Science & Cooking: From Haute Cuisine to Soft Matter Science | edX
Top chefs and Harvard researchers explore how everyday cooking and haute cuisine can illuminate basic principles in physics and engineering, and vice versa.
Free textbook: Abstract and Concrete Categories: The Joy of Cats
Abstract and Concrete Categories was published by John Wiley and Sons, Inc, in 1990, and after several reprints, the book has been sold out and unavailable for several years. We now present an improved and corrected version as an open access file. This was made possible due to the return of copyright to the authors, and due to many hours of hard work and the exceptional skill of Christoph Schubert, to whom we wish to express our profound gratitude. The illustrations of Edward Gorey are unfortunately missing in the current version (for copyright reasons), but fortunately additional original illustrations by Marcel Erné, to whom additional special thanks of the authors belong, counterbalance the loss.
Open access includes the right of any reader to copy, store or distribute the book or parts of it freely. (See the GNU Free Documentation License at the end of the text.)
#categorytheory #mathematics #textbook
"A few exciting words": information and entropy revisited | Lyn Robinson and David Bawden - Academia.edu
A review is presented of the relation between information and entropy, focusing on two main issues: the similarity of the formal definitions of physical entropy, according to statistical mechanics, and of information, according to information theory; and the possible subjectivity of entropy considered as missing information. The paper updates the 1983 analysis of Shaw and Davis. The difference in the interpretations of information given respectively by Shannon and by Wiener, significant for the information sciences, receives particular consideration. Analysis of a range of material, from literary theory to thermodynamics, is used to draw out the issues. Emphasis is placed on recourse to the original sources, and on direct quotation, to attempt to overcome some of the misunderstandings and oversimplifications that have occurred with these topics. While it is strongly related to entropy, information is neither identical with it, nor its opposite. Information is related to order and pattern, but also to disorder and randomness. The relations between information and the “interesting
complexity,” which embodies both patterns and randomness, are worthy of attention.
#informationtheory #entropy
"Waiting for Carnot": information and complexity | Lyn Robinson and David Bawden - Academia.edu
Abstract: The relationship between information and complexity is analysed, by way of a detailed literature analysis. Complexity is a multi‐faceted concept, with no single agreed definition. There are numerous approaches to defining and measuring complexity and organisation, all involving the idea of information. Conceptions of complexity, order, organization and ‘interesting order’ are inextricably intertwined with those of information. Shannon’s formalism captures information’s unpredictable creative contributions to organized complexity; a full understanding of information’s relation to structure and order is still lacking. Conceptual investigations of this topic should enrich the theoretical basis of the information science discipline, and create fruitful links with other disciplines which study the concepts of information and complexity.
#informationtheory #complexity
8th Annual North American School of Information Theory
(NASIT) - August 10-13, 2015 - UC San Diego, La Jolla, California
The School of Information Theory will bring together over 100 graduate students, postdoctoral scholars, and leading researchers for four action-packed days of learning, stimulating discussions, professional networking and fun activities, all on the beautiful campus of the University of California, San Diego (UCSD) and in the nearby beach town of La Jolla.
#NASIT #InformationTheory
[1012.5647] An informal introduction to topos theory
Author: Tom Leinster
This short expository text is for readers who are confident in basic category theory but know little or nothing about toposes. It is based on some impromptu talks given to a small group of category theorists.
Subjects: Category Theory (math.CT); Algebraic Geometry (math.AG); Logic (math.LO)
The Homological Nature of Entropy
We propose that entropy is a universal co-homological class in a theory associated to a family of observable quantities and a family of probability distributions. Three cases are presented: (1) classical probabilities and random variables; (2) quantum probabilities and observable operators; (3) dynamic probabilities and observation trees. This gives rise to a new kind of topology for information processes, that accounts for the main information functions: entropy, mutual-informations at all orders, and Kullback–Leibler divergence and generalizes them in several ways. The article is divided into two parts, that can be read independently. In the first part, the introduction, we provide an overview of the results, some open questions, future results and lines of research, and discuss briefly the application to complex data. In the second part we give the complete definitions and proofs of the theorems A, C and E in the introduction, which show why entropy is the first homological invariant of a structure of information in four contexts: static classical or quantum probability, dynamics of classical or quantum strategies of observation of a finite system.
Shannon information; #homology theory; #entropy; #quantuminformation; homotopy of links; mutual informations; Kullback–Leiber divergence; trees; monads; partitions; #informationtheory
The Simons Institute is doing some interesting things with information theory, complexity, cryptography, economics, and evolutionary theory this year.
Current & Future Programs | Simons Institute for the Theory of Computing
Microformats 2 Version of Underscores Starter Theme with #Indieweb Support for #Wordpress via @dshanske
Loving that @dshanske is building a custom theme for #WordPress and #IndieWebCamp
Despite privacy policy, RadioShack customer data up for sale in auction | Ars Technica
Apparently pride also goeth during the fall as well
#privacy
Neural networks and deep learning
Michael Nielsen has a free online book: Neural Networks and Deep Learning
[1503.02776] The Emergence of Life as a First Order Phase Transition
We demonstrate a phase transition from non-life to life, defined as non-replicating and replicating systems respectively, and characterize some of its dynamical properties. The transition is first order and demonstrates many characteristics one might expect from a newly emergent biosphere. During the phase transition the system experiences an explosive growth in diversity, with restructuring of both the extant replicator population and the environment. The observed dynamics have a natural information-theoretic interpretation, where the probability for the transition to occur depends on the mutual information shared between replicators and environment. Through the transition, the system undergoes a series of symmetry breaking transitions whereby the information content of replicators becomes increasingly distinct from that of their environment. Thus, the replicators that nucleate the transition in the non-life phase are often not those which are ultimately selected in the life phase. We discuss the implications of these results for understanding the emergence of life, and natural selection more broadly.
#arXiv, #itbio