Nociceptors lacking TRPV1 and TRPV2 have normal heat responses.

链条的强度取决于它的薄弱环节英语作文全文共5篇示例，供读者参考篇1The Strength of a Chain Depends on Its Weakest LinkHi everyone! My name is Tommy and I'm going to tell you about something super important called "The strength of a chain depends on its weakest link." It's a saying that grown-ups like to use, but it's actually pretty easy to understand, even for a kid like me!Have you ever played that game where you and your friends make a human chain by holding hands? You link up and see how long you can keep the chain together without breaking. Well, one time, my friend Jacob wasn't holding on very tightly. He was the weakest link! And you know what happened? Yup, the whole chain fell apart because of him!That's what the saying means. A chain is only as strong as its weakest part. If one of the links is loose or broken, it doesn't matter how tight and strong the other links are. The entire chain will come undone!This idea applies to so many things in life, not just actual chains. Let me give you some examples that might help you understand better.篇2The Strength of a Chain Depends on Its Weakest LinkHi friends! Today I want to tell you about something really important I learned. It's all about chains and how strong they are. You might be thinking "Huh? Chains? That's boring!" But trust me, this is actually super interesting and useful to know!Have you ever seen one of those big heavy chains before? Maybe it was being used to pull a truck that got stuck. Or keeping a gate closed. Or even just being used as a swing at the park. Chains are made up of lots of little metal rings all linked together. And those rings have to be pretty strong to hold everything together, right?Well, here's the really cool thing I learned. You know how I said those rings have to be strong? It turns out that the strength of the whole chain depends on its weakest link! Whoa, mind blown! Let me explain what that means.Let's imagine we have a chain with 100 rings in it. 99 of those rings are made out of super tough steel. But one of the rings ismade out of butter! Yeah, you read that right - butter! Now obviously butter is not very strong at all. In fact, it's really weak and soft.So even though the other 99 rings are crazy strong, that one butter ring makes the whole chain weak. It's kind of like the butter ring is dragging the whole chain down. No matter how strong the other rings are, the chain itself can't be stronger than its absolute weakest part.If you tried to use that chain to pull a truck or hold up a heavy gate, it would totally break at the butter ring. The strong steel rings wouldn't be able to make up for that one weak, melty link made of butter. Crazy, right?!This idea of the weakest link being so important doesn't just apply to actual chains though. It's a good lesson for all kinds of things in life. Let me give you some examples to help you understand:Let's say you're on a soccer team, and you're really, really good at scoring goals. Like, you're an amazing shooter. But the rest of your team can't pass or defend very well at all. Even with you being so talented, your team is going to struggle to win games because the other players are the "weak links."Or let's say you're building a model rocket to launch into the sky. You use a super strong body tube and fins. You pack in a powerful engine. But you use a cheap, flimsy nose cone made of paper. When you launch it, the nose cone is probably going to crumple, and the whole rocket will tumble out of control. So that weak nose cone ruins the whole project!Okay, one more example because this is just so interesting! Imagine you're making a chain of paper clips for a class project. You interlock a bunch of clips together one by one. But there's one paper clip that's slightly bent and doesn't connect perfectly. When you go to pick up the chain, it's going to break right at that little bent link. Bummer!Do you see what I mean now? The overall strength of something depends on its weakest part. Whether it's an actual metal chain or a team or a rocket or whatever, you always have to consider the weak links.The good news is, if you can identify the weak links, you can work on making them stronger! For the soccer team, you can practice passing and defense more. For the rocket, you can reinforce the nose cone. For the paper clip chain, you can find the bad link and replace it.By finding and fixing the weak points, you can make the whole thing stronger. A chain is only as strong as its weakest link, but that also means a chain can become super strong if all the links are strong!So keep an eye out for weak links, whether it's with actual chains or any other system like a team or project. Weak links are important to address so they don't drag everything else down. But weak links can also be opportunities to improve and build up your overall strength!I hope this all makes sense. Learning about weak links and how they affect overall strength was a huge eye opener for me. It's going to make me think twice anytime I'm working on something important. I'll be sure to analyze every part to identify potential weak spots and reinforce them. With no more weak links left, I'll be unstoppable!Alright friends, that's all I've got for you today on the importance of weak links. Thanks for reading my essay! Let me know if you have any other questions about this concept. For now, I'm going to go practice my clarinet playing...wouldn't want my pinky finger dexterity to be the weak link holding me back! See ya!篇3The Strength of a Chain Depends on Its Weakest LinkHi friends! My name is Emma and I'm going to tell you all about chains and how their strength depends on the weakest link. This is something I learned about in science class and I thought it was really interesting!First, let me explain what a chain is. A chain is made up of lots of little metal rings that are all connected together. The rings are linked to each other to form one long line. Chains are super strong and can be used to lift really heavy things like cars or anchors for big ships. But even though chains seem really tough, they have one weakness - the weakest link!You see, each metal ring in the chain is a "link." And no matter how strong the other links are, if just one link is weak or damaged, then the whole chain could break apart! The strongest chain in the world is only as strong as its weakest link. If that one link fails, then everything falls apart.It's kind of like if you had a team working together to pull a heavy truck. Let's say there were 10 people all pulling on one big rope that was attached to the truck. If 9 of those people were really strong, but 1 person was really weak, then the whole teammight not be able to pull the truck because of that one weak link! The weak person would be the weakest link and they could make the whole chain or team fail.In science class, we did an experiment to see how this works with actual chains. We took two chains - one that was brand new and one that was kind of old and rusty. The rusty chain had some weak links because the metal was getting worn down. We attached some weights to each chain to see how much they could hold before breaking.The new chain held a ton of weights no problem! But the old rusty chain with the weak links? It couldn't hold nearly as much weight before one of the weak links broke and caused the whole chain to snap apart. Just that one damaged link made the chain way weaker than it should have been. Really cool to see it in action!This idea about chains and their weakest links can apply to so many things in life too, not just actual metal chains. For example, let's say you were part of a team working on a big project for school. Maybe your team had some members who worked really hard and did an awesome job on their parts. But if there was one person who slacked off and didn't put in any effort,their laziness could bring down the whole project! Their poor work ethic would be the weakest link that failed the whole team.Or think about a company that makes toys. They might have a great design team that comes up with fun new toy ideas. And they might have an amazing production team that can make the toys quickly and perfectly. But if they have a weak link in their sales team that can't sell the toys well, then the whole business could suffer!You can apply this idea to just about anything - sports teams, friend groups, families, you name it. The strengths of the whole group depend on not having any weak links that could fail. Whether it's an actual metal chain or a figurative "chain" of people, the weakest link determines the overall strength.Of course, this doesn't mean that if one link is weak, everything is automatically ruined. But it does mean you have to work extra hard to make up for that weakness and strengthen the other links. Like if there was one weak kid on a tug-of-war team, the other kids would have to pull extra hard to make up for the weak link. It's possible to overcome a weak link, but it makes things way harder.In my opinion, the best way to make a strong chain is to simply get rid of the weak links entirely. Whether it's replacing arusty chain link or removing the lazy kid from your project team, dealing with the weak link directly is often the easiest solution. That way you can make sure every single link is as strong as possible.Though sometimes you can't just get rid of the weak link. Like if the weak link was someone really important or someone you really care about. If your buddy or family member was being a weak link by making poor choices, you wouldn't just ditch them. Instead, you'd try your best to strengthen them and turn them into a strong link again through hard work and perseverance.No chain is perfect and every chain will have some links that are stronger than others. But by being aware of your weakest links and either removing them or working hard to improve them, you can make sure your "chain" is as strong as it can possibly be. Never underestimate the importance of your weakest links!Well, that's all I've got to say about chains and their weakest links. I hope this essay taught you something new and interesting. Thanks for reading, friends! Time for me to go practice my tug-of-war skills so I'll never be the weak link on the team. See ya!篇4The Strength of a Chain Depends on its Weakest LinkHi friends! Today I want to tell you about something really important that I learned. It's all about chains and how strong they are. You might be thinking "Chains? That's boring!" But trust me, this is actually a super cool idea that can teach us a lot about life.You see, chains are made up of lots of little metal rings all linked together. If you look at one ring on its own, it seems pretty strong and hard to break, right? But here's the crazy thing - it doesn't matter how strong those individual rings are. The strength of the whole chain depends on the weakest link!What does that mean? Well, let's imagine there's one ring in the chain that is a little bit bent or has a tiny crack in it. That one weak ring is like the chain's achilles heel. No matter how perfect all the other rings are, if you pull hard enough on the chain, it's going to break at that one weak spot. The whole chain is only as strong as its weakest link!When I first learned about this, it blew my mind. I pictured a tough, strong chain just falling apart because of one tiny faulty ring. It seems so unfair! Why should the entire chain be ruined by one little problem?But the more I thought about it, the more I realized that this "weakest link" idea applies to so many things in life, not just chains. Like if you're part of a soccer team, you might be the fastest runner and have the best kicks, but if the rest of your team doesn't work well together, your team is going to struggle. The team is only as good as its weakest link!Or let's say you're building a cool fort out of popsicle sticks and glue. You glue down 100 sticks perfectly, but there's one stick that isn't stuck down properly. Guess what? When you go to add more levels to your fort, the whole thing is going to wobble and could easily collapse - all because of that one loose popsicle stick!It's kind of scary to think that one small mistake or weakness can make something strong become incredibly fragile. But understanding this principle can also help us work harder to identify and fix our weaknesses.Like when I was learning math last year, I was awesome at addition and subtraction, but those pesky multiplication tables were my weakest link. No matter how great I was at other stuff, I struggled with lots of math problems because I didn't have the multiplication basics down perfectly. Once I realized multiplication was the weak link for me, I practiced it like crazyuntil I got it down pat. Then the rest of math became much easier!Or when we're working on a group project at school, it's important for our team to keep an eye out for any members who are falling behind or not pulling their weight. If we have one "weak link" on our team, it can really hold all of us back unless we find a way to bring that person up to the same level as the rest of us.The more I think about it, the more examples I can see of the "weakest link" principle all around me:A sports team with one player who doesn't practice as hard as the othersA video game where you get hugely powerful except for one area you neglected to level upA group of friends where one person always starts dramaEven making a cake where you miss one ingredient - your dessert will be the weakest link!Everywhere you look, chains (both literal and metaphorical) are vulnerable to their weakest links. It seems kind of sad that all our efforts can be undermined by one small flaw or weak spot.But that's also what makes the "weakest link" principle so powerful and inspiring.Instead of pretending weaknesses don't exist or making excuses for them, we need to directly identify and strengthen those weakest links. We have to work hard at our rough edges and flaws until they are no longer liabilities. By eliminating our biggest weaknesses and leveling up our areas of struggle, we can overcome obstacles and achieve bigger and better things.A chain is truly no stronger than its weakest link - but the awesome thing is that we all have the ability to strengthen those weakest links through hard work and determination. Whether it's a skill we need to improve, a bad habit we need to break, or a mindset we need to change, we can overcome any weakness that might be holding us back.So yes, the strength of a chain does depend on its weakest link - but that just means we need to reinforce those weak links until they become some of the strongest parts of our chain. Then we'll be unbreakable! Pretty cool, right? The "weakest link" idea might seem discouraging at first, but I think it's one of the most motivating principles I've learned.Whenever I feel frustrated about struggling with something, I remind myself that identifying and working on my weakest linksis how I'll get strong enough to achieve my goals. I am the chain, and it's up to me to make sure I don't have any weak, vulnerable links that could make me break. It's a simple idea, but one that can inspire us to always work on improving ourselves in every possible way.So what do you think, friends? Are you ready to find your weakest links and get started strengthening those areas? I'm going to keep practicing and reinforcing any weak spots until my chain is stronger than ever. Then nothing can hold me back or cause me to break! Let's get strengthening - our futures depend on our ability to eliminate those weakest links.篇5The Strength of a Chain is as Strong as Its Weakest LinkHi! My name is Tommy and I'm going to tell you about something really important that I learned. It's all about chains and how strong they are. You might be thinking "Who cares about dumb old chains?" But trust me, this is actually super interesting and important!You see, chains are made up of lots of little metal rings all connected together. If you look at a chain, you'll see that eachlittle ring is linked to the ones next to it. The rings form this cool twisty pattern that goes around and around. Pretty neat, huh?Now, here's the key thing about chains that I learned. Let's say you had a chain and one of the little metal rings was kind of bent or rusty or just not as strong as the others. That one weak ring is what they call the "weakest link" in the chain. And get this - the strength of the entire chain depends on that one weak link!It doesn't matter if the other rings are super strong and sturdy. If there's just one ring that's weaker, then the whole chain is only as strong as that weakest link. If you pull really hard on the chain, it's going to break at that one spot where the weak link is. Wild, right?My teacher showed us a video of someone trying to pull apart this huge, thick chain made of big sturdy rings of steel. You'd think there's no way that chain could possibly break, right? Wrong! There was one little ring that was just a tiny bit more worn down than the others. And sure enough, when they pulled as hard as they could, that one weak link snapped and the whole chain fell apart. Mind = blown.After seeing that, I couldn't stop thinking about how chains are kind of like a team or a family or a friend group. Stay with me here...let's say your family is like a chain where each person isone of the little rings. Maybe your dad is a super hard worker and your mom is really good at taking care of everyone. Those would be the strong links.But what if your little brother struggles in school and doesn't have very good focus? He would be the weakest link in the family chain. And if he really starts failing classes and getting in trouble, that's going to weaken the whole family just like the weak link in a chain. See what I mean?The same thing happens with friend groups too. If you have a bunch of great friends who are nice, fun to hang out with, do their homework on time, etc. they would be the strong links. But if one friend starts ditching class, getting into fights, or doing other bad stuff, that person is the weakest link. And just like with the chain, if that one friend gets into really big trouble, it's going to cause problems for the whole friend group.It works the same way with teams too! Let's say there's a sports team or a group working on a project together. If everyone on the team is working really hard, doing their jobs, and working together well, those would be the strong links. But if there's one person who isn't pulling their weight, slacking off, or causing drama, that person is the weak link dragging the whole team down.Isn't that crazy how one weak person in a group can make everything fall apart? That's why it's so important for everyone to be a strong link and do their part. We can't just rely on other people to carry us. We all have to give 100% effort and live up to our responsibilities. Otherwise we'll be the weakest link that breaks the chain!I really took this whole "weak link" thing to heart. Now whenever I'm being lazy about my schoolwork or chores, I remind myself that I can't be the weak link in my family chain. And when I'm playing soccer, I always give it my full effort because I don't want to let my teammates down and be the weak link on the team. It's such an important lesson about putting in your best and not being the one who lets everyone else down.So there you have it - the whole scoop on why a chain is only as strong as its weakest link. Who knew chains could teach us such a valuable lesson, right? Just look at any chain and remember, we've all got to hold up our end with hard work and dedication. Otherwise the whole thing falls apart. Let's all aim to be the strongest possible links we can be!。

最开始编程的困难英文范文Embarking on the journey of programming is akin to learning a new language, a medium through which one communicates with machines. It is a path filled with challenges and triumphs, where each step forward is a puzzle solved, a line of code that brings a creation closer to reality. The initial phase of this journey is often the most daunting, as one grapples with unfamiliar concepts and the relentless demand for precision.In the beginning, the syntax of programming languages can seem cryptic. Each language, with its unique rules and structure, requires a level of detail that is unforgiving to the uninitiated. A missing semicolon, an unclosed bracket, or a mistyped command can lead to errors that are not always easy to decipher. The process of debugging, which is integral to programming, becomes a test of patience and attention to detail.Moreover, the logic and structure of programming demand a new way of thinking. One must learn to break down complex problems into smaller, manageable components, a skill that is not naturally acquired. This computational thinking extends beyond writing code; it influences how one approaches problem-solving in general. The transition from linear thinking to this segmented approach can be challenging, as it requires a shift in mindset that is not immediately intuitive.Another hurdle is the understanding of abstract concepts such as algorithms and data structures. These are the building blocks of efficient programming, yet they are concepts that cannot be touched or seen, only imagined and implemented. Grasping these abstractions is essential, but it often involves a steep learning curve. The ability to visualize data flowing through an algorithm or the manipulation of elements within a data structure is a skill honed over time with practice and experience.The vastness of the field can also be overwhelming. With an ever-expanding array of languages, frameworks, and tools, it is easy to feel lost in the sea of information. Deciding where to focus one's efforts and what to learn next can be paralyzing. The fearof missing out on important knowledge or falling behind the latest trends can add to the stress of the learning process.Despite these difficulties, the rewards of programming are manifold. The satisfaction of solving a problem, the joy of seeing one's code come to life, and the endless possibilities of creation are what drive many to persevere. Each obstacle overcome is a step towards mastery, and with each line of code, the language becomes more familiar, the logic clearer, and the abstract more concrete.As one progresses, the community of programmers becomes an invaluable resource. The shared experiences, the collective knowledge, and the support available through forums, social media, and collaborative projects can lighten the burden of the initial struggles. Learning from others' mistakes, asking for guidance, and contributing one's own solutions are all part of the growth process.In conclusion, the early stages of learning to program are fraught with challenges that test one's resolve, patience, and ability to think logically. Yet, it is these very challenges that sharpen the mind, foster creativity, and ultimately lead to a rewarding journey. As with any skill, proficiency comes with practice, and the difficulties faced at the start are but stepping stones to becoming a competent programmer. The key is to persist, stay curious, and embrace the learning process, for the world of programming offers endless opportunities to those who are willing to explore it. 。

芯片短缺有所缓解英语作文Title: Mitigation of Chip Shortages。

In recent times, the global electronics industry has been grappling with a significant challenge: chip shortages. This shortage has had widespread implications acrossvarious sectors, from automotive to consumer electronics, impacting production timelines and supply chains. However, there are indications that the situation is gradually improving, albeit with some caveats.First and foremost, the easing of chip shortages can be attributed to increased production capacity by semiconductor manufacturers. Companies within the industry have been investing heavily in expanding theirmanufacturing capabilities to meet the surging demand for chips. This strategic move has started to bear fruit, with reports indicating a gradual increase in chip supplies reaching the market.Furthermore, concerted efforts by governments and industry stakeholders have played a pivotal role in mitigating chip shortages. Governments have beenincentivizing semiconductor companies to ramp up production through various means, including tax breaks, subsidies, and infrastructure support. Additionally, collaborations between different players in the supply chain havefacilitated smoother coordination and allocation ofavailable chip resources.Another factor contributing to the alleviation of chip shortages is the optimization of supply chain management practices. Companies have been adopting agile and resilient supply chain strategies to navigate through theuncertainties caused by the shortage. This includes diversifying sourcing channels, optimizing inventory levels, and enhancing communication and collaboration with suppliers.Moreover, advancements in technology have enabled more efficient utilization of existing chip inventories. Innovations such as chip stacking, multi-chip modules, andimproved design methodologies have enabled manufacturers to maximize the performance of available chips, thereby stretching their supply further.However, despite these positive developments, it's essential to acknowledge that challenges still persist. While chip supplies are gradually increasing, the demand continues to outstrip supply in some segments of the market. This could potentially lead to continued disruptions and delays, particularly in industries heavily reliant on chips, such as automotive and consumer electronics.Additionally, the global semiconductor industry remains susceptible to various macroeconomic factors andgeopolitical tensions. Supply chain disruptions, trade policies, and geopolitical conflicts can significantly impact the availability of chips, adding another layer of complexity to the situation.In conclusion, while there are signs of improvement in alleviating chip shortages, the road ahead remains challenging. It requires continued collaboration,innovation, and strategic planning from all stakeholders involved. By addressing these challenges collectively, the industry can strive towards a more resilient and sustainable chip ecosystem, ensuring smoother operations and uninterrupted supply for various sectors reliant on semiconductor technology.。

9/06 IOM-AOS-ECM Installation and Operation Manual AO Smith ECM MotorNailor Industries Inc. reserves the right to change any information concerning product or specification without notice or obligation.Page 1 of 1NOTICE:POWER MUST BE REMOVED FROM THE CONTROLLER WHENEVER CONNECTIONS OR DISCONNECTIONS ARE BEING MADE. FAILURE TO DO SO COULD RESULT IN IRREPARABLE DAMAGE.NOTICE:BEFORE PROCEEDING WITH ANY ADDITIONAL TROUBLESHOOTING, ENSURE THAT THE POLARITY OF THE 24 VAC SUPPLY TO THE CONTROLLER IS CORRECT. (SEE FIGURE 1). IF THE POLARITY IS NOT CORRECT, REMOVE THE CONNECTORS AND RECONNECT OBSERVING PROPER POLARITY. RECHECK THE SYSTEM FOR PROPER OPERATION.1.Inspect the unit to make sure that there are no foreign objectsblocking fan operation. Turn the wheel by hand to verify that it moves freely.2.Energize the unit at the unit disconnect switch. Adjust thecontrols to call for the fan motor to run.Setting the Fan Airflow in the Manual Mode 1.Attach the leads of a DC voltmeter to the "METER"and "COM"terminals on the volume controller card. Read the DC volts.2.Refer to the Fan Calibration Table inside the line voltageenclosure. Select the voltage that corresponds to the desired airflow (cfm or l/s) set point.3.Adjust the potentiometer on the ECM card to the desiredvoltage.Troubleshooting1.Confirm the jumper on the ECM card is in the correct position. The jumper should be in the "MAN"position for adjustment of fan speed at the unit.2.If the motor does not run, turn off the power to the unit and verify that the power plug and the control plug are firmly and correctly attached to the motor. Then, turn the unit power back on and wait for the motor to start. If it has not started within 20 seconds, turn off power and repeat this step.3.If the motor still does not start, unplug both wiring harnesses from the motor. IMPORTANT: Do not jam the voltmeter leads into the connectors. This will swage out the connectors and cause them to not make contact when the unit is plugged back in.Insert the probes into the plugs until they touch the pins. Do not penetrate the pins.4.Energize the unit. Check the AC voltage at the power plug. You should have full voltage between the neutral and power lines, or between the two power lines in case of 240 VAC. If this is the case, go to step5. If there is not a full voltage signal at this point, check the voltage at the incoming power terminal block. If there is not a full voltage signal at this point, turn off the power to the box and fix the problem with the electrician. If there is a full voltage signal at the incoming terminal block, turn off the power to the box and reinstall the power cable harness.5.If there is a full voltage signal, and if the ground wire is properly connected, check the voltage at the ECM card. Be sure that you have 24 - 28.5 VAC at the 24 VAC terminals. If you do not have voltage at this point, check the transformer.6.If you have the correct input voltage, place meter on the "GND" and "VDC" meter terminals where you should be reading a magnitude between 0 and 10 VDC. Using a screwdriver, move the potentiometer to verify that the magnitude varies.If you do not have the proper voltages, replace the ECM card. 7.If all the voltages check out, it is possible that the pins may not be connecting properly and it may be a good idea to recheck them at the plug near the motor.The ECM card provides a visual airflow indicator. A green LED located on the controller circuit board flashes in response to the airflow indicator pulses provided by the control board located in the motor. Each pulse is 100 cfm (47.2 l/s). The last pulse is scaled.Figure 1. AO Smith ECM Card.Contractors check box to confirm steps 1–7 have been addressed. After addressing 1–7 please return to manufacturerfor warranty action.InspectorsSignature:–––––––––––––––––––––––––––––––––––––––––CABLEPLUGMETERGNDPOTENTIOMETER。

Huawei's Breakthrough in Self-Developed Chips: Overcoming Technological BlockadesHuawei has emerged as a global leader in the technology sector, particularly in telecommunications and consumer electronics. However, the company has faced significant challenges due to geopolitical tensions and subsequent technological blockades imposed by various countries. In response to these hurdles, Huawei has made remarkable strides in self-developing its own chips, showcasing its resilience and innovation. This essay explores the significance of Huawei's breakthrough in chip development and its implications for the global tech industry.The imposition of technological blockades on Huawei, particularly by the United States, has created substantial obstacles for the company. These restrictions have limited Huawei's access to critical components and technologies, especially those involving semiconductors and advanced chipsets. As a result, Huawei faced the daunting task of maintaining its competitive edge and ensuring the continuity of its product lines without relying on foreign suppliers.In response to these challenges, Huawei embarked on an ambitious journey towards self-reliance. The company invested heavily in research and development, allocating significant resources to its semiconductor subsidiary, HiSilicon. This strategic move aimed to reduce Huawei's dependence on external suppliers and establish a robust in-house capability for chip design and manufacturing.The breakthrough came with the development of Huawei's Kirin series of processors, which are used in the company’s smartphones and other devices. These chips, designed by HiSilicon, demonstrated competitive performance and efficiency, positioning Huawei as a formidable player in the semiconductor industry. The latest iterations of Kirin chips have showcased advanced features, including artificial intelligence capabilities and 5G compatibility, further cementing Huawei's technological prowess.Huawei's successful development of its own chips has significant implications for the global tech industry. Firstly, it highlights the potential for companies to innovate and overcome external pressures through substantial investment in research and development. Huawei's achievements can serve as an inspiration for other firms facing similar challenges, encouraging them to pursue self-reliance and innovation.Secondly, Huawei's breakthrough underscores the shifting dynamics of the global semiconductor market. Traditionally dominated by a few key players,the market is now witnessing the rise of new contenders from diverse regions. This increased competition can drive further innovation and potentially lead to more affordable and advanced technologies for consumers worldwide.Furthermore, Huawei's advancements in chip technology can contribute to the development of a more resilient global supply chain. By diversifying sources of critical components, the tech industry can reduce vulnerabilities and mitigate the risks associated with geopolitical tensions and trade restrictions.In conclusion, Huawei's breakthrough in self-developing chips represents a significant milestone in the face of technological blockades. Through substantial investment in research and development, the company has demonstrated its resilience and capability to innovate independently. This achievement not only strengthens Huawei's position in the global tech industry but also has broader implications for innovation, competition, and supply chain resilience. As Huawei continues to push the boundaries of technology, it serves as a powerful example of how challenges can be transformed into opportunities for growth and advancement.。

Sparse Solution of Underdetermined Linear Equationsby Stagewise Orthogonal Matching PursuitDavid L.Donoho1,Yaakov Tsaig2,Iddo Drori1,Jean-Luc Starck3March2006AbstractFinding the sparsest solution to underdetermined systems of linear equations y=Φx is NP-hard in general.We show here that for systems with‘typical’/‘random’Φ,a good approximation to thesparsest solution is obtained by applying afixed number of standard operations from linear algebra.Our proposal,Stagewise Orthogonal Matching Pursuit(StOMP),successively transforms the signal into a negligible residual.Starting with initial residual r0=y,at the s-th stage it formsthe‘matchedfilter’ΦT r s−1,identifies all coordinates with amplitudes exceeding a specially-chosenthreshold,solves a least-squares problem using the selected coordinates,and subtracts the least-squaresfit,producing a new residual.After afixed number of stages(e.g.10),it stops.In contrastto Orthogonal Matching Pursuit(OMP),many coefficients can enter the model at each stage inStOMP while only one enters per stage in OMP;and StOMP takes afixed number of stages(e.g.10),while OMP can take many(e.g.n).StOMP runs much faster than competing proposals for sparsesolutions,such as 1minimization and OMP,and so is attractive for solving large-scale problems.We use phase diagrams to compare algorithm performance.The problem of recovering a k-sparse vector x0from(y,Φ)whereΦis random n×N and y=Φx0is represented by a point(n/N,k/n)in this diagram;here the interesting range is k<n<N.For n large,StOMP correctly recovers(anapproximation to)the sparsest solution of y=Φx over a region of the sparsity/indeterminacy planecomparable to the region where 1minimization is successful.In fact,StOMP outperforms both 1minimization and OMP for extremely underdetermined problems.We rigorously derive a conditioned Gaussian distribution for the matchedfiltering coefficients at each stage of the procedure and rigorously establish a large-system limit for the performancevariables of StOMP.We precisely calculate large-sample phase transitions;these provide asymptot-ically precise limits on the number of samples needed for approximate recovery of a sparse vector byStOMP.We give numerical examples showing that StOMP rapidly and reliablyfinds sparse solutions in compressed sensing,decoding of error-correcting codes,and overcomplete representation.Keywords:compressed sensing,decoding error-correcting codes,sparse overcomplete representation. phase transition,large-system limit.random matrix theory.Gaussian approximation. 1minimization. stepwise regression.thresholding,false discovery rate,false alarm rate.MIMO channel,mutual access interference,successive interference cancellation.iterative decoding.Acknowledgements This work was supported by grants from NIH,ONR-MURI,a DARPA BAA, and NSF DMS00-77261,DMS01-40698(FRG)and DMS05-05303.1:Department of Statistics,Stanford University,Stanford CA,943052:Institute for Computational Mathematics in Engineering,Stanford University,Stanford CA,94305 3:DAPNIA/SEDI-SAP,Service d’Astrophysique,Centre Europeen d’Astronomie/Saclay,F-91191Gif-sur-Yvette Cedex France.1IntroductionThe possibility of exploiting sparsity in signal processing is attracting growing attention.Over the years, several applications have been found where signals of interest have sparse representations and exploiting this sparsity offers striking benefits;see for example[11,28,26,25,7].At the ICASSP2005conference a special session addressed the theme of exploiting sparsity,and a recent international workshop,SPARS05, was largely devoted to this topic.Very recently,considerable attention has focused on the following Sparse Solutions Problem(SSP). We are given an n×N matrixΦwhich is in some sense‘random’,for example a matrix with iid Gaussian entries.We are also given an n-vector y and we know that y=Φx0where x0is an unknown sparse vector.We wish to recover x0;however,crucially,n<N,the system of equations is underdetermined and so of course,this is not a properly-stated problem in linear algebra.Nevertheless,sparsity of x0is a powerful property that sometimes allows unique solutions.Applications areas for which this model is relevant include:App1:Compressed Sensing.x0represents the coefficients of a signal or image in a known basis which happens to sparsely represent that signal or image.Φencodes a measurement operator,i.e.an operator yielding linear combinations of the underlying object.Here n<N means that we collect fewer data than unknowns.Despite the indeterminacy,sparsity of x0allows for accurate recon-struction of the object from what would naively seem to be‘too few samples’[17,8,48].App2:Error rmation is transmitted in a coded block in which a small fraction of the entries may be corrupted.From the received data,one constructs a system y=Φx0;here x0 represents the values of errors which must be identifed/corrected,y represents(generalized)check sums,andΦrepresents a generalized checksum operator.It is assumed that the number of errors is smaller than a threshold,and so x0is sparse.This sparsity allows to perfectly correct the gross errors[9,48,28].App3:Sparse Overcomplete Representation.x0represents the synthesis coefficients of a signal y,which is assumed to be sparsely represented from terms in an overcomplete expansion;those terms are the columns ofΦ.The sparsity allows to recover a unique representation using only a few terms, despite the fact that representation is in general nonunique[43,11,21,20,50,51].In these applications,several algorithms are available to pursue sparse solutions;in some cases attractive theoretical results are known,guaranteeing that the solutions found are the sparsest possible solutions. For example,consider the algorithm of 1minimization,whichfinds the solution to y=Φx having minimal 1norm.Also called Basis Pursuit(BP)[11],this method enjoys some particularly striking theoretical properties,such as rigorous proofs of exact reconstruction under seemingly quite general circumstances[21,35,32,7,16,8,17,18]Unfortunately,some of the most powerful theoretical results are associated with fairly heavy com-putationally burdens.The research reported here began when,in applying the theory of compressed sensing to NMR spectroscopy,we found that a straightforward application of the 1minimization ideas in[17,58]required several days solution time per(multidimensional)spectrum.This seemed prohibitive computational expense to us,even though computer time is relatively less precious than spectrometer time.In fact,numerous researchers have claimed that general-purpose 1minimization is much too slow for large-scale applications.Some have advocated a heuristic approach,Orthogonal Matching Pursuit (OMP),(also called greedy approximation and stepwise regression in otherfields)[43,52,53,55,54], which though often effective in empirical work,does not offer the strong theoretical guarantees that attach to 1minimization.(For other heuristic approaches,see[50,51,29].)In this paper we describe Stagewise Orthogonal Matching Pursuit(StOMP),a method for approx-imate sparse solution of underdetermined systems with the property either thatΦis‘random’or that the nonzeros in x0are randomly located,or both.StOMP is significantly faster than the earlier methods BP and OMP on large-scale problems with sparse solutions.Moreover,StOMP permits a theoretical analysis showing that StOMP is similarly succcessful to BP atfinding sparse solutions.Our analysis uses the notion of comparison of phase transitions as a performance metric.We con-sider the phase diagram,a2D graphic with coordinates measuring the relative sparsity of x0(numberof nonzeros in x0/number of rows inΦ),as well as the indeterminacy of the system y=Φx(number of rows inΦ/number of columns inΦ).StOMP’s large-n performance exhibits two phases(success/failure) in this diagram,as does the performance of BP.The“success phase”(the region in the phase diagram where StOMP successfullyfinds sparse solutions)is large and comparable in size to the success phase for 1minimization.In a sense StOMP is more effective atfinding sparse solutions to large extremely under-determined problems than either 1minimization or OMP;its phase transition boundary is even higher at extreme sparsity than the other methods.Moreover,StOMP takes a few seconds to solve problems that may require days for 1solution.As a result StOMP is well suited to large-scale applications.Indeed we give several explicitly worked-out examples of realistic size illustrating the performance benefits of this approach.Our analysis suggests the slogannoiseless underdetermined problems behave like noisy well-determined problems,i.e.coping with incompleteness of the measurement data is(for‘randomΦ’)similar to coping with Gaus-sian noise in complete measurements.At each StOMP stage,the usual set of matchedfilter coefficients is a mixture of‘noise’caused by cross-talk(non-orthogonality)and true signal;setting an appropriate threshold,we can subtract identified signal,causing a reduction in cross-talk at the next iteration.This is more than a slogan;we develop a theoretical framework for rigorous asymptotic analysis.Theorems 1-3below allow us to track explicitly the successful capture of signal,and the reduction in cross-talk, stage by stage,rigorously establishing(asymptotic)success below phase transition,together with the failure that occurs above phase transition.The theory agrees with empiricalfinite-n results.Our paper is organized as follows.Section2presents background on the sparse solutions problem; Section3introduces the StOMP algorithm and documents its favorable performance;Section4develops a performance measurement approach based on the phase diagram and phase transition.Section5analyzes the computational complexity of the algorithm.Section6develops an analytic large-system-limit for predicting phase transitions which agree with empirical performance characteristics of StOMP.Section 7develops the Gaussian noise viewpoint which justifies our thresholding rules.Section8describes the performance of StOMP under variations[adding noise,of distribution of nonzero coefficients,of matrix ensemble]and documents the good performance of StOMP under all these variations.Section9presents computational examples in applications App1-App3that document the success of the method in simulated model problems.Section10describes the available software package which reproduces the results in this paper and Section11discusses the relationship of our results to related ideas in multiuser detection theory and to previous work in the sparse solutions problem.2Sparse Solution PreliminariesRecall the Sparse Solutions Problem(SSP)mentioned in the introduction.In the SSP,an unknown vector x0∈R N is of interest;it is assumed sparse,which is to say that the number k of nonzeros is much smaller than N.We have the linear measurements y=Φx0whereΦis a known n by N matrix, and wish to recover x0.Of course,ifΦwere a nonsingular square matrix,with n=N,we could easily recover x from y; but we are interested in the case where n<N.Elementary linear algebra tells us that x0is then not uniquely recoverable from y by linear algebraic means,as the equation y=Φx may have many solutions.However,we are seeking a sparse solution,and for certain matricesΦ,sparsity will prove a powerful constraint.Some of the rapidly accumulating literature documenting this phenomenon includes [21,20,32,55,56,50,51,8,18,16,57,58,48].For now,we consider a specific collection of matrices where sparsity proves valuable.Until we say otherwise,letΦbe a random matrix taken from the Uniform Spherical ensemble(USE);the columns of Φare iid points on the unit sphere S n−1[16,17].Later,several other ensembles will be introduced.3Stagewise Orthogonal Matching PursuitStOMP aims to achieve an approximate solution to y=Φx0whereΦcomes from the USE and x0is sparse.In this section,we describe its basic ingredients.In later sections we document and analyse itsMatched Filter"T r s Projection "I s T "I s ()#1"I s T y Interference Construction "x sFigure 1:Schematic Representation of the StOMP algorithm.performance.3.1The ProcedureStOMP operates in S stages,building up a sequence of approximations x 0,x 1,...by removing detected structure from a sequence of residual vectors r 1,r 2,....Figure 1gives a diagrammatic representation.StOMP starts with initial ‘solution’x 0=0and initial residual r 0=y .The stage counter s starts at s =1.The algorithm also maintains a sequence of estimates I 1,...,I s of the locations of the nonzeros in x 0.The s -th stage applies matched filtering to the current residual,getting a vector of residual correlationsc s =ΦT r s −1,which we think of as containing a small number of significant nonzeros in a vector disturbed by Gaussian noise in each entry.The procedure next performs hard thresholding to find the significant nonzeros;the thresholds,are specially chosen based on the assumption of Gaussianity [see below].Thresholding yields a small set J s of “large”coordinates:J s ={j :|c s (j )|>t s σs };here σs is a formal noise level and t s is a threshold parameter.We merge the subset of newly selected coordinates with the previous support estimate,thereby updating the estimate:I s =I s −1∪J s .We then project the vector y on the columns of Φbelonging to the enlarged support.Letting ΦI denote the n ×|I |matrix with columns chosen using index set I ,we have the new approximation x s supported in I s with coefficients given by (x s )I s =(ΦT I s ΦI s )−1ΦT I s y.The updated residual isr s =y −Φx s .We check a stopping condition and,if it is not yet time to stop,we set s :=s +1and go to the next stage of the procedure.If it is time to stop,we set ˆx S =x s as the final output of the procedure.Remarks:1.The procedure resembles Orthogonal Matching Pursuit(known to statisticians as Forward StepwiseRegression).In fact the two would give identical results if S were equal to n and if,by coincidence, the threshold t s were set in such a way that a single new term were obtained in J s at each stage.2.The thresholding strategy used in StOMP(to be described below)aims to have numerous termsenter at each stage,and aims to have afixed number of stages.Hence the results will be different from OMP.3.The formal noise levelσs= r s 2/√n,and typically the threshold parameter takes values in therange2≤t s≤3.4.There are strong connections to:stagewise/stepwise regression in statistical model building;succes-sive interference cancellation multiuser detectors in digital communications and iterative decoders in error-control coding.See the discussion in Section11.Our recommended choice of S(10)and our recommended threshold-setting procedures(see Section 3.4below)have been designed so that when x0is sufficiently sparse,the following two conditions are likely to hold upon termination:•All nonzeros in x0are selected in I S.•I S has no more than n entries.The next lemma motivates this design criterion.Recall thatΦis sampled from the USE and so columns ofΦare in general position.The following is proved in Appendix A.Lemma3.1Let the columns ofΦbe in general position.Let I S denote the support ofˆx S.Suppose that the support I0of x0is a subset of I S.Suppose in addition that#I S≤n.Then we have perfect recovery:ˆx S=x0.(3.1)3.2An ExampleWe give a simple example showing that the procedure works in a special case.We generated a coefficient vector x0with k=32nonzeros,having amplitudes uniformly distributed on[0,1].We sampled a matrixΦat random from the USE with n=256,N=1024,and computed a linear measurement vector y=Φx0.Thus the problem of recovering x0given y is1:4underdetermined (i.e.δ=n/N=.25),with underlying sparsity measureρ=k/n=.125.To this SSP,we applied StOMP coupled with the CFAR threshold selection rule to be discussed below.The results are illustrated in Figure2.Panels(a)-(i)depict each matchedfiltering output,its hard thresholding and the evolving approxi-mation.As can be seen,after3stages a result is obtained which is quite sparse and,as thefinal panel shows,matches well the object x0which truly generated the data.In fact,the error at the end of the third stage measures ˆx3−x0 2/ x0 2=0.022,i.e.a mere3stages were required to achieve an accuracy of2decimal digits.3.3Approximate Gaussianity of Residual MAIAt the heart of our procedure are two thresholding schemes often used in Gaussian noise removal.(N.B. at this point we assume there is no noise in y!)To explain the relevance of Gaussian‘noise’concepts, note that at stage1,the algorithm is computing˜x=ΦT y;this is essentially the usual matchedfilter estimate of x0.If y=Φx0and x0vanishes except in one coordinate,the matchedfilter output˜x equals x0perfectly.Hence z=˜x−x0is a measure of the disturbance to exact reconstruction caused by multiple nonzeros in x0.The same notion arises in digital communications where it is called Multiple-Access Interference(MAI)[60].Perhaps surprisingly-because there is no noise in the problem-the MAI in our setting typically has a Gaussian behavior.MoreFigure2:Progression of the StOMP algorithm.Panels(a),(d),(g):successive matchedfiltering outputs c1,c2,c3;Panels(b),(e),(h):successive thresholding results;Panels(c),(f),(i):successive partial solutions. In this example,k=32,n=256,N=1024.specifically,ifΦis a matrix from the USE and if n and N are both large,then the entries in the MAI vector z have a histogram which is nearly Gaussian with standard deviationσ≈ x0 2/√n.(3.2)The heuristic justification is as follows.The MAI has the formz(j)=˜x(j)−x0(j)=j=φj,φ x0( ).The thing we regard as‘random’in this expression is the matrixΦ.The termξjk ≡ φj,φk measures theprojection of a random point on the sphere S n−1onto another random point.This random variable has approximately a Gaussian distribution N(0,1n).ForΦfrom the USE,for a givenfixedφj,the differentrandom variables(ξjk :k=j)are independently distributed.Hence the quantity z(j)is an iid sum ofapproximately normal r.v.’s,and so,by standard arguments,should be approximately normal with mean 0and varianceσ2j=V ar[j= ξjx0( )]=(j=x0( )2)·V ar(ξj1)≈n−1 x0 22Settingσ2= x0 2/n,this justifies(3.2).Computational experiments validate Gaussian approximation for the MAI.In Figure3,Panels(a),(d),(g) display Gaussian QQ-plots of the MAI in the sparse case with k/n=.125,.1875and.25,in the Uniform Spherical Ensemble with n=256and N=1024.In each case,the QQ-plot appears straight,as the Gaussian model would demand.Through the rest of this paper,the phrase Gaussian approximation means that the MAI has an approximately Gaussian marginal distribution.(The reader interested in formal proofs of Gaussian approximation can consult the literature of multiuser detection e.g.[46,61,12];such a proof is implicitin the proofs of Theorems1and2below.The connection between our work and MUD theory will be amplified in Section11below).Properly speaking,the term‘MAI’applies only at stage1of StOMP.At later stages there is residual MAI,i.e.MAI which has not yet been cancelled.This can be defined asz s(j)=x0(j)−φT j r s/ P Is−1φj 22,j∈I s−1;Figure3:QQ plots comparing MAI with Gaussian distribution.Left column:k/n=.125,middle column:k/n=.1875,right column:k/n=.25.Top row:USE,middle row:RSE,bottom row:URP. The RSE and URP ensembles are discussed in Section8.The plots all appear nearly linear,indicating that the MAI has a nearly Gaussian distribution.the coordinates j∈I s−1are ignored at stage s-the residual in those coordinates is deterministically0.Empirically,residual MAI has also a Gaussian behavior.Figure4shows quantile-quantile plots for the first few stages of the CFAR variant,comparing the residual MAI with a standard normal distribution. The plots are effectively straight lines,illustrating the Gaussian ter,we provide theoretical support for a perturbed Gaussian approximation to residual MAI.3.4Threshold SelectionOur threshold selection proposal is inspired by the Gaussian behavior of residual MAI.We view the vector of correlations c s at stage s as consisting of a small number of‘truly nonzero’entries,combined with a large number of‘Gaussian noise’entries.The problem of separating‘signal’from‘noise’in such problems has generated a large literature including the papers[24,27,26,1,23,37],which influenced our way of thinking.We adopt language from statistical decision theory[39]and thefield of multiple comparisons[38]. Recall that the support I0of x0is being(crudely)estimated in the StOMP algorithm.If a coordinate belonging to I0does not appear in I S,we call this a missed detection.If a coordinate not in I0does appear in I S we call this a false alarm.The coordinates in I S we call discoveries,and the coordinates in I S\I0we call false discoveries.(Note:false alarms are also false discoveries.The terminological distinction is relevant when we normalize to form a rate;thus the false alarm rate is the number of false alarms divided by the number of coordinates not in I0;the false discovery rate is the fraction of false discoveries within I S.)We propose two strategies for setting the threshold.Ultimately,each strategy should land us in a position to apply Lemma3.1:i.e.to arrive at a state where#I S≤n and there are no missed detections. Then,Lemma3.1assures us,we perfectly recover:ˆx S=x.The two strategies are:•False Alarm Control.We attempt to guarantee that the number of total false alarms,across all stages,does not exceed the natural codimension of the problem,defined as n−k.Subject to this, we attempt to make the maximal number of discoveries possible.To do so,we choose a threshold so the False Alarm rate at each stage does not exceed a per-stage budget.•False Discovery Control.We attempt to arrange that the number of False Discoveries cannot exceedFigure4:QQ plots comparing residual MAI with Gaussian distribution.Quantiles of residual MAI at different stages of StOMP are plotted against Gaussian quantiles.Near-linearity indicates approximate Gaussianity.afixed fraction q of all discoveries,and to make the maximum number of discoveries possible subject to that constraint.This leads us to consider Simes’rule[2,1].The False Alarm Control strategy requires knowledge of the number of nonzeros k or some upper bound.False Discovery Control does not require such knowledge,which makes it more convenient for applications,if slightly more complex to implement and substantially more complex to analyse[1].The choice of strategy matters;the basic StOMP algorithm behaves differently depending on the threshold strategy,as we will see below.Implementation details are available by downloading the software we have used to generate the results in this paper;see Section10below.4Performance Analysis by Phase TransitionWhen does StOMP work?To discuss this,we use the notions of phase diagram and phase transition.4.1Problem Suites,Performance MeasuresBy problem suite S(k,n,N)we mean a collection of Sparse Solution Problems defined by two ingredients: (a)an ensemble of random matricesΦof size n by N;(b)an ensemble of k-sparse vectors x0.By standard problem suite S st(k,n,N)we mean the suite withΦsampled from the uniform spherical ensemble,with x0a random variable having k nonzeros sampled iid from a standard N(0,1)distribution.For a given problem suite,a specific algorithm can be run numerous times on instances sampled from the problem suite.Its performance on each realization can then be measured according to some numerical or qualitative criterion.If we are really ambitious,and insist on perfect recovery,we use the performancemeasure1{ˆxS =x0}.More quantitative is the 0-norm, ˆx S−x0 0,the number of sites at which the twovectors disagree.Both these measures are inappropriate for use withfloating point arithmetic,which does not produce exact agreement.We prefer to use instead 0, ,the number of sites at which the reconstruction and the target disagree by more than =10−4.We can also use the quantitative measure relerr2= ˆx S−x0 2/ x0 2,declaring success when the measure is smaller than afixed threshold(say ).For a qualitative performance indicator we simply report the fraction of realizations where the qual-itative condition was true;for a quantitative performance measure,we present the mean value across instances at a given k,n,N.Figure5:Phase Diagram for 1minimization.Shaded attribute is the number of coordinates of recon-struction which differ from optimally sparse solution by more than10−4.The diagram displays a rapid transition from perfect reconstruction to perfect disagreement.Overlaid red curve is theoretical curve ρ1.4.2Phase DiagramA phase diagram depicts performance of an algorithm at a sequence of problem suites S(k,n,N).The average value of some performance measure as displayed as a function ofρ=k/n andδ=n/N.Both of these variablesρ,δ∈[0,1],so the diagram occupies the unit square.To illustrate such a phase diagram,consider a well-studied case where something interesting happens. Let x1solve the optimization problem:(P1)min x 1subject to y=Φx.As mentioned earlier,if y=Φx0where x0has k nonzeros,we mayfind that x1=x0exactly when k is small enough.Figure5displays a grid ofδ−ρvalues,withδranging through50equispaced points in the interval[.05,.95]andρranging through50equispaced points in[.05,.95];here N=800.Each point on the grid shows the mean number of coordinates at which original and reconstruction differ by more than10−4,averaged over100independent realizations of the standard problem suite S st(k,n,N). The experimental setting just described,i.e.theδ−ρgrid setup,the values of N,and the number of realizations,is used to generate phase diagrams later in this paper,although the problem suite being used may change.This diagram displays a phase transition.For smallρ,it seems that high-accuracy reconstruction is obtained,while for largeρreconstruction fails.The transition from success to failure occurs at different ρfor different values ofδ.This empirical observation is explained by a theory that accurately predicts the location of the observed phase transition and shows that,asymptotically for large n,this transition is perfectly sharp. Suppose that problem(y,Φ)is drawn at random from the standard problem suite,and consider the event E k,n,N that x0=x1i.e.that 1minimization exactly recovers x0.The paper[19]defines a functionρ1(δ)(called thereρW)with the following property.Consider sequences of(k n),(N n)obeying k n/n→ρand n/N n→δ.Suppose thatρ<ρ1(δ).Then as n→∞P rob(E kn ,n,N n)→1.On the other hand,suppose thatρ>ρ1(δ).Then as n→∞P rob(E kn ,n,N n)→0.The theoretical curve(δ,ρ1(δ))described there is overlaid on Figure5,showing good agreement betweenasymptotic theory and experimental results.Figure6:Phase diagram for CFAR thresholding.Overlaid red curve is heuristically-derived analytical curveρF AR(see Appendix B).Shaded attribute:number of coordinates wrong by more than10−4 relative error.4.3Phase Diagrams for StOMPWe now use phase diagrams to study the behavior of StOMP.Figure6displays performance of StOMP with CFAR thresholding with per-iteration false alarm rate(n−k)/(S(N−k)).The problem suite and un-derlying problem size,N=800,are the same as in Figure5.The shaded attribute again portrays the number of entries where the reconstruction misses by more than10−4.Once again,for very sparse problems(ρsmall),the algorithm is successful at recovering(a good approximation to)x0,while for less sparse problems(ρlarge),the algorithm fails.Superposed on this display is the graph of a heuristically-derived functionρF AR,which we call the Predicted Phase transition for CFAR thresholding.Again the agreement between the simulation results and the predicted transition is reasonably good.AppendixB explains the calculation of this predicted transition,although it is best read only afterfirst reading Section6.Figure7shows the number of mismatches for the StOMP algorithm based on CFDR thresholding with False Discovery Rate q=1/2.Here N=800and the display shows that,again,for very sparse problems(ρsmall),the algorithm is successful at recovering(a good approximation to)x0,while for less sparse problemsρlarge,the algorithm fails.Superposed on this display is the graph of a heuristically-derived functionρF DR,which we call the Predicted Phase transition for CFDR thresholding.Again the agreement between the simulation results and the predicted transition is reasonably good,though visibly not quite as good as in the CFAR case.5ComputationSince StOMP seems to work reasonably well,it makes sense to study how rapidly it runs.5.1Empirical ResultsTable1shows the running times for StOMP equipped with CFAR and CFDR thresholding,solving an instance of the problem suite S st(k,n,N).We compare thesefigures with the time needed to solve the same problem instance via 1minimization and OMP.Here 1minimization is implemented using Michael Saunders’PDCO solver[49].The simulations used to generate thefigures in the table were all executed on a3GHz Xeon workstation,comparable with current desktop CPUs.Table1suggests that a tremendous saving in computation time is achieved when using the StOMP schemeover traditional 1minimization.The conclusion is that CFAR-and CFDR-based methods have a large。

2025年全国大学英语CET四级考试复习试题及解答参考一、写作（15分）Part I Writing (30 points)Directions: For this part, you are allowed 30 minutes to write a short essay on the topic “The Impact of Artificial Intelligence on Daily Life.” You should start your essay with a brief introduction to the topic, then give specific examples to illustrate your point, and finally, provide a conclusion with your personal view. Your essay should be about 120 to 150 words but no less than 100 words.Writing Sample:The advent of artificial intelligence (AI) has revolutionized our daily lives in numerous ways. From smart homes to advanced medical diagnosis, AI has become an integral part of modern society.In smart homes, AI systems like voice assistants and smart security cameras enhance our convenience and safety. These systems learn from our habits and preferences, making our homes more comfortable and efficient. Moreover, in the healthcare sector, AI algorithms are being used to analyze medical images and identify potential diseases at an early stage, which can significantly improvepatient outcomes.However, the rise of AI also brings challenges. For example, job displacement is a major concern, as AI can perform certain tasks more efficiently than humans. Additionally, there are ethical questions about privacy, data security, and the potential misuse of AI technology.In conclusion, while AI has brought substantial benefits to our daily lives, we must also address its challenges to ensure a balanced and ethical integration of AI into our society.Writing Analysis:•Introduction: The essay starts with a clear introduction to the topic of AI and its impact on daily life, providing a broad perspective.•Body Paragraphs: The body of the essay presents two distinct impacts of AI:•The positive impact of AI in smart homes and healthcare.•The negative impacts of job displacement and ethical concerns.•Conclusion: The essay concludes with a balanced view, acknowledging both the benefits and challenges of AI, and emphasizing the need for ethical considerations.•Structure and Coherence: The essay has a clear structure and is well-organized, making the flow of ideas easy to follow.•Length: The essay meets the required word count, with 120 words, demonstrating the writer’s ability to convey the main points concisely.二、听力理解-短篇新闻（选择题，共7分）第一题News:In recent years, global attention has been drawn to the rapid development of electric vehicles (EVs). According to a recent report by the International Energy Agency (IEA), the number of electric vehicles on the roads worldwide reached 13 million in 2021, up from just 2 million in 2015. The report also indicates that by 2030, the number of electric vehicles is expected to surpass 145 million.Question 1:What has the number of electric vehicles on the roads reached as of 2021 according to the recent report by the IEA?A) 1 millionB) 13 millionC) 2 millionAnswer: BQuestion 2:How many years is it mentioned from 2015 to 2021 in the report?A) 5 yearsB) 6 yearsC) 7 yearsAnswer: BQuestion 3:What is the expected number of electric vehicles by 2030 according to the report?A) 13 millionB) 2 millionC) 145 millionAnswer: C第二题News Item 1:A new study reveals that the global use of electric scooters has increased significantly in recent years. These scooters are becoming a popular form of transportation in cities around the world. However, the study also highlights the environmental and safety concerns associated with the rapid growth in electric scooter usage.Cities are faced with the challenge of managing the increased demand for parking spaces, as well as the potential risks of accidents involving these scooters. Improved infrastructure and regulations are being considered to address these issues.Questions:1、What is the primary topic of the news item?A. The decline of traditional scootersB. The environmental impact of electric scootersC. The safety concerns of using electric scootersD. The rise in global use of electric scooters2、“These scooters are becoming a popular form of transportation in cities around the world.” Which of the following is true regarding the use of electric scooters?A. They are only popular in developed countries.B. They have no environmental impact.C. They are causing a decrease in car usage.D. They have become a common mode of transportation globally.3、“Improved infrastructure and regulations are being considered to address these issues.” What is the implied issue that needs to be addressed?A. The overuse of public transportation.B. The need for more parking spaces for cars.C. The decline in bicycle usage.D. The potential safety risks and management challenges posed by electric scooters.Answers:1.D2.D3.D三、听力理解-长对话（选择题，共8分）First QuestionConversationA: Hey, Sarah! Did you finish listening to the podcast this morning?B: Yeah, I did. It was quite fascinating. Have you checked the transcript on their webpage?A: Not yet. I plan to review what we heard today after work. By the way, I was thinking it would be nice to form a study circle this semester.B: That sounds like a good idea. Could you host a meeting this weekend?A: Sure, I can. I’ll prepare some questio ns for us to discuss, and you can bring in your notes. It’ll make our learning more productive.B: Great! Should we stick to the topics in the podcast or choose something else?A: Let’s talk about the topics in the podcast first. That way, it’ll help us understand the context better.B: Sounds perfect. I have a couple of questions for you. How long have you been listening to podcasts?A: Since about a year now. I find it’s a great way to learn English while doing something productive.B: I agree. What’s your favorite podcast?A: Hmm, I really like “The Economist Briefing.” It covers current events and history, which are topics I find interesting.B: Nice choice. I’m a fan of “TED Talks Daily.” It’s a bit different from “The Economist Briefing” but still educational.A: That’s true. We can switch up the topics as we like. What are youstudying?B: I’m majoring in international relations. The podcast really helps me get more insights into what I’m studying.A: That’s awesome. What about yo ur plans for the future?B: I hope to travel around Europe for my study abroad program next year, so I’m trying to learn more European languages. It would be a great opportunity to practice my English as well.A: That sounds exciting! This weekend, let’s m eet for an hour at my place, okay?B: Sure, that works for me.Q1. What is one reason Sarah likes listening to this podcast?a)To practice her English.b)To pass CET-4.c)To prepare for a trip.d)To learn her major subject.Answer: aQ2. How long has the speaker been listening to podcasts?a)One yearb)Two yearsc)Three yearsd)Half a yearAnswer: aQ3. Who does the speaker admire for choosing “TED Talks Daily”?a)Sarahb) A friendc) A professord)Another studentAnswer: aQ4. What will they do this weekend?a)Meet for an hour at the speaker’s place.b)Join a club activity.c)Go to a coffee shop.d)Attend a lecture on English.Answer: aQuestion 2:Why does Liu feel a bit nervous about the exam?A) He is preparing for it for too long.B) He hasn’t studied hard enough.C) His friends are also enrolled in CET-4 course classes.D) He needs to take a break soon.Answer: AQuestion 3:What advice does Amy give to Liu?A) Enroll in a CET-4 course class.B) Review the past papers.C) Study every day.D) Take a break.Answer: BQuestion 4:What can be inferred about Liu from the conversation?A) He is confident about the exam.B) He has been preparing for the exam for a long time.C) He is ready for the upcoming exam.D) He doesn’t like studying hard.Answer: B四、听力理解-听力篇章（选择题，共20分）第一题Directions: In this section, you will hear a passage. Listen carefully and answer the questions that follow.Passage:In today’s fast-paced digital world, it has become increasingly important for businesses to adopt technologies that improve their efficiency and customer satisfaction. The rise of artificial intelligence (AI) and machine learning (ML) has led to significant advancements in the field of business operations. Companies are now exploring various ways to integrate these technologies to enhance their processes.1、What aspect of business operations has seen significant advancements dueto AI and ML integration?A) Customer serviceB) LogisticsC) Financial managementD) A2、Why is the adoption of AI and ML technologies regarded as important for businesses?A) To reduce operational costsB) To improve customer satisfactionC) To increase operational efficiencyD) C3、Which of the following is NOT an example of how businesses can integrate AI and ML?A) Enhancing predictive analyticsB) Automating routine tasksC) Increasing manual data entryD) C第二题Passage 1The globalization of the economy has brought about significant changes in the world, and one area that has been heavily affected is the sports industry. In this essay, we will explore how globalization has impacted the sports industry,focusing on the growth of international sports events and the role of sports in global culture.1、Why is globalization having a profound impact on the sports industry?A) Because it allows sports to be practiced anywhere in the world.B) Because it has led to the growth of international sports events.C) Because it has changed the way people culture around the world.D) Because it has increased the salaries of professional athletes.2、Which of the following is not mentioned as a change brought about by globalization in the sports industry?A) The increase in cross-cultural interactions.B) The decline in local sports teams.C) The rise of regional sports leagues.D) The increase in global fan bases for various sports.3、What is the main argument made by the essay about the role of sports in global culture?A) Sports have a单一 focus on winning and losing.B) Sports help to foster national pride and identity.C) Sports have become a way for countries to cooperatively compete.D) Sports have lost their relevance due to increased commercialization.Answer Key:1、B2、BThird Question: Listening Comprehension - Listening PassagePassage:Welcome to our final research trip to India. We are in a small village in the state of Kerala, known for its rich cultural heritage and scenic beauty. The village, named Paravoor, has a population of approximately 15,000. Today, we focus on the local economy, which is largely dependent on farming, tourism, and small-scale industries. Currently, the village is facing several challenges, including water scarcity and lack of proper infrastructure. The government plans to implement a new irrigation project, which will provide a significant boost to the agricultural sector. In addition, the village is promoting eco-tourism to diversify its economic base. However, these initiatives require support and investment from both the government and the local community.1、Which of the following is NOT a challenge facing Paravoor Village?A、Water scarcityB、Lack of proper infrastructureC、Dependence on large-scale industriesD、C、2、What is the villagers’ plan to diversify their economic base?A、Developing new industriesB、Promoting eco-tourismC、Increasing agricultural production3、Which of the following is a potential benefit of the new irrigation project?A、It will help diversify the local economy.B、It will improve the infrastructure.C、It will provide water to the entire state.D、C、五、阅读理解-词汇理解（填空题，共5分）第一题Reading PassageAlice, receiving a ring, was extremely pleased. Her father promptly asked, “Have you made up your mind, my dear?” “Not quite,” said Alice ominously, stepping out of her ring. “But I will do so directly,” she declared.With a faint shiver of delight, the father experienced her civil but firm decision and then together they went to bet {?1?} her little servant girl a seventeen-pound horse. While they were thus occupied, the children saw their disagreement. The richest and keenest-uprisinguchepest, perfectly struck their fancy, and though their(Game) competitive position was, by no means, satisfactory, they had no objection to feel very sorry for the seller.1、civil A. 非常高兴的B. 礼貌的；文明的C. 无数的；无休止的D. 非常出色的2、competititive A. 竞争性的；竞赛的B. 嫉妒的；充满敌意的C. 令人厌恶的；讨厌的D. 无能的；不称职的3、keen A. 苦涩的；尖利的B. 明锐的；敏锐的C. 高兴的；愉快的D. 枯燥的；乏味的4、Ominous A. 不吉利的；不祥的B. 温和的；文雅的C. 欢快的；愉快的D. 兴奋的；激动的5、shiver A. 战栗；发抖B. 淡水C. 快速降雨D. 柔软的动物答案:1、B2、A3、B4、A5、A第二题Directions: Read the following text and complete the sentences below. There is one word or phrase missing in each sentence. Choose the most appropriate word or phrase from the options given below each sentence.Reading Passage:The rapid growth of technology has profoundly transformed our social fabric. From the emergence of the internet to the advent of smartphones, our daily interactions and work routines have been fundamentally altered. These technological advancements have not only facilitated instant communication but also expanded our access to information. However, this shift comes with its own set of challenges. For instance, while the internet provides a vast array of resources, it also exposes us to misinformation and the need for digital literacy is increasingly important. Moreover, the reliance on technology in the workplace has raised concerns about job security, as automation and artificial intelligence continue to evolve and change the nature of work.1、The word “fabric” (Line 1) most closely r elates to the following word: _[Options: a) fabric b) structure c) society d) clothing_]•1、c) society2、The phrase “emergence of the internet” (Line 3) can be replaced with which of the following: _[Options: a) the start of the internet b) the appearance of the internet c) the deployment of the internet d) the invention of the internet_]•2、b) the appearance of the internet3、The word “instant” (Line 4) is synonymous with: _[Options: a) immediate b) brief c) quick d) rapid_]•3、a) immediate4、The challenge mentioned in the passage regarding the internet is: _[Options: a) accessing information b) exposure to misinformation c) maintaining digital literacy d) balancing physical and digital interactions_]•4、b) exposure to misinformation5、The phrase “nature of work” (Line 7) refers to: _[Options: a) the quality of work b) the purpose of work c) the essence of work d) the value of work_]•5、c) the essence of work六、阅读理解-长篇阅读（选择题，共10分）第一题Reading Passage OneIt is widely accepted that education is of great importance to all people. However, there are many arguments on its necessity. While some people believe it is important to receive an education, others argue that education is not essential in one’s life.One of the main arguments for education is that it offers opportunities for personal development. With a good education, individuals can acquire the knowledge and skills needed to succeed in life. They can also improve theircritical thinking abilities and make informed decisions. Furthermore, an education can help individuals become more adaptable and flexible, enabling them to thrive in a changing world.Opponents of education argue that people can succeed without it. They cite examples of successful individuals who dropped out of school, such as Steve Jobs and比尔·盖茨. They believe that talent and opportunities can compensate for a lack of formal education.In the following passage, there are some statements about education. Choose the most suitable answer for each of the following questions.Questions 1-51、Which of the following is the main issue discussed in the reading passage?A. The benefits of educationB. The drawbacks of educationC. The importance of personal developmentD. The relationship between education and success2、What do the proponents of education believe about the role of education in personal development?A. Education hinders personal growth.B. Education does not contribute to skill acquisition.C. Education improves critical thinking and decision-making skills.D. Education makes individuals less adaptable.3、What is the main argument against education mentioned in the passage?A. Education limits personal development.B. Successful individuals can compensate for a lack of education.C. Education stifles creativity and innovation.D. Education takes away opportunities for self-betterment.4、Which of the following does the reading passage NOT mention as a reason for supporting education?A. Increased opportunities for employment.B. Enhanced critical thinking abilities.C. Improved adaptability and flexibility.D. Theernenment in international cooperation.5、What is the author’s attitude towards the debate on education?A. The author believes that education is unnecessary.B. The author supports the idea that education is essential for personal development.C. The author prefers talent and opportunities over education.D. The author is neutral on the issue of education.Answer Key:1、A2、C3、B4、D5、B第二题Passage:The concept of cloud computing has been discussed for decades, but it has only recently become a practical solution for businesses and individuals. Itall began with the idea of using the Internet as a transmission medium for data and applications. As technology advanced, the costs of storage and bandwidth became more affordable, making cloud computing a viable option. Today, cloud services range from simple file storage to complex application delivery, and they are accessible via web browsers or special software applications.The benefits of cloud computing are numerous. First, there is no need for costly hardware or maintenance. Cloud providers handle all the backend operations, ensuring that the service runs smoothly without requiring any intervention from users. Second, cloud services are highly scalable, meaning they can handle sudden increases in demand without additional investment. Third, cloud computing encourages collaboration and mobility, as users can access data and applications from anywhere with an internet connection. Finally, cloud services often come with robust security features, which are continuously updated, minimizing the risk of data breaches.However, cloud computing also comes with challenges. Security remains a significant concern, as data is stored remotely and vulnerable to cyberattacks. Additionally, there is the issue of data sovereignty, where data stored outside a country’s borders may be subject to the laws of that country. Furthermore, some companies may be hesitant to switch to cloud services due to the lack of control over their data, a common concern known as “control issues.”Questions:1、What is the main idea of the passage?a) The history of cloud computing.b) The benefits and challenges of cloud computing.c) The security concerns of cloud computing.d) The scalability of cloud computing.2、Why did cloud computing become practical recently?a) Because of the decreased costs of storage and bandwidth.b) Because of the widespread availability of the Internet.c) Because of the advancement in technology.d) Because of the decreasing demand for hardware.3、What are the benefits of cloud computing mentioned in the passage?a) No need for costly hardware, scalability, collaboration and mobility, and robust security features.b) High scalability, easy maintenance, and data sovereignty.c) Low costs, easy access, and increased data security.d) Remote access, data availability, and decreased bandwidth requirements.4、Which of the following is a challenge of cloud computing?a) The lack of mobility.b) The high costs of hardware.c) The security risks associated with remote data storage.d) The limited availability of web browsers.5、What is the common concern known as “control issues” mentioned in the passage?a) Users have no control over their data.b) Users have control over their data, but it is stored remotely.c) Data stored outside a country’s borders may be subject to the laws of that country.d) Users can choose to control their data through special software applications.Answers:1、b) The benefits and challenges of cloud computing.2、a) Because of the decreased costs of storage and bandwidth.3、a) No need for costly hardware, scalability, collaboration and mobility, and robust security features.4、c) The security risks associated with remote data storage.5、a) Users have no control over their data.七、阅读理解-仔细阅读（选择题，共20分）First Reading Comprehension Part AReading PassageThe following is a passage about the importance of exercise for mental health and productivity. This passage is followed by some questions to which the answers can be found in the passage.In today’s fast-paced world, stress has become an integral part of our lives. It’s essential to find ways to manage and reduce stress to maintain both our mental and physical health. One effective way to combat stress is through regularexercise. Research has consistently shown that physical activity can have a profound impact on our mental well-being and productivity.1.Physical activity has been found to:A) improve mental healthB) enhance productivityC) both improve mental health and enhance productivityD) have no effect on mental health2.The passage primarily discusses:A) the negative impact of stress on mental healthB) the benefits of exercise in reducing stressC) the effectiveness of various stress management techniquesD) the effects of different types of stress on the body3.It is mentioned that physical activity can have a “profound impact” on our:A) attention spanB) moodC) ability to sleepD) All of the above4.The word “integral” in the first paragraph most closely means:A) essentialB) foundationC) simpleD) occasional5.According to the passage, what is one effective way to combat stress?A) Avoiding situations that cause stressB) Seeking professional helpC) Regular physical activityD) Meditating for a few minutes dailyOptions:1、C2、B3、D4、A5、C第二题阅读下面的文章，然后回答问题。

遇到的编程上的困难用英语作文Encountering Difficulties in ProgrammingIn the field of programming, I have encountered numerous challenges that have tested my skills and problem-solving abilities. These difficulties have often pushed me to think critically and find innovative solutions. In this essay, I will discuss some of the most significant programming challenges I have faced and how I have overcome them.One of the common difficulties I have encountered is debugging code. Debugging is an essential part of programming, but it can be time-consuming and frustrating. When faced with a bug, I have learned to approach the problem systematically.I start by understanding the error message or unexpected behavior that occurs. Then, I carefully review the code, checking for syntax errors, logical flaws, or incorrect variable assignments. If the bug is not apparent, I use tools like print statements or debugging software to track the program's execution and identify the issue. Patience and persistence are crucial in this process, as it may require multiple iterations to locate and fix the bug.Another challenge I have faced is understanding complex algorithms and data structures. Programming often involves implementing intricate algorithms or utilizing advanced data structures to optimize performance. To overcome this difficulty, I dedicate time to studying and researching these concepts. I read textbooks, watch online tutorials, and participate in coding competitions to enhance my understanding. Additionally, I practice implementing these algorithms in small projects to gain hands-on experience. Breaking down complex algorithms into smaller, manageable parts and analyzing their time and space complexities has been instrumental in my learning process.Working on large-scale projects with a team has also presented its own set of challenges. Collaborating with others requires effective communication and coordination. Miscommunication or differences in coding styles can lead to conflicts and delays. To address this, I make a conscious effort to maintain clear and open lines of communication with my team members. Regular meetings, code reviews, and documentation help ensure that everyone is on the same page. Additionally,I have learned to be adaptable and flexible, considering different perspectives and incorporating feedback from team members. This collaborative approach has not only improved the quality of the projects but also fostered a positive and productive working environment.Lastly, staying updated with the rapidly evolving programming languages, frameworks, and tools can be overwhelming. New technologies are constantly emerging, and it can be challenging to keep up with the latest trends. To overcome this difficulty, I prioritize continuous learning. I follow industry blogs, attend webinars, and participate in online courses to stay updated with the latest advancements. Moreover, I engage in personal projects that allow me to experiment with new technologies and expand my skill set. By embracing a growth mindset and being proactive in my learning, I can adapt to new technologies and remain competitive in the programming field.虽然在编程领域中遇到了许多困难，但我通过不断的学习和实践，克服了这些困难。

科技英语试题及答案一、选择题（每题2分，共20分）1. The term "nanotechnology" refers to the manipulation of matter on an atomic, molecular, and supramolecular scale.A. TrueB. False2. Which of the following is NOT a characteristic of renewable energy sources?A. Infinite in supplyB. Environmentally friendlyC. Dependent on weather conditionsD. Non-renewable3. The process of converting solar energy into electrical energy is known as:A. SolarizationB. Photovoltaic effectC. Solar distillationD. Thermal radiation4. In the context of computer science, what does "AI" stand for?A. Artificial IntelligenceB. Advanced InterfaceC. Automated InputD. Application Interface5. The term "genome" is associated with:A. The complete set of genes in an organismB. The structure of a cellC. The study of geneticsD. The process of cell division6. What is the primary function of a transistor in an electronic circuit?A. To amplify signalsB. To store dataC. To convert light into electricityD. To filter signals7. The "Internet of Things" (IoT) refers to:A. A network of interconnected devicesB. The global network of computersC. A collection of internet protocolsD. The study of internet security8. Which of the following is a type of biotechnology?A. Genetic engineeringB. Quantum computingC. NanolithographyD. Nuclear fusion9. The "Greenhouse Effect" is related to:A. The warming of the Earth's surfaceB. The cooling of the Earth's surfaceC. The process of photosynthesisD. The formation of the ozone layer10. What does "CRISPR" stand for in the field of molecular biology?A. Clustered Regularly Interspaced Short Palindromic RepeatsB. Computer-Aided Research in Scientific ProjectsC. Comprehensive Research in Innovative ScienceD. Computational Research in Systematic Processes二、填空题（每题1分，共10分）1. The unit of electrical resistance is the ______.2. The process of converting sound waves into electrical signals is known as ______.3. In physics, the term "entropy" is used to describe the level of ______ in a system.4. The study of the chemical composition of planets is known as ______.5. The term "cybersecurity" refers to the protection of______ from cyber threats.6. The process of converting electrical energy into light is known as ______.7. The smallest unit of life that can replicate itself is called a ______.8. The process of creating new substances from existing ones is known as ______.9. The study of the structure and function of cells is known as ______.10. The process of converting light energy into chemical energy is known as ______.三、简答题（每题5分，共30分）1. Explain the concept of "machine learning" in artificialintelligence.2. Describe the role of a semiconductor in modern electronics.3. What is the significance of biodiversity in the context of environmental science?4. Discuss the potential impact of nanotechnology on medicine.四、论述题（共40分）1. Discuss the ethical considerations involved in the development and use of genetic engineering technologies. (20分)2. Analyze the potential benefits and challenges of implementing a global Internet of Things (IoT) network. (20分)答案：一、选择题1. A2. D3. B4. A5. A6. A7. A8. A9. A10. A二、填空题1. ohm2. transduction3. disorder4. cosmochemistry5. information systems6. electroluminescence7. cell8. synthesis9. cytology10. photosynthesis三、简答题1. Machine learning is a subset of artificial intelligence that enables computers to learn from and make decisions based on data, improving at tasks over time through experience without being explicitly programmed.2. Semiconductors are materials with electrical conductivity between that of a conductor and an insulator. They arecrucial in electronic devices like transistors and diodes, allowing for the control of electrical current and the amplification of signals.3. Biodiversity is significant in environmental science as it ensures the stability of ecosystems, supports ecological processes, and provides a variety of services and resources that are vital for human survival and well-being.4. Nanotechnology has the potential to。

BF, BG and G-SeriesA Wholly Owned Subsidiary of Flanders CorporationOperation andMaintenance ManualPB-1311-0207Bag-In/Bag-Out Manual Operation & Maintenance ManualImportant Message.....................................................................Inside Front Cover Quality Assurance Program.. (4)Introduction (5)BF Gel Seal Design Concept (8)BG Gasket Seal Design Concept (9)G-Series Design Concept (10)Handling and Storage of Filter Elements Prior to Installation (11)Installation of New Filter Housings (12)Filter Housing Start-up Procedures (14)Installation of New Filter Elements (15)Filter Change-Out (Replacing Dirty Filters) (26)System Maintenance (39)Replacement of Access Door Gasket (40)Replacement of BF-Series Gel Seal Locking Mechanism (43)Replacement of BG-Series Gasket Seal Locking Mechanism(Optional Clamping Mechanism) (47)Spare Parts (51)4Flanders/CSC’s Quality Assurance Program was established to address the eighteen criteria structure of ASME NQA-1 (formally N45.2), “Quality Assurance Requirements for Nuclear Facility Applications”. As suppliers of High Efficiency Air Filtration products and services, there are three standards that govern the majority of Flanders/CSC’s activities.1. ASME N509-1989 (reaffirmed 1996)“Nuclear Power Plant Air-cleaning Units and Components”2.ASME N510-1989 (reaffirmed 1995)“Testing of Nuclear Air Treatment Systems”3.ASME AG-1- 1997“Code on Nuclear Air and Gas Treatment”These standards and our customer’s specifications invoke many other standards and codes the Flanders/CSC’s Quality Assurance Program incorporates as standard practice.There are a variety of Quality Assurance Programs that manufacturer’s implement to ensure product and service quality, two such systems are ISO-9001and ASME NQA-1.Abstracts of these programs include:ISO 9001:2000 specifies requirements for a Quality Management System where an organization 1.Needs to demonstrate its ability to consistently provide product that meets customer and applicable regulatory requirements, and 2.Aims to enhance customer satisfaction through the effective application of the sys-tem, including processes for continual im-provement of the system and the assurance of conformity to customer and applicable regu-latory requirements.All requirements of this international standard are generic and are intended to be applicable to all organizations, regardless of type, size and product provided.1ASME NQA-1: This Standard sets forth requirements for the establishment and execution of quality assurance programs for the siting, design,construction, operation, and decommissioning of nuclear facilities. Nonmandatory guidance is provided in the Appendices. NQA-1 establishes 18criteria covering all aspects of quality, from purchase of raw materials, to design and testing. 2Because ASME NQA-1 applies to the Nuclear Industry where containment and safety are of paramount concern, it is generally seen to establish more checks and balances.Containment air filtration started out as a critical requirement in the Nuclear industry to protect workers, the public and the environment. Today,containment air filtration is a critical issue in a variety of industries and applications; from pharmaceutical,health care, military, and the original nuclear applications among others. Because of the critical safety requirements of the nuclear industry, ASME N509, ASME N510, and ASME AG-1 are recognized as the standards for design and testing of containment air filtration systems. Each of these standards requires a Quality Assurance Program that meets the requirements of ASME NQA-1.Flanders/CSC maintains a full scope Quality Assurance Program that meets the requirements of ASME NQA-1, 10 CFR 50 Appendix B, and DOE O 414 1A. Customers that require the stringent application of quality principles that only a mature and developed program can offer routinely audit this Quality Assurance program.Flanders/CSC has evaluated the possibility of certification to ISO-9001 and determined that an ASME NQA-1 program better meets the critical needs of our customers. Although the two programs are comparable, an ASME study indicates that a ISO-9001 Quality Assurance Program will not meet the requirements of ASME NQA-1 without substantial modification. 3parison NQA 1 and ISO 9001 Technical Report,available from 5IntroductionTypical 1 high 1 wide filter housing module for a single primary filter.Five (5) 2 high 2 wide filter housing modules welded together to create a 2 high 2 wide, 5 stage filter train.Flanders/CSC’s line of bag-In/bag-out filter housings for gel or gasket seal primary filters are side-loading filter housings which have been designed to meet the air filtration needs of industries and research facilities that handle dangerous or toxic biological, radiological, or carcinogenic material. To minimize exposure to this harmful contamination while replacing and handling dirty filters, the housing incorporates a ribbed bag-in/bag-out ring, over which a heavy duty plastic bag is attached.Once the initial filters are installed and the first bag attached, all filters ¾ both dirty and new ¾ are handled through the bag using the procedures described in detail throughout this manual, hence the name Bag-In/Bag-Out.Depending upon the user’s requirements, the housing may have an assortment of filter arrangements, including the prefilters, HEPA filters,and/or carbon adsorbers. No matter what type of filters are contained within the housing, the filter change-out procedure is the same.Remember: A filter change-out is not complete until the new filters have been sealed to the housing frame and an in-place leak test has been performed.6Access DoorPrefilter Flanges for Duct ConnectionRibbed Bagging RingHEPA (or Adsorber) FilterSecurity StrapBag Stub Removal Glove SleeveFilter (or Adsorber)Locking MechanismPrimary Filter Removal RodChange-Out Bag (Plastic)Cinching StrapAccess Door KnobIllustration of Bag-In/Bag-Out ComponentsFilter HandlingGlove SleeveThe plan view illustrations below are the basic steps involved in changing contaminated filters in a Bag-In/Bag-Out containment housing. A complete step-by-step change-out instruction manual is furnished with each housing or system.•Extend bag and place arms in filter handlingglove sleeves of bag.•Remove access door.Figure 2Figure 1HEPA FilterPlastic BagPlastic BagHandling Glove SleeveHEPA FilterBag Stub Removal Glove SleeveAccess DoorBag-In/Bag-Out Operation & Maintenance Manual8The standard locking mechanism is manufactured ofType 300 Series stainless steel.3W BF-Series Housing Showing Locking Mechanism and Filter Removal RodHousing Knife Edge Front and BottomHousing Knife Edge Front and TopDescription of the BF-Series Filter Locking SystemThe BF-Series housing has a filter locking arm in each tier to operate the replaceable filter locking mechanism. By operating the internal filter locking arm inside the PVC bag and access door, the filter is engaged on, or disengaged from, the housing knife edge (internal sealing frame). The filter locking arm and the access door interface in such a manner that minimizes the possibility of the door being closed until the filters are correctly sealed in the housing and sealed to the mounting frame.Gel Seal Design ConceptThe filter-to-housing gel seal is effected by means of a continu-ous knife edge on the interior of the housing, which mates into the gel-filled perimeter channel on the face of the filter. T o effect the seal, the locking mechanism forces the filter against the knife edge. The knife edge penetrates the gel and a uniform seal is pro-duced on the filter face.Blu-Jel SealKnife EdgeHousingLockingArmFilterGel-Filled ChannelAir Flow®9The filter to housing gasket seal is effected by means of a con-tinuous flat mounting surface on the interior of the housing,which mates to a perimeter gasket on the filter.To effect the seal, the locking mechanism forces the filter against the mounting surface.BG-Series Gasket Seal Housing inside view showing the filter locking mechanism. Note the exterior drive bolts and spring-loaded mechanism.The BG-Series Gasket Seal Design ConceptThe BG-Series Gasket Seal DescriptionBy turning a drive bolt located at the front exte-rior of the BG-Series housing, the independent pressure bars with pre-loaded springs, located in the filter locking mechanism, force the filter against the interior mounting frame. Pre-loaded springs on each pressure bar, for each filter element, ap-ply consistent pressure to maintain filter seal.The applied force has a minimum clamping load of 1,400 pounds per full width filter or 1,050 pounds per half width filter. This force is applied as an even, uniform load along the top and bottom of each filter frame. The standard locking mechanism is manufactured of Type 300 Series stainless steel with brass pivot blocks.Air FlowHousingHousingFilterFilter Locking MechanismGasketThe standard locking mechanism is manufactured ofType 300 Series stainless steel and brass10The G-Series Housing Design ConceptI n addition to the BF-Series side load Bag-In/Bag-Out housing, Flanders/CSC offers round filter housing for in-line applications. The G-Series hous-ing is designed for single filter replacement from the top of the unit. The housing can be installed for side access, but Flanders/CSC does not rec-ommend that the unit be supported by the inlet and outlet connections. Instead, a mounting stand or some other means of support should be used.There is no specific diameter for inlet and outlet connections for the G-Series housing, sincerequirements vary. The purchaser must specify the required pipe sizes and lengths.The G-Series inlet and outlet connection can be a standard rolled stainless steel sheet metal nipple or optional stainless steel piping or tubing.Gel seal filters used in the round housing do not require filter clips.The G-Series housings have a different locking mechanism from the standard BF or BG Series housing.G-Series Round Housing for in-line applicationsFilter Clamping Arm Pressure BarsFilter clamping arm pressure bars secure the filter during operation. Filter elements that are 12 inch x 12 inch require two clamps and filter elements that are 24 inch x 24 inch require four clamps.The clamps are spring loaded and have a “T” handle that is turned 90° by the operator to lock the filter in the sealed position.Gel Seal Clamping Arms for a G1F Housing In a G-Series round housing, the filter is held in place by with spring loaded clamps for the G1F gel seal or pressure bars, for the G1G gasket seal one (1), two(2) or four(4) compression points are used; depending upon the filter size.Gasket Seal Locking Mechanism for a G1G HousingCompression SpringClamping Arm PressureBarPressure Bar StopsClamping Arm HandleFilter Sealing SurfaceCrank and brass port block, optional 300 series staniless steel designKnife Edge Sealing SurfaceFilter Clamping Arms11Handling and Storage of Filter Elements Prior to InstallationParticulate FiltersParticulate filters include a wide range of filter types, sizes, and performance capabilities.Particulate filters are designed to remove airborne particulates from an airstream while carbon adsorbers (see below) remove contaminate gas molecules from an airstream. Particulate filters can be small, disposable, 30% efficient by ASHRAE “Prefilters” or expensive HEPA (High Efficiency Particulate Air) filters with an efficiency of 99.97% by DOP or better.Generally, all types of particulate filters are very fragile and should be handled with a great deal of care. The following precautions should be observed:•Store in a clean, dry environment.•Store filters in correct orientation.(Check marking arrows on cartons.)•Store filters with tagging information easily visible.•Store away from heavy traffic areas.•Do not stack HEPA filters more than three filters high during storage and handling.•Store filters in factory-packed carton and do not remove from carton until just prio to installation into the filter housing.•Do not move stored filters from place to place. Moving filters can cause damage to the filters.Carbon AdsorbersAdequate care should be provided for packaged adsorber cells to assure optimum initial performance. It is important to minimize the exposure of the adsorbers to moisture, since moisture adversely affects the carbon and the special impregnates (if carbon is impregnated).It is important to store adsorbers in a temperature-controlled environment (0° — 120°F). The following precautions should be observed:•Store in a clean, dry environment.•Store adsorbers in correct orientation.(Check marking arrows on cartons.)•Store filters with tagging information easily visible.•Store away from heavy traffic areas.•Store filters in factory-packed carton and do not remove from carton until just prior to installation into the filter housing.•Immediately prior to installation of the adsorbers into the filter housing, insure that filter housing and ductwork is free of loose construction debris. Flanders/CSC recommends operating the system for approximately two (2) hours with prefilters (and HEPA filters, if used) in place before installing adsorbers.•If the adsorbers are exposed to paint fumes or other solvents, the carbon in the adsorbers will be poisoned and the life of the carbon is shortened. Make sure adequate paint drying time is allowed (usually 24-48 hours) before exposing the adsorbers to the paint fumes.Shelf Life InformationFlanders/CSC recommends that every filter be stored in its original shipping carton to prevent it from being exposed to ultraviolet rays, moisture,and possible damage to the filter media. The filter should be stored in a controlled area (0° — 120°F),and it should not be exposed to ozone depleting sources. If these parameters are satisfied and storage requirements as detailed are maintained,the filter shelf life should be three (3) years from gasket cure date or three (3) years from manufacturing date for gel seal filters.121.Be sure position of housing accessdoor(s) and direction of air flow is correct prior to connecting ductwork.2.The housing should be permanentlyconnected to the ductwork by welding or gasketing and bolting before installation of the filters.Installation of New BF-Series and BG-Series HousingsCaution: RTV caulking compounds may deteriorate in service. They are not recommended for permanent installations. (Check your site specifications.)3.Following installation of the housing(s),the system should be cleaned toremove construction dust, etc. before installing any of the filters.DUCT CONNECTION:Welded or bolted; if bolted, use gasket material to insure leak tightness. (Flanders/CSC provides gasket material with factory drilled flanges.)ACCESS DOOR:Face housing so air flow would strike your back. If door is on your right. Then, housing is right-hand access and vice versa to make it left hand access.Allow minimum of 4 ft. clearance for filter changeoutWall, Support Column,or Other ObstructionsPREFILTER:Normally located on upstream side ofhousingPLAN VIEWPRIMARY FILTER:Normally seals on downstream side of housing when prefilter is behind the same door (shown); seals on up-stream side of housing when prefilter has a separate door or if there is no prefilterDOWNSTREAM DUCT :(by others)UPSTREAM DUCT :(by others)131.Be sure the position of housing accessdoor(s) and direction of air flow is correct prior to connecting ductwork.2.The housing should be permanentlyconnected to the ductwork before the filters are installed. G-Series housings are frequently supplied without flanges for butt welding of piping in the field,but may be supplied with separate flanges for installation in the field.Installation of New G-Series Filter HousingsIf flanges are supplied, they are usually bolted when the housing is properly aligned to mating flanges in the field.(Construction plans should be consulted for details.)3.Following installation of the housing(s),the system should be cleaned toremove construction dust, etc. before installing the filters.Allow a minimum of 4 ft. clearance to remove filters from the housing.PROVIDE STAND OR BAG-OUT SHELFProvide a suitable stand or support shelf for filter change. The shelf should be strong enough to support a fully-loaded HEPA filter or carbon adsorber. If the access door is on the side of the housing, locate the stand just outside of and a few inches beneath the bottom of the door. If the ac-cess door is located on the top of the housing, place the stand alongside and level with the top of the door.Note: A filter removal tray is available fromFlanders/CSC for convenient filter change-out.4 Ft.ClearanceRecommendedBag-In/Bag-Out Manual: Start-Up Procedures15Installation of New Filters in New (Uncontaminated) HousingsMaterials and Tools Required:Rest filter on floor whileremoving carton.Remove packing materials.Turn filter over.BF-Series and G-Series Gel Seal Housings •No tools are requiredBG-Series, Gasket Seal Housings •Standard ratchet with short extension and 3/4 inch socket •Filter release agent (silicone grease)All bag-in/bag-out housings•New filters or adsorbers (Check for correct quantity, type, size and model number.)•New plastic change-out bags(Check for correct quantity, type, size and model number.)•One (1) security strap per access door16STEP 1: BF-Series,BG-Series, and G-Series Remove the housing access door by the following method:•Remove the four (4)aluminum knobs.•Grasp handles on thefront of the door.•Pull the door straightforward, toward yourself.Remove aluminum knobs.Note: The access door on the G-Series is round; however, it is removed in the same manner.Pull door forward.Door Latches on BF-Series and BG-Series Standard latches are threaded studs with removable knobs.The studs align with the retainers provided at each corner of the door and are secured with hand knobs, as shown.Swivel Door Latch (Standard on G-Series; optional on BF-Series and BG-Series)Swivel latches swing away from the door to facilitate its removal during the bag-in/bag-out procedure. The hand knobs are held captive on the swivel latch assembly as a precaution against dropping or losing them.Swivel Latch in Closed PositionSwivel Latch in Swing-Away PositionCaution: Avoid contacting door gasket with door bolts as door is removed to prevent damage to gasket material. Also, the door must be positioned in a way to prevent the gasket frombeing damaged.17STEP 2: BF-Series•Release primary filter locking mechanism handle from handle latch.•Swing handle to full open position.Release filter locking arm from handle latch.Filter Locking Arm in Full Open PositionSTEP 3: BF-Series•Insure that filter clips are alignedproperly on the mechanism angle.(Refer to the filter manufacturer’s instructions if clips have not been factory installed.)•Filter clips must interface with filter locking mechanism angle at top and bottom of filter, as shown:Filter Clip to Mechanism Angle DetailFilter ClipFilter Locking Mechanism AngleFilter Frame (Wood or Metal)18STEP 4: BF-Series•Load filter(s) into housing insuring the filter(s) is installed in the correct position.•When air flow is horizontal,separators — or pleats — of prefilter(s) and HEPA filter(s) must run vertical and carbon beds of carbon ad-sorbers must run horizontal .•When sliding the filter(s) in the hous-ing, use the locking mechanism angles as guides by aligning filter clips over mechanism angles and gently but firmly pushing the filter(s) until ittouches the back of the housing or as far as can be reached.•On multi-wide filter housings, repeat procedure for each filter until all filters are installed.•On three-wide filter housings, it may be necessary to use the second filter to push the filter all the way to the back of the housing.Install HEPA filters with pleatsin vertical position.Install adsorbers with beds in horizontal position.STEP 5: BF-Series•Lock filter(s) in place to the housing’sfilter sealing knife-edge by swinging the locking mechanism handle to theclosed position (towards handle latch).Locking Mechanism Latched with Filters InstalledNote: Air flow arrows on filters normally indicate thedirection of air flow during the manufacturer’s factory testing. When installed in a system (filter housing),air may flow through a HEPA filter or adsorber from both directions. It is important that the filter sealing gel filled channel is in contact with the filter housing’s knife edge sealing surface.Note: The locking mechanism handle isdesigned to provide tension against the handle latch with filters installed. Apply the required pressure to the handle with one hand and swing the handle latchover the handle with the other hand.19STEP 6: BG-Series •Be sure the filter locking mechanism is completely open by turning each mechanism counterclockwise with the standard ratchet until you feel it bottom out .Operator Cranking Top Locking Mechanism← Operator Cranking Bottom Locking MechanismATTENTION:Recommended Step for BG and G1GTo prevent filter gasket from sticking to the housing sealing surface after being compressed for an extended period, the entire face of each new filter gasket must be coated with a silicone grease (Flanders/CSC’s Part Number 03-009)before being installed. A 1/8 - 3/16 inch diameter bead of silicone grease should be applied to the middle of the entire 3/4 inch wide filter gasket.The grease should then be spread evenly across the entire gasket face. This thin coating of sili-cone grease acts as a release agent and will also help achieve and maintain a good filter-to-housing seal.Caution: Do not use RTV (Room TemperatureVulcanizing). RTV would stick filter to housing, thereby compounding potential problems of filter removal.Apply bead of grease on center of gasket strips.Evenly spread grease over entire gasket.20STEP 7: BG-Series•Load filter(s) into housing insuring the filter(s)is installed in the correct position.•When air flow is horizontal, separators —or pleats — of prefilter(s) and HEPAfilter(s) must run vertical and carbon beds of carbon adsorbers must run horizontal .•When sliding the filter(s) in the housing, it is helpful to use the pressure bars on the locking mechanism as guides by butting the non-gasket side of the filter(s) to the bars and gently but firmly pushing the filter(s) until it touches the back of the housing, or as far as can be reached.•On multi-wide filter housings, repeatprocedure for each filter until all filters are installed.•On three-wide filter housings, it may be necessary to use the second filter to push the filter all the way to the back of the housing.Note: Air flow arrows on filters normally indicate the direction of air flow during the manufacturer’s factory testing. When installed in a system (filter housing), air may flow through a HEPA filter or adsorber from either direction. It is important that the filter sealing gasket is in contact with the filter housing’s sealing surface.One of the features unique to some of Flanders/CSC’s generic seismic qualified filter housing designs is the filter retaining clips. These clips are required on housings with specific seismic loads. The retaining clips are required to keep the filters stable and functioning during a seismic event.During installation or change-out of filters, care should be taken to avoid contact between clips and filters.Caution for Seismic BF and BG-Series Housing Designs OnlyInstall HEPA filters with pleatsin vertical position.Install adsorbers with bedsin horizontal position.FilterRetaining Clip(Typical Top and Bottom of Filter)Bagging Ring Filter Seal SurfaceHousingTop of FilterSTEP 8: BG-Series•Lock filter(s) in place to the housingsealing surface by alternating from top locking mechanism to bottom locking mechanism.•First, turn top locking mechanismclockwise with ratchet until filter(s)is snug, not completely tightened.•Second, turn bottom lockingmechanism until filter is completely tightened. There are factory-installed stops to determine when the filter is sealed.•Third, completely tighten the top locking mechanism. There arefactory-installed stops to determine when the filter is sealed.•The filter(s) is now sealed.Note: Refer to chart below for maximum recommended torque for locking mechanism of various size housings.STEP 10: G1F and G1G Series•Pick up the filter by the frame, taking care not totouch the filter element. If the door is on the side of the housing, turn the filter so that the pleats in the medium are vertical. The filter seal-ing surface must face toward the housing seal surface. Take care not to hit the clamp arm handles with the filter. The clamp arms will help guide the filter onto the knife edge. When the filter in G1F housings meets the knife edge, there will be some resistance; however, push the fil-ter frame firmly until it will go no further. This mates the knife edge into the gel-filled channel.For G1G housing see step 6 to help prevent fil-ter gasket from sticking to the housing.STEP 9: G1F and G1G Series•If the clamp arm handles are pointing towardthe center of the housing, they will not permit filter installation.Pull the handles and turn 90° to one side.(Stops will permit turning in one direction only.)Filter Clamping Mechanism for G-Series*Exceeding these limits could damage mechanismFilter Seal SurfacePressure BarGel-Filled Channel orGasketFilter Locking Mechanism Torque Requirements Maximum Torque* LimitHousing FilterWidth Normal Torque Required to SealFilter(s)(3)Three filters wide(2)Two filters wide (1)One filter wide 11-13 ft. lbs.22-23 ft. lbs.32-38 ft. lbs.18 ft. lbs.28 ft. lbs.43 ft. lbs.STEP 11: G1F and G1G SeriesFilter Locked into Place on G-Series HousingSTEP 12: BF-Series, BG-Series, andG-Series•Place plastic bag over bag-in/bag-out ring.Shock cord of plastic bag is to be located between second rib of bag-in/bag-out ring and the housing frame.It is easier to work bag from bottom to topof bag-in/bag-out ring. Locate seam of bag at top of ring, so gloves in bag are inthe correct position.•Turn the clamp arm handles 90° toward the filter.Each handle will snap into place, indicating thatthe clamping mechanism is locked, holding thefilter onto the knife edge of the G1F housing.•Turn the “T” handles on the clamping arm untilthe clamping arm pressure bar bottoms out onthe preesure bar stops for the G1G housing.HousingShock CordSecurityStrapSecond RibBagging RingFirst RibBag•Locate security strap between first and second ribs of the bag-in/bag-out ring.•Loop the end of the security strap through the D-ring.•Tighten security strap and secure any excess strap so it won’t interfere with the door seal when it is replaced.STEP 13:BF-Series, BG-Series, andG-Series Locate D-Ring on strap at top of bag-in/bag-out ring before tightening.Pull strap until it is tight around the bag-in/bag-out ring. Press Velcro together. Secure excess strapso it will not interfere with the door seal.STEP 14: BF-Series, BG-Series, andG-Series•Gather bag at a point near the lip ofthe bag-in/bag-out ring, drawing the bag taut (being careful not to pull the bag off the bag-in/bag-out ring); allow the slack to fall off to the side.•Place the cinching strap aroundbag and pull taut.The nylon cinching strap helps minimize the possibility of the bag being drawn into the housing during operation.。