**MY-ASSIGNMENTEXPERT™**可以为您提供sydney. **CSYS5030 Information Theory**信息论课程的代写代考和辅导服务！

**MY-ASSIGNMENTEXPERT™**

#### 这是悉尼大学信息论课程的代写成功案例。

**CSYS5030**课程简介

The dynamics of complex systems are often described in terms of how they process information and self-organise; for example regarding how genes store and utilise information, how information is transferred between neurons in undertaking cognitive tasks, and how swarms process information in order to collectively change direction in response to predators. The language of information also underpins many of the central concepts of complex adaptive systems, including order and randomness, self-organisation and emergence. Shannon information theory, which was originally founded to solve problems of data compression and communication, has found contemporary application in how to formalise such notions of information in the world around us and how these notions can be used to understand and guide the dynamics of complex systems. This unit of study introduces information theory in this context of analysis of complex systems, foregrounding empirical analysis using modern software toolkits, and applications in time-series analysis, nonlinear dynamical systems and data science. Students will be introduced to the fundamental measures of entropy and mutual information, as well as dynamical measures for time series analysis and information flow such as transfer entropy, building to higher-level applications such as feature selection in machine learning and network inference. They will gain experience in empirical analysis of complex systems using comprehensive software toolkits, and learn to construct their own analyses to dissect and design the dynamics of self-organisation in applications such as neural imaging analysis, natural and robotic swarm behaviour, characterisation of risk factors for and diagnosis of diseases, and financial market dynamics.

## Prerequisites

At the completion of this unit, you should be able to:

**LO1**. critically evaluate investigations of self-organisation and relationships in complex systems using information theory, and the insights provided**LO2**. develop scientific programming skills which can be applied in complex system analysis and design**LO3**. apply and make informed decisions in selecting and using information-theoretic measures, and software tools to analyse complex systems**LO4**. create information-theoretic analyses of real-world data sets, in particular in a student’s domain area of expertise**LO5**. understand basic information-theoretic measures, and advanced measures for time-series, and how to use these to analyse and dissect the nature, structure, function, and evolution of complex systems**LO6**. understand the design of, and to extend the design of a piece of software using techniques from class, and your own readings.

**CSYS5030 Information Theory** HELP（EXAM HELP， ONLINE TUTOR）

A sequence of six symbols are independently drawn according to the distribution of the random variable $X$. The sequence is encoded symbol-by-symbol using an optimal (Huffmann) code. The resulted binary string is 10110000101 . We know that the source alphabet has five elements, but we only know that the distribution is one of the two distributions ${0,4 ; 0,3 ; 0,2 ; 0,05 ; 0,05}$ and ${0,3 ; 0,25 ; 0,2 ; 0,2 ; 0,05}$. Determine the distribution of $X$.

We are asked to determine an object by asking yes-no questions. The object is drawn randomly from a finite set according to a certain distribution. Playing optimally, we need 38.5 questions on the average to find the object. At least how many elements does the finite set have?

Problem 19 (Shortest codeword of Huffmann codes) Suppose that we have an optimal binary prefix code for the distribution $\left(p_1, \ldots, p_n\right)$, where $p_1>p_2>\ldots, p_n>0$. Show that

- If $p_1>2 / 5$ then the corresponding codeword has length 1 .
- If $p_1<1 / 3$ then the corresponding codeword has length at least 2.

(Basketball PLAY-Offs) The play-offs of NBA are played between team $A$ and team $B$ in a seven-game series that terminates as soon as one of the teams wins four games. Let the random variable $X$ represent the outcome of the series of games (possible values of $X$ are $A A A A$ or $B A B A B A B$ or $A A A B B B B$ ). Let $Y$ denote the number of games played. Assuming that the two teams are equally strong, determine the values of $H(X), H(Y), H(Y \mid X)$ and $H(X \mid Y)$.

(Cryptography) Let $X$ and $Z$ be binary 0-1 valued independent random variables, whose distribution is given by $\mathbf{P}{X=1}=p$ and $\mathbf{P}{Z=1}=1 / 2$. Define $Y=X \oplus Z$, where $\oplus$ denotes mod 2 summation. $X$ may be thought of as the message, $Z$ is the secret key, and $Y$ is the encrypted message. Determine the following quantities: $H(X), H(X \mid Z), H(X \mid Y), H(X \mid Y, Z), I(X ; Y), I(X ; Z), I(X ;(Y, Z))$. Interpret the results. What does the value of $I(X ; Y)$ tell you?

Problem 22 (Inequalities) Let $X, Y$ and $Z$ be arbitrary (finite) random variables. Prove the following inequalities.

- $H(X, Y \mid Z) \geq H(X \mid Z)$,
- $I((X, Y) ; Z) \geq I(X ; Z)$,
- $H(X, Y, Z)-H(X, Y) \leq H(X, Z)-H(X)$.

**MY-ASSIGNMENTEXPERT™**可以为您提供SYDNEY. **CSYS5030 INFORMATION THEORY**信息论课程的代写代考和辅导服务！