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## Introduction to Large Deviation Theory

*M. Vidyasagar*

### in Hidden Markov Processes: Theory and Applications to Biology

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691133157
- eISBN:
- 9781400850518
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691133157.003.0005
- Subject:
- Mathematics, Probability / Statistics

This chapter provides an introduction to large deviation theory. It begins with an overview of the motivatio n for the problem under study, focusing on probability distributions and how to construct ... More

## Entropy

*Robert Alicki and Mark Fannes*

### in Quantum Dynamical Systems

- Published in print:
- 2001
- Published Online:
- February 2010
- ISBN:
- 9780198504009
- eISBN:
- 9780191708503
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504009.003.0009
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter begins with the discussion of various meanings of the entropy: Boltzmann entropy, Shannon entropy, von Neumann entropy. It then presents the basic properties of the von Neumann entropy ... More

## Introduction to Information Theory

*M. Vidyasagar*

### in Hidden Markov Processes: Theory and Applications to Biology

- Published in print:
- 2014
- Published Online:
- October 2017
- ISBN:
- 9780691133157
- eISBN:
- 9781400850518
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691133157.003.0002
- Subject:
- Mathematics, Probability / Statistics

This chapter provides an introduction to some elementary aspects of information theory, including entropy in its various forms. Entropy refers to the level of uncertainty associated with a random ... More

## Quantum information I

*Vlatko Vedral*

### in Introduction to Quantum Information Science

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the ... More

## Measures of entanglement

*Vlatko Vedral*

### in Introduction to Quantum Information Science

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses how entangled two states are. One obvious way is to consider the distillation procedure, in which the entanglement of any state is quantified by how many fully entangled qubits ... More

## Quantum information II

*Vlatko Vedral*

### in Introduction to Quantum Information Science

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements ... More

## Generalized Information Measures and the Analysis of Brain Electrical Signals

*A. Plastino, M.T. Martin, and O. Rosso*

### in Nonextensive Entropy: Interdisciplinary Applications

- Published in print:
- 2004
- Published Online:
- November 2020
- ISBN:
- 9780195159769
- eISBN:
- 9780197562024
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780195159769.003.0020
- Subject:
- Earth Sciences and Geography, Atmospheric Sciences

The traditional way of analyzing brain electrical activity, on the basis of electroencephalogram (EEG) records, relies mainly on visual inspection and years of training. Although it is quite ... More

## The Metrics of Info-Metrics

*Amos Golan*

### in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199349524
- eISBN:
- 9780199349555
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199349524.003.0003
- Subject:
- Economics and Finance, Econometrics

In this chapter I present the key ideas and develop the essential quantitative metrics needed for modeling and inference with limited information. I provide the necessary tools to study the ... More

## Prior Information

*Amos Golan*

### in Foundations of Info-Metrics: Modeling, Inference, and Imperfect Information

- Published in print:
- 2017
- Published Online:
- November 2017
- ISBN:
- 9780199349524
- eISBN:
- 9780199349555
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199349524.003.0008
- Subject:
- Economics and Finance, Econometrics

In this chapter I introduce and quantify prior information and show how to incorporate it into the info-metrics framework. The priors developed arise from fundamental properties of the system, from ... More

## Large Deviations Principle for Diffusions

*Gopinath Kallianpur and P. Sundar*

### in Stochastic Analysis and Diffusion Processes

- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780199657063
- eISBN:
- 9780191781759
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199657063.003.0012
- Subject:
- Mathematics, Probability / Statistics, Applied Mathematics

Large deviations theory formulated by Varadhan has made a tremendous impact in a variety of fields such as mathematical physics, control theory, and statistics, to name a few. After a brief ... More

## Population Dynamics

*Daniel Friedman, Barry Sinervo, Daniel Friedman, Barry Sinervo, Daniel Friedman, and Barry Sinervo*

### in Evolutionary Games in Natural, Social, and Virtual Worlds

- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.003.0001
- Subject:
- Economics and Finance, Behavioural Economics

The chapter introduces the concept of fitness, and focuses on the distribution of traits or behaviors within each population. The traits may be biological and governed by genes, or may instead have a ... More

## The Blessing and the Curse of the Multiplicative Updates

*Daniel Friedman and Barry Sinervo*

### in Evolutionary Games in Natural, Social, and Virtual Worlds

- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780199981151
- eISBN:
- 9780190466657
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199981151.003.0010
- Subject:
- Economics and Finance, Behavioural Economics

This chapter shows how replicator dynamics (in a setting with no frequency dependence) correspond to multiplicative updates studied by computer scientists in the context of online learning. The ... More

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