Computation at the Nanoscale:
|
|
- Jean Griffin
- 5 years ago
- Views:
Transcription
1 Computation at the Nanoscale: thoughts on information processing in novel materials, molecules, & atoms Jim Crutchfield Complexity Sciences Center Physics Department University of California at Davis Telluride Summer workshop on The Complexity of Dynamics & Kinetics in Many Dimensions Telluride, Colorado 16 June 2013 Joint work with Dowman Varn (UCD) & Paul Riechers (UCD) Copyright James P. Crutchfield 1
2 Agenda History of Substrates Information Processing Intrinsic Computation Applications Looking Forward 2
3 History of Computing Substrates Mechanical: Gears Electron tube circuits Gates: Electron tubes, semiconductors Memory: Mercury delay lines, storage scopes,... Molecular Computing (1970s) Physics and Computation (MIT Endicott House 1981) Quantum Computing (Feynman there) Josephson Junction Computers (IBM 1980s) Nanotech (Drexler/Merkle XEROX PARC 1990s) Design goal: Useful computing 3
4 History Of Intrinsic Computing Nature already computes Information: H(Pr(X)) (Shannon 1940s) In chaotic dynamics: (Kolmogorov 1950s) h µ Physics and Computation (MIT Endicott House 1981) Intrinsic computing there too! 4
5 Information Processing 5
6 Information-Theoretic Analysis of Complex Systems... Process Pr( X, X ) is a communication channel X X from the past to the future : Past Present Future Channel 6
7 Information-Theoretic Analysis of Complex Systems... Process Pr( X, X ) is a communication channel X X from the past to the future : Past Present Future Information Rate h µ Channel Capacity C 6
8 Information-Theoretic Analysis of Complex Systems... Process Pr( X, X ) is a communication channel X X from the past to the future : Past Present Future Information Rate h µ Channel Capacity C Channel Utilization: Excess Entropy E = I[ X ; X ] 6
9 Roadmap to Information(s) H(L) µ E + h L H(L) E Block Entropy H(L) H[! X L ] E T h L µ 0 0 L J. P. Crutchfield and D. P. Feldman, Regularities Unseen, Randomness Observed: Levels of Entropy Convergence, CHAOS 13:1 (2003)
10 Is Information Theory Sufficient? No! Measurements = process states? Wrong! Hidden processes No direct measure of structure 8
11 Intrinsic Computation (1) How much of past does process store? (2) In what architecture is that information stored? (3) How is stored information used to produce future behavior? 9
12 Computational Mechanics: What are the hidden states? Group all histories that give same prediction: ( x )={ x : Pr( X x ) = Pr( X x )} Equivalence relation: x x Equivalence classes are process s causal states: S = Pr( X, X )/!-Machine: Optimal, minimal, unique predictor. J. P. Crutchfield, K. Young, Inferring Statistical Complexity, Physical Review Letters 63 (1989)
13 Computational Mechanics!-Machine: M = S, {T (x) : x A} Dynamic: State State A B Transient States T (x), = Pr(,x) C , S Recurrent States D 11
14 Varieties of ε-machine Denumerable Causal States Fractal J. P. Crutchfield, Calculi of Emergence: Computation, Dynamics, and Induction, Physica D 75 (1994) Continuous 12
15 Kinds of Intrinsic Computing Directly from!-machine: Stored information (Statistical complexity): C µ = Pr( ) log 2 Pr( ) S Information production (Entropy rate): h µ = S Pr( ) S,s A Pr( s ) log 2 Pr( s ) 13
16 Computational Mechanics Theorem (Causal Shielding): Pr( X, X S) = Pr( X S)Pr( X S) Theorem (Optimal Prediction): Pr( X S) = Pr( X X ) Corollary (Capture All Shared Information): I[S; X ]=E (Prescient models) Theorem:!-Machine is smallest prescient model C µ H[S] H[R] 14
17 Prediction V. Modeling Hidden: State information via measurement. So, how accessible is state information? How do measurements reveal internal states? Quantitative version: Prediction ~ Modeling ~ E C µ 15
18 Information Accessibility How hidden is a hidden Process? Crypticity: = C µ E Stored Information Apparent Information 16
19 Summary Information stored in the present is not that shared between the past and the future. 17
20 Cautionary Cryptic Processes: Excess IC entropy can be arbitrarily small ( E 0). Even for very structured ( ) processes. C µ 1 Care when applying informational analyses to complex systems. Best to focus on causal architecture, then calculate what you need. 18
21 Intrinsic Computation (1) How much of past does process store? (2) In what architecture is that information stored? (3) How is stored information used to produce future behavior? 19
22 Intrinsic Computation (1) How much of past does process store? C µ (2) In what architecture is that information stored? (3) How is stored information used to produce future behavior? 19
23 Intrinsic Computation (1) How much of past does process store? (2) In what architecture is that information stored? n o S, {T (s),s2a} (3) How is stored information used to produce future behavior? C µ 19
24 Intrinsic Computation (1) How much of past does process store? (2) In what architecture is that information stored? n o S, {T (s),s2a} (3) How is stored information used to produce future behavior? C µ h µ 19
25 Applications Chaotic Crystallography Single Molecule Dynamics Atomic Computing 20
26 Chaotic Crystallography via ε-machine Spectral Reconstruction Close-packed structures: Polytypes (semiconductors) ε-msr D. P. Varn, G. S. Canright, and J. P. Crutchfield, "ε-machine spectral reconstruction theory: A direct method for inferring planar disorder and structure from X-ray diffraction studies", Acta Cryst. Sec. A 69:2 (2013)
27 Designer Semiconductors Hypothesis: Structure key to computational & physical properties.!msr: New theory of structure in disordered materials Infer intrinsic computation Calculate new physical properties (length scales, interaction energy,...) Exotic semiconductors = Rational design of polytypes: Identify!M with desired physical+informational properties Run!MSR backwards to assemble polytypic materials Desired properties in an ensemble of realizations, reduces complexity of assembly 22
28 Molecular Dynamics Spectroscopy C.-B. Li, H. Yang, & T. Komatsuzaki, Proc. Natl. Acad. Sci USA 105:2 (2008)
29 Atomic Computing Chaotic ionization mechanism: Nonlinear turnstiles Momentum pr Rydberg atoms: Isolated, highly excited electron states K. Burke, K. Mitchell, B. Wyker, S.Ye, and F. B. Dunning, Demonstration of Turnstiles as a Chaotic Ionization Mechanism in Rydberg Atoms, Physical Review Letters 107 (2011)
30 Atomic Computing Measured ionization well predicted (classically!) Current work: Phase shift as a function of T. Small displacements in T are applied to 1D and experimental data to separate markers. Intrinsic computational analysis via!m Embed logic gates in turnstile dynamics 25
31 Atomic Computing Couple to build circuits... Rydberg Computers? Optical lattice of Rydberg atoms: Rydberg atoms in solid-state materials? 26
32 Looking forward Theory of Computational Mechanics: Complete, closed-form analysis of intrinsic computing. Experiment: Analyze intrinsic computation in dynamic, nonlinear nanosystems. Information Engine UC Davis: Workshops, visit Davis, collaborate,...! 27
33 Thanks! J. P. Crutchfield, C. J. Ellison, and J. R. Mahoney, Time's Barbed Arrow: Irreversibility, Crypticity, and Stored Information, Physical Review Letters 103:9 (2009) C. J. Ellison, J. R. Mahoney, and J. P. Crutchfield, Prediction, Retrodiction, and the Amount of Information Stored in the Present, Journal of Statistical Physics 137:6 (2009) J. P. Crutchfield, C. J. Ellison, J. R. Mahoney, and R. G. James, Synchronization and Control in Intrinsic and Designed Computation: An Information-Theoretic Analysis of Competing Models of Stochastic Computation, CHAOS 20:3 (2010) J. P. Crutchfield, Between Order and Chaos, Nature Physics 8 (January 2012) D. P. Varn, G. S. Canright, and J. P. Crutchfield, "!-Machine spectral reconstruction theory: A direct method for inferring planar disorder and structure from X-ray diffraction studies", Acta Cryst. Sec. A 69:2 (2013)
Demon Dynamics: Deterministic Chaos, the Szilard Map, & the Intelligence of Thermodynamic Systems.
Demon Dynamics: Deterministic Chaos, the Szilard Map, & the Intelligence of Thermodynamic Systems http://csc.ucdavis.edu/~cmg/ Jim Crutchfield Complexity Sciences Center Physics Department University of
More informationHierarchical Thermodynamics
Hierarchical Thermodynamics James P Crutchfield Complexity Sciences Center Physics Department University of California, Davis http://csc.ucdavis.edu/~chaos/ Workshop on Information Engines at the Frontier
More informationReconstruction Deconstruction:
Reconstruction Deconstruction: A Brief History of Building Models of Nonlinear Dynamical Systems Jim Crutchfield Center for Computational Science & Engineering Physics Department University of California,
More informationStatistical Complexity of Simple 1D Spin Systems
Statistical Complexity of Simple 1D Spin Systems James P. Crutchfield Physics Department, University of California, Berkeley, CA 94720-7300 and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501
More informationThe Past and the Future in the Present
The Past and the Future in the Present James P. Crutchfield Christopher J. Ellison SFI WORKING PAPER: 2010-12-034 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily
More informationQuantum versus Classical Measures of Complexity on Classical Information
Quantum versus Classical Measures of Complexity on Classical Information Lock Yue Chew, PhD Division of Physics and Applied Physics School of Physical & Mathematical Sciences & Complexity Institute Nanyang
More informationε-machine Spectral Reconstruction Theory Applied to Discovering Planar Disorder in Close-Packed Stuctures Dowman P Varn
ε-machine Spectral Reconstruction Theory Applied to Discovering Planar Disorder in Close-Packed Stuctures Dowman P Varn dpv@complexmatter.org 23 May 2013 Readings for this lecture: BTFM1 and BTFM2 articles
More informationOptimal Causal Inference
Optimal Causal Inference Susanne Still James P. Crutchfield Christopher J. Ellison SFI WORKING PAPER: 007-08-04 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily
More informationPrediction, Retrodiction, and the Amount of Information Stored in the Present
Prediction, Retrodiction, and the Amount of Information Stored in the Present Christopher J. Ellison John R. Mahoney James P. Crutchfield SFI WORKING PAPER: 2009-05-017 SFI Working Papers contain accounts
More informationReconstruction. Reading for this lecture: Lecture Notes.
ɛm Reconstruction Reading for this lecture: Lecture Notes. The Learning Channel... ɛ -Machine of a Process: Intrinsic representation! Predictive (or causal) equivalence relation: s s Pr( S S= s ) = Pr(
More informationInformation Accessibility and Cryptic Processes
Information Accessibility and Cryptic Processes John R. Mahoney Christopher J. Ellison James P. Crutchfield SFI WORKING PAPER: 2009-05-08 SFI Working Papers contain accounts of scientific work of the author(s)
More informationNatural Computation. Transforming Tools of NBIC: Complex Adaptive Systems. James P. Crutchfield Santa Fe Institute
Natural Computation Transforming Tools of NBIC: Complex Adaptive Systems James P. Crutchfield www.santafe.edu/~chaos Santa Fe Institute Nanotechnology, Biotechnology, Information Technology, and Cognitive
More informationInformation Theoretic Properties of Quantum Automata
Information Theoretic Properties of Quantum Automata D. Gier Department of Physics and Astronomy, The University of Kansas, Lawrence, KS 66045 and Complexity Sciences Center and Physics Department, University
More informationIntrinsic Quantum Computation
Intrinsic Quantum Computation James P. Crutchfield Karoline Wiesner SFI WORKING PAPER: 2006-11-045 SFI Working Papers contain accounts of scientific work of the author(s and do not necessarily represent
More informationDynamical Embodiments of Computation in Cognitive Processes James P. Crutcheld Physics Department, University of California, Berkeley, CA a
Dynamical Embodiments of Computation in Cognitive Processes James P. Crutcheld Physics Department, University of California, Berkeley, CA 94720-7300 and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe,
More informationInformational and Causal Architecture of Discrete-Time Renewal Processes
Entropy 2015, 17, 4891-4917; doi:10.3390/e17074891 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Informational and Causal Architecture of Discrete-Time Renewal Processes Sarah
More informationInferring planar disorder in close-packed structures via ɛ-machine spectral reconstruction theory: examples from simulated diffraction spectra
Acta Crystallographica Section A Foundations of Crystallography ISSN 0108-7673 Inferring planar disorder in close-packed structures via ɛ-machine spectral reconstruction theory: examples from simulated
More informationInformation Symmetries in Irreversible Processes
Information Symmetries in Irreversible Processes Christopher J. Ellison John R. Mahoney R. G. James James P. Crutchfield Joerg Reichardt SFI WORKING PAPER: 0-07-08 SFI Working Papers contain accounts of
More informationComplex Systems Methods 3. Statistical complexity of temporal sequences
Complex Systems Methods 3. Statistical complexity of temporal sequences Eckehard Olbrich MPI MiS Leipzig Potsdam WS 2007/08 Olbrich (Leipzig) 02.11.2007 1 / 24 Overview 1 Summary Kolmogorov sufficient
More informationSharpening Occam s Razor with Quantum Mechanics
Sharpening Occam s Razor with Quantum Mechanics ternative is more efficient and thus superior; it demands only a single bit of input, when the original model required two. Preference for efficient models
More informationAnatomy of a Bit. Reading for this lecture: CMR articles Yeung and Anatomy.
Anatomy of a Bit Reading for this lecture: CMR articles Yeung and Anatomy. 1 Information in a single measurement: Alternative rationale for entropy and entropy rate. k measurement outcomes Stored in log
More informationComputational Mechanics of the Two Dimensional BTW Model
Computational Mechanics of the Two Dimensional BTW Model Rajesh Kommu kommu@physics.ucdavis.edu June 8, 2010 Abstract Some aspects of computational mechanics in two dimensions are investigated in this
More informationComputation in Sofic Quantum Dynamical Systems
Santa Fe Institute Working Paper 07-05-007 arxiv:0704.3075 Computation in Sofic Quantum Dynamical Systems Karoline Wiesner 1, and James P. Crutchfield 1, 1 Center for Computational Science & Engineering
More informationUltralow-Power Reconfigurable Computing with Complementary Nano-Electromechanical Carbon Nanotube Switches
Ultralow-Power Reconfigurable Computing with Complementary Nano-Electromechanical Carbon Nanotube Switches Presenter: Tulika Mitra Swarup Bhunia, Massood Tabib-Azar, and Daniel Saab Electrical Eng. And
More informationTransient Dissipation and Structural Costs of Physical Information Transduction
Santa Fe Institute Working Paper 2017-01-01 arxiv.org:1612.08616 [cond-mat.stat-mech] Transient Dissipation and Structural Costs of Physical Information Transduction Alexander B. Boyd, 1, Dibyendu Mandal,
More informationEnumerating Finitary Processes
Enumerating Finitary Processes B. D. Johnson J. P. Crutchfield C. J. Ellison C. S. McTague SFI WORKING PAPER: 200--027 SFI Working Papers contain accounts of scientific work of the author(s) and do not
More informationExact Synchronization for Finite-State Sources
Santa Fe Institute Woring Paper 10-11-031 arxiv.org:1008.4182 [nlin.cd] Exact Synchronization for Finite-State Sources Nicholas F. Travers 1, 2, 1, 2, 3, 4, and James P. Crutchfield 1 Complexity Sciences
More informationRegularities Unseen, Randomness Observed: Levels of Entropy Convergence
Regularities Unseen, Randomness Observed: evels of Entropy Convergence James P. Crutchfield David P. Feldman SFI WORKING PAPER: -- SFI Working Papers contain accounts of scientific work of the author(s)
More informationScientific Computing II
Scientific Computing II Molecular Dynamics Numerics Michael Bader SCCS Technical University of Munich Summer 018 Recall: Molecular Dynamics System of ODEs resulting force acting on a molecule: F i = j
More informationPermutation Excess Entropy and Mutual Information between the Past and Future
Permutation Excess Entropy and Mutual Information between the Past and Future Taichi Haruna 1, Kohei Nakajima 2 1 Department of Earth & Planetary Sciences, Graduate School of Science, Kobe University,
More informationCharge Excitation. Lecture 4 9/20/2011 MIT Fundamentals of Photovoltaics 2.626/2.627 Fall 2011 Prof. Tonio Buonassisi
Charge Excitation Lecture 4 9/20/2011 MIT Fundamentals of Photovoltaics 2.626/2.627 Fall 2011 Prof. Tonio Buonassisi 1 2.626/2.627 Roadmap You Are Here 2 2.626/2.627: Fundamentals Every photovoltaic device
More informationII. Spatial Systems A. Cellular Automata 8/24/08 1
II. Spatial Systems A. Cellular Automata 8/24/08 1 Cellular Automata (CAs) Invented by von Neumann in 1940s to study reproduction He succeeded in constructing a self-reproducing CA Have been used as: massively
More informationII. Spatial Systems. A. Cellular Automata. Structure. Cellular Automata (CAs) Example: Conway s Game of Life. State Transition Rule
II. Spatial Systems A. Cellular Automata B. Pattern Formation C. Slime Mold D. Excitable Media A. Cellular Automata 1/18/17 1 1/18/17 2 Cellular Automata (CAs) Invented by von Neumann in 1940s to study
More informationFPGA IMPLEMENTATION OF BASIC ADDER CIRCUITS USING REVERSIBLE LOGIC GATES
FPGA IMPLEMENTATION OF BASIC ADDER CIRCUITS USING REVERSIBLE LOGIC GATES B.Ravichandra 1, R. Kumar Aswamy 2 1,2 Assistant Professor, Dept of ECE, VITS College of Engineering, Visakhapatnam (India) ABSTRACT
More informationExtreme Quantum Advantage when Simulating Strongly Coupled Classical Systems
Santa Fe Institute Working Paper -09-XXX arxiv:09.xxxx Extreme Quantum Advantage when Simulating Strongly Coupled Classical Systems Cina Aghamohammadi, John R. Mahoney, and James P. Crutchfield Complexity
More informationAnalysis of flip flop design using nanoelectronic single electron transistor
Int. J. Nanoelectronics and Materials 10 (2017) 21-28 Analysis of flip flop design using nanoelectronic single electron transistor S.Rajasekaran*, G.Sundari Faculty of Electronics Engineering, Sathyabama
More informationOptimal predictive inference
Optimal predictive inference Susanne Still University of Hawaii at Manoa Information and Computer Sciences S. Still, J. P. Crutchfield. Structure or Noise? http://lanl.arxiv.org/abs/0708.0654 S. Still,
More informationMechanisms of Emergent Computation in Cellular Automata
Mechanisms of Emergent Computation in Cellular Automata Wim Hordijk, James P. Crutchfield, Melanie Mitchell Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, 87501 NM, USA email: {wim,chaos,mm}@santafe.edu
More informationTest Code : CSB (Short Answer Type) Junior Research Fellowship (JRF) in Computer Science
Test Code : CSB (Short Answer Type) 2016 Junior Research Fellowship (JRF) in Computer Science The CSB test booklet will have two groups as follows: GROUP A A test for all candidates in the basics of computer
More informationThe Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications
The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications James P. Crutchfield SFI WORKING PAPER: 2017-10-035 SFI Working Papers contain accounts of scienti5ic work
More informationNanomaterials and their Optical Applications
Nanomaterials and their Optical Applications Winter Semester 2013 Lecture 02 rachel.grange@uni-jena.de http://www.iap.uni-jena.de/multiphoton Lecture 2: outline 2 Introduction to Nanophotonics Theoretical
More informationQuantum Computing. Joachim Stolze and Dieter Suter. A Short Course from Theory to Experiment. WILEY-VCH Verlag GmbH & Co. KGaA
Joachim Stolze and Dieter Suter Quantum Computing A Short Course from Theory to Experiment Second, Updated and Enlarged Edition WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Preface XIII 1 Introduction and
More informationWhat is Chaos? Implications of Chaos 4/12/2010
Joseph Engler Adaptive Systems Rockwell Collins, Inc & Intelligent Systems Laboratory The University of Iowa When we see irregularity we cling to randomness and disorder for explanations. Why should this
More informationShannon Information (very briefly!) Lecture 4. Maximum and Minimum Entropy. Entropy. Entropy of Transition Rules. Entropy Examples
Lecture 4 9/4/07 1 Shannon Information (very briefly!) Information varies directly with surprise Information varies inversely with probability Information is additive The information content of a message
More informationarxiv: v3 [cs.fl] 16 Dec 2012
Santa Fe Institute Working Paper 0--027 arxiv.org:0.0036 [cs.fl] Enumerating Finitary Processes arxiv:0.0036v3 [cs.fl] 6 Dec 202 Benjamin D. Johnson,, 2, James P. Crutchfield,, 2, 3, 4, Christopher J.
More informationIBM quantum experience: Experimental implementations, scope, and limitations
IBM quantum experience: Experimental implementations, scope, and limitations Plan of the talk IBM Quantum Experience Introduction IBM GUI Building blocks for IBM quantum computing Implementations of various
More informationStat Mech: Problems II
Stat Mech: Problems II [2.1] A monatomic ideal gas in a piston is cycled around the path in the PV diagram in Fig. 3 Along leg a the gas cools at constant volume by connecting to a cold heat bath at a
More informationChapter 2 Review of Classical Information Theory
Chapter 2 Review of Classical Information Theory Abstract This chapter presents a review of the classical information theory which plays a crucial role in this thesis. We introduce the various types of
More informationHow Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos
How Random is a Coin Toss? Bayesian Inference and the Symbolic Dynamics of Deterministic Chaos Christopher C. Strelioff Center for Complex Systems Research and Department of Physics University of Illinois
More informationInformation Entropy Theory of Physics
Information Entropy Theory of Physics Abstract... 1 Considering the chess game as a model of physics... 1 Using this model in physics... 4 Quantum Information Science... 4 Quantum Computing Research...
More informationJ. P. Crutchfield R. G. James S. Marzen D. P. Varn
Understanding and Designing Complex Systems: Response to A Framework for Optimal High- Level Descriptions in Science and Engineering -- Preliminary Report J. P. Crutchfield R. G. James S. Marzen D. P.
More information*WILEY- Quantum Computing. Joachim Stolze and Dieter Suter. A Short Course from Theory to Experiment. WILEY-VCH Verlag GmbH & Co.
Joachim Stolze and Dieter Suter Quantum Computing A Short Course from Theory to Experiment Second, Updated and Enlarged Edition *WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface XIII 1 Introduction
More informationStructure or Noise? Susanne Still James P. Crutchfield SFI WORKING PAPER:
Structure or Noise? Susanne Still James P. Crutchfield SFI WORKING PAPER: 2007-08-020 SFI Working Papers contain accounts of scientific work of the author(s) and do not necessarily represent the views
More informationTowards a Theory of Information Flow in the Finitary Process Soup
Towards a Theory of in the Finitary Process Department of Computer Science and Complexity Sciences Center University of California at Davis June 1, 2010 Goals Analyze model of evolutionary self-organization
More informationarxiv: v1 [cond-mat.stat-mech] 9 Dec 2014
Santa Fe Institute Working Paper 4-2-XXX arxiv.org:42.xxxx [cond-mat.stat-mech] Circumventing the Curse of Dimensionality in Prediction: Causal Rate-Distortion for Infinite-Order Markov Processes arxiv:42.2859v
More informationNanotechnology-inspired Information Processing Systems of the Future
Nanotechnology-inspired Information Processing Systems of the Future Lav R. Varshney University of Illinois at Urbana-Champaign August 31, 2016 Cross-cutting Panel 3 Putting intelligence in (trillions
More informationStochastic Model for Adaptation Using Basin Hopping Dynamics
Stochastic Model for Adaptation Using Basin Hopping Dynamics Peter Davis NTT Communication Science Laboratories 2-4 Hikaridai, Keihanna Science City, Kyoto, Japan 619-0237 davis@cslab.kecl.ntt.co.jp Abstract
More informationInferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: ɛ-machine Spectral Reconstruction Theory
Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: ɛ-machine Spectral Reconstruction Theory D. P. Varn, 1, 2 G. S. Canright, 2, 3 and J. P. Crutchfield 1
More informationTitle of file for HTML: Supplementary Information Description: Supplementary Figures and Supplementary References
Title of file for HTML: Supplementary Information Description: Supplementary Figures and Supplementary References Supplementary Figure 1. SEM images of perovskite single-crystal patterned thin film with
More informationDESIGN OF A COMPACT REVERSIBLE READ- ONLY-MEMORY WITH MOS TRANSISTORS
DESIGN OF A COMPACT REVERSIBLE READ- ONLY-MEMORY WITH MOS TRANSISTORS Sadia Nowrin, Papiya Nazneen and Lafifa Jamal Department of Computer Science and Engineering, University of Dhaka, Bangladesh ABSTRACT
More informationwhere n = (an integer) =
5.111 Lecture Summary #5 Readings for today: Section 1.3 (1.6 in 3 rd ed) Atomic Spectra, Section 1.7 up to equation 9b (1.5 up to eq. 8b in 3 rd ed) Wavefunctions and Energy Levels, Section 1.8 (1.7 in
More informationTheory Component of the Quantum Computing Roadmap
3.2.4 Quantum simulation Quantum simulation represents, along with Shor s and Grover s algorithms, one of the three main experimental applications of quantum computers. Of the three, quantum simulation
More informationMultiple Exciton Generation in Quantum Dots. James Rogers Materials 265 Professor Ram Seshadri
Multiple Exciton Generation in Quantum Dots James Rogers Materials 265 Professor Ram Seshadri Exciton Generation Single Exciton Generation in Bulk Semiconductors Multiple Exciton Generation in Bulk Semiconductors
More informationNeural Networks for Machine Learning. Lecture 11a Hopfield Nets
Neural Networks for Machine Learning Lecture 11a Hopfield Nets Geoffrey Hinton Nitish Srivastava, Kevin Swersky Tijmen Tieleman Abdel-rahman Mohamed Hopfield Nets A Hopfield net is composed of binary threshold
More informationPHYSICS (PHYS) Physics (PHYS) 1. PHYS 5880 Astrophysics Laboratory
Physics (PHYS) 1 PHYSICS (PHYS) PHYS 5210 Theoretical Mechanics Kinematics and dynamics of particles and rigid bodies. Lagrangian and Hamiltonian equations of motion. PHYS 5230 Classical Electricity And
More informationThe Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing
Santa Fe Institute Working Paper 8-6-XXX arxiv.org:86.4789 [nlin.cd] The Organization of Intrinsic Computation: Complexity-Entropy Diagrams and the Diversity of Natural Information Processing David P.
More informationPattern Discovery in Time Series, Part I: Theory, Algorithm, Analysis, and Convergence
Journal of Machine earning Research? (2002)?? Submitted 0/28; Published?/02 Pattern Discovery in Time Series, Part I: Theory, Algorithm, Analysis, and Convergence Cosma Rohilla Shalizi shalizi@santafe.edu
More informationAnalyzing Line Emission Spectra viewed through a Spectroscope using a Smartphone
Energy (ev) Analyzing Line Emission Spectra viewed through a Spectroscope using a Smartphone Eugene T. Smith, PhD Goals: 1. Calibrate spectroscope using mercury emission source or fluorescent bulb. 2.
More informationOroville Union High School District Science Curriculum
Oroville Union High School District Science Curriculum Science - Physics Physics COURSE TITLE: Physics LENGTH OF COURSE: One Year TYPE OF CREDIT: Science (10 credits) GRADE Level: 10-12 PREREQUISITE: One
More informationAppendix 1: List of symbols
Appendix 1: List of symbols Symbol Description MKS Units a Acceleration m/s 2 a 0 Bohr radius m A Area m 2 A* Richardson constant m/s A C Collector area m 2 A E Emitter area m 2 b Bimolecular recombination
More informationPhysics for Scientists & Engineers with Modern Physics Douglas C. Giancoli Fourth Edition
Physics for Scientists & Engineers with Modern Physics Douglas C. Giancoli Fourth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the
More informationAsynchronous updating of threshold-coupled chaotic neurons
PRAMANA c Indian Academy of Sciences Vol. 70, No. 6 journal of June 2008 physics pp. 1127 1134 Asynchronous updating of threshold-coupled chaotic neurons MANISH DEV SHRIMALI 1,2,3,, SUDESHNA SINHA 4 and
More informationChirikov standard map Dima Shepelyansky
Chirikov standard map Dima Shepelyansky www.quantware.ups-tlse.fr/chirikov (959) Chirikov criterion (969) Classical map: p = p + K sin x x = x + p (979) Quantum map (kicked rotator): ψ = e iˆp2 /2 e ik/
More informationLecture Notes 2 Charge-Coupled Devices (CCDs) Part I. Basic CCD Operation CCD Image Sensor Architectures Static and Dynamic Analysis
Lecture Notes 2 Charge-Coupled Devices (CCDs) Part I Basic CCD Operation CCD Image Sensor Architectures Static and Dynamic Analysis Charge Well Capacity Buried channel CCD Transfer Efficiency Readout Speed
More informationExact Synchronization for Finite-State Sources
Santa Fe Institute Woring Paper 10-08-XXX arxiv.org:1008.4182 [nlin.cd] Exact Synchronization for Finite-State Sources Nicholas F. Travers 1, 2, 1, 2, 3, 4, and James P. Crutchfield 1 Complexity Sciences
More informationLong-Term Prediction, Chaos and Artificial Neural Networks. Where is the Meeting Point?
Engineering Letters, 5:, EL_5 Long-Term Prediction, Chaos and Artificial Neural Networks. Where is the Meeting Point? Pilar Gómez-Gil Abstract This paper presents the advances of a research using a combination
More informationRegularities unseen, randomness observed: Levels of entropy convergence
CHAOS VOUME 13, NUMBER 1 MARCH 2003 Regularities unseen, randomness observed: evels of entropy convergence James P. Crutchfield a) Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501 David
More informationRydberg excited Calcium Ions for quantum interactions. Innsbruck Mainz Nottingham
Rydberg excited Calcium Ions for quantum interactions Innsbruck Mainz Nottingham Brussels 26.03.2013 The R-ION Consortium Ferdinand Schmidt-Kaler University of Mainz/Germany Trapped ions Experiment Jochen
More informationLecture 11: Quantum Information III - Source Coding
CSCI5370 Quantum Computing November 25, 203 Lecture : Quantum Information III - Source Coding Lecturer: Shengyu Zhang Scribe: Hing Yin Tsang. Holevo s bound Suppose Alice has an information source X that
More informationEmergent proper+es and singular limits: the case of +me- irreversibility. Sergio Chibbaro Institut d Alembert Université Pierre et Marie Curie
Emergent proper+es and singular limits: the case of +me- irreversibility Sergio Chibbaro Institut d Alembert Université Pierre et Marie Curie Introduction: Definition of emergence I J Kim 2000 The whole
More informationAn Introduction to Quantum Computation and Quantum Information
An to and Graduate Group in Applied Math University of California, Davis March 13, 009 A bit of history Benioff 198 : First paper published mentioning quantum computing Feynman 198 : Use a quantum computer
More informationphys4.20 Page 1 - the ac Josephson effect relates the voltage V across a Junction to the temporal change of the phase difference
Josephson Effect - the Josephson effect describes tunneling of Cooper pairs through a barrier - a Josephson junction is a contact between two superconductors separated from each other by a thin (< 2 nm)
More informationNon-traditional methods of material properties and defect parameters measurement
Non-traditional methods of material properties and defect parameters measurement Juozas Vaitkus on behalf of a few Vilnius groups Vilnius University, Lithuania Outline: Definition of aims Photoconductivity
More informationCellular Automata CS 591 Complex Adaptive Systems Spring Professor: Melanie Moses 2/02/09
Cellular Automata CS 591 Complex Adaptive Systems Spring 2009 Professor: Melanie Moses 2/02/09 Introduction to Cellular Automata (CA) Invented by John von Neumann (circa~1950). A cellular automata consists
More informationTHIELE CENTRE. Disordered chaotic strings. Mirko Schäfer and Martin Greiner. for applied mathematics in natural science
THIELE CENTRE for applied mathematics in natural science Disordered chaotic strings Mirko Schäfer and Martin Greiner Research Report No. 06 March 2011 Disordered chaotic strings Mirko Schäfer 1 and Martin
More informationFault Tolerance Technique in Huffman Coding applies to Baseline JPEG
Fault Tolerance Technique in Huffman Coding applies to Baseline JPEG Cung Nguyen and Robert G. Redinbo Department of Electrical and Computer Engineering University of California, Davis, CA email: cunguyen,
More informationHugh Everett III s Many Worlds
236 My God, He Plays Dice! Hugh Everett III s Many Worlds Many Worlds 237 Hugh Everett III s Many Worlds Hugh Everett III was one of John Wheeler s most famous graduate students. Others included Richard
More informationParallel Ensemble Monte Carlo for Device Simulation
Workshop on High Performance Computing Activities in Singapore Dr Zhou Xing School of Electrical and Electronic Engineering Nanyang Technological University September 29, 1995 Outline Electronic transport
More informationhttp://www.physics.ucdavis.edu/condensed_matter.html A brief introduction to Condensed Matter Physics at Davis and an overview of the Condensed Matter Experiment Group The Past-- 30 Years of Nobel Prizes
More informationINTRODUCTION TO SUPERCONDUCTING QUBITS AND QUANTUM EXPERIENCE: A 5-QUBIT QUANTUM PROCESSOR IN THE CLOUD
INTRODUCTION TO SUPERCONDUCTING QUBITS AND QUANTUM EXPERIENCE: A 5-QUBIT QUANTUM PROCESSOR IN THE CLOUD Hanhee Paik IBM Quantum Computing Group IBM T. J. Watson Research Center, Yorktown Heights, NY USA
More informationNONLINEAR AND ADAPTIVE (INTELLIGENT) SYSTEMS MODELING, DESIGN, & CONTROL A Building Block Approach
NONLINEAR AND ADAPTIVE (INTELLIGENT) SYSTEMS MODELING, DESIGN, & CONTROL A Building Block Approach P.A. (Rama) Ramamoorthy Electrical & Computer Engineering and Comp. Science Dept., M.L. 30, University
More informationA Novel Ternary Content-Addressable Memory (TCAM) Design Using Reversible Logic
2015 28th International Conference 2015 on 28th VLSI International Design and Conference 2015 14th International VLSI Design Conference on Embedded Systems A Novel Ternary Content-Addressable Memory (TCAM)
More informationThe Modeling and Complexity of Dynamical Systems by Means of Computation and Information Theories
Proceedings of the nd Central European Conference on Information and Intelligent Systems 8 The Modeling and Complexity of Dynamical Systems by Means of Computation and Information Theories Robert Logozar
More informationDESIGN AND ANALYSIS OF A FULL ADDER USING VARIOUS REVERSIBLE GATES
DESIGN AND ANALYSIS OF A FULL ADDER USING VARIOUS REVERSIBLE GATES Sudhir Dakey Faculty,Department of E.C.E., MVSR Engineering College Abstract The goal of VLSI has remained unchanged since many years
More informationGroup Members: Your Name In Class Exercise #6. Photon A. Energy B
Group Members: Your Name In Class Exercise #6 Shell Structure of Atoms Part II Photoelectron Spectroscopy Photoelectron spectroscopy is closely related to the photoelectric effect. When high energy photons
More informationarxiv:cs/ v3 [cs.lg] 27 Nov 2002
Journal of Machine earning Research? (2003)?? Submitted 11/02; Published?/? An Algorithm for Pattern Discovery in Time Series arxiv:cs/0210025v3 [cs.g] 27 Nov 2002 Cosma Rohilla Shalizi shalizi@santafe.edu
More informationRecall the essence of data transmission: How Computers Work Lecture 11
Recall the essence of data transmission: How Computers Work Lecture 11 Q: What form does information take during transmission? Introduction to the Physics of Computation A: Energy Energy How Computers
More informationLECTURE 15. Last time: Feedback channel: setting up the problem. Lecture outline. Joint source and channel coding theorem
LECTURE 15 Last time: Feedback channel: setting up the problem Perfect feedback Feedback capacity Data compression Lecture outline Joint source and channel coding theorem Converse Robustness Brain teaser
More informationEarly Quantum Theory and Models of the Atom
Early Quantum Theory and Models of the Atom Electron Discharge tube (circa 1900 s) There is something ( cathode rays ) which is emitted by the cathode and causes glowing Unlike light, these rays are deflected
More informationPHYSICS QUESTION PAPER CLASS-XII
PHYSICS QUESTION PAPER CLASS-XII Time : 3.00 Hours] [Maximum Marks : 100 Instructions : There are four sections and total 60 questions in this question paper. ( 1) (2) All symbols used in this question
More information