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Information Theory and the Length Distribution of All Discrete Systems
Information Theory and the Length Distribution of all Discrete Systems Les Hatton1* Gregory Warr2** 1 Faculty of Science, Engineering and Computing, Kingston University, London, UK 2 Medical University of South Carolina, Charleston, South Carolina, USA. * [email protected] ** [email protected] Revision: $Revision: 1.35 $ Date: $Date: 2017/09/06 07:30:43 $ Abstract We begin with the extraordinary observation that the length distribution of 80 million proteins in UniProt, the Universal Protein Resource, measured in amino acids, is qualitatively identical to the length distribution of large collections of computer functions measured in programming language tokens, at all scales. That two such disparate discrete systems share important structural properties suggests that yet other apparently unrelated discrete systems might share the same properties, and certainly invites an explanation. We demonstrate that this is inevitable for all discrete systems of components built from tokens or symbols. Departing from existing work by embedding the Conservation of Hartley-Shannon information (CoHSI) in a classical statistical mechanics framework, we identify two kinds of discrete system, heterogeneous and homogeneous. Heterogeneous systems contain components built from a unique alphabet of tokens and yield an implicit CoHSI distribution with a sharp unimodal peak asymptoting to a power-law. Homogeneous systems contain components each built from arXiv:1709.01712v1 [q-bio.OT] 6 Sep 2017 just one kind of token unique to that component and yield a CoHSI distribution corresponding to Zipf’s law. This theory is applied to heterogeneous systems, (proteome, computer software, music); homogeneous systems (language texts, abundance of the elements); and to systems in which both heterogeneous and homogeneous behaviour co-exist (word frequencies and word length frequencies in language texts). -
Conformational Transition in Immunoglobulin MOPC 460" by Correction. in Themembership List of the National Academy of Scien
Corrections Proc. Natl. Acad. Sci. USA 74 (1977) 1301 Correction. In the article "Kinetic evidence for hapten-induced Correction. In the membership list of the National Academy conformational transition in immunoglobulin MOPC 460" by of Sciences that appeared in the October 1976 issue of Proc. D. Lancet and I. Pecht, which appeared in the October 1976 Natl. Acad. Sci. USA 73,3750-3781, please note the following issue of Proc. Nati. Acad. Sci. USA 73,3549-3553, the authors corrections: H. E. Carter, Britton Chance, Seymour S. Cohen, have requested the following changes. On p. 3550, right-hand E. A. Doisy, Gerald M. Edelman, and John T. Edsall are affil- column, second line from bottom, and p. 3551, left-hand col- iated with the Section ofBiochemistry (21), not the Section of umn, fourth line from the top, "Fig. 2" should be "Fig. 1A." Botany (25). In the legend of Table 2, third line, note (f) should read "AG, = -RTlnKj." On p. 3553, left-hand column, third paragraph, fifth line, "ko" should be replaced by "Ko." Correction. In the Author Index to Volume 73, January-De- cember 1976, which appeared in the December 1976 issue of Proc. Natl. Acad. Sci. USA 73, 4781-4788, the limitations of Correction. In the article "Amino-terminal sequences of two computer alphabetization resulted in the listing of one person polypeptides from human serum with nonsuppressible insu- as the author of another's paper. On p. 4786, it should indicate lin-like and cell-growth-promoting activities: Evidence for that James Christopher Phillips had an article beginning on p. -
Victorian Metrics and Mechanized Scansion
1 Mechanized Metrics: From Verse Science to Laboratory Prosody, 1880–1918 Jason David Hall University of Exeter ABSTRACT: From roughly the 1880s on, a methodical verse “science” was beginning to assert itself. Gripped by the thought of articulating an objective, fact-based metrics, poetry scientists brought to bear on the traditional verse-line principles of observation and, later, on full-blown experimental practices—not to mention a curious array of instrumentation. By the turn of the century, metrical verse was being subjected to a rigorous measurement regime, which employed techniques and apparatuses derived from the new disciplines of experimental physiology and psychology. Proponents of this newly mechanized metrics pitched themselves enthusiastically into the turn-of-the-century prosody fray, believing they could resolve, once and for all, some of the fundamental dilemmas of versification. Mechanical Meters In 1857, just a few months before Coventry Patmore published the first version of his influential “Essay on English Metrical Law” in the respectable North British Review, a series of short articles titled “A Chapter or Two on Meters” appeared in a general-interest magazine called The Friendly Companion and Illustrated Instructor. These “meters,” however, were not precisely the kind that Patmore’s essay was given over to theorizing, and readers expecting something along the lines of a prosodical digest may have been perplexed (and quite possibly relieved) to find, in place of remarks on the iambus or dactylic hexameters, an alphabetically arranged catalog of measurement apparatuses. The first of three monthly installments contained three entries: actinometer (“for measuring the intensity of solar or terrestrial radiation”), aerometer (“for correctly ascertaining the mean bulk of gases”), and barometer (“for ascertaining the weight of the atmosphere”). -
Copyright by Xue Chen 2018 the Dissertation Committee for Xue Chen Certifies That This Is the Approved Version of the Following Dissertation
Copyright by Xue Chen 2018 The Dissertation Committee for Xue Chen certifies that this is the approved version of the following dissertation: Using and Saving Randomness Committee: David Zuckerman, Supervisor Dana Moshkovitz Eric Price Yuan Zhou Using and Saving Randomness by Xue Chen DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN May 2018 Dedicated to my parents Daiguang and Dianhua. Acknowledgments First, I am grateful to my advisor, David Zuckerman, for his unwavering support and encouragements. David has been a constant resource for providing me with great advice and insightful feedback about my ideas. Besides these and many fruitful discussions we had, his wisdom, way of thinking, and optimism guided me through the last six years. I also thank him for arranging a visit to the Simons institute in Berkeley, where I enrich my understanding and made new friends. I could not have hoped for a better advisor. I would like to thank Eric Price. His viewpoints and intuitions opened a different gate for me, which is important for the line of research presented in this thesis. I benefited greatly from our long research meetings and discussions. Besides learning a lot of technical stuff from him, I hope I have absorbed some of his passion and attitudes to research. Apart from David and Eric, I have had many mentors during my time as a student. I especially thank Yuan Zhou, who has been an amazing collaborator and friend since starting college. -
Shannon's Formula Wlog(1+SNR): a Historical Perspective
Shannon’s Formula W log(1 + SNR): A Historical· Perspective on the occasion of Shannon’s Centenary Oct. 26th, 2016 Olivier Rioul <[email protected]> Outline Who is Claude Shannon? Shannon’s Seminal Paper Shannon’s Main Contributions Shannon’s Capacity Formula A Hartley’s rule C0 = log2 1 + ∆ is not Hartley’s 1 P Many authors independently derived C = 2 log2 1 + N in 1948. Hartley’s rule is exact: C0 = C (a coincidence?) C0 is the capacity of the “uniform” channel Shannon’s Conclusion 2 / 85 26/10/2016 Olivier Rioul Shannon’s Formula W log(1 + SNR): A Historical Perspective April 30, 2016 centennial day celebrated by Google: here Shannon is juggling with bits (1,0,0) in his communication scheme “father of the information age’’ Claude Shannon (1916–2001) 100th birthday 2016 April 30, 1916 Claude Elwood Shannon was born in Petoskey, Michigan, USA 3 / 85 26/10/2016 Olivier Rioul Shannon’s Formula W log(1 + SNR): A Historical Perspective here Shannon is juggling with bits (1,0,0) in his communication scheme “father of the information age’’ Claude Shannon (1916–2001) 100th birthday 2016 April 30, 1916 Claude Elwood Shannon was born in Petoskey, Michigan, USA April 30, 2016 centennial day celebrated by Google: 3 / 85 26/10/2016 Olivier Rioul Shannon’s Formula W log(1 + SNR): A Historical Perspective Claude Shannon (1916–2001) 100th birthday 2016 April 30, 1916 Claude Elwood Shannon was born in Petoskey, Michigan, USA April 30, 2016 centennial day celebrated by Google: here Shannon is juggling with bits (1,0,0) in his communication scheme “father of the information age’’ 3 / 85 26/10/2016 Olivier Rioul Shannon’s Formula W log(1 + SNR): A Historical Perspective “the most important man.. -
Quantum Management – Quantum Quality Model Rakesh Kumari M.Sc
International Journal of Scientific & Engineering Research Volume 9, Issue 6, June-2018 1143 ISSN 2229-5518 Quantum Management – Quantum Quality model Rakesh Kumari M.Sc. (Physics), M.Ed., Fellow, Gujarat India. Abstract – This paper proposes the Quantum Quality Model (Q2M), a quality inventiveness, a merger application of Quantum science and Human psychology on Management science to improve/enhance the quality performance of managers/leaders/employees working in an organization. The foun- dational pillar to this model is Quantum skills model and Quantum Organization. Quantum skills model is the unification of physics, psychology and some glimpses of spiritual domain. And Quantum organization has following features - value-centered, all-inclusive, bottom-up, self-organizing, emer- gent, believes in the potentiality more than actuality, flexible and responsive in-on-out the chaos situations, follows adaptive evolution through multiple alteration, thinks that presence and participation of every employee affects the organizational success, considers human and non- human dimensions. Considering Managers/Leaders/Employees as a Particle (the microcosm) of the organization (the macrocosm), the Q2M proposes Particle domain (internal state) and the Organizational domain (outer state) of the Particle and by cultivating both domains the quality performance (in terms of Seeing-Knowing, Thinking-Acting, Feeling-Trusting) of the Particle can be improved/enhanced at workplace. The aim of this paper to improve/enhance the qualitative attributes of the Particles and quantify their quality performance. Simple Random sampling method (Probability sampling) is used for sampling with set criteria that the Particles should be working with at least Graduation (in any sub- ject) degree, no upper limit for the qualification, the age limit is 30-60 years, and open to all gender with no geographical limits. -
Maxwell's Demon: Entropy, Information, Computing
Complex Social Systems a guided exploration of concepts and methods Information Theory Martin Hilbert (Dr., PhD) Today’s questions I. What are the formal notions of data, information & knowledge? II. What is the role of information theory in complex systems? …the 2nd law and life… III. What is the relation between information and growth? Complex Systems handle information "Although they [complex systems] differ widely in their physical attributes, they resemble one another in the way they handle information. That common feature is perhaps the best starting point for exploring how they operate.” (Gell-Mann, 1995, p. 21) Source: Gell-Mann, M. (1995). The Quark and the Jaguar: Adventures in the Simple and the Complex. New York: St. Martin’s Griffin. Complex Systems Science as computer science “What we are witnessing now is … actually the beginning of an amazing convergence of theoretical physics and theoretical computer science” Chaitin, G. J. (2002). Meta-Mathematics and the Foundations of Mathematics. EATCS Bulletin, 77(June), 167–179. Society computes Numerical: Analytical: Agent-based models Information Theory Why now? Thermodynamics: or ? Aerodynamics: or ? Hydrodynamics: or ? Electricity: or ? etc… Claude Shannon Alan Turing John von Neumann Bell, D. (1973). The Coming of Post- Industrial Society: A Venture in Social Forecasting. New York, NY: Basic Books. “industrial organization of goods” => “industrial organization of information” 15,000 citations 35,000 citations Beniger, J. (1986). The Control Revolution: Castells, M. (1999). The Information Technological and Economic Origins of the Age, Volumes 1-3: Economy, Society Information Society. Harvard University Press and Culture. Cambridge (Mass.); “exploitation of information” Oxford: Wiley-Blackwell. -
Information Basics Observer and Choice
information basics observer and choice Information is defined as “a measure of the freedom from choice with which a message is selected from the set of all possible messages” Bit (short for binary digit) is the most elementary choice one can make Between two items: “0’ and “1”, “heads” or “tails”, “true” or “false”, etc. Bit is equivalent to the choice between two equally likely alternatives Example, if we know that a coin is to be tossed, but are unable to see it as it falls, a message telling whether the coin came up heads or tails gives us one bit of information 1 Bit of uncertainty 1 Bit of information H,T? uncertainty removed, choice between 2 symbols information gained recognized by an observer INDIANA [email protected] UNIVERSITY informatics.indiana.edu/rocha Fathers of uncertainty-based information Information is transmitted through noisy communication channels Ralph Hartley and Claude Shannon (at Bell Labs), the fathers of Information Theory, worked on the problem of efficiently transmitting information; i. e. decreasing the uncertainty in the transmission of information. Hartley, R.V.L., "Transmission of Information", Bell System Technical Journal, July 1928, p.535. C. E. Shannon [1948], “A mathematical theory of communication”. Bell System Technical Journal, 27:379-423 and 623-656 C. E. Shannon, “A Symbolic analysis of relay and switching circuits” .MS Thesis, (unpublished) MIT, 1937. C. E. Shannon, “An algebra for theoretical genetics.” Phd Dissertation, MIT, 1940. INDIANA [email protected] UNIVERSITY informatics.indiana.edu/rocha Let’s talk about choices Multiplication Principle “If some choice can be made in M different ways, and some subsequent choice can be made in N different ways, then there are M x N different ways these choices can be made in succession” [Paulos] 3 shirts and 4 pants = 3 x 4 = 12 outfit choices INDIANA [email protected] UNIVERSITY informatics.indiana.edu/rocha Hartley Uncertainty Nonspecificity A = Set of Hartley measure Alternatives The amount of uncertainty associated with a set of alternatives (e.g. -
Active Regression Via Linear-Sample Sparsification
Active Regression via Linear-Sample Sparsification Xue Chen∗ Eric Pricey [email protected] [email protected] Northwestern University The University of Texas at Austin March 25, 2019 Abstract We present an approach that improves the sample complexity for a variety of curve fitting problems, including active learning for linear regression, polynomial regression, and continuous sparse Fourier transforms. In the active linear regression problem, one would like to estimate the ∗ n×d least squares solution β minimizing kXβ − yk2 given the entire unlabeled dataset X 2 R but only observing a small number of labels yi. We show that O(d) labels suffice to find a constant factor approximation βe: 2 ∗ 2 E[kXβe − yk2] ≤ 2 E[kXβ − yk2]: This improves on the best previous result of O(d log d) from leverage score sampling. We also present results for the inductive setting, showing when βe will generalize to fresh samples; these apply to continuous settings such as polynomial regression. Finally, we show how the techniques yield improved results for the non-linear sparse Fourier transform setting. arXiv:1711.10051v3 [cs.LG] 21 Mar 2019 ∗Supported by NSF Grant CCF-1526952 and a Simons Investigator Award (#409864, David Zuckerman), part of this work was done while the author was a student in University of Texas at Austin and visiting the Simons Institute for the Theory of Computing. yThis work was done in part while the author was visiting the Simons Institute for the Theory of Computing. 1 Introduction We consider the query complexity of recovering a signal f(x) in a given family F from noisy observations. -
Physiological Psychology, Applied Psychology, and Film Theory: the Reception of Hugo Münsterberg in Modern Japan
Ars Vivendi Journal No.6 (March 2014): 29-49 Physiological Psychology, Applied Psychology, and Film Theory: the reception of Hugo Münsterberg in modern Japan Ryo SHINOGI* *Research Fellow of the Japan Society for the Promotion of Science,Ritsumeikan University, Kyoto, Japan 1. Introduction This paper aims at showing how Hugo Münsterberg [1863-1916] and his work were understood by the contemporaneous Japanese scholars[1]. Münsterberg was a psychologist and philosopher, who moved from Germany to the United States in the late 19th century. He made the earliest contributions to many fields of applied psychology (Münsterberg, 1914b), specifically, art (Münsterberg, 1904), law (Münsterberg, 1908, 1914a), psychotherapy (Münsterberg, 1909a), education (Münsterberg, 1909b), industry (Münsterberg, 1913, 1915), and film (Münsterberg, 1916). So many researchers have already written about his life and work (Münsterberg, M. 1922; Keller, 1979; Hale, 1980; Landy, 1992; Spillmann & Spillmann, 1993). As they put it, his fame and the evaluation of his work had their ups and downs. In the late 19th and early 20th century, many Japanese scholars studied psychology in the United States and introduced the discipline to Japan. Further, most scholars in Japan enthusiastically wrote about contemporaneous German and American psychology, and Münsterberg was one of the psychologists they often referred to. However it is only since the 1970s that most historians have begun to pay attention to Münsterberg.(Keller, 1979; Hale, 1980; Landy, 1992; Spillmann & Spillmann, 1993). The reasons for his changing fortunes can be found in Münsterberg's psychology, his personality and in historical circumstances. First, many psychologists contemporary to Münsterberg often thought that only experimental psychology was important and disdained applied psychology. -
Sounds of Science – Schall Im Labor (1800–1930)
MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2008 PREPRINT 346 Julia Kursell (ed.) Sounds of Science – Schall im Labor (1800–1930) TABLE OF CONTENTS Introductory Remarks Julia Kursell 3 „Erzklang“ oder „missing fundamental“: Kulturgeschichte als Signalanalyse Bernhard Siegert 7 Klangfiguren (a hit in the lab) Peter Szendy 21 Sound Objects Julia Kursell 29 A Cosmos for Pianoforte d’Amore: Some Remarks on “Miniature Estrose” by Marco Stroppa Florian Hoelscher 39 The “Muscle Telephone”: The Undiscovered Start of Audification in the 1870s Florian Dombois 41 Silence in the Laboratory: The History of Soundproof Rooms Henning Schmidgen 47 Cats and People in the Psychoacoustics Lab Jonathan Sterne 63 The Resonance of “Bodiless Entities”: Some Epistemological Remarks on the Radio-Voice Wolfgang Hagen 73 VLF and Musical Aesthetics Douglas Kahn 81 Ästhetik des Signals Daniel Gethmann 89 Producing, Representing, Constructing: Towards a Media-Aesthetic Theory of Action Related to Categories of Experimental Methods Elena Ungeheuer 99 Standardizing Aesthetics: Physicists, Musicians, and Instrument Makers in Nineteenth-Century Germany Myles W. Jackson 113 Introductory Remarks The following collection of papers documents the workshop “Sounds of Science – Schall im Labor, 1800 to 1930,” carried out at the Max Planck Institute for the History of Science, Berlin October 5 to 7, 2006. It was organized within the context of the project “Experimentalization of Life: Configurations between Science, Art, and Technology” situated in Department III of the Institute. While the larger project has discussed topics such as “Experimental Cultures,” the “Materiality of Time Relations in Life Sciences, Art, and Technology (1830-1930),” “Science and the City,” “Relations between the Living and the Lifeless,” and the “Shape of Experiment” in workshops and conferences, this workshop asked about the role sound plays in the configurations among science, technology and the arts, focusing on the years between 1800 and 1930. -
Backward Chaining –! Bayesian Belief Network –! Explanation
Information, Search, and Expert Systems ! Robert Stengel! Robotics and Intelligent Systems MAE 345 ! Princeton University, 2017 •! Communication/Information Theory –! Wiener vs. Shannon –! Entropy •! Finding Decision Rules in Data –! ID3 Algorithm •! Graph and Tree Search •! Expert Systems –! Forward and Backward Chaining –! Bayesian Belief Network –! Explanation Copyright 2017 by Robert Stengel. All rights reserved. For educational use only. 1 http://www.princeton.edu/~stengel/MAE345.html “Communication Theory” or “Information Theory”? •! Prodigy at Harvard, professor at MIT •! Cybernetics •! Feedback control •! Communication theory Dark Hero Of The Information Age: In Search of Norbert Wiener, the Father of Cybernetics, Flo Norbert Wiener Conway and Jim Siegelman, 2005. Basic Books (1894-1964) •! University of Michigan, MIT (student), Bell Labs, MIT (professor) •! Boolean algebra •! Cryptography, telecommunications •! Information theory Claude The Information: A History, A Theory, A Flood, Shannon James Gleick, 2011, Pantheon. (1916-2001) 2 Information, Noise, and Observation S = Information (Signal) Power, e.g., watts N = Noise Power, e.g., watts ()S + N = Observed Power, e.g., watts 3 Communication: Separating Signals from Noise Signal-to-Noise Ratio, SNR Signal Power S SNR = ! Noise Power N 2 ! signal watts = (zero-mean), e.g., ! 2 noise watts SNR often expressed in decibels 2 Signal Power (Signal Amplitude) SNR(dB) = 10log10 = 10log10 2 Noise Power (Noise Amplitude) Signal Amplitude = 20log = S(dB) ! N(dB) 10 Noise Amplitude 4 Communication: