Algorithmic Probability

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Algorithmic Probability

Author : Marcel F. Neuts
Publisher : CRC Press
ISBN 13 : 9780412996917
Total Pages : 488 pages
Book Rating : 4.9/5 (969 download)

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Book Synopsis Algorithmic Probability by : Marcel F. Neuts

Download or read book Algorithmic Probability written by Marcel F. Neuts and published by CRC Press. This book was released on 1995-07-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique text collects more than 400 problems in combinatorics, derived distributions, discrete and continuous Markov chains, and models requiring a computer experimental approach. The first book to deal with simplified versions of models encountered in the contemporary statistical or engineering literature, Algorithmic Probability emphasizes correct interpretation of numerical results and visualization of the dynamics of stochastic processes. A significant contribution to the field of applied probability, Algorithmic Probability is ideal both as a secondary text in probability courses and as a reference. Engineers and operations analysts seeking solutions to practical problems will find it a valuable resource, as will advanced undergraduate and graduate students in mathematics, statistics, operations research, industrial and electrical engineering, and computer science.

Algorithmic Probability

Author : Fouad Sabry
Publisher : One Billion Knowledgeable
ISBN 13 :
Total Pages : 129 pages
Book Rating : 4.:/5 (661 download)

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Book Synopsis Algorithmic Probability by : Fouad Sabry

Download or read book Algorithmic Probability written by Fouad Sabry and published by One Billion Knowledgeable. This book was released on 2023-06-28 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: What Is Algorithmic Probability In the field of algorithmic information theory, algorithmic probability is a mathematical method that assigns a prior probability to a given observation. This method is sometimes referred to as Solomonoff probability. In the 1960s, Ray Solomonoff was the one who came up with the idea. It has applications in the theory of inductive reasoning as well as the analysis of algorithms. Solomonoff combines Bayes' rule and the technique in order to derive probabilities of prediction for an algorithm's future outputs. He does this within the context of his broad theory of inductive inference. How You Will Benefit (I) Insights, and validations about the following topics: Chapter 1: Algorithmic Probability Chapter 2: Kolmogorov Complexity Chapter 3: Gregory Chaitin Chapter 4: Ray Solomonoff Chapter 5: Solomonoff's Theory of Inductive Inference Chapter 6: Algorithmic Information Theory Chapter 7: Algorithmically Random Sequence Chapter 8: Minimum Description Length Chapter 9: Computational Learning Theory Chapter 10: Inductive Probability (II) Answering the public top questions about algorithmic probability. (III) Real world examples for the usage of algorithmic probability in many fields. (IV) 17 appendices to explain, briefly, 266 emerging technologies in each industry to have 360-degree full understanding of algorithmic probability' technologies. Who This Book Is For Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of algorithmic probability.

Universal Artificial Intelligence

Author : Marcus Hutter
Publisher : Springer Science & Business Media
ISBN 13 : 3540268774
Total Pages : 294 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Universal Artificial Intelligence by : Marcus Hutter

Download or read book Universal Artificial Intelligence written by Marcus Hutter and published by Springer Science & Business Media. This book was released on 2005-12-29 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: Personal motivation. The dream of creating artificial devices that reach or outperform human inteUigence is an old one. It is also one of the dreams of my youth, which have never left me. What makes this challenge so interesting? A solution would have enormous implications on our society, and there are reasons to believe that the AI problem can be solved in my expected lifetime. So, it's worth sticking to it for a lifetime, even if it takes 30 years or so to reap the benefits. The AI problem. The science of artificial intelligence (AI) may be defined as the construction of intelligent systems and their analysis. A natural definition of a system is anything that has an input and an output stream. Intelligence is more complicated. It can have many faces like creativity, solving prob lems, pattern recognition, classification, learning, induction, deduction, build ing analogies, optimization, surviving in an environment, language processing, and knowledge. A formal definition incorporating every aspect of intelligence, however, seems difficult. Most, if not all known facets of intelligence can be formulated as goal driven or, more precisely, as maximizing some utility func tion. It is, therefore, sufficient to study goal-driven AI; e. g. the (biological) goal of animals and humans is to survive and spread. The goal of AI systems should be to be useful to humans.

Algorithmic Probability and Combinatorics

Author : Manuel Lladser
Publisher : American Mathematical Soc.
ISBN 13 : 082184783X
Total Pages : 251 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Algorithmic Probability and Combinatorics by : Manuel Lladser

Download or read book Algorithmic Probability and Combinatorics written by Manuel Lladser and published by American Mathematical Soc.. This book was released on 2010-07-30 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Sessions on Algorithmic Probability and Combinatories held at DePaul University on October 5-6, 2007 and at the University of British Columbia on October 4-5, 2008. This volume collects cutting-edge research and expository on algorithmic probability and combinatories. It includes contributions by well-established experts and younger researchers who use generating functions, algebraic and probabilistic methods as well as asymptotic analysis on a daily basis. Walks in the quarter-plane and random walks (quantum, rotor and self-avoiding), permutation tableaux, and random permutations are considered. In addition, articles in the volume present a variety of saddle-point and geometric methods for the asymptotic analysis of the coefficients of single-and multivariable generating functions associated with combinatorial objects and discrete random structures. The volume should appeal to pure and applied mathematicians, as well as mathematical physicists; in particular, anyone interested in computational aspects of probability, combinatories and enumeration. Furthermore, the expository or partly expository papers included in this volume should serve as an entry point to this literature not only to experts in other areas, but also to graduate students.

Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence

Author : David L. Dowe
Publisher : Springer
ISBN 13 : 3642449581
Total Pages : 457 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence by : David L. Dowe

Download or read book Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence written by David L. Dowe and published by Springer. This book was released on 2013-10-22 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic probability and friends: Proceedings of the Ray Solomonoff 85th memorial conference is a collection of original work and surveys. The Solomonoff 85th memorial conference was held at Monash University's Clayton campus in Melbourne, Australia as a tribute to pioneer, Ray Solomonoff (1926-2009), honouring his various pioneering works - most particularly, his revolutionary insight in the early 1960s that the universality of Universal Turing Machines (UTMs) could be used for universal Bayesian prediction and artificial intelligence (machine learning). This work continues to increasingly influence and under-pin statistics, econometrics, machine learning, data mining, inductive inference, search algorithms, data compression, theories of (general) intelligence and philosophy of science - and applications of these areas. Ray not only envisioned this as the path to genuine artificial intelligence, but also, still in the 1960s, anticipated stages of progress in machine intelligence which would ultimately lead to machines surpassing human intelligence. Ray warned of the need to anticipate and discuss the potential consequences - and dangers - sooner rather than later. Possibly foremostly, Ray Solomonoff was a fine, happy, frugal and adventurous human being of gentle resolve who managed to fund himself while electing to conduct so much of his paradigm-changing research outside of the university system. The volume contains 35 papers pertaining to the abovementioned topics in tribute to Ray Solomonoff and his legacy.

Probability and Computing

Author : Michael Mitzenmacher
Publisher : Cambridge University Press
ISBN 13 : 9780521835404
Total Pages : 372 pages
Book Rating : 4.8/5 (354 download)

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Book Synopsis Probability and Computing by : Michael Mitzenmacher

Download or read book Probability and Computing written by Michael Mitzenmacher and published by Cambridge University Press. This book was released on 2005-01-31 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool.

Algorithmic Information Dynamics

Author : Hector Zenil
Publisher : Cambridge University Press
ISBN 13 : 1108659268
Total Pages : 346 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Algorithmic Information Dynamics by : Hector Zenil

Download or read book Algorithmic Information Dynamics written by Hector Zenil and published by Cambridge University Press. This book was released on 2023-05-25 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Biological systems are extensively studied as interactions forming complex networks. Reconstructing causal knowledge from, and principles of, these networks from noisy and incomplete data is a challenge in the field of systems biology. Based on an online course hosted by the Santa Fe Institute Complexity Explorer, this book introduces the field of Algorithmic Information Dynamics, a model-driven approach to the study and manipulation of dynamical systems . It draws tools from network and systems biology as well as information theory, complexity science and dynamical systems to study natural and artificial phenomena in software space. It consists of a theoretical and methodological framework to guide an exploration and generate computable candidate models able to explain complex phenomena in particular adaptable adaptive systems, making the book valuable for graduate students and researchers in a wide number of fields in science from physics to cell biology to cognitive sciences.

Algorithmic Learning in a Random World

Author : Vladimir Vovk
Publisher : Springer Science & Business Media
ISBN 13 : 9780387001524
Total Pages : 344 pages
Book Rating : 4.0/5 (15 download)

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Book Synopsis Algorithmic Learning in a Random World by : Vladimir Vovk

Download or read book Algorithmic Learning in a Random World written by Vladimir Vovk and published by Springer Science & Business Media. This book was released on 2005-03-22 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algorithmic Learning in a Random World describes recent theoretical and experimental developments in building computable approximations to Kolmogorov's algorithmic notion of randomness. Based on these approximations, a new set of machine learning algorithms have been developed that can be used to make predictions and to estimate their confidence and credibility in high-dimensional spaces under the usual assumption that the data are independent and identically distributed (assumption of randomness). Another aim of this unique monograph is to outline some limits of predictions: The approach based on algorithmic theory of randomness allows for the proof of impossibility of prediction in certain situations. The book describes how several important machine learning problems, such as density estimation in high-dimensional spaces, cannot be solved if the only assumption is randomness.

Formulas and Theorems in Pure Mathematics

Author : George Shoobridge Carr
Publisher : Chelsea Publishing Company, Incorporated
ISBN 13 :
Total Pages : 1014 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Formulas and Theorems in Pure Mathematics by : George Shoobridge Carr

Download or read book Formulas and Theorems in Pure Mathematics written by George Shoobridge Carr and published by Chelsea Publishing Company, Incorporated. This book was released on 1970 with total page 1014 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Methods and Applications of Algorithmic Complexity

Author : Hector Zenil
Publisher : Springer Nature
ISBN 13 : 3662649853
Total Pages : 270 pages
Book Rating : 4.6/5 (626 download)

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Book Synopsis Methods and Applications of Algorithmic Complexity by : Hector Zenil

Download or read book Methods and Applications of Algorithmic Complexity written by Hector Zenil and published by Springer Nature. This book was released on 2022-05-16 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores a different pragmatic approach to algorithmic complexity rooted or motivated by the theoretical foundations of algorithmic probability and explores the relaxation of necessary and sufficient conditions in the pursuit of numerical applicability, with some of these approaches entailing greater risks than others in exchange for greater relevance and applicability. Some established and also novel techniques in the field of applications of algorithmic (Kolmogorov) complexity currently coexist for the first time, ranging from the dominant ones based upon popular statistical lossless compression algorithms (such as LZW) to newer approaches that advance, complement, and also pose their own limitations. Evidence suggesting that these different methods complement each other for different regimes is presented, and despite their many challenges, some of these methods are better grounded in or motivated by the principles of algorithmic information. The authors propose that the field can make greater contributions to science, causation, scientific discovery, networks, and cognition, to mention a few among many fields, instead of remaining either as a technical curiosity of mathematical interest only or as a statistical tool when collapsed into an application of popular lossless compression algorithms. This book goes, thus, beyond popular statistical lossless compression and introduces a different methodological approach to dealing with algorithmic complexity. For example, graph theory and network science are classic subjects in mathematics widely investigated in the twentieth century, transforming research in many fields of science from economy to medicine. However, it has become increasingly clear that the challenge of analyzing these networks cannot be addressed by tools relying solely on statistical methods. Therefore, model-driven approaches are needed. Recent advances in network science suggest that algorithmic information theory could play an increasingly important role in breaking those limits imposed by traditional statistical analysis (entropy or statistical compression) in modeling evolving complex networks or interacting networks. Further progress on this front calls for new techniques for an improved mechanistic understanding of complex systems, thereby calling out for increased interaction between systems science, network theory, and algorithmic information theory, to which this book contributes.

From Parallel to Emergent Computing

Author : Andrew Adamatzky
Publisher : CRC Press
ISBN 13 : 1351681915
Total Pages : 601 pages
Book Rating : 4.3/5 (516 download)

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Book Synopsis From Parallel to Emergent Computing by : Andrew Adamatzky

Download or read book From Parallel to Emergent Computing written by Andrew Adamatzky and published by CRC Press. This book was released on 2019-03-13 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern computing relies on future and emergent technologies which have been conceived via interaction between computer science, engineering, chemistry, physics and biology. This highly interdisciplinary book presents advances in the fields of parallel, distributed and emergent information processing and computation. The book represents major breakthroughs in parallel quantum protocols, elastic cloud servers, structural properties of interconnection networks, internet of things, morphogenetic collective systems, swarm intelligence and cellular automata, unconventionality in parallel computation, algorithmic information dynamics, localized DNA computation, graph-based cryptography, slime mold inspired nano-electronics and cytoskeleton computers. Features Truly interdisciplinary, spanning computer science, electronics, mathematics and biology Covers widely popular topics of future and emergent computing technologies, cloud computing, parallel computing, DNA computation, security and network analysis, cryptography, and theoretical computer science Provides unique chapters written by top experts in theoretical and applied computer science, information processing and engineering From Parallel to Emergent Computing provides a visionary statement on how computing will advance in the next 25 years and what new fields of science will be involved in computing engineering. This book is a valuable resource for computer scientists working today, and in years to come.

An Introduction to Kolmogorov Complexity and Its Applications

Author : Ming Li
Publisher : Springer Science & Business Media
ISBN 13 : 1475726066
Total Pages : 655 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis An Introduction to Kolmogorov Complexity and Its Applications by : Ming Li

Download or read book An Introduction to Kolmogorov Complexity and Its Applications written by Ming Li and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 655 pages. Available in PDF, EPUB and Kindle. Book excerpt: Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).

Uncertainty in Artificial Intelligence

Author : L.N. Kanal
Publisher : Elsevier
ISBN 13 : 1483296520
Total Pages : 522 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Uncertainty in Artificial Intelligence by : L.N. Kanal

Download or read book Uncertainty in Artificial Intelligence written by L.N. Kanal and published by Elsevier. This book was released on 2014-06-28 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to deal with uncertainty is a subject of much controversy in Artificial Intelligence. This volume brings together a wide range of perspectives on uncertainty, many of the contributors being the principal proponents in the controversy.Some of the notable issues which emerge from these papers revolve around an interval-based calculus of uncertainty, the Dempster-Shafer Theory, and probability as the best numeric model for uncertainty. There remain strong dissenting opinions not only about probability but even about the utility of any numeric method in this context.

Randomness And Undecidability In Physics

Author : Karl Svozil
Publisher : World Scientific
ISBN 13 : 9814522929
Total Pages : 310 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Randomness And Undecidability In Physics by : Karl Svozil

Download or read book Randomness And Undecidability In Physics written by Karl Svozil and published by World Scientific. This book was released on 1993-10-05 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent findings in the computer sciences, discrete mathematics, formal logics and metamathematics have opened up a royal road for the investigation of undecidability and randomness in physics. A translation of these formal concepts yields a fresh look into diverse features of physical modelling such as quantum complementarity and the measurement problem, but also stipulates questions related to the necessity of the assumption of continua.Conversely, any computer may be perceived as a physical system: not only in the immediate sense of the physical properties of its hardware. Computers are a medium to virtual realities. The foreseeable importance of such virtual realities stimulates the investigation of an “inner description”, a “virtual physics” of these universes of computation. Indeed, one may consider our own universe as just one particular realisation of an enormous number of virtual realities, most of them awaiting discovery.One motive of this book is the recognition that what is often referred to as “randomness” in physics might actually be a signature of undecidability for systems whose evolution is computable on a step-by-step basis. To give a flavour of the type of questions envisaged: Consider an arbitrary algorithmic system which is computable on a step-by-step basis. Then it is in general impossible to specify a second algorithmic procedure, including itself, which, by experimental input-output analysis, is capable of finding the deterministic law of the first system. But even if such a law is specified beforehand, it is in general impossible to predict the system behaviour in the “distant future”. In other words: no “speedup” or “computational shortcut” is available. In this approach, classical paradoxes can be formally translated into no-go theorems concerning intrinsic physical perception.It is suggested that complementarity can be modelled by experiments on finite automata, where measurements of one observable of the automaton destroys the possibility to measure another observable of the same automaton and it vice versa.Besides undecidability, a great part of the book is dedicated to a formal definition of randomness and entropy measures based on algorithmic information theory.

Advances In Cognitive Science

Author : Manfred Kochen
Publisher : CRC Press
ISBN 13 : 0429713061
Total Pages : 247 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Advances In Cognitive Science by : Manfred Kochen

Download or read book Advances In Cognitive Science written by Manfred Kochen and published by CRC Press. This book was released on 2019-04-23 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a collection of papers on both natural (biological) and artificial (computer) approaches to several facets of intelligent behavior from the primary viewpoint of the convergence of computer science and biology in the theory of cognitive science. .

Probability and Bayesian Modeling

Author : Jim Albert
Publisher : CRC Press
ISBN 13 : 1351030132
Total Pages : 553 pages
Book Rating : 4.3/5 (51 download)

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Book Synopsis Probability and Bayesian Modeling by : Jim Albert

Download or read book Probability and Bayesian Modeling written by Jim Albert and published by CRC Press. This book was released on 2019-12-06 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probability and Bayesian Modeling is an introduction to probability and Bayesian thinking for undergraduate students with a calculus background. The first part of the book provides a broad view of probability including foundations, conditional probability, discrete and continuous distributions, and joint distributions. Statistical inference is presented completely from a Bayesian perspective. The text introduces inference and prediction for a single proportion and a single mean from Normal sampling. After fundamentals of Markov Chain Monte Carlo algorithms are introduced, Bayesian inference is described for hierarchical and regression models including logistic regression. The book presents several case studies motivated by some historical Bayesian studies and the authors’ research. This text reflects modern Bayesian statistical practice. Simulation is introduced in all the probability chapters and extensively used in the Bayesian material to simulate from the posterior and predictive distributions. One chapter describes the basic tenets of Metropolis and Gibbs sampling algorithms; however several chapters introduce the fundamentals of Bayesian inference for conjugate priors to deepen understanding. Strategies for constructing prior distributions are described in situations when one has substantial prior information and for cases where one has weak prior knowledge. One chapter introduces hierarchical Bayesian modeling as a practical way of combining data from different groups. There is an extensive discussion of Bayesian regression models including the construction of informative priors, inference about functions of the parameters of interest, prediction, and model selection. The text uses JAGS (Just Another Gibbs Sampler) as a general-purpose computational method for simulating from posterior distributions for a variety of Bayesian models. An R package ProbBayes is available containing all of the book datasets and special functions for illustrating concepts from the book. A complete solutions manual is available for instructors who adopt the book in the Additional Resources section.

Networks of Networks in Biology

Author : Narsis A. Kiani
Publisher : Cambridge University Press
ISBN 13 : 1108428878
Total Pages : 215 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Networks of Networks in Biology by : Narsis A. Kiani

Download or read book Networks of Networks in Biology written by Narsis A. Kiani and published by Cambridge University Press. This book was released on 2021-04 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces network inspired approaches for the analysis and integration of large, heterogeneous data sets in the life sciences.