Decision theory and information propagation in quantum physics
Alan Forrester
15 Linden Road
Northampton
NN3 2JJ
alan_forrester2@https://www.doczj.com/doc/2b8891288.html,
Abstract
In recent papers, Zurek (2005) has objected to the decision-theoretic approach of (Deutsch, 1999) and (Wallace, 2003) to deriving the Born rule for quantum probabilities on the grounds that it courts circularity. Deutsch and Wallace assume that the many worlds theory is true and that decoherence gives rise to a preferred basis. However, decoherence arguments use the reduced density matrix, which relies upon the partial trace and hence upon the Born Rule for its validity. Using the Heisenberg Picture and quantum Darwinism – the notion that classical information is quantum information that can proliferate in the environment pioneered in (Olliver et al. 2005 and 2006) – I show that measurement interactions between two systems only create correlations between a specific set of commuting observables of system 1 and a specific set of commuting observables of system 2. This argument picks out a unique basis in which information flows in the correlations between those sets of commuting observables. I then derive the
Born rule for both pure and mixed states and answer some other criticisms of the decision theoretic approach to quantum probability.
Keywords: multiverse, parallel universes, decision theory, quantum computation, information flow, Heisenberg Picture.
1. Introduction
The basic equations of quantum mechanics are uncontroversial, but the explanation (interpretation) of these equations is still very controversial. According to the many worlds interpretation quantum physics should be taken literally – in particular when its equations say that physical objects exist in multiple versions this should be taken to mean that these other versions do actually exist (Everett, 1957; Deutsch, 1997 and 2002). One of the problems with this view is that one cannot experiment directly on these other versions of objects, but can only do so indirectly through interference. If the many worlds theory is true, that must presumably be because physical reality (in this context called the multiverse) is divided approximately into separate layers, each of which resembles the world of classical physics to some extent, for some demonstrable reason. One approach to securing this conclusion has been decoherence: every system interacts with an environment to some extent, and the hope was that by tracing the environmental degrees of freedom out of the density matrix of a system it could be shown that open quantum systems have a ‘pointer basis’ in which they act classically to a suitable degree of approximation. Calculations and computer simulations of decoherence seemed to indicate
that there is a pointer basis for many interesting systems (Zurek, 1991). However, as
Zurek (2005) pointed out, decoherence arguments assume that the partial trace procedure
for extracting reduced density matrices is valid and this in turn assumes that the Born rule
is valid (Neilsen and Chuang, 2000, p. 107; Landau, 1927). The Born Rule states that for
a quantum observable ?A of a system in a state ρ the expectation value of ?A is given by:
?A=Trρ?A
() (1) where Tr is the trace function.
Another problem is that quantum systems do not obey the axioms of standard probability
theory (see e.g. (Deutsch, Ekert and Luppachini, 2000) – for instance, there is no way of
assigning probabilities obeying the chain rule, to values of observables at times when
they are not ‘observed’). Hence, the Born rule for obtaining probabilities from quantum
systems is not generally applicable while interference processes are under way. So the
question arises: under what circumstances do quantum systems obey the Born rule? There
have been many unsuccessful approaches to this problem using the frequency
interpretation of probability, which is unviable because it relies on the unphysical notion
of an infinite set of measurements. More recently there have been some approaches to
probability via decision theory (Deutsch, 1999; DeWitt, 1998; Wallace, 2003). Decision
theory describes the behaviour of agents or decision makers who assign ‘values’ to
different games in a way that satisfies the ‘rationality’ requirement, namely that for any
two games G
1 and G
2
either the value of G
1
is greater than that of G
2
, or it is less than
that of G
2 or it is equal in value to G
2
. If the value of G
1
is greater than that of G
2
, the
agent will willingly give up an opportunity to experience G
2
for an opportunity to
experience G
1
and if the ranking is reversed his preferences will reverse too. If their value
is equal he will be indifferent between experiencing G
1 and experiencing G
2
. If, as in
quantum physics, a game has many possible outcomes then he will assign probabilities to the different possible outcomes to assign the game a value.It may be thought that decision theory is irrelevant to the laws of physics. However this objection is wrong because any real agent must be a physical system. In particular, if the laws of physics allow the existence of agents who act in the manner described above, then decision theory is applicable to physics; otherwise decision theory is not applicable to physics. If decision theory is applicable to physics then in some sense the laws of rationality are laws of physics because they predict the behaviour of a certain physical systems – decision theoretic agents. This argument also answers the objection that the laws of physics, including the Born rule should underwrite decision theory and not the other way around. Previous quantum mechanical decision theoretic arguments assumed that decoherence selects a preferred basis that evolves classically to a good approximation and so that information could only propagate in this preferred basis. As agents have to be able to receive information and use it to change their environment – perhaps by placing bets – they could only care about a set of outcomes in the preferred basis. In this approach, it was argued that quantum physics in the Schr?dinger Picture (with static observables and an evolving global state) is compatible with decision theory in the sense that under suitable circumstances the Born rule (and, indeed, only it) satisfies the rationality requirement and the axioms of probability theory in the Everett interpretation.
Zurek (2005) argues that the decision theoretic approach courts circularity because the decision-theoretic arguments proposed to date take for granted that decoherence provides
a preferred ‘pointer basis’ and this relies on the partial trace which relies on the Born rule (Neilsen and Chuang, 2000, p.107; Landau, 1927). Zurek then derives the probability rule using either decision theory or the relative frequency approach, using certain invariance properties of Schr?dinger states of systems that have been measured. He calls this approach envariance.
By contrast with Deutsch and Wallace, I will not assume that decoherence gives rise to a preferred basis. Instead I show that a measurement interaction between two systems only create correlations between observable ?A
t() of a system S1 and observable ?A2t() of
1
. This picks out a unique basis in which information flows in the another system S
2
correlations between observables of these quantum systems. The properties of these measurement interactions place substantial restrictions on the information that can propagate in the environment and so on the information that an agent can get about a system and I use these restrictions to derive the Born rule by treating decision theoretic agents as information-processing systems. (Ollivier et al., 2004 and 2005) have also discussed the constraints on what sort of information about a quantum system can spread widely in the environment. Unlike Ollivier et al., I use the Heisenberg Picture because the Schr?dinger picture (with its global but evolving state) is not as useful for the study of information propagation as is the Heisenberg Picture (with its static state and local evolving observables), as Deutsch and Hayden (2000) have pointed out. Of course, it is possible to trace the flow of information in the Schr?dinger Picture as it is mathematically equivalent to the Heisenberg Picture, and it has been used to prove results about the flow of information in quantum systems in (Tipler, 2000; Page, 1982), so these
results could be derived in the Schr?dinger Picture, but the argument would be more difficult to follow. Ollivier et al. also discuss quantitative issues of how to decide how much information flows out of a system into the environment. In this paper I discuss only qualitative issues of quantum Darwinism that have a bearing on quantum decision theory. In Section 2 I derive the relevant part of quantum Darwinism using the Heisenberg Picture. In Section 3 I use the results of Section 2 together with decision theory to derive the Born rule. In Section 4 I discuss the result and some criticisms of the decision theoretic approach.
2. Quantum Darwinism in the Heisenberg picture
First I shall explain the formalism that I will use to obtain the results in this paper. In the
Heisenberg Picture, an arbitrary observable ?A 1t () of a system S 1
with an N -dimensional Hilbert space is a Hermitian operator which can be written as
? A 1t ()=α1a ? B 1A a t ()a =0
N ?1
∑, (2) where the α1a are static, real c-numbers and the ? B 1A a t () are Hermitian operators such that ?B 1A a t ()?B 1A b t ()=δa b ?B 1A a t ()?B 1A a
t ()=?1a =0N ?1
∑ , (3)
where ? 1 is the unit observable. Thus the ? B 1A a
t () are a set of commuting projectors. (I have used this notation to avoid confusion between projectors and payoff functions, see Section 3.) I shall discuss he role of the static Heisenberg state below. Observables of S 1
that do not commute with ?A 1t () have different sets of projectors from ?A 1
t (), but the
equation for those observables in terms of those different projectors has the same form of as equation (2).
So the ? B 1A a t () do not span the full vector space of the observables of S 1 so some more operators are needed. The operators S 1A a b t () are defined to have the properties S 1A a b t ()S 1A c d t ()=δb c S 1A a d t ()
S 1A a a t ()=? B 1A a
t (). (4)
In other words, these operators have the same algebra as matrices with a 1 in the a ,b ()th slot and 0 elsewhere. The S 1A a b t () are a full basis of the vector space of the observables of S 1. (However, the S 1A a b t () are not all observables since they are not all Hermitian.) An arbitrary observable ? C 1t () of S 1 that is not equal to ?A 1t () may be written as ? C 1t ()=γ1c ? B 1C c t ()
c =0N ?1
∑? B 1C c t ()=β1c d e S 1A d e t ()
c =0
N ?1
∑ , (5)
where the γ1c are real, static c-numbers (the eigenvalues of ? C 1t ()) and the β1c d e
are complex static c-numbers such that the projectors ? B 1C c t () obey the algebra (3).
An arbitrary observable ? A 1
t () evolves as ?A 1t ()=U t ??A 10()U t
U t
?U t
=U t
U t
?=?1
, (6)
where U t ? is the Hermitian conjugate of U t . U t may or may not depend only on descriptors of S 1. The S 1A a b t () are linear combinations of observables and so they also
evolve according to this rule. I will suppose for the rest of this paper, with no relevant loss of generality, that the systems investigated evolve in steps of unit duration and the observables will be considered only at the end of each step. The generality follows from the fact that a quantum computational network evolving in the manner described may simulate any transformation undergone by any finite quantum system with arbitrary accuracy (Deutsch, 1989). Nothing would be lost by discarding this assumption, except for some clarity. A computer is a physical system composed of subsystems S 1,S 2... with associated observable quantities that can take on some discrete range of values. The computer evolves in discrete steps during which only some finite number of subsystems interact with one another. The motion undergone by the computer is called a computation.
I shall now explain in what sense a quantum system can perform a classical computation – that is, a computation that could be performed by a Turing Machine obeying classical physics as defined by Turing (1936) – and how information propagates between quantum systems. Consider a specific example of motion of a quantum system:
U =exp i φb ()S 1A b πb ()0()b =0
N ?1
∑, (7)
where π is a permutation of the integers 0...N ?1 and the φb are arbitrary real numbers. Then
? A 11()=α1a ? B 1A πa ()0()a =0N ?1
∑, (8)
so this motion has just permuted the eigenvalues corresponding to each of the projectors
associated with ? A
1
t() and the phases φb don’t matter so far as the evolution of this observable under U is concerned.
However, U has a very different effect on the ? B
1C c
t() (and hence on the arbitary
observable? C
1
t() provided it does not commute with ? A 1t()):
? B 1C c 1()=exp iφd?φe
()
[]β1c d e S1Aπd()πe()0()
c=0
N?1
∑. (9)
The phases φ
b do matter to ? C
1
t() and this evolution does not permute the ? B 1C c t().
Since the evolution of ? A
1
t() under U values permutes projectors that can be labelled with the integers from 0 to N?1 and any algorithm that permutes integers from 0 to N?1
could be performed by a Turing machine obeying classical physics, the evolution of ? A
1
t() under U performs N classical computations evaluating the same function of the integers from 0 to N?1 with different initial values. Each of these is locally and possibly globally a branch of the multiverse – that is to say, a structure within which information
flows perfectly about values of observables ? A
1
t() at an earlier time. (See (Deutsch, 2002) for an elaboration of this argument.) A branch of the multiverse must be a structure within which information flows because one of the characteristic features of the macroscopic world is that information does flow in the sense that it is possible to infer some features of the past from records and to predict some features of the future from the present state of the world. Furthermore as I show below information flows perfectly between systems only in branches characterised by classical computation. The evolution
of ? C 1t () under U does not perform a classical computation and does not constitute a branch of the multiverse. As I will discuss below a system may branch in different ways at different times so a branch may not survive for very long. If a branch continues to exist on large ‘classical’ scales I will call it a ‘world’.
In the many worlds theory, a measurement of a quantum system produces correlations between observables of the measured system and the measuring system and does not select one possible value of that observable as “the value” of that observable. Nevertheless, observers and measuring instruments do not observe all of the possible values of an observable.
The standard proof that, in the many worlds interpretation, observers and measuring instruments do not observe all of the possible values of an observable runs as follows. Let
S 1 and S 2 be two systems with N -dimensional Hilbert spaces H 1 and H 2 respectively
with the joint system S 1S 2 having Hilbert space H 1?H 2. Consider the observables ? A 1t () and ? A 2t () of S 1 and S 2 respectively ? A 1t ()=α1a ? B 1A a t ()
a =0N ?1
∑? A 2t ()=α2b ? B 2A b t ()
b =0
N ?1
∑, (10)
where these two observables have identical spectra. And let
? C 1t ()=γ1c ? B 1C c t ()
c =0
N ?1
∑? B 1C c
t ()=β
1c d e S
1A d e
t ()
d ,
e =0
N ?1
∑? C 2t ()=γ2c ? B 2C c t ()
c =0
N ?1
∑? B 2C c
t ()=β
1c d e S
1A d e
t ()
d ,
e =0
N ?1
∑, (11)
where the observables ? C 1t () and ? C 2t () have the same spectra as the observables ? A 1t () and ? A 2t () but do not commute with ? A 1t () and ? A 2t ().
Consider the motion described by
U M 1=
exp i φa b
()? B
1A a
0()S 2A b a ⊕N b
0()a ,b =0N ?1
∑, (12)
where
a ⊕N
b ≡a +b ()mod N . (13) Then
? A 11()=α1a ? B 1A a 0()=a =0N ?1
∑? A 1
0()? A 2
1()=α
2b
? B 1A a 0()? B 2A a ⊕N b 0()
a ,
b =0
N ?1
∑. (14)
So ? A 1t () is unaffected but ? A 2t () now depends on the values of a and b and so this is called a perfect measurement of ? A 1t () by ? A 2t () as it perfectly correlates ? A 2t () with ? A 1t (). Furthermore, (12) performs a classical computation on ? A 1t () and ? A 2t () in the sense described above. As such there are N independent branches and in each version the measuring instrument measures only one version of the measured system.
However, ? C
1
t() and ? C 2t() respond very differently:
? C 11()=exp iφd b?φa b
()
[]γ1cβ1c a d S1A a d0()
a,b,c,d=0
N?1
∑S2A a⊕
N
b d⊕N b
0()
? C 21()=exp iφa d?φa b
()
[]γ2cβ2c b d? B 1A a0()S2A a⊕N b a⊕N d0()
a,b,c,d=0
N?1
∑
. (15)
? C
1
t() and ? C 2t() are not perfectly correlated with one another or with anything else and
do not evolve classically under (12). Thus (12) perfectly correlates ? A
1
t() and ? A 2t(), but
not ? C
1
t() and ? C 2t(). Hence the form of the measurement interaction selects a preferred pointer basis: it induces the existence of branches down which information flows
characterised by different values of ? A
1
t(), but not of ? C 1t(). Furthermore, (14) and (15) illustrate that measurement can only copy information about eigenvalues of commuting sets of observables. Since information does get copied from one system to another (e.g. – from the document I am writing to other identical copies of this document that other people will read) and measurements of the kind described above are classical
computations on ? A
1
t() and ? A 2t() branches must be characterised by classical evolution.
What happens if ? C
1
t(), which isn’t correlated with anything is measured onto ? A 2t()?
First, between times 1 and 2, S
1
evolves so that
? A
1
2()=? C 11(). (16) If the measurement
U M 2=
exp i φab
()?B
a 1
2()S 2Aba ⊕N b
2()a ,b =0
N ?1
∑ (17)
is then performed the result is ? A 2
3()=α
2b
? B 1A a 2()a ,b =0N ?1
∑? B 2A a ⊕N b 2()
=
α
2b β
1a e a ⊕N b
exp i φa ⊕N b d ?φc d ()[]
S 1A e a ⊕N b 0()S 2A e ⊕N d a ⊕N b ⊕N c 0()
a ,
b ,
c ,
d ,
e =0
N ?1
∑. (18)
This is effectively a measurement of ? C 1t () onto ? A 2t (). From (18) it can be seen that the observable still has a branching structure in a suitably chosen basis but each branch that existed at time 0 is not associated with a single branch at time 2 but instead with multiple branches. As such not all the classical information that was recorded in ? A 2t () before the measurement has been retained.
So if measurements are always made in the same basis then the measured observable and the measuring observable may be regarded as a perfect channel for information about the results of classical computations. Otherwise it may not. And that is the main point of quantum Darwinism. Even here, however, the observables will carry N versions of this information as all classical evolution changes all N versions of a particular system. Quantum Darwinism in the sense used here is somewhat stricter than the sense in which the term is used in (Ollivier et al., 2004 and 2005). I discuss the issue of the relationship between the two ideas in Section 4.
A system that processes classical information – such as the human brain, or a decision theoretic agent – only does so in some of its observables. Thus, a classical computation,
such as human thought, must be instantiated only on some of the observables describing the physical object performing the computation. Even a quantum computer can only contain an answer to a problem in some commuting set of observables if that answer is to be propagated and used. And in general since the classically evolving observable is doing many classical computations an observer can experience only one of these computations, the particular computation that instantiates him, and so each copy of the observer can observe only one of the possible values of an observable after a measurement. The constant Heisenberg relative state ρ, a positive operator with trace 1, contains information about what observables carry information and what their values are in the world under consideration. This information is necessary for making predictions. In this sense, the state is an emergent feature of information flow between observables in quantum systems. The existence of the state is a consequence of measurement theory in the many worlds theory and is not needed to derive measurement theory. So quantum Darwinism is more fundamental than envariance, which relies on the existence of the relative state. The information that can be accessed in the state ρ by an observer about an t() is contained in ρ? A 1t(). And since measurement has the form of classical observable ? A
1
evolution in the sense described above an observer cannot access any phase information t(). When some observable has a definite value in the world under consideration in ρ? A
1
the state is said to be pure. A pure state obeys the equationρ2=ρ and so the state is equal to the product of projectors for some set of observables at equal times for all of the subsystems of the system of interest. For a pure state there is an observable ? A
t() of the
1
whole system for which
ρ? A
t()=α1aρ, (19) 1
In all of the worlds in the region of the multiverse described by the state ρ the observable ? A 1t () has value α1a . If there is no such observable then the state is said to be mixed.
I will need one more form of measurement to provide a proof of the Born rule. Sometimes an observable on an N -dimensional Hilbert space H 1 may be measured onto an observable of an M -dimensional Hilbert space H 1 with M >N . To do this H 2 is divided into a subspaces H 2a of dimension m a so that
H 2=?a =0N ?1H 2a . (20)
The observables ? A 1t () and ? A 2t () with spectra α1a and α2b with a =0...N ?1,b =0...M ?1 respectively then evolve such that
? A 1t +1()=α1a ? B 1A a t ()
a =0
N ?1
∑? A 2t +1()=? B 1A a t ()α2b ? B 2A b t ()b =γa ?1
γa ∑? ? ? ? ?
? ? ? a =0N ?1
∑γj =m k
k =0
j
∑. (21) This measurement differs from the ones above only in that for every possible value α1a many possible values of the measuring observable act as indicators of that value of ? A 1t (). This kind of measurement gives the same information as the earlier simpler measurements like (17) and (12).
3. Decision theory and quantum probability
Decision theory concerns rational agents, that is, physical objects such as persons that rank different physical states of affairs on a single scale of value. These agents may be considered as playing games in which each possible consequence of a particular action has some payoff associated with it. The value of a game is the payoff such that the agent is neutral between receiving that payoff and playing the game. In the context of quantum theory an agent is an information-processing system that obeys quantum physics and a physical state of affairs consists of an observable to be measured and a state in which it will be measured. By using this approach do I presuppose the Born rule? Unitary evolution does not presuppose the Born rule and indeed some unitary evolution changes amplitudes in ways that violate the Born rule as mentioned in Section 1. The measurement theory of Section 2 is about the creation of perfect correlations between observables and so explains what information an agent can extract from a system. In Section 2 I made no reference to probability and did not use the Born rule.
More explicitly, a quantum game consists of (1) an observable to be measured ? A
t(), the
1 measurement results being the consequences of the agent’s decision to play that particular
t() is measured, (3) a payoff function P that gives game, (2) a state ρ in which ? A
1
t() that is observed information on how much the agent gets for each eigenvalue of ? A
1
t() to the real numbers) and (4) a value (i.e. – it is a function from the eigenvalues of ? A
1
t(), the state ρ and the payoff function P to a real number function V which maps ? A
1
that is the value of the game.
In addition there is a set of acts that may be performed upon the system S
1
that has
observable ? A
1
t() and ancillary systems to change one game into another – unitary operations.
I should briefly discuss assumption (3) because some physicists apparently regard it as problematic. For an example see (Barnum et al., 2000, Section III) in which they complain that Deutsch assumes that when the eigenvalues are the same in each branch the player always gets the same payoff. As noted above when one observable is measured onto another, the measurement only conveys information about that observable and those observables of the measured system with which it commutes. Moreover, in each branch only information about the specific value that has been measured in that branch is available and can affect what happens in that branch. So attempts to argue that payoffs should not be associated with eigenvalues of the measured observable are perverse.
The result that I will derive is
Vρ,?A
1t(),P0
()=Trρ?A1t()
(), (22)
where P
0 is the payoff function that gives payoffs equal to the eigenvalues of ? A
1
t() in
each branch. That is, the expectation value Trρ?A
1t()
() predicted by the Born Rule will
be shown to be the same as the value of the game in state ρ, observable ? A
1
t() and payoff
function P
. So any quantum measurement may be interpreted as a quantum game with specific payoffs and expectation values.
If a particular game is changed in any of the attributes listed (1) – (3) then it becomes a different game. If two games have the same value they may be said to be equivalent because the agent is indifferent between playing them. The following properties of the value function follow from the general description of a game above and the discussion of Section 2:
An agent must be able to retain information about the value of an observable he has experienced if he is to keep the payoff associated with that value. Otherwise he will forget the value and the associated payoff. So he must get the payoff by measuring commuting observables and keeping the records in observables that commute with the observables that will be measured by other systems. And as each memory record within the agent may be measured by other observables that constitute the agent, all the observables in which the records are kept must commute with one another. This means that the agent cannot care about phases in the product ρ? A
t() that provides him with all
1
t(). This property of rational agents is called
the information he can access about ? A
1
phase indifference.
If an act U is a classical computation relative to the observable ? A
t() to be measured and
1
U?ρU=UρU?=ρ then U does not change the game’s value and I will call U a classical act. U just permutes which of the possible values of the observable are associated with which branch with respect to the observable concerned and with respect to the state picking out the world in which the game takes place. That is, the agent cares
about the consequences associated with being in a branch, not how the branches happen to be labelled. This principle is called classical act neutrality .
Physicality If there are two observables ? A 1t () and ? A 2
t () such that ρ? A 1t +Δt ()=ρ? A 2t (), (23) then
V ρ,? A 1t +Δt (),P ()=V ρ,? A 2t (),P ()
, (24) where P is an arbitrary payoff function.
I have argued that all of the information available about an arbitrary observable ? A 1t () is contained in ρ? A 1t () and the physicality principle is a direct consequence of this.
Dominance Let P 1 and P 2 be payoff functions such that P 1≥P 2 for all members of the
spectrum of ? A 1
t () then V ρ,? A 1t (),P 1()≥V ρ,? A 1t (),P 2()
. (25)
This amounts to the reasonable assumption that if in every world a player gets a greater payoff when he plays game G 1 then he does if he plays game G 2 then he will prefer to play game G 1.
Additivity Let P 1 and P 2 be arbitrary payoff functions, then
V ρ,? A 1t (),P 1+P 2()=V ρ,? A 1t (),P 1()+V ρ,? A 1t (),P 2
()
. (26)
This means that placing one bet whose payoff function is P 1+P 2 on a particular physical situation (i.e. – a particular instance of ρ and ? A 1t ()) is the same as placing two separate bets on the same physical situation whose payoff functions are P 1 and P 2 respectively. To see why this is true consider a game with state ρ, observable ? A 1
t () and payoff function P 1. This is equivalent to measuring the observable P 1? A 1
t ()()
P 1? A 1t ()()
=P 1α1a ()a =0
N ?1
∑? B 1A a
t () (27) with the payoff function P 0 since these give the same payoff in every branch. Similarly for another payoff function P 2 measuring P 2? A 1t ()()
and getting the payoff P 0 is the same as measuring ? A 1t () and getting payoff P 2. The observables ? A 1t (), P 1? A 1t ()(), P 2? A 1t ()()
and P 1+P 2()? A 1t ()()
all commute with one another and so records of the results of measuring all of these observables do not conflict with one another. So an agent could measure P 1? A 1t ()() and P 2? A 1t ()()
separately with payoff P 0 and receive a payoff P 1+P 2()α1a () in the a th branch just as he would if he measured P 1+P 2()? A 1t ()().
I will now prove the Born rule in four stages, the first three of which concern only the value of games played with pure states. All of the games below will consist of a measurement of ? A 10() in the state ρ with payoff function P 0 unless otherwise specified.
软件公司市场部的工作职责 进入IT行业，更准确的说是进入ERP行业，很真切的感受到行业的不同对市场部岗位设置要求的不同。 传统营销理论谈的是：4P，price价格、product产品、place渠道、promotion促销，市场部的主要工作职责可能也是围绕这些方面。但ERP软件公司很不同，比如：product：一套软件产品的生命周期通常在3-5年，软件的开发、需求确定等往往由技术部门主导，虽然有的大公司设有产品经理（理论上说也属于市场范畴），但大部分中小软件企业的市场部不包括产品开发该职能。Price：目前随着ERP市场竞争的激烈，随着客户成熟度的提高，目前一套ERP产品的售价往往取决与客户的议价能力、预算范围及竞争压力。在此方面，市场部起到的作用也不是非常大。Place：如果软件厂商没有设置代理商，市场部也没有用武之地了。Promotion：ERP产品面对的客户都是企业组织，属于组织购买行为，不是普通的广告、促销就能打动的了的。 那么软件公司是不是就没有必要设置市场部了？ 当然不是，而是在ERP行业，市场部的职责不同于其他行业。 对ERP等软件公司而言，最重要的是品牌建设及销售促进。软件公司的市场部，更应该以4C理论为指导：customer needs，cost，communication，convience。 细化一下，软件公司市场部的主要工作职责可以分为一下几类： 1、市场调研：关注行业动态，了解目标市场发展趋势及技术趋势等。 2、竞争者分析：对竞争对手历史、技术实力、成功失败案例、商务政策等要有一个基本的认识和了解。分为几个层次：知道竞争对手是谁；知道竞争对手做了什么；知道竞争对手未来会做什么；影响竞争对手策略。 3、品牌建设与推广。包括媒体宣传、网络营销、参加行业展会论坛等。 4、市场活动的策划与组织。 5、公关关系的维护，包括政府、协会、媒体等。 6、合作伙伴关系维护。 7、客户关系维护。软件公司更多的是关系影响，塑造标杆客户等非常重要。
上海交通大学医学院附属瑞金医院放射科简介 瑞金医院放射科目前为影像医学与核医学专业硕士、博士及博士后培养点，上海市住院医师规范化培训考核基地。科室现有高级职称人员18名，博士生导师2名，硕士生导师4名，在读博士研究生和硕士研究生20余名，每年招收进修医师25-30名。拥有多层螺旋CT 4台，磁共振检查仪3台，平板DSA设备3台及数字胃肠机、数字平板钼靶机、DR、CR等大型医疗设备。放射科已有完整的PACS和RIS系统，放射科的数字化建设已走在全国的前列。每年承办国家级继续教育学习班3-4项，主持国际多中心研究多项。近年来成功地主办、协办了多次大型国际性及区域性会议。科室与比利时、法国、美国等相关大学医院建立了多项合作交流项目，每年接待国外来访学者多批，并每年排除进修人员多名。2006年同比利时自由大学医院共同举办了中比神经影像研讨会，在上海、北京、杭州三地举行，受到了相当的好评。科室具有较强的师资队伍，在法文、英文教学方面具有特色，目前承担了上海市教委的影像学精品课程项目。 放射专业逐步形成了骨关节疾病、内分泌疾病、消化道和胰腺疾病、乳腺疾病、颅神经病变等方面的传统诊疗特色，开展了众多具有国际先进水平的特色项目：各类肿瘤或肿瘤样病变CT导引下的穿刺病理活检术；全身范围的多层CTA 检查；面肌痉挛和三叉神经痛的磁共振诊断；磁共振功能成像对脑认知的研究；乳腺癌影像学早期诊断；肾上腺病变的介入性治疗；肾动脉球囊扩张或内支架成形术治疗肾血管性高血压；CT引导下经皮治疗腰突症所致的坐骨神经根炎；半导体激光对原发及转移性肿瘤的姑息治疗；半导体激光治疗骨样骨瘤等。学科目前承担国家自然科学基金1项、上海市重大课题项目4项、市科委、市教委、市卫生局等基金及其它各类基金近20项；近年来获上海市科学技术进步“三等奖”2项、上海市医学科技奖“三等奖”2项。 联系导师简介 陈克敏，男，1951年1月出生，教授、主任医师 放射科主任，1976年毕业于上海第二医学院医学系，长期从事放射诊断和介入治疗的临床、教学和研究工作。目前担任中华医学会放射学分会委员、中国医学影像技术研究协会放射学分会副主任委员、上海放射学会副主任委员、国家
岗位：项目经理 主要职责： 1、计划： a)项目范围、项目质量、项目时间、项目成本的确认。 b)项目过程/活动的标准化、规范化。 c)根据项目范围、质量、时间与成本的综合因素的考虑，进行项目的总体规划与阶段计划。 d)各项计划得到上级领导、客户方及项目组成员认可。 2、组织： a)组织项目所需的各项资源。 b)设置项目组中的各种角色，并分配好各角色的责任与权限。 c)定制项目组内外的沟通计划。（必要时可按配置管理要求写项目策划目录中的《项目沟通计划》） d)安排组内需求分析师、客户联系人等角色与客户的沟通与交流。 e)处理项目组与其它项目干系人之间的关系。 f)处理项目组内各角色之间的关系、处理项目组内各成员之间的关系。 g)安排客户培训工作。 3、领导： a)保证项目组目标明确且理解一致。 b)创建项目组的开发环境及氛围，在项目范围内保证项目组成员不受项目其它方面的影响。 c)提升项目组士气，加强项目组凝聚力。 d)合理安排项目组各成员的工作，使各成员工作都能达到一定的饱满度。 e)制定项目组需要的招聘或培训人员的计划。 f)定期组织项目组成员进行相关技术培训以及与项目相关的行业培训等。 g)及时发现项目组中出现的问题。 h)及时处理项目组中出现的问题。 4、控制 a)保证项目在预算成本范围内按规定的质量和进度达到项目目标。 b)在项目生命周期的各个阶段，跟踪、检查项目组成员的工作质量； c)定期向领导汇报项目工作进度以及项目开发过程中的难题。 d)对项目进行配置管理与规划。 e)控制项目组各成员的工作进度，即时了解项目组成员的工作情况，并能快速的解决项目组成员所碰到的难题。 f)不定期组织项目组成员进行项目以外的短期活动，以培养团队精神。 结语： 项目经理是在整个项目开发过程中项目组内对所有非技术性重要事情做出最终决定的人。 岗位：系统架构师（技术总监） 主要功能及职责：
硕037班 刘文3110038020 2011/4/20交互式多模型仿真与分析IMM算法与GBP算法的比较，算法实现和运动目标跟踪仿真，IMM算法的特性分析 多源信息融合实验报告
交互式多模型仿真与分析 一、 算法综述 由于混合系统的结构是未知的或者随机突变的，在估计系统状态参数的同时还需要对系统的运动模式进行辨识，所以不可能通过建立起一个固定的模型对系统状态进行效果较好的估计。针对这一问题，多模型的估计方法提出通过一个模型集{}(),1,2,,j M m j r == 中不同模型的切换来匹配不同目标的运动或者同一目标不同阶段的运动，达到运动模式的实时辨识的效果。 目前主要的多模型方法包括一阶广义贝叶斯方法（BGP1），二阶广义贝叶斯方法（GPB2）以及交互式多模型方法等（IMM ）。这些多模型方法的共同点是基于马尔科夫链对各自的模型集进行切换或者融合，他们的主要设计流程如下图： M={m1,m2,...mk} K 时刻输入 值的形式 图一 多模型设计方法 其中，滤波器的重初始化方式是区分不同多模型算法的主要标准。由于多模型方法都是基于一个马尔科夫链来切换与模型的，对于元素为r 的模型集{}(),1,2,,j M m j r == ，从0时刻到k 时刻，其可能的模型切换轨迹为 120,12{,,}k i i i k trace k M m m m = ，其中k i k m 表示K-1到K 时刻，模型切换到第k i 个， k i 可取1,2,,r ，即0,k trace M 总共有k r 种可能。再令1 2 1 ,,,,k k i i i i μ+ 为K+1时刻经由轨迹0,k trace M 输入到第1k i +个模型滤波器的加权系数，则输入可以表示为 0,11 2 1 12|,,,,|,,,???k k trace k k k i M k k i i i i k k i i i x x μ++=?∑ 可见轨迹0,k trace M 的复杂度直接影响到算法计算量和存储量。虽然全轨迹的
?哈弗曼编码 A method for the construction of minimum-re-dundancy codes, 耿国华1数据结构1北京:高等教育出版社,2005:182—190 严蔚敏,吴伟民.数据结构(C语言版)[M].北京:清华大学出版社,1997. 冯桂,林其伟,陈东华.信息论与编码技术[M].北京:清华大学出版社,2007. 刘大有,唐海鹰,孙舒杨,等.数据结构[M].北京:高等教育出版社,2001 ?压缩实现 速度要求 为了让它(huffman.cpp)快速运行，同时不使用任何动态库，比如STL或者MFC。它压缩1M数据少于100ms（P3处理器，主频1G）。 压缩过程 压缩代码非常简单，首先用ASCII值初始化511个哈夫曼节点： CHuffmanNode nodes[511]; for(int nCount = 0; nCount < 256; nCount++) nodes[nCount].byAscii = nCount; 其次，计算在输入缓冲区数据中，每个ASCII码出现的频率： for(nCount = 0; nCount < nSrcLen; nCount++) nodes[pSrc[nCount]].nFrequency++; 然后，根据频率进行排序： qsort(nodes, 256, sizeof(CHuffmanNode), frequencyCompare); 哈夫曼树，获取每个ASCII码对应的位序列： int nNodeCount = GetHuffmanTree(nodes); 构造哈夫曼树 构造哈夫曼树非常简单，将所有的节点放到一个队列中，用一个节点替换两个频率最低的节点，新节点的频率就是这两个节点的频率之和。这样，新节点就是两个被替换节点的父
2019年中国大学软件工程专业大学排名和 大学名单 中国大学软件工程专业大学排名和大学名单 在最新公布的中国校友会网中国大学软件工程专业大学排名和大学名单中，北京大学、清华大学、国防科学技术大学的软件工程专业荣膺中国六星级学科专业，入选中国顶尖学科专业，位居全国高校第一；浙江大学、北京航空航天大学、华东师范大学的软件工程专业荣膺中国五星级学科专业美誉，跻身中国一流学科专业。上海交通大学、复旦大学、武汉大学、南京大学、吉林大学、中山大学、华中科技大学、四川大学、中国科学技术大学、山东大学、西安交通大学、哈尔滨工业大学、同济大学、天津大学、东南大学、湖南大学、西北工业大学、大连理工大学、北京理工大学、重庆大学、东北大学、西北大学、苏州大学、南京航空航天大学、北京邮电大学、北京工业大学、解放军理工大学等高校的软件工程专业入选中国四星级学科专业，跻身中国高水平学科专业。 2014中国大学软件工程专业排行榜 名次一级学科学科专业星级学科专业层次学校名称2014综合排名办学类型办学层次1软件工程6星级中国顶尖学科专业北京大学1中国研究型中国顶尖大学1软件工程6星级中国顶尖学
科专业清华大学2中国研究型中国顶尖大学1软件工程6星级中国顶尖学科专业国防科学技术大学中国研究型中国一流大学4软件工程5星级中国一流学科专业浙江大学6中国研究型中国一流大学4软件工程5星级中国一流学科专业北京航空航天大学21中国研究型中国一流大学4软件工程5星级中国一流学科专业华东师范大学24中国研究型中国一流大学7软件工程4星级中国高水平学科专业上海交通大学3中国研究型中国一流大学7软件工程4星级中国高水平学科专业复旦大学4中国研究型中国一流大学7软件工程4星级中国高水平学科专业武汉大学5中国研究型中国一流大学7软件工程4星级中国高水平学科专业南京大学8中国研究型中国一流大学7软件工程4星级中国高水平学科专业吉林大学9中国研究型中国一流大学7软件工程4星级中国高水平学科专业中山大学10中国研究型中国一流大学7软件工程4星级中国高水平学科专业华中科技大学12中国研究型中国一流大学7软件工程4星级中国高水平学科专业四川大学13中国研究型中国一流大学7软件工程4星级中国高水平学科专业中国科学技术大学14中国研究型中国一流大学7软件工程4星级中国高水平学科专业山东大学16中国研究型中国一流大学7软件工程4星级中国高水平学科专业西安交通大学18中国研究型中国一流大学7软件工程4星级中国高水平学科专业哈尔滨工业大学20中国研究型中国一流大学7软件工程4星级中国高水平学科专业同济大学22中国研究型中国一流大学7软件工程4星级中国高水平学科专业天津大学23中国研究型中国一流大学7软件工程4星级中国高水平学科专业东南大学25中国研究型中国一流大学7软件工程4星级中国高水平学科专业湖南大学28中国研究型中国高水平大学7软件工程4星级中国高水平学
更多资料请访问.(.....) 软件部经理岗位职责 职位名称：软件部经理 所属部门：软件部 直属上级：技术总监 职位概要：负责软件工程项目的具体实施、自有产品及基础技术的开发。 工作内容：管理、组建公司开发团队，参与公司相关政策的制定；拟定和执行本部门年度、月度目标、工作计划及总结；设计、开发、维护、管理软件产品。 一、直接职责 1、拟定本部门年度、月度目标、工作计划及总结； 2、负责本部门的成本控制工作以及本部门员工的绩效考评及监督、管理工作； 3、参与技术业务制定流程及与其他部门的协调工作； 4、领导技术团队并组织实施年度工作计划，完成年度任务目标； 5、负责管理公司的整体核心技术，组织制定和实施重大技术决策和技术方案； 6、负责协调项目开发或实施的各个环节，把握项目的整体进度； 7、指导、审核项目总体技术方案，对各项目结果进行最终质量评估； 8、会同项目经理共同审核项目组内部测试计划，并组织项目组负责软件项目的后期维护工作； 9、针对部门的发展计划，向公司提供部门员工的培训要求，抓好部门员工的专业培训工作； 10、本部门的发展规划，组织审定部门各项技术标准，编制、完善软件开发流程； 11、负责与其他部门之间的沟通与协作，满足和协调公司各相关部门提出的系统更新、新产品等技术需求； 12、关注国内外软件市场的发展动向、最新技术及信息，组织内部技术交流。一三、配合市场部门开展工作，向市场部门提供必要的技术支持。
14、需求调研中，配合项目经理进行需求调研工作，并对生成的需求调研报告进行审核评定。 一五、明确文档编写种类及格式，对项目组需要生成的文档进行质量、数量和时间控制，并组织召开评审会； 16、制度本部门人员短期和长期需求计划，并配合行政部的人员招聘工作； 二、管理职责 1、抓好本部门项目组总结分析报告工作，定期进行项目分析、总结经验、找出存在的问题，提出改进工作的意见和建议，并组织本部门员工学习，为公司领导决策提供专题分析报告或综合分析资料； 2、开展公司的市场经营和客户服务工作，组织开展市场调查、经营分析，掌握竞争对手动态，及时组织竞争方案的制定和实施，确保公司在市场竞争中的主动； 3、组织实施公司机构和人员的调整设置、绩效考核及二级薪酬分配，提出员工的招聘和使用计划，保证公司内部考核、薪酬分配制度的合理完善及人力资源的有效配置，推进公司目标的实现。提供项目的设计方案，协助公司顺利接下项目； 4、参与工程项目的洽谈、制定和审核工作，对公司所签合同有关软件技术合同部分中工期、技术方案、软件合同额等方面提供技术支持； 5、推进公司企业文化建设，掌握员工主要思想动态，倡导队伍的创新和团队精神，提升公司核心竞争能力； 6、规范部门内部管理，提高员工整体技术水平，把握技术发展方向，使得技术发展方向与主流技术合拍； 7、定期组织部门人员培训，组建一个高效、有朝气、技术过硬的开发团队； 三、工作权限 1、对本部职责范围内的工作有指导、协调、监督管理的权力； 2、下属人员的工作态度，工作岗位等考核权、指导权、分配权； 3、所属人员的违纪、违规纠正权及事实处理权或处理申报权； 4、对本部门项目资金使用的额度内审核权； 5、对软件部人员及公司其他相关人员的技术培训提出指导建议权； 四、管辖范围 软件部所工作及总经理授权范畴。 五、工作标准（或要求） 1、严格遵守公司的各项管理制度，认真履行工作职责，行使公司给予的管理权力，软件部统一对外出口为软件部经理； 2、有效、合理的部署全部门的工作安排； 3、及时掌握客户的需求，针对项目方案做出分析； 4、对软件的整体设计以及调研进行审核及补救； 5、调动部门员工的工作热情，使部门形成良好风气； 6、处理部门突发事件，组织人员及时处置； 六、入职要求 1、计算机及其相关专业，大本以上学历。 2、4年以上软件开发经验及2年研发团队管理经验，有独立带领技术团队开发软件产品的成功案例； 3、精通各类型数据库，并能熟练编写数据库存储过程，触发器，熟悉、模式的项目开发； 4、有制造业项目经验，如仓库管理、车间管理、等；
作业参考答案——10-特殊图 1.(a)(c)(d)是欧拉图，(a)(b)(c)(d)(e)可以一笔画，(a)(b)(c)(d)(e)(f)(g)是 哈密顿图。 2.根据给定条件建立一个无向图G=
数至少为2，而V2中的每个结点度数至多为2，从而它满足t条件t=1，因此存在从V1到V2的匹配，故可分配。 5.此平面图具有五个面，如下图所示。 a b c d e f g r1r2 r3 r4 r5 ?r1，边界为abca，D(r1)=3; ?r2，边界为acga，D(r2)=3; ?r3，边界为cegc，D(r3)=3; ?r4，边界为cdec，D(r4)=3; ?r5，边界为abcdefega，D(r5)=8;无限面 6.设该连通简单平面图的面数为r，由欧拉公式可得，6?12+r=2，所以 r=8，其8个面分别设为r1,r2,r3,r4,r5,r6,r7,r8。因是简单图，故每个面至少由3条边围成。只要有一个面是由多于3条边所围成的，那就有所有面的次数之和 8∑ i=1 D(r i)>3×8=24。但是，已知所有面的次数之和等于边数的两倍，即2×12=24。因此每个面只能由3条边围成。 2
LZ77压缩算法实验报告 一、实验内容 使用C++编程实现LZ77压缩算法的实现。 二、实验目的 用LZ77实现文件的压缩。 三、实验环境 1、软件环境：Visual C++ 6.0 2、编程语言：C++ 四、实验原理 LZ77 算法在某种意义上又可以称为“滑动窗口压缩”，这是由于该算法将一个虚拟的，可以跟随压缩进程滑动的窗口作为术语字典，要压缩的字符串如果在该窗口中出现，则输出其出现位置和长度。使用固定大小窗口进行术语匹配，而不是在所有已经编码的信息中匹配，是因为匹配算法的时间消耗往往很多，必须限制字典的大小才能保证算法的效率；随着压缩的进程滑动字典窗口，使其中总包含最近编码过的信息，是因为对大多数信息而言，要编码的字符串往往在最近的上下文中更容易找到匹配串。 五、LZ77算法的基本流程 1、从当前压缩位置开始，考察未编码的数据，并试图在滑动窗口中找出最长的匹 配字符串，如果找到，则进行步骤2，否则进行步骤3。 2、输出三元符号组( off, len, c )。其中off 为窗口中匹
配字符串相对窗口边 界的偏移，len 为可匹配的长度，c 为下一个字符。然后将窗口向后滑动len + 1 个字符，继续步骤1。 3、输出三元符号组( 0, 0, c )。其中c 为下一个字符。然后将窗口向后滑动 len + 1 个字符，继续步骤1。 六、源程序 /********************************************************************* * * Project description: * Lz77 compression/decompression algorithm. * *********************************************************************/ #include 2019年陕西师范大学招生计划录取人数及招生专业目录(文科理科) 陕西师范大学招生计划录取人数及招生专业目录(文科理科) 更新：2018-11-29 11:48:29 2019年陕西师范大学招生计划录取人数及招生专业目录(文科理科) 选择可以说在很大程度上影响着考生后半生的生活方向和轨迹，很多考生因为高考填志愿时没有足够重视，要么浪费了不少分数；要么学了不喜欢的专业，在大学里感觉“痛不欲生”。 俗话说“七分考，三分报”，正是说明志愿填报的重要性。那么如何填报志愿，填报志愿时选大学应主要考虑哪些指标？其中一个重要指标就是大学招生计划人数和招生专业。今日将带你一起了解关于陕西师范大学招生计划和招生人数、陕西师范大学招生专业目录等相关知识。 注：2019年陕西师范大学招生专业和招生计划人数截至发稿前官方暂未公布，所以小编先整理了2018年陕西师范大学的招生计划专业的信息。考生务必以官方发布的信息为准，本文只作参考！ 2018年陕西师范大学招生计划人数和招生专业在陕西招生计划 专业名称计划类型层次科类计划数外国语言文学类 (含英语(创新试验班),翻译)非定向本科文史15哲学非定向本科文史11日语非定向本科文史11法学非定向本科文史15行政管理非定向本科文史10新闻传播学类 (含新闻学,编辑出版学,网络与新媒体专业)非定向本科文史17公共事业管理非定向本科文史10旅游管理非定向本科文史5社会学非定向本科文史14思想政治教育 (创新试验班)非定向本科文史10历史学类 (含历史学(创新试验班),文物与博物馆学,古典文献学专业)非定向本科文史22中国语言文学类 (含汉语言文学(基地班),汉语言文学(创新试验班),秘书学,汉语国际教育专业)非定向本科文史40预科班非定向本科文史10俄语非定向本科文史10数学类 (含数学与应用数学(创新试验班)、信息与计算科学、统计学专业)非定向本科理工43心理学类 (含心理学,应用心理学专业)非定向本科理工24计算机类 (含计算机科学与技术(创新试验班)软件工程,信息管理与信息系统专业)非定向本科理工57旅游管理非定向本科理工9生物科学类 (含生物科学(基地班),生物技术,生态学专业)非定向本科理工51食品科学与工程类 (含食品科学与工程,食品质量与安全专业)非定向本科理工34物理学类 (含物理学(创新试验班)电子信息科学与技术专业)非定向本科理工22新闻传播学类 (含新闻学,编辑出版学,网络与新媒体专业)非定向本科理工 上海交通大学医学院附属瑞金医院北院 2018年度决算 目录 第一部分上海交通大学医学院附属瑞金医院北院概况 一、主要职能 二、机构设置 第二部分上海交通大学医学院附属瑞金医院北院2018年度决算表 一、收入支出决算总表 二、收入决算表 三、支出决算表 四、财政拨款收入支出决算总表 五、一般公共预算财政拨款支出决算表 六、一般公共预算财政拨款基本支出决算表 七、一般公共预算财政拨款“三公”经费及机关运行经费支出决算表 八、政府性基金预算财政拨款支出决算表 九、资产负债情况表 第三部分上海交通大学医学院附属瑞金医院北院2018年度决算情况说明 第四部分名词解释 第一部分上海交通大学医学院附属瑞金医院北院概况 一、主要职能 上海交通大学医学院附属瑞金医院北院是“郊区新建三级 综合医院项目”（“5+3+1”工程）的重要组成部分之一，位于嘉 定新城，于2009 年12月奠基，2012 年12月17日开始试运营。全院占地面积210亩，建筑面积72,000平方米，核定床位600张,核定编制800人，医院目前现有职工（含瑞金派驻及退 休回聘）903人，其中研究生学历272人，中高级职称320人，已开放临床医技科室41个，其中血液科、内分泌科、普外科等 多个瑞金母院固有的优势、重点学科在新院得到了有效的延伸 与发展。 瑞金医院北院的发展将本着“落户嘉定、服务周边”，改善 区域居民对优质医疗资源可及性的建设目标，继续朝着符合公 立医院综合改革总体思想和目标，紧密结合瑞金医院母院，有 所侧重，有所互补，捆绑错位发展；积极融合嘉定，与二级医 院和社区形成三级服务网络，更好地发挥在疑难复杂病例、危 急重症救治等方面的综合服务能力，切实为老百姓带来优质的 医疗服务。 二、机构设置 实验名称：LZSS压缩算法实验报告 一、实验内容 使用Visual 6..0 C++编程实现LZ77压缩算法。 二、实验目的 用LZSS实现文件的压缩。 三、实验原理 LZSS压缩算法是词典编码无损压缩技术的一种。LZSS压缩算法的字典模型使用了自适应的方式，也就是说，将已经编码过的信息作为字典， 四、实验环境 1、软件环境：Visual C++ 6.0 2、编程语言：C++ 五、实验代码 #include -- need byte-swap function for big endian CPU */ #define READ_LE32(X) *(uint32_t *)(X) #define WRITE_LE32(X,Y) *(uint32_t *)(X) = (Y) /* this assumes sizeof(long)==4 */ typedef unsigned long uint32_t; /* text (input) size counter, code (output) size counter, and counter for reporting progress every 1K bytes */ static unsigned long g_text_size, g_code_size, g_print_count; /* ring buffer of size N, with extra F-1 bytes to facilitate string comparison */ static unsigned char g_ring_buffer[N + F - 1]; /* position and length of longest match; set by insert_node() */ static unsigned g_match_pos, g_match_len; /* left & right children & parent -- these constitute binary search tree */ static unsigned g_left_child[N + 1], g_right_child[N + 257], g_parent[N + 1]; /* input & output files */ static FILE *g_infile, *g_outfile; /***************************************************************************** initialize trees *****************************************************************************/ static void init_tree(void) { unsigned i; /* For i = 0 to N - 1, g_right_child[i] and g_left_child[i] will be the right and left children of node i. These nodes need not be initialized. Also, g_parent[i] is the parent of node i. These are initialized to NIL (= N), which stands for 'not used.' For i = 0 to 255, g_right_child[N + i + 1] is the root of the tree for strings that begin with character i. These are initialized to NIL. Note there are 256 trees. */ for(i = N + 1; i <= N + 256; i++) g_right_child[i] = NIL; for(i = 0; i < N; i++) g_parent[i] = NIL; } /***************************************************************************** Inserts string of length F, g_ring_buffer[r..r+F-1], into one of the trees (g_ring_buffer[r]'th tree) and returns the longest-match position and length via the global variables g_match_pos and g_match_len. If g_match_len = F, then removes the old node in favor of the new one, because the old one will be deleted sooner. （岗位职责）软件公司各岗 位描述 软件公司岗位说明书 版本号V2010 岗位说明 岗位：项目经理 主要职责： 1、计划： a)项目范围、项目质量、项目时间、项目成本的确认。 b)项目过程/活动的标准化、规范化。 c)根据项目范围、质量、时间和成本的综合因素的考虑，进行项目的总体规划和阶段计划。 d)各项计划得到上级领导、客户方及项目组成员认可。 2、组织： a)组织项目所需的各项资源。 b)设置项目组中的各种角色，且分配好各角色的责任和权限。 c)定制项目组内外的沟通计划。（必要时可按配置管理要求写项目策划目录中的《项目沟通计划》） d)安排组内需求分析师、客户联系人等角色和客户的沟通和交流。 e)处理项目组和其它项目干系人之间的关系。 f)处理项目组内各角色之间的关系、处理项目组内各成员之间的关系。 g)安排客户培训工作。 3、领导： a)保证项目组目标明确且理解壹致。 b)创建项目组的开发环境及氛围，于项目范围内保证项目组成员不受项目其它方面的影响。 c)提升项目组士气，加强项目组凝聚力。 d)合理安排项目组各成员的工作，使各成员工作均能达到壹定的饱满度。 e)制定项目组需要的招聘或培训人员的计划。 f)定期组织项目组成员进行关联技术培训以及和项目关联的行业培训等。 g)及时发现项目组中出现的问题。 h)及时处理项目组中出现的问题。 4、控制 a)保证项目于预算成本范围内按规定的质量和进度达到项目目标。 b)于项目生命周期的各个阶段，跟踪、检查项目组成员的工作质量； c)定期向领导汇报项目工作进度以及项目开发过程中的难题。 d)对项目进行配置管理和规划。 e)控制项目组各成员的工作进度，即时了解项目组成员的工作情况，且能快速的解决项目组成员所碰到的难题。 f)不定期组织项目组成员进行项目以外的短期活动，以培养团队精神。 结语：项目经理是于整个项目开发过程中项目组内对所有非技术性重要事情做出最终决定的人。 多媒体数据压缩实验报告 篇一：多媒体实验报告_文件压缩 课程设计报告 实验题目：文件压缩程序 姓名：指导教师：学院：计算机学院专业：计算机科学与技术学号： 提交报告时间：20年月日 四川大学 一，需求分析： 有两种形式的重复存在于计算机数据中，文件压缩程序就是对这两种重复进行了压 缩。 一种是短语形式的重复，即三个字节以上的重复，对于这种重复，压缩程序用两个数字：1.重复位置距当前压缩位置的距离；2.重复的长度，来表示这个重复，假设这两个数字各占一个字节，于是数据便得到了压缩。 第二种重复为单字节的重复，一个字节只有256种可能的取值，所以这种重复是必然的。给 256 种字节取值重新编码，使出现较多的字节使用较短的编码，出现较少的字节使用较长的编码，这样一来，变短的字节相对于变长的字节更多，文件的总长度就会减少，并且，字节使用比例越不均 匀，压缩比例就越大。 编码式压缩必须在短语式压缩之后进行，因为编码式压缩后，原先八位二进制值的字节就被破坏了，这样文件中短语式重复的倾向也会被破坏（除非先进行解码）。另外，短语式压缩后的结果：那些剩下的未被匹配的单、双字节和得到匹配的距离、长度值仍然具有取值分布不均匀性，因此，两种压缩方式的顺序不能变。 本程序设计只做了编码式压缩，采用Huffman编码进行压缩和解压缩。Huffman编码是一种可变长编码方式，是二叉树的一种特殊转化形式。编码的原理是：将使用次数多的代码转换成长度较短的代码，而使用次数少的可以使用较长的编码，并且保持编码的唯一可解性。根据 ascii 码文件中各 ascii 字符出现的频率情况创建 Huffman 树，再将各字符对应的哈夫曼编码写入文件中。同时，亦可根据对应的哈夫曼树，将哈夫曼编码文件解压成字符文件. 一、概要设计： 压缩过程的实现: 压缩过程的流程是清晰而简单的: 1. 创建 Huffman 树 2. 打开需压缩文件 3. 将需压缩文件中的每个 ascii 码对应的 huffman 编码按 bit 单位输出生成压缩文件压缩结束。 信息工程专业介绍: 1．专业简介：信息技术是衡量一个国家现代化水平的重要标志，我国把信息技术列为21世纪发展战略计划的首位。信息工程是一门研究信息的产生、获取、传输、存储和显示技术的学科。信息工程专业培养在信息工程，重点是光电信息工程领域具有宽厚的理论基础、扎实的专业知识和熟练的实验技能的高级信息工程科技人才。毕业生将在光电信号的采集、传输、处理、存储和显示的科学研究、工程设计、技术开发和企业管理中展示才华。 2．主修课程：光电信息物理基础、光电子学、信号与系统、通信原理、图像处理、传感器原理技术、光电检测技术、自动控制理论、光纤通信、计算机通讯网络、工程光学、微机原理、计算机软件技术基础、计算机网络技术、计算机辅助设计、数字与模拟电子技术基础、电路基础以及有关数理基础和工程基础方面的课程。 3．毕业去向：本专业历年输送了大量优秀毕业生攻读硕士、博士学位。除此之外，主要为科研单位、高等院校、电信部门、信息产业部门、企事业单位及有关公司录用，从事光电信息工程与技术、通信工程与技术、光电信号检测、处理及控制技术等领域的研究、设计、开发应用和管理等工作。 电子信息工程专业 业务培养目标： 业务培养目标：本专业培养具备电子技术和信息系统的基础知识，能从事各类电子设备和信息系统的研究、设计、制造、应用和开发的高等工程技术人才。 业务培养要求：本专业是一个电子和信息工程方面的较宽口径专业。本专业学生主要学习信号的获取与处理、电厂设备信息系统等方面的专业知识，受到电子与信息工程实践的基本训练，具备设计、开发、应用和集成电子设备和信息系统的基本能力。 电子信息工程已经涵盖很广的范围。电话交换局里怎样处理各种电话信号，手机是怎样传递我们的声音甚至图象，我们周围的网络怎么样传递数据，甚至信息化时代军队的信息传递中如何保密等知识。我们通过一些基础知识的学习认识这些东西，并能够进行维护和更先进的技术和新产品的开发。 你首先要有扎实的数学知识，要学习许多电路知识，电子技术，信号与系统，计算机控制原理，信号与系统，通信原理等基本课程。自己还要动手设计、连接一些电路以及结合计算机的实验。譬如自己连接传感器的电路，用计算机自己设置小的通信系统，还会参观一些大的公司的电子和信息处理设备，对整体进行了解，理解手机信号、有线电视是如何传输的等，并能有机会在老师指导下参与大的工程的设计。 随着计算机和互联网日益深入到社会生活的多个层面，社会需求量相当大。现在是一个热门专业。 毕业后干什么——从事电子设备和信息系统的设计、应用开发以及技术管理等 随着社会信息化的深入，各行业大都需要本专业人才，而且薪金很高。可成为： 电子工程师——设计开发一些电子，通信器件，起薪一般2000元——6000元/月； 项目主管—策划一些大的系统，经验、知识要求很高，起薪一般4000元/月以上； 还可以继续进修成为教师，进行科研项目等 专业是个好专业：适用面比较宽，和计算机、通信、电子都有交叉；但是这行偏电，因此动手能力很重要；另外，最好能是本科，现在专科找工作太难了！当然大虾除外 本专业对数学和英语要求不低，学起来比较郁闷要拿高薪，英语是必需的； 吃技术这碗饭，动手能力和数学是基本功当然，也不要求你成为数学家，只要能看懂公式就可以了，比如微积分和概率统计公式，至少知道是在说些什么而线性代数要求就高一些，因为任何书在讲一个算法时，最后都会把算法化为矩阵计算（这样就能编程实现了，而现代的电子工程相当一部分工作都是编程） 对于动手能力，低年级最好能焊接装配一些小电路，加强对模拟、数字、高频电路（这三门可是电子线路的核心）的感性认识；工具吗就找最便宜的吧！电烙铁、万用表是必需的，如果有钱可以买个二手示波器电路图吗，无线电杂志上经常刊登，无线电爱好者的入门书对实际操作很有好处 综合排名： 综合排名比得主要是综合医院，专科医院就不参与了，这当中也包括三甲中医院，因为现在三甲中医院也是科室齐全，只不过多了个“中”字而已 1，复旦大学附属上海华山医院 上海人心中的永远的金字招牌，无论关于上海哪家医院排第一的理论到底有多多，最起码，华山医院这上海第一在上海人心中是肯定的！再看，《2007年全国医院排名》华山医院全国第三，上海第一；2009年全年门急诊量279万，全国第二，仅次于解放军总医院的300万；2009年出院人数4.7万，少于瑞金医院的5.5万，上海第二，综上，华山医院上海第一无可厚非。中国科学院院士一人，中国工程院院士两人，上海第一家接受JCI评审的综合医院，10个国家重点科室上海第一，全国仅次于协和医院......华山医院上海第一，想必应该如此2，上海交大附属瑞金医院 《2007年全国排名》全国第五，上海第二，2009年全员出院人次上海第一，中国科学院院士人，中国工程院院士2人，瑞金的实力无需多说，和华山不相上下。 3，复旦大学附属上海中山医院 虽然《2007年全国医院排名》把仁济医院排在全国第八，上海第三，但拥有中国科学院院士，工程院院士各1人，还有那么多重点专科的中山医院......够了，不多说。 争议就从第四名开始了 以下都是我个人意见： 4，上海交大附属仁济医院 5，第二军医大附属长海医院 6，上海交大附属新华医院 7，第二军医大附属长征医院 8，上海中医药大学附属曙光医院 9，上海中医药大学附属龙华医院 10，同济大学附属上海同济医院 分科排名（分科排名就不列举前10了，有名的我就写上，也算是指导大家去上海就医的选择吧） 内科： 神经内科：1，复旦大学附属上海华山医院；2，复旦大学附属上海中山医院；3，复旦大学附属儿科医院 心内科：1，复旦大学附属上海中山医院；2，复旦大学附属上海新华医院；3，复旦大学附属上海华山医院 消化内科：1，上海交大附属仁济医院；2，复旦大学附属上海中山医院；3，上海交大附属瑞金医院 呼吸内科：1，上海交大附属新华医院；2，第二军医大附属长海医院；3，同济大学附属上海同济医院 内分泌科：1，上海交大附属瑞金医院；2，上海交大附属仁济医院；3，同济大学附属上海同济医院陕西师范大学招生计划录取人数及招生专业目录(文科理科).doc
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