A Note on Amplifying the Error-Tolerance of Locally Decodable Codes
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Q1126pis Rev 01/221Product InformationQ Sepharose ® Fast FlowQ1126Product DescriptionQ Sepharose ® Fast Flow is an ion exchangechromatography resin with a quaternary amine (Q) functional group [-CH 2-N +(CH 3)3] attached to Sepharose ® Fast Flow. The Q group serves as astrong anion exchanger, which is completely ionized over a broad pH range. The terms “s trong" and"weak" in ion exchange chromatography refer to the extent of ionization with pH, and not to the binding strength of the functional group to the target species. The parent Sepharose ® Fast Flow is a cross-linked derivative of Sepharose ®. The particle size range is 45-165 µm. The average bead diameter is ~90 µm. The counterion in the product is sulfate (SO 4-2). Recommended cation buffers to use with Q Sepharose ® Fast Flow include alkylamines,ammonium, ethylenediamine, imidazole, pyridine, or Tris. In terms of pH, it is suggested to operate within 0.5 pH unit of the buffer's pK a . With proteins, it is suggested to operate at least 1 pH unit above the pI of the protein, to facilitate binding. Oxidizing agents, and anionic detergents and buffers, should not be used with Q Sepharose ® Fast Flow. Likewise,extended exposure of Q1126 to pH < 4 should be avoided. Several publications 1,2 and dissertations 3-5 cite use of product Q1126 in their research.ReagentQ Sepharose ® Fast Flow is offered as a suspension in 20% ethanol.Approximate Exclusion Limit: average molecular mass of ~4 × 106 DaltonsIonic Capacity: 0.18-0.24 mmol Cl -/mL gel Binding Capacity: ~42 mg BSA per mL gel pH Stability: 2-12Working temperature: 4-40 °CPrecautions and DisclaimerFor R&D use only. Not for drug, household, or other uses. Please consult the Safety Data Sheet for information regarding hazards and safe handling practices. General Resin Preparation Procedure1. Allow the ion exchange medium and ~10 columnvolumes (CV) of buffer to equilibrate to thetemperature chosen for the chromatographic run. 2. Mix the pre-swollen suspension with startingbuffer to form a moderately thick slurry, which consists of ~75% settled gel and 25% liquid. 3. Degas the gel under vacuum at the temperatureof column operation.4. Mount the column vertically on a suitable stand,out of the way of direct sunlight or drafts, which may cause temperature fluctuations.5. Pour a small amount of buffer into the emptycolumn. Allow the buffer to flow through spaces to eliminate air pockets.6. Pour the suspension of ion exchange mediumprepared in Step 3 into the column by allowing it to flow gently down the side of the tube, to avoid bubble formation.7. For consistent flow rates and reproducibleseparations, connect a pump to the column. 8. Fill the remainder of the column to the top withbuffer. Allow ~5 CV of buffer to drain through the bed at a flow rate at least 133% of the flow rate to be used in the procedure. The bed height should have settled to a constant height.9. Using a syringe or similar instrument, apply thesample dissolved in starting buffer to the column. For isocratic separations, the sample volumeshould range from 1-5% of the column volume. If the chromatographic run involves elution with a gradient, the applied sample mass is of much greater importance than the sample volume, and the sample should be applied in a low ionicstrength medium. Ion exchange is used both to concentrate and to fractionate the sample. 10. Elution:• If only unwanted substances in the sample areadsorbed, or if sample components aredifferentially retarded under isocratic conditions, the starting buffer can also be used as the eluent.The life science business of Merck operates as MilliporeSigma in the U.S. and Canada.Merck and Sigma-Aldrich are trademarks of Merck KGaA, Darmstadt, Germany or its affiliates. All other trademarks are the property of their respective owners. Detailed information on trademarks is available via publicly accessible resources.© 2022 Merck KGaA, Darmstadt, Germany and/or its affiliates. All Rights Reserved. Q1126pis Rev 01/22 JJJ,MAM,GCY2•Normally, however, separation and elution are achieved by selectively decreasing the affinity of the molecules for the charged groups on the resin by changing the pH and/or ionic strength of the eluent. This procedure is termed gradient elution. 11. Regeneration: •Either (a) washing the column with a high ionic strength salt solution, such as 1 M NaCl, or (b) changing the pH to the tolerable low and high pH extremes, is usually sufficient to remove reversibly bound material.• When needed, lipids and precipitated proteins canbe removed by washing with 1 CV of 1-2 M NaCl, followed by 1 CV of 0.1 M NaOH in 0.5 M NaCl. • Rinse with several CV of water. Thenre-equilibrate the resin with starting buffer.• If base such as NaOH was used, adjust the pH ofthe resin to neutral before storing or using.12. Storage: Q Sepharose ® Fast Flow may be storedat 2-8 °C in water with 20% ethanol added as an antibacterial agent.General NotesCation versus Anion Exchanger• If sample components are most stable below their pI values, a cation exchanger should be used. • If sample components are most stable above their pI values, an anion exchanger should be used. •If stability is good over a wide pH range on both sides of the pI, either or both types of ion exchanger may be used.Strong versus Weak Ion Exchanger•Most proteins have pI values within the range 5.5-7.5, and can thus be separated on both strong and weak ion exchangers.•When maximum resolution occurs at an extreme pH and the molecules of interest are stable at that pH, a strong ion exchanger should be used. Choice of Buffer, pH, and Ionic Strength• The highest ionic strength which permits binding should normally be used.•The required buffer concentration varies fromsubstance to substance. Usually, an ionic strength of at least 10 mM is required to ensure adequate buffering capacity.•As salts (such as buffers) help to stabilize proteins in solution, their concentration should be highenough to prevent denaturation and precipitation.References1. López, G. et al ., Eukaryot. Cell , 14(6), 564-577(2015).2. Bhargava, V. et al ., Dev. Cell., 52(1), 38-52.e10(2020).3. Fu , Yinan, “Structure and dynamics ofPseudomonas aeruginosa ICP”. University ofGlasgow, Ph.D. dissertation, p. 126 (April 2009). 4. Redmond, Miranda , “The Role of N-TerminalAcidic Inserts on the Dynamics of the Tau Protein ”. University of Vermont, Ph.D. dissertation, p. 22 (May 2017).5. Taylor-Whiteley, Teresa Rachel , “RecapitulatingParkinson’s disease pathology in athree-dimensional neural cell culture mode ”. Sheffield Hallam University, Ph.D. dissertation, p. 58 (September 2019).NoticeWe provide information and advice to our customers on application technologies and regulatory matters to the best of our knowledge and ability, but without obligation or liability. Existing laws and regulations are to be observed in all cases by our customers. This also applies in respect to any rights of third parties. Our information and advice do not relieve ourcustomers of their own responsibility for checking the suitability of our products for the envisaged purpose. The information in this document is subject to change without notice and should not be construed as acommitment by the manufacturing or selling entity, or an affiliate. We assume no responsibility for any errors that may appear in this document.Technical AssistanceVisit the tech service page at /techservice .Standard WarrantyThe applicable warranty for the products listed in this publication may be found at /terms .Contact InformationFor the location of the office nearest you, go to /offices .。
A v i a t i o nPhone: (860) 526-9504Internet: Sales/Service e-mail: info@©2016 Whelen Aerospace Technologies Form No. 14986A (062119)Installation Guide/ICA:Model 9035450P/N 01-0790354-50LED Tail Navigation and Anti-Collision Light AssemblyThe conditions and tests required for TSO approval of this article are minimum performance standards.Those installing this article either on or within a specific type or class of aircraft must determine that the aircraft installation conditions are within the TSO standards which include any accepted integrated non-TSO functions. TSO articles and any accepted integrated non-TSO function(s) must have separate approval for installation in an aircraft. The article may be installed only according to 14 CFR part 43 or the applicable airworthiness requirements.WARNING: This product can expose you to chemicals including Methylene Chloride which is known to the State of California to cause cancer, and Bisphenol A, which is known to the State of California to cause birth defects or other reproductive harm. For more information go to .TSO-C30c TYPE III APPROVEDTSO-C96a CLASS II APPROVED1.651.82 3.88 4.851.65DrainPassagesPIN-OUT CONNECTIONSD38999/20FB5PNPINABCDE28VDC POSITION GROUND 28VDC ACL GROUND SYNCHRONIZE**OUTPUT ONLYSIGNAL (2.11) 1.581.031SPECIFICATIONS:Nominal Operational Voltage:......................28 VDC (operational from 24-32VDC)With 7114801 Flasher Anti-CollisionAverage Current..............................0.53 ampsPulse Current:.................................2.8 amps@250 ms Flashrate.........................................45± 5 per min.NavigationCurrent............................................0.16 ampsEQUIPMENT LIMITATIONS:An approved lighting system consists of three lights, one located on the tail and one located on each wingtip. Model 9035450 is a tail position and anti-collision light. The assembly should be mounted as far aft on the aircraft as practicable on a thermally conductive surface. The baseplate must be mounted parallel to the vertical and horizontal centerlines of the aircraft to project the patterns properly.Certain types of installations may require additional testing.AIRWORTHINESS LIMITATIONS: The Airworthiness Limitations section is FAA approved and specifies inspections and other maintenance required under §43.16 and §91.403 of the Federal Aviation Regulations, unless an alternative program has been approved.No airworthiness limitations are associated with the installation of the light assembly.CONTINUED AIRWORTHINESS:The tail navigation light is designed with 4 LEDs. The anti-collision light is designed with 30 LEDs. If any one LED fails, the unit must be repaired or replaced. NOTE: To reduce eye strain, use an optical filter such as dark glasses or a blue covering dome during LED inspection. Inspect the lens.Replace if there is excessive scratching, pitting, discoloration or cracking. For additional lens maintenance detail, see SAE ARP5637.Note: The anti-collision light has an internal diagnostic circuit that will shut-off after 20-25 flashes if a failure is detected.PERIODIC INSPECTIONS: An annual inspection shall be performed unless the OEM specifies a shorter interval. INSTALLATION PROCEDURES:1.Using the mounting detail information provided, prepare the aircraft for means to secure the light assembly.2.Remove the 2, #6 Phillips head screws and lens retainers. Carefully remove lens. Remove 3 Phillips head screws securing the baseplate to the light assembly. Remove the baseplate. CAUTION: Do not touch LEDs with either fingers or sharp objects. This could soil and/or damage the LED, effecting the optical performance of the light.ing the appropriate hardware, install the baseplate directly to the aircraft, making sure the single post end is up.4.Route the wires through the opening in the baseplate. Connect the light inputs according to the chart shown. Connect the power lead to an appropriately sized breaker. Connections to be in accordance with FAA approved methods.Note: SYNC is a low-power, output control signal. Connecting to the synchronize signal of any WAT LED anti-collision assembly will cause the lights to flash at the same time. If synchronization is not necessary, the connection may be left open.5.Reinstall the light assembly onto the baseplate and insure that all leads are clear of any obstructions and secured as required. Note that proper orientation is achieved with the drain holes down.6.Reinstall the lens and secure using the retainers and screws. Note:Visually confirm that the lens, gasket and retainers are fully and properly seated.7.When necessary, waterproof the light base to the aircraft. Apply single part silicone (RTV) or equivalent around any open area where water could get in. Do not cover the drain holes.8.Check all avionics systems for interference from this installation.9. A flight check should be performed by a properly certified pilot.10.If required, update aircraft records utilizing FAA Field Approval (Form 337) or equivalent.。
NAMESoX − Sound eXchange, the Swiss Army knife of audio manipulationSYNOPSISsox[global-options][format-options]infile1[[format-options]infile2]... [format-options]outfile[effect[effect-options]] ...play[global-options][format-options]infile1[[format-options]infile2]... [format-options][effect[effect-options]] ...rec[global-options][format-options]outfile[effect[effect-options]] ...DESCRIPTIONIntroductionSoX reads and writes audio files in most popular formats and can optionally apply effects to them. It can combine multiple input sources, synthesise audio, and, on many systems, act as a general purpose audio player or a multi-track audio recorder.It also has limited ability to split the input into multiple output files.All SoX functionality is available using just the sox command. To simplify playing and recording audio, if SoX is invoked as play,the output file is automatically set to be the default sound device, and if invoked as rec,the default sound device is used as an input source.Additionally,the soxi(1) command provides a con-venient way to just query audio file header information.The heart of SoX is a library called libSoX.Those interested in extending SoX or using it in other pro-grams should refer to the libSoX manual page:libsox(3).SoX is a command-line audio processing tool, particularly suited to making quick, simple edits and to batch processing. If you need an interactive,graphical audio editor,use audacity(1).***The overall SoX processing chain can be summarised as follows:Input(s)→Combiner→Effects→Output(s)Note however, that on the SoX command line, the positions of the Output(s) and the Effects are swapped w.r.t. the logical flow just shown. Note also that whilst options pertaining to files are placed before their respective file name, the opposite is true for effects. To show how this works in practice, here is a selection of examples of how SoX might be used.The simplesox recital.au recital.wavtranslates an audio file in Sun AU format to a Microsoft WA Vfile, whilstsox recital.au −b 16 recital.wav channels 1 rate 16k fade 3 norm performs the same format translation, but also applies four effects (down-mix to one channel, sample rate change, fade-in, nomalize), and stores the result at a bit-depth of 16.sox −r 16k −e signed −b 8 −c 1 voice-memo.raw voice-memo.wav converts ‘raw’ (a.k.a. ‘headerless’) audio to a self-describing file format,sox slow.aiff fixed.aiff speed 1.027adjusts audio speed,sox short.wav long.wav longer.wavconcatenates two audio files, andsox −m music.mp3 voice.wav mixed.flacmixes together two audio files.play "The Moonbeams/Greatest/*.ogg" bass +3plays a collection of audio files whilst applying a bass boosting effect,play −n −c1 synth sin %−12 sin %−9 sin %−5 sin %−2 fade h 0.1 1 0.1 plays a synthesised ‘A minor seventh’ chord with a pipe-organ sound,rec −c 2 radio.aiff trim 0 30:00records half an hour of stereo audio, andplay −q take1.aiff & rec −M take1.aiff take1-dub.aiff(with POSIX shell and where supported by hardware) records a new track in a multi-track recording.Finally,rec −r 44100 −b 16 −s −p silence 1 0.50 0.1% 1 10:00 0.1% | \ sox −p song.ogg silence 1 0.50 0.1% 1 2.0 0.1% : \newfile : restartrecords a stream of audio such as LP/cassette and splits in to multiple audio files at points with 2 seconds of silence. Also,it does not start recording until it detects audio is playing and stops after it sees 10 minutes of silence.N.B. The above is just an overview of SoX’s capabilities; detailed explanations of how to use all SoX parameters, file formats, and effects can be found below in this manual, in soxformat(7), and in soxi(1). File Format TypesSoX can work with ‘self-describing’ and ‘raw’ audio files.‘self-describing’ formats (e.g. W A V,FLAC, MP3) have a header that completely describes the signal and encoding attributes of the audio data that fol-lows. ‘raw’ or ‘headerless’ formats do not contain this information, so the audio characteristics of these must be described on the SoX command line or inferred from those of the input file.The following four characteristics are used to describe the format of audio data such that it can be pro-cessed with SoX:sample rateThe sample rate in samples per second (‘Hertz’ or ‘Hz’).Digital telephony traditionally uses asample rate of 8000Hz (8kHz), though these days, 16 and even32kHz are becoming more com-mon. Audio Compact Discs use 44100Hz (44.1kHz). Digital Audio Tape and many computersystems use 48 kHz. Professional audio systems often use 96 kHz.sample sizeThe number of bits used to store each sample.Today,16-bit is commonly used. 8-bit was popularin the early days of computer audio. 24-bit is used in the professional audio arena. Other sizes arealso used.data encodingThe way in which each audio sample is represented (or ‘encoded’).Some encodings have variantswith different byte-orderings or bit-orderings.Some compress the audio data so that the storedaudio data takes up less space (i.e. disk space or transmission bandwidth) than the other formatparameters and the number of samples would monly-used encoding types includefloating-point,µ-law, ADPCM, signed-integer PCM, MP3, and FLAC.channelsThe number of audio channels contained in the file.One (‘mono’) and two(‘stereo’) are widelyused. ‘Surround sound’ audio typically contains six or more channels.The term ‘bit-rate’ is a measure of the amount of storage occupied by an encoded audio signal over a unit of time.It can depend on all of the above and is typically denoted as a number of kilo-bits per second (kbps). An A-law telephony signal has a bit-rate of 64 kbs. MP3-encoded stereo music typically has a bit-rate of 128−196 kbps. FLAC-encoded stereo music typically has a bit-rate of 550−760 kbps.Most self-describing formats also allow textual ‘comments’ to be embedded in the file that can be used to describe the audio in some way,e.g. for music, the title, the author,etc.One important use of audio file comments is to convey ‘Replay Gain’ information.SoX supports applying Replay Gain information, but not generating it.Note that by default, SoX copies input file comments to output files that support comments, so output files may contain Replay Gain information if some was present in the input file.In this case, if anything other than a simple format conversion was performed then the output file Replay Gain information is likely to be incorrect and so should be recalculated using a tool that supports this (not SoX).The soxi(1) command can be used to display information from audio file headers.Determining & Setting The File FormatThere are several mechanisms available for SoX to use to determine or set the format characteristics of an audio file.Depending on the circumstances, individual characteristics may be determined or set using dif-ferent mechanisms.To determine the format of an input file, SoX will use, in order of precedence and as given or available:mand-line format options.2.The contents of the file header.3.The filename extension.To set the output file format, SoX will use, in order of precedence and as given or available:mand-line format options.2.The filename extension.3.The input file format characteristics, or the closest that is supported by the output file type.For all files, SoX will exit with an error if the file type cannot be determined. Command-line format options may need to be added or changed to resolve the problem.Playing & Recording AudioThe play and rec commands are provided so that basic playing and recording is as simple as play existing-file.wavandrec new-file.wavThese two commands are functionally equivalent tosox existing-file.wav −dandsox −d new-file.wavOf course, further options and effects (as described below) can be added to the commands in either form.***Some systems provide more than one type of (SoX-compatible) audio driver, e.g. ALSA & OSS, or SUNAU & AO.Systems can also have more than one audio device (a.k.a. ‘sound card’).If more than one audio driver has been built-in to SoX, and the default selected by SoX when recording or playing is not the one that is wanted, then the AUDIODRIVER environment variable can be used to override the default.For example (on many systems):set AUDIODRIVER=ossplay ...The AUDIODEV environment variable can be used to override the default audio device, e.g.set AUDIODEV=/dev/dsp2play ...sox ... −t ossorset AUDIODEV=hw:soundwave,1,2play ...sox ... −t alsaNote that the way of setting environment variables varies from system to system—for some specific exam-ples, see ‘SOX_OPTS’ below.When playing a file with a sample rate that is not supported by the audio output device, SoX will automati-cally invoke the rate effect to perform the necessary sample rate conversion. For compatibility with old hardware, the default rate quality level is set to ‘low’. This can be changed by explicitly specifying the rate effect with a different quality level, e.g.play ... rate −mor by using the−−play−rate−arg option (see below).***On some systems, SoX allows audio playback volume to be adjusted whilst using play.Where supported, this is achieved by tapping the ‘v’ & ‘V’ keys during playback.To help with setting a suitable recording level, SoX includes a peak-level meter which can be invoked (before making the actual recording) as follows:rec −nThe recording level should be adjusted (using the system-provided mixer program, not SoX) so that the meter is at most occasionally full scale, and never‘in the red’ (an exclamation mark is shown). See also−S below.AccuracyManyfile formats that compress audio discard some of the audio signal information whilst doing so. Con-verting to such a format and then converting back again will not produce an exact copy of the original audio. This is the case for many formats used in telephony(e.g. A-law, GSM) where low signal bandwidth is more important than high audio fidelity,and for many formats used in portable music players (e.g. MP3, V orbis) where adequate fidelity can be retained even with the large compression ratios that are needed to make portable players practical.Formats that discard audio signal information are called ‘lossy’.Formats that do not are called ‘lossless’.The term ‘quality’ is used as a measure of how closely the original audio signal can be reproduced when using a lossy format.Audio file conversion with SoX is lossless when it can be, i.e. when not using lossy compression, when not reducing the sampling rate or number of channels, and when the number of bits used in the destination for-mat is not less than in the source format. E.g. converting from an 8-bit PCM format to a 16-bit PCM for-mat is lossless but converting from an 8-bit PCM format to (8-bit) A-law isn’t.N.B.SoX converts all audio files to an internal uncompressed format before performing any audio process-ing. This means that manipulating a file that is stored in a lossy format can cause further losses in audio fidelity.E.g. withsox long.mp3 short.mp3 trim 10SoX first decompresses the input MP3 file, then applies the trim effect, and finally creates the output MP3file by re-compressing the audio—with a possible reduction in fidelity above that which occurred when the input file was created.Hence, if what is ultimately desired is lossily compressed audio, it is highly recom-mended to perform all audio processing using lossless file formats and then convert to the lossy format only at the final stage.N.B.Applying multiple effects with a single SoX invocation will, in general, produce more accurate results than those produced using multiple SoX invocations.DitheringDithering is a technique used to maximise the dynamic range of audio stored at a particular bit-depth. Any distortion introduced by quantisation is decorrelated by adding a small amount of white noise to the signal.In most cases, SoX can determine whether the selected processing requires dither and will add it during output formatting if appropriate.Specifically,by default, SoX automatically adds TPDF dither when the output bit-depth is less than 24 and any of the following are true:•bit-depth reduction has been specified explicitly using a command-line option•the output file format supports only bit-depths lower than that of the input file format•an effect has increased effective bit-depth within the internal processing chainFor example, adjusting volume with vol0.25requires two additional bits in which to losslessly store its results (since 0.25 decimal equals 0.01 binary).So if the input file bit-depth is 16, then SoX’s internal rep-resentation will utilise 18 bits after processing this volume change.In order to store the output at the same depth as the input, dithering is used to remove the additional bits.Use the−V option to see what processing SoX has automatically added. The−D option may be given to override automatic dithering.To inv o ke dithering manually (e.g. to select a noise-shaping curve), see the dither effect.ClippingClipping is distortion that occurs when an audio signal level(or ‘volume’) exceeds the range of the chosen representation. In most cases, clipping is undesirable and so should be corrected by adjusting the level prior to the point (in the processing chain) at which it occurs.In SoX, clipping could occur,as you might expect, when using the vol or gain effects to increase the audio volume. Clipping could also occur with many other effects, when converting one format to another,and ev e n when simply playing the audio.Playing an audio file often involves resampling, and processing by analogue components can introduce a small DC offset and/or amplification, all of which can produce distortion if the audio signal level was ini-tially too close to the clipping point.For these reasons, it is usual to make sure that an audio file’s signal level has some ‘headroom’, i.e. it does not exceed a particular level below the maximum possible level for the given representation. Some stan-dards bodies recommend as much as 9dB headroom, but in most cases, 3dB (≈70% linear) is enough.Note that this wisdom seems to have been lost in modern music production; in fact, many CDs, MP3s, etc.are now mastered at levels above0dBFS i.e. the audio is clipped as delivered.SoX’s stat and stats effects can assist in determining the signal level in an audio file. The gain or vol effect can be used to prevent clipping, e.g.sox dull.wav bright.wav gain −6 treble +6guarantees that the treble boost will not clip.If clipping occurs at any point during processing, SoX will display a warning message to that effect.See also−G and the gain and norm effects.Input File CombiningSoX’s input combiner can be configured (see OPTIONS below) to combine multiple files using any of the following methods: ‘concatenate’, ‘sequence’, ‘mix’, ‘mix-power’, ‘merge’, or ‘multiply’.The default method is ‘sequence’ for play,and ‘concatenate’ for rec and sox.For all methods other than ‘sequence’, multiple input files must have the same sampling rate. If necessary, separate SoX invocations can be used to make sampling rate adjustments prior to combining.If the ‘concatenate’ combining method is selected (usually,this will be by default) then the input files must also have the same number of channels.The audio from each input will be concatenated in the order given to form the output file.The ‘sequence’ combining method is selected automatically for play.It is similar to ‘concatenate’ in that the audio from each input file is sent serially to the output file. However, here the output file may be closed and reopened at the corresponding transition between input files. This may be just what is needed when sending different types of audio to an output device, but is not generally useful when the output is a normal file.If either the ‘mix’ or ‘mix-power’ combining method is selected then two or more input files must be given and will be mixed together to form the output file.The number of channels in each input file need not be the same, but SoX will issue a warning if they are not and some channels in the output file will not contain audio from every input file.A mixed audio file cannot be un-mixed without reference to the original input files.If the ‘merge’ combining method is selected then two or more input files must be given and will be merged together to form the output file.The number of channels in each input file need not be the same.A merged audio file comprises all of the channels from all of the input files. Un-merging is possible using multiple invocations of SoX with the remix effect. For example, two mono files could be merged to form one stereo file. The first and second mono files would become the left and right channels of the stereo file.The ‘multiply’ combining method multiplies the sample values of corresponding channels (treated as num-bers in the interval −1 to +1).If the number of channels in the input files is not the same, the missing chan-nels are considered to contain all zero.When combining input files, SoX applies any specified effects (including, for example, the vol volume adjustment effect) after the audio has been combined. However, it is often useful to be able to set the vol-ume of (i.e. ‘balance’) the inputs individually,before combining takes place.For all combining methods, input file volume adjustments can be made manually using the−v option (below) which can be given for one or more input files. If it is given for only some of the input files then the others receive no volume adjustment.In some circumstances, automatic volume adjustments may be applied (see below).The−V option (below) can be used to show the input file volume adjustments that have been selected (either manually or automatically).There are some special considerations that need to made when mixing input files:Unlike the other methods, ‘mix’ combining has the potential to cause clipping in the combiner if no balanc-ing is performed.In this case, if manual volume adjustments are not given, SoX will try to ensure that clip-ping does not occur by automatically adjusting the volume (amplitude) of each input signal by a factor of ¹/n,where n is the number of input files.If this results in audio that is too quiet or otherwise unbalanced then the input file volumes can be set manually as described ing the norm effect on the mix is another alternative.If mixed audio seems loud enough at some points but too quiet in others then dynamic range compression should be applied to correct this—see the compand effect.With the ‘mix-power’ combine method, the mixed volume is approximately equal to that of one of the input signals. This is achieved by balancing using a factor of ¹/√n instead of ¹/n.Note that this balancing factor does not guarantee that clipping will not occur,but the number of clips will usually be low and the resultant distortion is generally imperceptible.Output FilesSoX’s default behaviour is to take one or more input files and write them to a single output file.This behaviour can be changed by specifying the pseudo-effect ‘newfile’ within the effects list.SoX will then enter multiple output mode.In multiple output mode, a newfile is created when the effects prior to the ‘newfile’ indicate they are done.The effects chain listed after ‘newfile’ is then started up and its output is saved to the newfile.In multiple output mode, a unique number will automatically be appended to the end of all filenames.If the filename has an extension then the number is inserted before the extension. This behaviour can be custom-ized by placing a %n anywhere in the filename where the number should be substituted.An optional num-ber can be placed after the % to indicate a minimum fixed width for the number.Multiple output mode is not very useful unless an effect that will stop the effects chain early is specified before the ‘newfile’. If end of file is reached before the effects chain stops itself then no newfile will be cre-ated as it would be empty.The following is an example of splitting the first 60 seconds of an input file into two30second files and ignoring the rest.sox song.wav ringtone%1n.wav trim 0 30 : newfile : trim 0 30Stopping SoXUsually SoX will complete its processing and exit automatically once it has read all available audio data from the input files.If desired, it can be terminated earlier by sending an interrupt signal to the process (usually by pressing thekeyboard interrupt key which is normally Ctrl-C).This is a natural requirement in some circumstances, e.g.when using SoX to make a recording. Note that when using SoX to play multiple files, Ctrl-C behaves slightly differently: pressing it once causes SoX to skip to the next file; pressing it twice in quick succession causes SoX to exit.Another option to stop processing early is to use an effect that has a time period or sample count to determine the stopping point. The trim effect is an example of this.Once all effects chains have stopped then SoX will also stop.FILENAMESFilenames can be simple file names, absolute or relative path names, or URLs (input files only).Note that URL support requires that wget(1) is available.Note: Giving SoX an input or output filename that is the same as a SoX effect-name will not work since SoX will treat it as an effect specification.The only work-around to this is to avoid such filenames. This is generally not difficult since most audio filenames have a filename ‘extension’, whilst effect-names do not.Special FilenamesThe following special filenames may be used in certain circumstances in place of a normal filename on the command line:−SoX can be used in simple pipeline operations by using the special filename ‘−’ which, if used as an input filename, will cause SoX will read audio data from ‘standard input’ (stdin), and which, ifused as the output filename, will cause SoX will send audio data to ‘standard output’ (stdout).Note that when using this option for the output file, and sometimes when using it for an input file,the file-type (see−t below) must also be given."|program[options]..."This can be used in place of an input filename to specify the the given program’s standard output(stdout) be used as an input file.Unlike−(above), this can be used for several inputs to one SoXcommand. For example, if ‘genw’ generates mono W A V formatted signals to its standard output,then the following command makes a stereo file from two generated signals:sox −M "|genw −−imd −" "|genw −−thd −" out.wavFor headerless (raw) audio,−t(and perhaps other format options) will need to be given, precedingthe input command."wildcard-filename"Specifies that filename ‘globbing’ (wild-card matching) should be performed by SoX instead of bythe shell.This allows a single set of file options to be applied to a group of files.For example, ifthe current directory contains three ‘vox’ files, file1.vox, file2.vox, and file3.vox, thenplay −−rate 6k *.voxwill be expanded by the ‘shell’ (in most environments) toplay −−rate 6k file1.vox file2.vox file3.voxwhich will treat only the first vox file as having a sample rate of 6k.Withplay −−rate 6k "*.vox"the given sample rate option will be applied to all three vox files.−p,−−sox−pipeThis can be used in place of an output filename to specify that the SoX command should be usedas in input pipe to another SoX command.For example, the command:play "|sox −n −p synth 2" "|sox −n −p synth 2 tremolo 10" stat plays two‘files’ in succession, each with different effects.−p is in fact an alias for ‘−t sox −’.−d,−−default−deviceThis can be used in place of an input or output filename to specify that the default audio device (ifone has been built into SoX) is to be used.This is akin to invoking rec or play(as describedabove).−n,−−nullThis can be used in place of an input or output filename to specify that a ‘null file’ is to be used.Note that here, ‘null file’ refers to a SoX-specific mechanism and is not related to any operating-system mechanism with a similar name.Using a null file to input audio is equivalent to using a normal audio file that contains an infiniteamount of silence, and as such is not generally useful unless used with an effect that specifies afinite time length (such as trim or synth).Using a null file to output audio amounts to discarding the audio and is useful mainly with effectsthat produce information about the audio instead of affecting it (such as noiseprof or stat).The sampling rate associated with a null file is by default 48kHz, but, as with a normal file, thiscan be overridden if desired using command-line format options (see below).Supported File & Audio Device TypesSee soxformat(7) for a list and description of the supported file formats and audio device drivers. OPTIONSGlobal OptionsThese options can be specified on the command line at any point before the first effect name.The SOX_OPTS environment variable can be used to provide alternative default values for SoX’s global options. For example:SOX_OPTS="−−buffer 20000 −−play-rate-arg −hs −−temp /mnt/temp"Note that setting SOX_OPTS can potentially create unwanted changes in the behaviour of scripts or other programs that invoke SoX. SOX_OPTS might best be used for things (such as in the given example) that reflect the environment in which SoX is being run.Enabling options such as−−no−clobber as default might be handled better using a shell alias since a shell alias will not affect operation in scripts etc.One way to ensure that a script cannot be affected by SOX_OPTS is to clear SOX_OPTS at the start of the script, but this of course loses the benefit of SOX_OPTS carrying some system-wide default options.An alternative approach is to explicitly invoke SoX with default option values, e.g.SOX_OPTS="−V −−no-clobber"...sox −V2 −−clobber $input $output ...Note that the way to set environment variables varies from system to system. Here are some examples:Unix bash:export SOX_OPTS="−V −−no-clobber"Unix csh:setenv SOX_OPTS "−V −−no-clobber"MS-DOS/MS-Windows:set SOX_OPTS=−V −−no-clobberMS-Windows GUI: via Control Panel : System : Advanced : Environment VariablesMac OS X GUI: Refer to Apple’s Technical Q&A QA1067 document.−−buffer BYTES,−−input−buffer BYTESSet the size in bytes of the buffers used for processing audio (default 8192).−−buffer applies toinput, effects, and output processing;−−input−buffer applies only to input processing (for whichit overrides−−buffer if both are given).Be aware that large values for−−buffer will cause SoX to be become slow to respond to requeststo terminate or to skip the current input file.−−clobberDon’t prompt before overwriting an existing file with the same name as that given for the outputfile. This is the default behaviour.−−combine concatenate|merge|mix|mix−power|multiply|sequenceSelect the input file combining method; for some of these, short options are available:−m selects ‘mix’,−M selects ‘merge’, and−T selects ‘multiply’.See Input File Combining above for a description of the different combining methods.−D,−−no−ditherDisable automatic dither—see ‘Dither’ above.An example of why this might occasionally be use-ful is if a file has been converted from 16 to 24 bit with the intention of doing some processing on it, but in fact no processing is needed after all and the original 16 bit file has been lost, then, strictly speaking, no dither is needed if converting the file back to 16 bit.See also the stats effect for how to determine the actual bit depth of the audio within a file.−−effects−file FILENAMEUse FILENAME to obtain all effects and their arguments. Thefile is parsed as if the values were specified on the command line.A new line can be used in place of the special ":" marker to sepa-rate effect chains.This option causes any effects specified on the command line to be discarded.−G,−−guardAutomatically invoke the gain effect to guard against clipping. E.g.sox −G infile −b 16 outfile rate 44100 dither −sis shorthand forsox infile −b 16 outfile gain −h rate 44100 gain −rh dither −s See also−V,−−norm,and the gain effect.−h,−−helpShow version number and usage information.−−help−effect NAMEShow usage information on the specified effect. The name all can be used to show usage on all effects.−−help−format NAMEShow information about the specified file format.The name all can be used to show information on all formats.−−i,−−infoOnly if given as the first parameter to sox,behave as soxi(1).−−interactiveDeprecated alias for−−no−clobber.−m|−MEquivalent to−−combine mix and−−combine merge,respectively.−−magicIf SoX has been built with the optional ‘libmagic’ library then this option can be given to enable its use in helping to detect audio file types.−−multi-threaded|−−single-threadedBy default, SoX is ‘single threaded’.If the−−multi-threaded option is given howev e r then SoX will process audio channels for most multi-channel effects in parallel on hyper-threading/multi-core architectures. This may reduce processing time, though sometimes it may be necessary to use this option in conjuction with a larger buffer size than is the default to gain any benefit from multi-threaded processing (e.g. 131072; see−−buffer above).−−no−clobberPrompt before overwriting an existing file with the same name as that given for the output file.N.B.Unintentionally overwriting a file is easier than you might think, for example, if you acci-dentally entersox file1 file2 effect1 effect2 ...when what you really meant was。
relative error例句1. The relative error of my measurement was only 0.5%, indicating high accuracy.2. The relative error in our experiment demonstrated a minimum of 4% difference.3. The calculated relative error shows that our model's prediction is reliable.4. Even though the relative error was small, it had a significant impact on our results.5. The researchers accounted for the relative error in their data analysis.6. The relative error of the machine learning algorithm was negligible.7. The relative error decreased as we refined our measuring techniques.8. The relative error exceeded our acceptable threshold, making us question our calculations.9. The relative error provides insight into the uncertainty of our measurements.10. The relative error increased when we used a larger sample size for testing.11. We need to calculate the relative error to assess the accuracy of our simulation.12. The relative error between the experimental and theoretical values was within an acceptable range.13. The relative error indicated that our measurement was close to the true value.14. The relative error was due to a systematic error in our experimental setup.15. We need to minimize the relative error to improve the precision of our results.16. The relative error was not significant enough to affect our conclusions.17. Our calculations were robust, and the relative error was minimal.18. The relative error in our analysis revealed discrepancies between the observed and expected values.19. The relative error helped us identify outliers in our dataset.20. The relative error influenced the significance of our statistical findings.21. We need to consider the relative error when interpreting our experimental results.22. The relative error was a result of measurement errors during data collection.23. The relative error was consistent across multiple trials, indicating high precision.24. Our measurements had a relative error of less than 2%, proving their accuracy.25. The relative error was due to limitations in our measuring instruments.26. The relative error highlighted the need for more precise measurement tools.27. The relative error was significantly higher than what we expected.28. By reducing the relative error, we can increase the reliability of our calculations.29. We need to quantify the relative error to validateour mathematical model.30. The relative error can be used as a measure of uncertainty in our results.31. The relative error increased as the variables in our experiment became more diverse.32. Our calculations had a small relative error, indicating high precision.33. The relative error affected our statistical analysis, leading to different conclusions.34. The relative error highlighted the need for recalibration of our measuring instruments.35. The 0.2% relative error indicated a high degree of accuracy in our measurements.36. The relative error was within the acceptable range, suggesting reliable results.37. We need to account for the relative error when reporting our findings.38. The relative error was consistent with previous studies, validating our results.39. The relative error demonstrated the sensitivity of our model to certain parameters.40. We aim to minimize the relative error to improve the reliability of our data.41. The relative error is an essential metric for assessing the quality of our measurements.42. Our calculations had a relative error of 1%, ensuring the accuracy of our results.。
编号报错提示1dat文件中出现----ERROR: 85 elements have missing property definitions. The elements have been identified in element set ErrElem Missing Section.2dat文件中出现----ERROR: in keyword *BEAMSECTION, file "1.inp", line 434056: OdbError: Material name is missing for this section.3dat文件中出现:***ERROR: The volume of 360 elements is zero, small, or negative. Checkcoordinates or node numbering, or modify the mesh seed. In the case of a tetrahedron this error may indicate that all nodes are locatedvery nearly in a plane. The elements have been identified in elementset ErrElemVolSmallNegZero.4dat文件中出现:***ERROR: THE DISTRIBUTING COUPLING WEIGHTS FOR COUPLING NODES LOCATED ON THE NODE-BASED SURFACE HM_COUPDIS_SURFACE_E1530 ARE ALL 0.0000. PLEASE SPECIFY A COUPLING WEIGHT ON THE SURFACE DEFINITION OPTION.5在单元上施加重力加速度的时候,报错如下。
PDE for Finance,Spring2003–Homework4Distributed3/10/03,due3/31/03.Problems1–4concern deterministic optimal control(Section4material);problems5–7 concern stochastic control(Section5material).Warning:this problem set is longer than usual(mainly because Problems1–4,though not especially difficult,are fairly laborious.)1)Consider thefinite-horizon utility maximization problem with discount rateρ.The dynamical law is thusdy/ds=f(y(s),α(s)),y(t)=x,and the optimal utility discounted to time0isu(x,t)=maxα∈ATte−ρs h(y(s),α(s))ds+e−ρT g(y(T)).It is often more convenient to consider,instead of u,the optimal utility discounted to time t;this isv(x,t)=eρt u(x,t)=maxα∈ATte−ρ(s−t)h(y(s),α(s))ds+e−ρ(T−t)g(y(T)).(a)Show(by a heuristic argument similar to those in the Section4notes)that v satisfiesv t−ρv+H(x,∇v)=0with HamiltonianH(x,p)=maxa∈A{f(x,a)·p+h(x,a)}andfinal-time datav(x,T)=g(x).(Notice that the PDE for v is autonomous,i.e.there is no explicit dependence on time.)(b)Now consider the analogous infinite-horizon problem,with the same equation of state,and value function¯v(x,t)=maxα∈A ∞te−ρ(s−t)h(y(s),α(s))ds.Show(by an elementary comparison argument)that¯v is independent of t,i.e.¯v=¯v(x) is a function of x alone.Conclude using part(a)that if¯v isfinite,it solves the stationary PDE−ρ¯v+H(x,∇¯v)=0.12)Recall Example1of the Section4notes:the state equation is dy/ds=ry−αwith y(t)=x,and the value function isu(x,t)=maxα≥0 τte−ρs h(α(s))dswith h(a)=aγfor some0<γ<1,andτ=first time when y=0if this occurs before time T T otherwise.(a)We obtained a formula for u(x,t)in the Section4notes,however our formula doesn’tmake sense whenρ−rγ=0.Find the correct formula in that case.(b)Let’s examine the infinite-horizon-limit T→∞.Following the lead of Problem1letus concentrate on v(x,t)=eρt u(x,t)=optimal utility discounted to time t.Show that¯v(x)=limT→∞v(x,t)=G∞xγifρ−rγ>0∞ifρ−rγ≤0with G∞=[(1−γ)/(ρ−rγ)]1−γ.(c)Use the stationary PDE of Problem1(b)(specialized to this example)to obtain thesame result.(d)What is the optimal consumption strategy,for the infinite-horizon version of thisproblem?3)Consider the analogue of Example1with the power-law utility replaced by the logarithm: h(a)=ln a.To avoid confusion let us write uγfor the value function obtained in the notes using h(a)=aγ,and u log for the value function obtained using h(a)=ln a.Recall that uγ(x,t)=gγ(t)xγwithgγ(t)=e−ρt1−γ1−γ1−γ.(a)Show,by a direct comparison argument,thatu log(λx,t)=u log(x,t)+1ρe−ρt(1−e−ρ(T−t))and g1is an as-yet unspecified function of t alone.2(b)Pursue the following scheme forfinding g1:Consider the utility h=1dγ(t)γ=0.(This leads to an explicit formula for g1but it’s messy;I’m not asking you to write it down.)(c)Indicate how g0and g1could alternatively have been found by solving appropriatePDE’s.(Hint:find the HJB equation associated with h(a)=ln a,and show that the ansatz u log=g0(t)ln x+g1(t)leads to differential equations that determine g0and g1.)4)Our Example1considers an investor who receives interest(at constant rate r)but no wages.Let’s consider what happens if the investor also receives wages at constant rate w. The equation of state becomesdy/ds=ry+w−αwith y(t)=x,and the value function isu(x,t)=maxα≥0 Tte−ρs h(α(s))dswith h(a)=aγfor some0<γ<1.Since the investor earns wages,we now permit y(s)<0, however we insist that thefinal-time wealth be nonnegative(y(T)≥0).(a)Which pairs(x,t)are acceptable?The strategy that maximizes y(T)is clearly toconsume nothing(α(s)=0for all t<s<T).Show this results in y(T)≥0exactly ifx+φ(t)w≥0whereφ(t)=1(d)In view of(a),a more careful definition of the value function for this control problemisu(x,t)=maxα≥0 τte−ρs h(α(s))dswhereτ=first time when y(s)+φ(s)w=0if this occurs before time T T otherwise.Use a verification argument to prove that the function v obtained in(c)is indeed the value function u defined this way.5)Our geometric Example2gave|∇u|=1in D(with u=0at∂D)as the HJB equation associated with starting at a point x in some domain D,traveling with speed at most1, and arriving at∂D as quickly as possible.Let’s consider what becomes of this problem when we introduce a little noise.The state equation becomesdy=α(s)ds+ dw,y(0)=x,whereα(s)is a(non-anticipating)control satisfying|α(s)|≤1,y takes values in R n,and each component of w is an independent Brownian motion.Letτx,αdenote the arrival time:τx,α=time when y(s)first hits∂D,which is of course random.The goal is now to minimize the expected arrival time at∂D,so the value function isu(x)=min|α(s)|≤1E y(0)=x{τx,α}.(a)Show,using an argument similar to that in the Section5notes,that u solves the PDE1−|∇u|+122u xx=0for−1<x<1u=0at x=±1.(a)Assuming that the solution u is unique,show it satisfies u(x)=u(−x).Conclude thatu x=0and u xx<0at x=0.Thus u has a maximum at x=0.4(b)Notice that v=u x solves1−|v|+δv x=0withδ=1。
• Built-in 5 common profiles, suitable for all 1/8 Racing, select and use instantly. (e.g. Zero timing-Blinky mode, 1/8 Off-Road Racing, 1/8 On-Road Racing, 1/8 GT Racing, 1/8 Sport mode).• There are 29 built-in adjustable parameters to set various power requirements. The parameters can be imported and exported, which is convenient for drivers to communicate with and learn from each other.• Support the firmware upgrade of the ESC (The multi-function LCD programming box G2 or OTA Programmer is needed to purchase). You can enjoy the latest functions. • Support 48 degrees Boost and Turbo timing. When matching with XERUN 4268/4274 G3 motor, the Max. Speed can be promoted by 50%, easily win your rival.• Multiple function: Low voltage protection, thermal protection of the ESC, motor and capacitor.• Built-in switch mode BEC with a maximum output of 15A and voltage adjustable from 6V to 8.4V (step: 0.1V) for usage with servos & other devices require different voltages.• The built-in reverse connection protection circuit of the ESC avoid the damage to the ESC due to reverse connection.• The record function of off-line data can read the Max. Temperature and RPM of the ESC and motor by Multifunction LCD Program Box (G2) or HW Link (OTA Programmer is needed to purchase), which is convenient for driver to analyze the running of the power system.• The record function of real-time data: Open this function by connecting the ESC with HW Link (OTA Programmer is needed to purchase) and mobile App can check throttle quantity, Voltage, Current, Temperature, RPM and other data in real time, and obtain the running status of the ESC and motor.03Features04Specifications06ESC Setup01DisclaimerPlease connect the wire correctly according to the instructions and drawing:1. Motor Wiring:There is difference between connection of sensored brushless motor and sensorless brushless motor. Please according to the following wiring method: A. Connect sensored brushless motor:There is strict wiring order from the ESC to the motor, the three A/B/C ESC wires must connect to the three A/B/C motor wires correspondingly. Next, connect the ESC sensor port and the motor sensor port with the stock 6-pin sensor cable. If you don’t plug the sensor cable in, your ESC will still work in sensorless mode even if you’re using a sensored motor. Note:If the forward and backward is reverse after installing the motor, please modify “no. 1I” parameters “Motor Rotation” to change the direction. B. Sensorless Motor Wiring:Users do not need to be worried in r egards to the connectivity with the A/B/C(ESC and motor) as ther e is no polarity. You may find it necessary to swap two wir es if the motor runs in reverse.2. Receiver Wiring:Insert the throttle control flat cable of ESC into the throttle channel (i.e. THROTTLE channel) of the receiver. Since the red line in the flat cable outputs 6-8.4v voltage to the receiver and steering servo. Please do not supply additional power to the receiver, otherwise the electric adjustment may be damaged. 3. Battery Wiring:Please make sure that the (+) pole of the ESC is connected to the (+) of the battery, and the (-) pole is connected to the (-). If connect reversely, the ESC cannot start up. (Add the picture of connecting battery here.)Warning!This is an extremely powerful system. For your safety and the safety of those around you, we strongly recommend removing the pinion gear attached to the motor before calibrating and setting this system. It is also advisable to keep the wheels in the air when you turn on the ESC.1) Illustration of power on/off: Short press the ON/OFF key to turn on the ESC in the off state, and long press the ON/OFF key to turn off the ESC.2) Beep illustration when turn on the ESC: When turn on ESC under normal conditions (i.e. it is started without pressing the SET key), the motor will emit several Beeps to indicate the LiPo cells. For example, "Beep, Beep, Beep" means 3S, "Beep, Beep, Beep, Beep" means 4S.XERUN XR8 Pro G2USER MANUALBrushless Electronic Speed Controller08Trouble ShootingIn order to make one firmware applicable to all different racing conditions, there are 5 groups of preset modes in the ESC. Users are able to change the settings of the modes provided and match suitable gear ratio. Plug-and -screw. Users can change the settings as per the control feel, track, and rename the setting mode. For example, the name can be changed from “1/8 Off-Road” to “NC2020-1900” to indicate the NC2020 uses 1900KV. This can be saved for future reference as well.Here is the method of setting parameters of ESC:1) LCD programming box set the parameters: (Please refer to the instructions of LCD programming box for detailes)parameters. You can adjust the setting via “ITEM” & “VALUE” buttons, and press the “OK(R/P)” button to save new settings to your ESC.Note: Only Multifunction LCD Program Box (G2) can work with this ESC!2) Use OTA Programmer to set parameters (Please refer to instructions of OTA Programmer for details) This ESC allows OTA Programmer connecting to the computer, that is, plug the programming wire of OTA Programmer to the programming port. Then use mobile phone to install HOBBYWING HW LINK App to set parameters.3) Data checking:recorded data to the designated area when you turn off the ESC after a run. You can check those data via a multifunction LCD program box whenever necessary. Users need to switch on the ESC after connection between the program box and the ESC has been established. Long Press the “OK(R/P)” button on any “item” page, followed by pressing the “ITEM” button again multiple times. The following 5 item pages will be displayed : Mode → ESC Temperature → Motor Temperature → Min Voltage → Max RPM. Attention!Press the “VALUE+/-” button on any profile page can get you into the next/prev preset mode. Please note that improper operation will get you into other preset mode(s).Here is the method of restore factory reset:1)Restore the default values with a multifunction LCD program boxAfter connecting the program box to the ESC, continue to press the “ITEM” button on the program box until you see the “RESTORE DEFAULT” item, and press “OK(R/P)” to factory reset your ESC.2)Restore the default values with a OTA Programmer (Use HW Link mobile phone App)Connect OTA Programmer to the ESC, enter into 【Parameters 】, click “reset” to factory reset your ESC.07Explanation for LED status1. During the Start-up Process• The RED LED keeps flashing rapidly indicating the ESC doesn't detect any throttle signal or the neutral throttle value stored on your ESC may be different from the current value stored on the transmitter. • The GREEN LED flashes “N” times indicating the number of LiPo cells you have connected to the ESC.2. In Operation• The throttle trigger is at the neutral: The RED LED turns on solid and the GREEN LED dies out when the throttle trigger is in the throttle neutral zone. The RED LED will blink to meet Blinky( Zero Timing) rules if the total value of Boost Timing and Turbo timing is 0.• Forward: The RED LED dies out and the GREEN LED blinks when your vehicle runs forward. The GREEN LED turns solid when pulling the throttle trigger to the full (100%) throttle endpoint. • Brake: The RED LED dies out and the GREEN LED blinks when you brake your vehicle. The GREEN LED turns solid when pushing the throttle trigger to the full brake endpoint and setting the ”Max. Brake Force” to 100%.• Backward: The RED LED dies out, the GREEN LED blinks when you reverse your vehicle. The GREEN LED turns solid when pushing the throttle trigger to the full brake endpoint and setting the ”reverse force” to 100%.3. When Some Protection is Activated• The RED LED flashes a short, single flash and repeats “☆, ☆, ☆” indicating the low voltage cutoff protection is activated. • The GREEN LED flashes a short, single flash and repeats “☆, ☆, ☆” indicating the ESC thermal protection is activated.• The GREEN LED flashes a short, double flash and repeats “☆☆, ☆☆, ☆☆” indicating the motor thermal protection is activated.• The GREEN LEDS flash a short, single flash and repeats “☆☆☆, ☆☆☆, ☆☆☆” indicating that the load of ESC is heavy, the Over-Current protection is activated.• The GREEN LEDS flash a short, single flash and repeats “☆☆☆☆☆,☆☆☆☆☆,☆☆☆☆☆” indicating that the temperature of ESC and capacitor is too high, the thermal protection of capacitor is activated.Programming:5Factory reset6Preset modes41A: Running Mode:Option 1: Forward with BrakeRacing mode. It has only forward and brake functions. Option 2: Forward/ Reverse with BrakeThis option is known to be the “training” mode with “Forwar d/ Reverse with Brake” functions. Hobbywing has adopted the “DO UBLE-CLICK” method, that is your vehicle only brakes on the 1st time you push the thr ottle trigger forward (brake) (1st push). The motor stops when you quickly r elease the throttle trigger and then r e-push the trigger quickly (2nd push), only then the vehicle will reverse. The reverse function will not work if your car does not come to a complete stop. The vehicle only reverses after the motor stops. This method is for preventing vehicle from being accidentally reversed.Option 3: Forward and ReverseThis mode is often used by special vehicles. It adopts the “SINGLE-CLICK” method. The vehicle will reverse immediately when you push the thr ottle trigger forward (brake).1B: Max. Reverse Force:The reverse force of the value will determine its speed. For the safety of your vehicle, we recommend using a low amount.1C: Lipo Cells:We strongly recommend that you set LiPo cells manually not automatically. When set automatically, the ESC can judge as 2S or 4S. If the battery voltage is lower than 9.5V after power on the ESC, it will be judged as 2S; if the battery voltage is between 9.5V ~13.6V, it will be judged as 3S; if higher than 13.6V, it will be judged as 4S. 1D: Cutoff Voltage:The ESC will monitor the battery voltage all the time, once the voltage is lower than the threshold value, the ESC will reduce the power to 50% instantly and cutoff the power output in 40 seconds. When enters into voltage protection, the RED LED will single flash that repeats (☆, ☆, ☆, ☆…….). Please set the “Cutoff Voltage” to “Disabled” or customized protection threshold value if you are using NiMH batteries. Option 1: DisabledThe ESC does not cut the power off due to low voltage. We do not recommend using this option when you use any LiPo battery as you will irreversibly damage the product. It is suggested to set to “Disabled”(But the battery would be damaged due to overcharged) Option 2: AutoThe ESC calculates the corresponding cutoff voltage as per the number of LiPo cells it detects and the “3.3V/cell” rule. For example, if the ESC detects a 4S, the cutoff voltage protection threshold value is 3.5x4=14.0V. Option 3: CustomizedThe customized cutoff threshold is a voltage for the whole battery pack (adjustable from 5.0V to 13.6V). Please calculate the value as per the number of LiPo cells you are using. For example, when you use a 4S and you want the cutoff voltage for each cell is 3.0V, you will need to set this item to 12V (3.0*4)1E: ESC Thermal Protection:The output from the ESC will be cut off with the value you have preset. The GREEN LED flashes (☆, ☆, ☆) when the ESC temperature reaches to the preset value. The output will not resume until the ESC temperature gets down.Warning! Please do not disable this function unless you’re in a competition. Otherwise the high temperature may damage your ESC and even your motor.1F: Motor Thermal Protection:The GREEN LED flashes (☆☆, ☆☆, ☆☆) when the motor temperature reaches to the preset value. The output will not resume until the motor temperature gets down.Warning! Please do not disable this function unless you’re in a competition. Otherwise the high temperature may damage your motor and even your ESC. For non-Hobbywing motor, the ESC may get this protection activated too early/late because of the different temperature sensor inside the motor. In this case, please disable this function and monitor the motor temperature manually.1G: BEC Voltage:BEC voltage can be adjusted between 6.0-8.4V. 6.0V is applicable to common servo. If use high-voltage servo, set to higher voltage according to voltage marking of servo. Warning: The setting BEC voltage should not be higher than the max. voltage of common servo, otherwise it will damage the servo or ESC. 1H: Sensor Mode:Option 1: Full SensoredIf use XERUN 4268/74-G2/G3 motor, it can set to full sensor mode. The power system will work in the “sensored” mode at all times. The efficiency and drivability of this mode is at the highest. And Boost 、Turbo timing can be used and get erupting power. Option 2: Sensored/Sensorless HybridThis is universal driving mode of current 1:8 power system. The ESC operates the motor in sensored mode during the low-speed start-up process, followed by switching to operating the motor in the “sensorless” mode when the RPM is increased.1I: Motor Rotation:With the motor shaft faces you (the rear end of the motor is away from you), increase the throttle input, the motor (shaft) will rotate in the CCW/CW direction if the “Motor Rotation/Direction” set to “CCW/CW”. Generally, the vehicle runs forward when the motor (shaft) rotates in the CCW direction. However, some vehicles only run forward when the motor rotates in the CW direction due to the different chassis design. In that case, you only need to set the “Motor Rotation/Direction” to “CW.1J: Phase-AC Swap:If the A/C wire of ESC connect to A/C wire of motor with crossed way (A wire of ESC connects to C wire of motor, C wire of ESC connects to A wire), set this item as Enable. Warning! When #A/#B/#C wire of ESC connect to #A/#B/#C wire of motor correspondingly, do not Set to Enable. Otherwise it will damage the ESC and motor.2A: Throttle Rate Control:This item is used to control the throttle response. It can be adjustable from 1 to 30 (step: 1), the lower the throttle rate, the more the limit will be on the throttle response. A suitable rate can help driver to control his vehicle properly during the starting-up process. Generally, you can set it to a high value to have a quick throttle response if you are proficient at throttle control.2B: Throttle Curve:The throttle curve parameter reconciles the position of the throttle trigger (in throttle zone) and the actual ESC throttle output. It is linear by default and we can change it to non-linear viaadjusting the throttle curve. For example, if adjust it to +EXP , the throttle output at the early stage will be higher (than the output when the curve is linear); if it is adjusted to –EXP , the throttle output at the early stage will be lower (than the output when the curve is linear.2C: Neutral Range:As not all transmitters have the same stability at “neutral position”, please adjust this parameter as per your preference. You can adjust to a bigger value when this happens.2D: Initial Throttle Force:It also called as minimum throttle force. You can set it according to wheel tire and traction. If the ground is slippery, please set a small throttle force. 2E: Coast:The RPM of the motor will be lowered gradually when throttle is reduced. The vehicle will not reduce speed abruptly when the throttle is reduced to return to the neutral position. The bigger the value, the more the “COAST” will be felt. Example, COAST of 0 deactivates, and a COAST of 20% would be the maximum amount of COAST. The advantages of COAST:When “TURBO DELAY” is set to “INSTANT”, the Turbo Timing will be activated right after the throttle trigger is moved to the full throttle position. When other value(s) is applied, you will needto hold the throttle trigger at the full throttle position (as you set) till the Turbo Timing initiates.5C: Turbo Increase Rate (deg/0.1sec):This item is used to define the “speed” at which Turbo Timing is released when the trigger condition is met. For example, “6 degs/0.1sec” refers to the Turbo Timing of 6 degrees that will be released in 0.1 second. Both the acceleration and heat is higher when the “Turbo increase rate” is of a larger value.5D: Turbo Decrease Rate (deg/0.1sec):After the Turbo Timing is activated and the trigger condition turns to not be met (i.e. vehicle slows down at the end of the straightaway and gets into a corner, full throttle turns to partialthrottle, the trigger condition for Turbo Timing turns to be not met), if you disable all the Turbo Timing in a moment, an obvious slow-down like braking will be felt and cause the control of vehicle to become bad. If the ESC can disable the Turbo Timing at some “speed”, the slow-down will be linear and the control will be improved.Warning !Boost Timing & Turbo Timing can effectively improve the motor efficiency; they are usually used in competitions. Please take some time to read this manual and then set these two items carefully, monitor the ESC & motor temperatures when you have a trial run and then adjust the Timing and FDR accordingly as aggressive Timings and FDR may cause your ESC or motor to be burnt.Note: Parameters 5A-5D only has function when you set the “Drive Mode” to “Full Sensored”.。
Error MessagesF9001 Error internal function call.F9002 Error internal RTOS function callF9003 WatchdogF9004 Hardware trapF8000 Fatal hardware errorF8010 Autom. commutation: Max. motion range when moving back F8011 Commutation offset could not be determinedF8012 Autom. commutation: Max. motion rangeF8013 Automatic commutation: Current too lowF8014 Automatic commutation: OvercurrentF8015 Automatic commutation: TimeoutF8016 Automatic commutation: Iteration without resultF8017 Automatic commutation: Incorrect commutation adjustment F8018 Device overtemperature shutdownF8022 Enc. 1: Enc. signals incorr. (can be cleared in ph. 2) F8023 Error mechanical link of encoder or motor connectionF8025 Overvoltage in power sectionF8027 Safe torque off while drive enabledF8028 Overcurrent in power sectionF8030 Safe stop 1 while drive enabledF8042 Encoder 2 error: Signal amplitude incorrectF8057 Device overload shutdownF8060 Overcurrent in power sectionF8064 Interruption of motor phaseF8067 Synchronization PWM-Timer wrongF8069 +/-15Volt DC errorF8070 +24Volt DC errorF8076 Error in error angle loopF8078 Speed loop error.F8079 Velocity limit value exceededF8091 Power section defectiveF8100 Error when initializing the parameter handlingF8102 Error when initializing power sectionF8118 Invalid power section/firmware combinationF8120 Invalid control section/firmware combinationF8122 Control section defectiveF8129 Incorrect optional module firmwareF8130 Firmware of option 2 of safety technology defectiveF8133 Error when checking interrupting circuitsF8134 SBS: Fatal errorF8135 SMD: Velocity exceededF8140 Fatal CCD error.F8201 Safety command for basic initialization incorrectF8203 Safety technology configuration parameter invalidF8813 Connection error mains chokeF8830 Power section errorF8838 Overcurrent external braking resistorF7010 Safely-limited increment exceededF7011 Safely-monitored position, exceeded in pos. DirectionF7012 Safely-monitored position, exceeded in neg. DirectionF7013 Safely-limited speed exceededF7020 Safe maximum speed exceededF7021 Safely-limited position exceededF7030 Position window Safe stop 2 exceededF7031 Incorrect direction of motionF7040 Validation error parameterized - effective thresholdF7041 Actual position value validation errorF7042 Validation error of safe operation modeF7043 Error of output stage interlockF7050 Time for stopping process exceeded8.3.15 F7051 Safely-monitored deceleration exceeded (159)8.4 Travel Range Errors (F6xxx) (161)8.4.1 Behavior in the Case of Travel Range Errors (161)8.4.2 F6010 PLC Runtime Error (162)8.4.3 F6024 Maximum braking time exceeded (163)8.4.4 F6028 Position limit value exceeded (overflow) (164)8.4.5 F6029 Positive position limit exceeded (164)8.4.6 F6030 Negative position limit exceeded (165)8.4.7 F6034 Emergency-Stop (166)8.4.8 F6042 Both travel range limit switches activated (167)8.4.9 F6043 Positive travel range limit switch activated (167)8.4.10 F6044 Negative travel range limit switch activated (168)8.4.11 F6140 CCD slave error (emergency halt) (169)8.5 Interface Errors (F4xxx) (169)8.5.1 Behavior in the Case of Interface Errors (169)8.5.2 F4001 Sync telegram failure (170)8.5.3 F4002 RTD telegram failure (171)8.5.4 F4003 Invalid communication phase shutdown (172)8.5.5 F4004 Error during phase progression (172)8.5.6 F4005 Error during phase regression (173)8.5.7 F4006 Phase switching without ready signal (173)8.5.8 F4009 Bus failure (173)8.5.9 F4012 Incorrect I/O length (175)8.5.10 F4016 PLC double real-time channel failure (176)8.5.11 F4017 S-III: Incorrect sequence during phase switch (176)8.5.12 F4034 Emergency-Stop (177)8.5.13 F4140 CCD communication error (178)8.6 Non-Fatal Safety Technology Errors (F3xxx) (178)8.6.1 Behavior in the Case of Non-Fatal Safety Technology Errors (178)8.6.2 F3111 Refer. missing when selecting safety related end pos (179)8.6.3 F3112 Safe reference missing (179)8.6.4 F3115 Brake check time interval exceeded (181)Troubleshooting Guide | Rexroth IndraDrive Electric Drivesand ControlsI Bosch Rexroth AG VII/XXIITable of ContentsPage8.6.5 F3116 Nominal load torque of holding system exceeded (182)8.6.6 F3117 Actual position values validation error (182)8.6.7 F3122 SBS: System error (183)8.6.8 F3123 SBS: Brake check missing (184)8.6.9 F3130 Error when checking input signals (185)8.6.10 F3131 Error when checking acknowledgment signal (185)8.6.11 F3132 Error when checking diagnostic output signal (186)8.6.12 F3133 Error when checking interrupting circuits (187)8.6.13 F3134 Dynamization time interval incorrect (188)8.6.14 F3135 Dynamization pulse width incorrect (189)8.6.15 F3140 Safety parameters validation error (192)8.6.16 F3141 Selection validation error (192)8.6.17 F3142 Activation time of enabling control exceeded (193)8.6.18 F3143 Safety command for clearing errors incorrect (194)8.6.19 F3144 Incorrect safety configuration (195)8.6.20 F3145 Error when unlocking the safety door (196)8.6.21 F3146 System error channel 2 (197)8.6.22 F3147 System error channel 1 (198)8.6.23 F3150 Safety command for system start incorrect (199)8.6.24 F3151 Safety command for system halt incorrect (200)8.6.25 F3152 Incorrect backup of safety technology data (201)8.6.26 F3160 Communication error of safe communication (202)8.7 Non-Fatal Errors (F2xxx) (202)8.7.1 Behavior in the Case of Non-Fatal Errors (202)8.7.2 F2002 Encoder assignment not allowed for synchronization (203)8.7.3 F2003 Motion step skipped (203)8.7.4 F2004 Error in MotionProfile (204)8.7.5 F2005 Cam table invalid (205)8.7.6 F2006 MMC was removed (206)8.7.7 F2007 Switching to non-initialized operation mode (206)8.7.8 F2008 RL The motor type has changed (207)8.7.9 F2009 PL Load parameter default values (208)8.7.10 F2010 Error when initializing digital I/O (-> S-0-0423) (209)8.7.11 F2011 PLC - Error no. 1 (210)8.7.12 F2012 PLC - Error no. 2 (210)8.7.13 F2013 PLC - Error no. 3 (211)8.7.14 F2014 PLC - Error no. 4 (211)8.7.15 F2018 Device overtemperature shutdown (211)8.7.16 F2019 Motor overtemperature shutdown (212)8.7.17 F2021 Motor temperature monitor defective (213)8.7.18 F2022 Device temperature monitor defective (214)8.7.19 F2025 Drive not ready for control (214)8.7.20 F2026 Undervoltage in power section (215)8.7.21 F2027 Excessive oscillation in DC bus (216)8.7.22 F2028 Excessive deviation (216)8.7.23 F2031 Encoder 1 error: Signal amplitude incorrect (217)VIII/XXII Bosch Rexroth AG | Electric Drivesand ControlsRexroth IndraDrive | Troubleshooting GuideTable of ContentsPage8.7.24 F2032 Validation error during commutation fine adjustment (217)8.7.25 F2033 External power supply X10 error (218)8.7.26 F2036 Excessive position feedback difference (219)8.7.27 F2037 Excessive position command difference (220)8.7.28 F2039 Maximum acceleration exceeded (220)8.7.29 F2040 Device overtemperature 2 shutdown (221)8.7.30 F2042 Encoder 2: Encoder signals incorrect (222)8.7.31 F2043 Measuring encoder: Encoder signals incorrect (222)8.7.32 F2044 External power supply X15 error (223)8.7.33 F2048 Low battery voltage (224)8.7.34 F2050 Overflow of target position preset memory (225)8.7.35 F2051 No sequential block in target position preset memory (225)8.7.36 F2053 Incr. encoder emulator: Pulse frequency too high (226)8.7.37 F2054 Incr. encoder emulator: Hardware error (226)8.7.38 F2055 External power supply dig. I/O error (227)8.7.39 F2057 Target position out of travel range (227)8.7.40 F2058 Internal overflow by positioning input (228)8.7.41 F2059 Incorrect command value direction when positioning (229)8.7.42 F2063 Internal overflow master axis generator (230)8.7.43 F2064 Incorrect cmd value direction master axis generator (230)8.7.44 F2067 Synchronization to master communication incorrect (231)8.7.45 F2068 Brake error (231)8.7.46 F2069 Error when releasing the motor holding brake (232)8.7.47 F2074 Actual pos. value 1 outside absolute encoder window (232)8.7.48 F2075 Actual pos. value 2 outside absolute encoder window (233)8.7.49 F2076 Actual pos. value 3 outside absolute encoder window (234)8.7.50 F2077 Current measurement trim wrong (235)8.7.51 F2086 Error supply module (236)8.7.52 F2087 Module group communication error (236)8.7.53 F2100 Incorrect access to command value memory (237)8.7.54 F2101 It was impossible to address MMC (237)8.7.55 F2102 It was impossible to address I2C memory (238)8.7.56 F2103 It was impossible to address EnDat memory (238)8.7.57 F2104 Commutation offset invalid (239)8.7.58 F2105 It was impossible to address Hiperface memory (239)8.7.59 F2110 Error in non-cyclical data communic. of power section (240)8.7.60 F2120 MMC: Defective or missing, replace (240)8.7.61 F2121 MMC: Incorrect data or file, create correctly (241)8.7.62 F2122 MMC: Incorrect IBF file, correct it (241)8.7.63 F2123 Retain data backup impossible (242)8.7.64 F2124 MMC: Saving too slowly, replace (243)8.7.65 F2130 Error comfort control panel (243)8.7.66 F2140 CCD slave error (243)8.7.67 F2150 MLD motion function block error (244)8.7.68 F2174 Loss of motor encoder reference (244)8.7.69 F2175 Loss of optional encoder reference (245)Troubleshooting Guide | Rexroth IndraDrive Electric Drivesand Controls| Bosch Rexroth AG IX/XXIITable of ContentsPage8.7.70 F2176 Loss of measuring encoder reference (246)8.7.71 F2177 Modulo limitation error of motor encoder (246)8.7.72 F2178 Modulo limitation error of optional encoder (247)8.7.73 F2179 Modulo limitation error of measuring encoder (247)8.7.74 F2190 Incorrect Ethernet configuration (248)8.7.75 F2260 Command current limit shutoff (249)8.7.76 F2270 Analog input 1 or 2, wire break (249)8.7.77 F2802 PLL is not synchronized (250)8.7.78 F2814 Undervoltage in mains (250)8.7.79 F2815 Overvoltage in mains (251)8.7.80 F2816 Softstart fault power supply unit (251)8.7.81 F2817 Overvoltage in power section (251)8.7.82 F2818 Phase failure (252)8.7.83 F2819 Mains failure (253)8.7.84 F2820 Braking resistor overload (253)8.7.85 F2821 Error in control of braking resistor (254)8.7.86 F2825 Switch-on threshold braking resistor too low (255)8.7.87 F2833 Ground fault in motor line (255)8.7.88 F2834 Contactor control error (256)8.7.89 F2835 Mains contactor wiring error (256)8.7.90 F2836 DC bus balancing monitor error (257)8.7.91 F2837 Contactor monitoring error (257)8.7.92 F2840 Error supply shutdown (257)8.7.93 F2860 Overcurrent in mains-side power section (258)8.7.94 F2890 Invalid device code (259)8.7.95 F2891 Incorrect interrupt timing (259)8.7.96 F2892 Hardware variant not supported (259)8.8 SERCOS Error Codes / Error Messages of Serial Communication (259)9 Warnings (Exxxx) (263)9.1 Fatal Warnings (E8xxx) (263)9.1.1 Behavior in the Case of Fatal Warnings (263)9.1.2 E8025 Overvoltage in power section (263)9.1.3 E8026 Undervoltage in power section (264)9.1.4 E8027 Safe torque off while drive enabled (265)9.1.5 E8028 Overcurrent in power section (265)9.1.6 E8029 Positive position limit exceeded (266)9.1.7 E8030 Negative position limit exceeded (267)9.1.8 E8034 Emergency-Stop (268)9.1.9 E8040 Torque/force actual value limit active (268)9.1.10 E8041 Current limit active (269)9.1.11 E8042 Both travel range limit switches activated (269)9.1.12 E8043 Positive travel range limit switch activated (270)9.1.13 E8044 Negative travel range limit switch activated (271)9.1.14 E8055 Motor overload, current limit active (271)9.1.15 E8057 Device overload, current limit active (272)X/XXII Bosch Rexroth AG | Electric Drivesand ControlsRexroth IndraDrive | Troubleshooting GuideTable of ContentsPage9.1.16 E8058 Drive system not ready for operation (273)9.1.17 E8260 Torque/force command value limit active (273)9.1.18 E8802 PLL is not synchronized (274)9.1.19 E8814 Undervoltage in mains (275)9.1.20 E8815 Overvoltage in mains (275)9.1.21 E8818 Phase failure (276)9.1.22 E8819 Mains failure (276)9.2 Warnings of Category E4xxx (277)9.2.1 E4001 Double MST failure shutdown (277)9.2.2 E4002 Double MDT failure shutdown (278)9.2.3 E4005 No command value input via master communication (279)9.2.4 E4007 SERCOS III: Consumer connection failed (280)9.2.5 E4008 Invalid addressing command value data container A (280)9.2.6 E4009 Invalid addressing actual value data container A (281)9.2.7 E4010 Slave not scanned or address 0 (281)9.2.8 E4012 Maximum number of CCD slaves exceeded (282)9.2.9 E4013 Incorrect CCD addressing (282)9.2.10 E4014 Incorrect phase switch of CCD slaves (283)9.3 Possible Warnings When Operating Safety Technology (E3xxx) (283)9.3.1 Behavior in Case a Safety Technology Warning Occurs (283)9.3.2 E3100 Error when checking input signals (284)9.3.3 E3101 Error when checking acknowledgment signal (284)9.3.4 E3102 Actual position values validation error (285)9.3.5 E3103 Dynamization failed (285)9.3.6 E3104 Safety parameters validation error (286)9.3.7 E3105 Validation error of safe operation mode (286)9.3.8 E3106 System error safety technology (287)9.3.9 E3107 Safe reference missing (287)9.3.10 E3108 Safely-monitored deceleration exceeded (288)9.3.11 E3110 Time interval of forced dynamization exceeded (289)9.3.12 E3115 Prewarning, end of brake check time interval (289)9.3.13 E3116 Nominal load torque of holding system reached (290)9.4 Non-Fatal Warnings (E2xxx) (290)9.4.1 Behavior in Case a Non-Fatal Warning Occurs (290)9.4.2 E2010 Position control with encoder 2 not possible (291)9.4.3 E2011 PLC - Warning no. 1 (291)9.4.4 E2012 PLC - Warning no. 2 (291)9.4.5 E2013 PLC - Warning no. 3 (292)9.4.6 E2014 PLC - Warning no. 4 (292)9.4.7 E2021 Motor temperature outside of measuring range (292)9.4.8 E2026 Undervoltage in power section (293)9.4.9 E2040 Device overtemperature 2 prewarning (294)9.4.10 E2047 Interpolation velocity = 0 (294)9.4.11 E2048 Interpolation acceleration = 0 (295)9.4.12 E2049 Positioning velocity >= limit value (296)9.4.13 E2050 Device overtemp. Prewarning (297)Troubleshooting Guide | Rexroth IndraDrive Electric Drivesand Controls| Bosch Rexroth AG XI/XXIITable of ContentsPage9.4.14 E2051 Motor overtemp. prewarning (298)9.4.15 E2053 Target position out of travel range (298)9.4.16 E2054 Not homed (300)9.4.17 E2055 Feedrate override S-0-0108 = 0 (300)9.4.18 E2056 Torque limit = 0 (301)9.4.19 E2058 Selected positioning block has not been programmed (302)9.4.20 E2059 Velocity command value limit active (302)9.4.21 E2061 Device overload prewarning (303)9.4.22 E2063 Velocity command value > limit value (304)9.4.23 E2064 Target position out of num. range (304)9.4.24 E2069 Holding brake torque too low (305)9.4.25 E2070 Acceleration limit active (306)9.4.26 E2074 Encoder 1: Encoder signals disturbed (306)9.4.27 E2075 Encoder 2: Encoder signals disturbed (307)9.4.28 E2076 Measuring encoder: Encoder signals disturbed (308)9.4.29 E2077 Absolute encoder monitoring, motor encoder (encoder alarm) (308)9.4.30 E2078 Absolute encoder monitoring, opt. encoder (encoder alarm) (309)9.4.31 E2079 Absolute enc. monitoring, measuring encoder (encoder alarm) (309)9.4.32 E2086 Prewarning supply module overload (310)9.4.33 E2092 Internal synchronization defective (310)9.4.34 E2100 Positioning velocity of master axis generator too high (311)9.4.35 E2101 Acceleration of master axis generator is zero (312)9.4.36 E2140 CCD error at node (312)9.4.37 E2270 Analog input 1 or 2, wire break (312)9.4.38 E2802 HW control of braking resistor (313)9.4.39 E2810 Drive system not ready for operation (314)9.4.40 E2814 Undervoltage in mains (314)9.4.41 E2816 Undervoltage in power section (314)9.4.42 E2818 Phase failure (315)9.4.43 E2819 Mains failure (315)9.4.44 E2820 Braking resistor overload prewarning (316)9.4.45 E2829 Not ready for power on (316)。
8Error messages and return codesContents8.1Making mistakes8.1.1Mistakes are forgiven8.1.2Mistakes stop user-written programs and do-files8.1.3Advanced programming to tolerate errors8.2The return message for obtaining command timings8.1Making mistakesWhen an error occurs,Stata produces an error message and a return code.For instance, .list myvarno variables definedr(111);We ask Stata to list the variable named myvar.Because we have no data in memory,Stata responds with the message“no variables defined”and a line that reads“r(111)”.The“no variables defined”is called the error message.The111is called the return code.You can click on blue return codes to get a detailed explanation of the error.8.1.1Mistakes are forgivenAfter“no variables defined”and r(111),all is forgiven;it is as if the error never occurred.Typically,the message will be enough to guide you to a solution,but if it is not,the numeric return codes are documented in[P]error.8.1.2Mistakes stop user-written programs and do-filesWhenever an error occurs in a user-written program or do-file,the program or do-file immediately stops execution and the error message and return code are displayed.For instance,consider the following do-file:begin myfile.do use https:///data/r18/autodecribelistend myfile.do Note the second line—you meant to type describe but typed decribe.Here is what happens when you execute this do-file by typing do myfile:.do myfile.use https:///data/r18/auto(1978automobile data)12[U]8Error messages and return codes.decribecommand decribe is unrecognizedr(199);end of do-filer(199);.Thefirst error message and return code were caused by the illegal decribe.This then caused the do-file itself to be aborted;the valid list command was never executed.8.1.3Advanced programming to tolerate errorsErrors are not only of the typographical kind;some are substantive.A command that is valid in one dataset might not be valid in another.Moreover,in advanced programming,errors are sometimes anticipated:use one dataset if it is there,but use another if you must.Programmers can access the return code to determine whether an error occurred,which they can then ignore,or,by examining the return code,code their programs to take the appropriate action.This is discussed in[P]capture.You can also prevent do-files from stopping when errors occur by using the do command’s nostop option..do myfile,nostop8.2The return message for obtaining command timingsIn addition to error messages and return codes,there is something called a return message,which you normally do not see.Normally,if you typed summarize tempjan,you would see .use https:///data/r18/citytemp(City temperature data).summarize tempjanVariable Obs Mean Std.dev.Min Maxtempjan95435.7489514.18813 2.272.6 If you were to type.set rmsg onr;t=0.0010:21:22sometime during your session,Stata would display return messages:.summarize tempjanVariable Obs Mean Std.dev.Min Maxtempjan95435.7489514.18813 2.272.6r;t=0.0110:21:26The line that reads r;t=0.0110:21:26is called the return message.The r;indicates that Stata successfully completed the command.The t=0.01shows the amount of time,in seconds,it took Stata to perform the command(timed from the point you pressed Enter to the time Stata typed the message).This command took a hundredth of a second.Stata also shows the time of day with a24-hour clock.This command completed at 10:21a.m.[U]8Error messages and return codes3 Stata can run commands stored infiles(called do-files)and can log output.Some usersfind the detailed return message helpful with do-files.They construct a long program and let it run overnight, logging the output.They come back the next morning,look at the output,and discover a mistake in some portion of the job.They can look at the return messages to determine how long it will take to rerun that portion of the program.You may set rmsg on whenever you wish.When you want Stata to stop displaying the detailed return message,type set rmsg off.There is another way to obtain timings of subsets of code that is of interest to programmers.See [P]timer.Stata,Stata Press,and Mata are registered trademarks of StataCorp LLC.Stata andStata Press are registered trademarks with the World Intellectual Property Organization®of the United Nations.Other brand and product names are registered trademarks ortrademarks of their respective companies.Copyright c 1985–2023StataCorp LLC,College Station,TX,USA.All rights reserved.。
Electronic Colloquium on Computational Complexity,Report No.134(2010)A Note on Amplifying the Error-Tolerance of LocallyDecodable CodesAvraham Ben-Aroya∗Klim Efremenko†Amnon Ta-Shma‡AbstractWe show a generic,simple way to amplify the error-tolerance of locally decodable codes.Specifically,we show how to transform a locally decodable code that can toleratea constant fraction of errors to a locally decodable code that can recover from a muchhigher error-rate.We also show how to transform such locally decodable codes to locallylist-decodable codes.The transformation involves a simple composition with an approximately locally(list) decodable ing a construction of such codes by Impagliazzo et al.[IJKW10],thetransformation incurs only a negligible growth in the length of the code and in the querycomplexity.1IntroductionLocally decodable codes(LDCs)are codes that allow retrieving any symbol of a message by reading only a constant number of symbols from its codeword,even if a large fraction of the codeword is corrupted.Formally,a code C is said to be locally decodable with parameters (q, ,δ)if it is possible to recover any symbol x i of a message x by making at most q queries to C(x),such that even if aδfraction of C(x)is corrupted,the decoding algorithm returns the correct answer with probability at least1− .Locally decodable codes play an important role in many areas in theoretical computer science.While thefirst formal definition of locally decodable codes was given by Katz and Trevisan[KT00],these codes implicitly appeared in previous works.The main line of research regarding LDCs seeks to identify the shortest possible code length,in terms of the message length n,while keeping the query complexity,the error-rate and the success probability constant.The Hadamard code is the best-known2-query locally decodable code and its length is2n.For2-query LDCs tight lower bounds on the code length of2θ(n)were given in[GKST02]for linear codes and in[KdW03]for general codes.For an arbitrary constant number of queries q,there are weak polynomial bounds,see ∗The Blavatnik School of Computer Science,Tel-Aviv University,Israel,69978.Supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities,by the Israel Science Foundation,by the Wolfson Family Charitable Trust,and by a European Research Council(ERC)Starting Grant.†The Blavatnik School of Computer Science,Tel-Aviv University,Israel,69978.Supported by the Israel Science Foundation,by the Wolfson Family Charitable Trust,and by Oded Regev’s European Research Council(ERC) Starting Grant.‡The Blavatnik School of Computer Science,Tel-Aviv University,Israel,69978.Supported by Israel Science Foundation grant217/05.[KT00,KdW03,Woo07].Thefirst subexponential LDCs(with a constant number of queries) were obtained by Yekhanin[Yek08].Yekhanin obtained3-query LDCs with subexponen-tial length under a highly believable number theoretic ter,Efremenko[Efr09], building on Yekhanin[Yek08]and Raghavendra[Rag07],gave an unconditional construction of subexponential length LDCs.This construction also allowed a tradeoff between the number of queries and the codeword length.Subsequently,the query complexity of this construction was improved in[IS08,MFL+10].The decoding algorithm in all of the aforementioned constructions is smooth,i.e.,each of its queries is uniformly distributed.The analysis of the decoding algorithm relied on all of the queried symbols being ing the union bound,one could obtain a decoder withsuccess probability greater than half,only if the error-rate was below12q .Another line of research focused on improving the error-tolerance of LDCs.Woodruff[Woo08]showed how to increase the handled error-rate from12q to1qover binary alphabets.Dvir,Gopalan and Yekhanin[DGY10],showed how to handle14fraction of errors for the codesof[Efr09].Ben-Aroya et.al.[BET10]showed the same codes could recover from any error-rate below12.Gal and Mills[GM09]obtained exponential lower bounds for3-query LDCs thatcan tolerate a high error-rate.When the error-rate is above half of the code’s distance,the information in a corrupted codeword is insufficient to uniquely identify the original(uncorrupted)codeword.Thus,in this case,we have to consider list-decoding.A code C is said to be(1−α,L)-list-decodable if for every word,the number of codewords within relative distance1−αfrom that word is at most L.The notion of list-decoding dates back to works by Elias[Eli57]and Wozencraft[Woz58]in the50s.Roughly speaking,a code C is locally list-decodable if it is(1−α,L)-list-decodable, and given a corrupted word w,an index k∈[L]and a target bit j,the decoder returns the j’th message bit of the k’th codeword that is close to w.As expected,there are some subtleties in the definition.The main issue is guaranteeing that for afixed k,all answers for inputs(k,j) correspond to the same codeword.More formally,a local list-decoding algorithm generates L machines{M k},such that the machine M k locally decodes one codeword that is close to w,and the machines{M k}together cover all the codewords that are close to w(for a formal definition,see Section2).The notion of local list-decoding is central in theoretical computer science.Itfirst im-plicitly appeared in the celebrated Goldreich-Levin result[GL89],that can be interpreted as a local list-decoding algorithm for the Hadamard ter on,many local list-decoding algo-rithms were studied,especially for Reed-Muller codes[GRS00,AS03,STV01,GKZ08],direct product and XOR codes[IW97,IJK06,IJKW08]and low-rate random codes[KS07,KS09]. In[BET10]it was shown how to locally list-decode the subexponential-length codes of[Efr09] with only a constant number of queries.Our Result.In this note we show a generic,simple transformation that takes a locally de-codable code C that can tolerate a low error-rate,and results in a code C that can tolerate a much higher fraction of errors.Our construction also works in the list-decoding regime,i.e., it can transform any LDC C to a code C which is locally list-decodable from an error-rate of 1−γ,for anyγ>0.Furthermore,the list-decoder for the new code outputs only a constant number of codewords.The transformation is based on the following idea.An error correcting code with relativedistance αis a function C :Σn →Σ¯nthat maps any two different strings,to two strings that differ in at least an αfraction of the coordinates.The decoding algorithm can therefore map any string ˜c with more than (1−α/2)n agreement with a codeword c =C (λ),to the correct message λ.We can view this as an α/2to 0error reduction:given a codeword with some α/2fraction of errors,one can correctly recover the original message.1.Similarly,one can define a related notion of codes that only amplify the error-tolerance,without completely correcting the corrupted word.That is,one can design a code C :Σn →Σ¯n ,such that given access to a corrupted word ˜c with γn agreement with some codeword c =C (λ),one can compute a message ˜λwith some larger β>γagreement with λ.We call such a code an approximately locally decodable code.When γis small,several codewords can be γ-close to ˜c and one has to resort to list-decoding.In this case,the code is called an approximately locally list-decodable code.Such codes naturally arise in hardness amplification (see,e.g.,[IJKW10]).For a formal definition see Section 2.Now,let us return to the problem of finding a good locally list-decodable code.Our ap-proach is to compose a locally decodable code (handling the α/2to 0error reduction)withan approximately locally list-decodable code (handling the 12− to α/2error reduction,forbinary codes).Namely,we first encode a message λwith a locally-decodable code C and then encode the result with an approximately locally list-decodable code to get the code C .To seethat it works,assume we are given a word with 12+ agreement with some codeword of C .Wefirst apply the approximate local list-decoder and get a list of words,each with 1−α/2agree-ment with some codeword of C .We then (uniquely)locally decode each of these corrupted codewords to get λi ,the i ’th symbol of the message λ.In fact,the local list-decoders of Reed-Muller codes [GRS00,AS03,STV01,GKZ08]and the Hadamard code [GL89],also have this two-step structure,combining an error-reduction step (that does not completely correct the corrupted word)with another unique decoding step.The main difference is that Reed-Muller and Hadamard codes are locally correctable ,i.e.,the first error-reduction step returns a close codeword,instead of close message.Therefore,these two steps can be done implicitly without the use of any general approximate list-decoding mechanism.In our case we present a generic transformation that may work with LDCs that are not known to be locally correctable (e.g.,the code of [Efr09])and we therefore need to compose the code with an approximately locally list-decodable code.Composing the locally decodable binary codes of [Efr09,MFL +10]with the binary ap-proximately locally list-decodable codes of [IJKW10]we get:Theorem 1.For every r ≥2there exists a binary code of lengthexp(exp(O (r log n (log log n )r −1))),which is locally list-decodable from an error-rate of 1/2−α.The list-decoding algorithmoutputs a list of size O (1α2)and uses at most O (log(1/ )α3)·3r/2queries.A locally list-decodable code of similar length was given in [BET10].However,the list size in the list-decoding algorithm of [BET10]was poly(n ),while in Theorem 1it is constant.The query complexity of the list-decoding algorithm of [BET10]was also worse than that of1For a treatment of the related notion of worst-case to average-case reduction and its relationship to error cor-recting codes see,e.g.,[IJKW10].Theorem1.On the other hand,the result in[BET10]shows the code of[Efr09]is locally list-decodable,while Theorem1only shows that some other(related)code is locally list-decodable, and does not state anything about the original code of[Efr09].2DefinitionsThe agreement between strings x and y is the fraction of coordinates i in which x i=y i.The agreement between x and y is denoted by Ag(x,y).Definition1.A probabilistic oracle machine M w locally outputs a string s with confidence1− ,if∀i Pr[M w(i)=s i]≥1− ,where the probability is over the randomness of M.Definition2.A deterministic oracle machine M w locally -approximates a string s,if[M w(i)=s i]≥1− ,Priwhere the probability is over a uniformly chosen i.Note that if M w locally outputs a string s with confidence1− then there is a way tofix its randomness such that it will locally -approximates a string s.Essentially,M w locally approximates a string s if it outputs a string that is close to s.Definition3(Local unique decoding).A code C:Σn→Σ¯n is(q, ,δ)locally decodable if there exists a probabilistic oracle machine M w(the decoding algorithm)with oracle access toa received codeword w such that:1.For every messageλ=(λ1,λ2,...λn)∈Σn and for every w∈Σ¯n such that Ag(C(λ),w)≥1−δit holds that M w locally outputsλwith confidence1− .2.M w(i)makes at most q queries to w for all i∈[n].It is possible to consider a more relaxed notion of local decoding,where the machine M wis not required to successfully decode every i.Instead,it is required to succeed on average overi:Definition4(Approximate local unique decoding).A code C over afieldΣ,C:Σn→Σ¯nis(q, ,δ)approximately locally decodable if there exists a deterministic oracle machine M w (the decoding algorithm)with oracle access to a received codeword w such that:1.For every messageλ=(λ1,λ2,...λn)∈Σn and for every w∈Σ¯n such that Ag(C(λ),w)≥1−δ,it holds that M w locally -approximatesλ.2.M w(i)makes at most q queries to w for all i∈[n].Although the definitions of locally decodable codes and approximately locally decodable codes are similar,it appears that it is much harder to construct locally decodable codes than ap-proximately locally decodable codes.While there exist constant-query approximately locally decodable codes of polynomial length,no such locally decodable codes are known.Approx-imately locally decodable are interesting when <δ,since the identity code is a(1, , ) approximately locally decodable code.A code C is list-decodable if for every word,there are a few codewords near it.Let C(y1),C(y2),...,C(y L)be the list of codewords near a word w.Roughly speaking,a code C is locally list-decodable if there exists a machine M,that given i,j and an oracle access to the received word w,outputs the j th symbol of y i.The locality property requires that the machine M makes a few queries to w.Formally:Definition5(Local list-decoding).Let C:Σn→Σ¯n be a code.A set of probabilistic oracle machines M1...M L with oracle queries to w,(α,L,q, )locally list-decodes C at the word w∈Σ¯n,if,•Every oracle machine M j makes at most q queries to the input word w.•For every codeword c∈C with Ag(c,w)≥α,there exists some k∈[L],such that M wk locally outputs c with confidence1− .We can also define approximate local list-decoding by relaxing the requirement that M w k successfully decodes c on every i.Instead,we require successful decoding on average over i. Definition6(Approximate local list-decoding).Let C:Σn→Σ¯n be a code.A set of de-terministic oracle machines M1...M L with oracle queries to w,(α,L,q, )approximately locally list-decodes C at the word w∈Σ¯n,if,•Every oracle machine M j makes at most q queries to the input word w.•For every codeword c∈C with Ag(c,w)≥α,there exists some k∈[L],such that M wk -approximates c.Definition7((Approximately)Locally list-decodable codes with deterministic reconstruction). Let C:Σn→Σ¯n be(α,L)list-decodable.A deterministic algorithm A(α,L,q, )(approx-imately)locally list-decodes C,if on input n,A outputs oracle machines M1...M L which (α,L,q, )(approximately)locally list-decode C at every word w∈Σ¯n.The code C is(α,L)list-decodable and therefore every w∈Σ¯n has at most L codewords c1,...,c L that areα-close to it.Each such codeword c i=C(λi)is represented by a proba-bilistic machine M i such that:•If the code is locally list-decodable then∀j M i(j)=λi j with probability at least1− .•If the code is approximately locally list-decodable then M i(j)=λi j for at least a1− fraction of the indices j.The algorithm A outputs L machines that are good for every w∈Σ¯n.One way to think about it is that i∈[L]is an advice that specifies which of the L solutions corresponds to the codeword we are interested in.Definition8(Locally list-decodable codes with probabilistic reconstruction).Let C:Σn→Σ¯n be(α,L)list-decodable.A probabilistic algorithm A(α,L,q, )locally list-decodes C, if on input n,A outputs probabilistic oracle machines M1...M L such that for every word w∈Σ¯n,with probability2/3over the random coins of A,the machines M1...M L locally list-decode C at w,i.e.,∀w∈F¯n PrA∀λAg(C(λ),w)≥α⇒∃i∀j Pr[M i(j)=λj]≥1−≥2/3.Definition9(Approximately locally list-decodable codes with probabilistic reconstruction). Let C:Σn→Σ¯n be(α,L)list-decodable.A probabilistic algorithm A(α,L,q, )ap-proximately locally list-decodes C,if on input n,A outputs deterministic oracle machines M1...M L such that for every word w∈Σ¯n,with probability2/3over the random coins of A,the machines M1...M L approximately locally list-decode C at w,i.e.,∀w∈F¯n PrA∀λAg(C(λ),w)≥α⇒∃i Prj[M i(j)=λj]≥1−≥2/3.The best approximately list-decodable codes currently known(to the best of our knowl-edge)are due to Impagliazzo et al.[IJKW10].In this note we focus on binary codes,although by using the non-binary codes of[IJKW10]one can also get non-binary list-decodable codes. Theorem2([IJKW10]2).For everyα, >0there exists a number f(α, )such that thereexists a code C App:{0,1}n→{0,1}f(α, )n5which is(1/2+α,O(1α2),O(log(1/ )α3), )ap-proximately locally list-decodable.3Composition TheoremOur main observation in this note is that if a code C LDC is locally decodable and a code C App is approximately locally decodable then by composing these two codes we get a code which is locally decodable,and can tolerate a higher error-rate.Theorem3.Let C LDC:Σn1→ΣN 2be(q, ,δ)locally decodable code and let C App:ΣN 2→ΣN3be an(q ,δ,δ )approximately locally decodable code.Then the code C=C App◦C LDC:Σn1→ΣN3defined by C(λ)=C App(C LDC(λ))is(q·q , ,δ )locally decodable.Thus,if we have a locally decodable code which can tolerate a small fraction of errors,the above theorem allows us to amplify the error-rate by using an approximately locally decodable code.We have similar theorem for the list-decoding regime:Theorem4.Let C LDC:Σn1→ΣN 2be(q, ,δ)locally decodable code and let C App:ΣN 2→ΣN3be an(α,L,q ,δ)approximately locally list-decodable code.Then the code C=C App◦C LDC:Σn1→ΣN3defined by C(λ)=C App(C LDC(λ))is(α,q·q ,L, )locally list-decodable.2The code we use is not explicit in[IJKW10],but it can be deduced from Section5in that paper.In Section5 it is shown that a longer code(the direct-product code,concatenated with Hadamard)is approximately locally list-decodable.However,the same proof carries over when using the derandomized direct-product code(concatenated with Hadamard).The parameter d(of[IJKW10])is set to5(this is affects the exponent in the codeword length). The number of queries is O(log(1/ )3)since we need to run the Goldreich-Levin algorithm O(log1/ )times,and each run requires1/α2queries.Proof:Let A denote the reconstruction algorithm for the code C App and let D w :[n ]→Σ1denote the unique decoding algorithm for the code C LDC .The reconstruction algorithm for the code C works as follows:it first applies the algorithm A to obtain a list of machines M 1,...,M L .For each machine M j ,it outputs the machine Z j defined by Z w j (i )=D M w j (i ).The bounds on the number of queries and the list size are immediate.Fix a word w ∈ΣN 3.The inner reconstruction algorithm A fails with probability at most 13.When it does not fail,wewill show that for every codeword with at least αagreement with w ,its message is outputted with confidence 1− by one of the output machines.Suppose that the agreement between C App (C LDC (λ))and w is at least α.Denote ζ=C LDC (λ).Since A did not fail,one of the machines M w j δ-approximates ζ.Thus,Z w j=D M w j locally outputs λwith confidence 1− .The above theorem give locally list-decodable codes which improve upon previously known constructions.Since we wish to get locally list-decodable codes with a constant query com-plexity,we need to use a locally decodable code with a constant query complexity.The best such codes currently known are due to [MFL +10]:Theorem 5([MFL +10]).For every r ≥2there exists a codeC LDC :{0,1}n →{0,1}exp(exp(O (r √log n (log log n )r −1)))which is (3r/2,γ,2·3r/2·γ)locally decodable,for every γ>0.Let C LDC and C App be the codes from Theorem 5and Theorem 2,respectively.Applying Theorem 4on these codes gives:Corollary 6(Theorem 1restated).For every r ≥2and every α, >0there exists a codeC :{0,1}n →{0,1}f (α, 2·3r/2)·exp(exp(O (r √log n (log log n )r −1)))which is (1/2+α,O (1α2),O (log(1/ )α3)·3r/2, )locally list-decodable,where f is the constant from Theorem 2.References[AS03]Sanjeev Arora and Madhu Sudan.Improved low-degree testing and its binatorica ,23(3):365–426,2003.[BET10]Avraham Ben-Aroya,Klim Efremenko,and Amnon Ta-Shma.Local list-decoding with a constant number of queries.In FOCS ,2010.[DGY10]Zeev Dvir,Parikshit Gopalan,and Sergey Yekhanin.Matching vector codes.Technical Report TR10-012,Electronic Colloquium on Computational Complex-ity (ECCC),2010.[Efr09]Klim Efremenko.3-query locally decodable codes of subexponential length.In STOC ,pages 39–44,2009.[Eli57]Peter.Elias.List decoding for noisy channels.Technical report,Research Labora-tory of Electronics,Massachusetts Institute of Technology,1957.[GKST02]Oded Goldreich,Howard J.Karloff,Leonard J.Schulman,and Luca Trevisan.Lower bounds for linear locally decodable codes and private information retrieval.In IEEE Conference on Computational Complexity,pages175–183,2002. 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