DOCSLIB.ORG

Analysis and Synthesis of Boolean Networks

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Analysis and Synthesis of Boolean Networks MING LIU Licentiate Thesis in Electronic and Computer Systems Stockholm, Sweden 2015 KTH School of Information and Communication Technology TRITA-ICT 2015:23 SE-164 40 Kista, Stockholm ISBN 978-91-7595-770-8 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av licentiatexamen i ämnet Elektronik och datorsystem fredag den 18 december 2015 klockan 09.00 i Sal B, Electrum, Kungl Tekniska högskolan, Kista 16440, Stockholm. © Ming Liu, November 2015 Tryck: Universitetsservice US AB iii Abstract In this thesis, we present techniques and algorithms for analysis and syn- thesis of synchronous Boolean and multiple-valued networks. Synchronous Boolean and multiple-valued networks are a discrete-space discrete-time model of gene regulatory networks. Their cycle of states, called attractors, are believed to give a good indication of the possible functional modes of the system. This motivates research on algorithms for finding at- tractors. Existing decision diagram-based approaches have limited capacity due to the excessive memory requirements of decision diagrams. Simulation- based approaches can be applied to large networks, however, their results are incomplete. In the first part of this thesis, we present an algorithm, which uses a SAT-based bounded model checking approach to find all attractors in a multiple-valued network. The efficiency of the presented algorithm is evaluated by analysing 30 network models of real biological processes as well as 35 000 randomly generated 4-valued networks. The results show that our algorithm has a potential to handle an order of magnitude larger models than currently possible. One of the characteristic features of genetic regulatory networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random faults. In the second part of this thesis, we focus on the robustness of a special kind of Boolean networks called Balanced Boolean Networks (BBNs). We formalize the notion of robustness and introduce a method to construct BBNs for 2-singleton attractors Boolean networks. The experiment results show that BBNs are capable of tolerating single stuck-at faults. Our method improves the robustness of random Boolean networks by at least 13% on average, and in some special case, up to 61%. In the third part of this thesis, we focus on a special type of synchronous Boolean networks, namely Feedback Shift Registers (FSRs). FSR-based filter generators are used as a basic building block in many cryptographic systems, e.g. stream ciphers. Filter generators are popular because their well-defined mathematical description enables a detailed formal security analysis. We show how to modify a filter generator into a nonlinear FSR, which is faster, but slightly larger, than the original filter generator. For example, the propagation delay can be reduced 1.54 times at the expense of 1.27% extra area. The presented method might be important for applications, which require very high data rates, e.g. 5G mobile communication technology. In the fourth part of this thesis, we present a new method for detect- ing and correcting transient faults in FSRs based on duplication and parity checking. Periodic fault detection of functional circuits is very important for cryptographic systems because a random hardware fault can compromise their security. The presented method is more reliable than Triple Modular Redundancy (TMR) for large FSRs, while the area overhead of the two ap- proaches are comparable. The presented approach might be important for cryptographic systems using large FSRs. iv Sammanfattning I denna avhandling presenterar vi metoder och algoritmer för analys och syntes av synkrona Booleska och flervärda nätverk. Synkrona Booleska och flervärda nätverk är rums-och tidsdiskret modell av regulatoriskt gennätverk. Deras fillständscykler, som kallas attractorer, tros ge en god indikation på möjliga funktionssätt i systemet. Detta motiverar forskning om algoritmer för att hitta attraktorer. Befintliga beslutsdiagram baserade metoder har begränsad kapacitet på grund av orimliga minneskrav. Simuleringsbaserade metoder kan tillämpas på stora nätverk, men ger ofull- ständiga resultat. I den första delen av denna avhandling presenterar vi en algoritm som använder en SAT-baserad modell för gränsvärdes kontroll för att hitta alla attraktorer i flervärda nätverk. Effektiviteten av den presenterade algoritmen utvärderas genom att analysera 30 nätverksmodeller av verkliga biologiska processer samt 35 000 slumpmässigt genererade 4-värda nätverk. Resultaten visar att vår algoritm har potential att hantera en storleksordning större modeller än vad som nu är möjligt. En karakteristisk egenskap hos regulatoriskt gennätverk är dess innebo- ende robusthet, det vill säga dess förmåga att bibehålla funktionalitet trots införandet av slumpmässiga fel. I den andra delen av denna uppsats fokuserar vi på robustheten hos en speciell typ av Booleska nätverk som kallas Balanse- rade Booleska Nätverk (BBN). Vi formaliserar begreppet robusthet och inför en metod för att bygga BBN för 2 -singleton attraktorer Booleska nätverk. Experimentets resultat visar att BBN har förmåga att tolerera enstaka fel. Vår metod förbättrar robustheten läsnings slumpmässigt genererade Booleska nätverk med minst 13% i genomsnitt och i vissa specialfall upp till 61%. I den tredje delen av denna uppsats fokuserar vi på en speciell typ av synkrona Booleska nätverk, nämligen Feedback Shift Register (FSR). FSR- baserade filtergeneratorer används som en grundläggande byggsten i många kryptografiska system, t.ex. strömchiffer. Filtergeneratorer är populära ef- tersom deras väldefinierade matematiska beskrivning möjliggör en detalje- rad formell säkerhetsanalys. Vi visar hur blir en filter generator i modifierad icke-linjärt FSR, snabbare, men något större, än den ursprungliga filterge- neratorn. Exempelvis kan utbredningsfördröjningen minskas 1,54 gånger på bekostnad av 1,27 % extra yta. De presenterade metoderna kan vara viktiga för tillämpningar som kräver mycket höga datahastigheter, t.ex. 5G mobil kommunikationsteknik. I den fjärde delen av denna avhandling presenterar vi en ny metod för att detektera och korrigera transienta fel i FSRer med hjälp av duplicering och paritetskontroll. Periodiskt fel-detektering av funktionella kretsar är mycket viktigt för krypteringssystem eftersom slumpmässiga hårdvarufel kan äventy- ra dess säkerhet. Denna metod är mer pålitlig än Triple Modular Redundancy (TMR) för stora FSRer, men med jämförbar area. Det presenterade tillväga- gångssättet kan vara viktigt för kryptografiska system som använder stora FSRer. Acknowledgements First of all, I would like to thank my supervisor, Professor Elena Dubrova, for inspiring me with so many topics and ideas, and especially, for all the patience and encouragement she offered me when I was in trouble. I would like to thank Professor Zhonghai Lu for reviewing this thesis. I would like to thank Professor Fredrik Jonsson for his help on the Swedish abstract. I would like to thank Ms. Alina Munteanu for her help on everything in school. I would like to thank all the professors and scholars who teach me, encourage me and enlighten my own research. I would like to thank all my colleagues and friends, Shaoteng Liu, Li Xie, Jue Shen, Pei Liu, Shuo Li, Yuan Yao, Xueqian Zhao, Fan Pan, Shao Tao, Nan Li and Shohreh Sharif Mansouri, for the discussions as well as happiness we shared together. Finally, I would like to thank my parents for their love and support. Thank you! Ming Liu Stockholm, November, 2015 v Contents Contents vii List of Figures ix List of Tablesx List of Abbreviations xi 1 Introduction1 1.1 Previous Work.........................................................1 1.2 Overview and Contributions of the Author..........................3 2 Background7 2.1 Notation................................................................7 2.2 Boolean Networks.....................................................9 2.3 Feedback Shift Registers.............................................. 11 2.4 Relationship between Boolean Networks and FSRs................. 13 3 Multiple-valued Networks 15 3.1 Multiple-valued Networks............................................. 15 3.2 Computation of Attractors........................................... 16 3.3 Converting GINML Format to CNET Format...................... 18 3.4 Conclusion............................................................. 19 4 Balanced Boolean Networks 21 4.1 Computational Scheme Based on Boolean Networks............... 21 4.2 Single Stuck-at Fault Model.......................................... 23 4.3 Robustness Evaluation................................................ 24 4.4 Balanced Boolean Networks.......................................... 25 4.5 Conclusion............................................................. 26 5 Design of Secure FSRs 27 5.1 Filter Generators...................................................... 27 vii viii CONTENTS 5.2 Main Ideas of the Presented Approach.............................. 29 5.3 The Fibonacci to Galois Transformation............................ 30 5.4 Example................................................................ 31 5.5 Conclusion............................................................. 35 6 Design of Reliable FSRs 37 6.1 Stream Ciphers........................................................ 37 6.2 Transient Faults and Triple Modular Redundancy.................
Recommended publications
  • Markov Model Checking of Probabilistic Boolean Networks Representations of Genes

    Markov Model Checking of Probabilistic Boolean Networks Representations of Genes

    Markov Model Checking of Probabilistic Boolean Networks Representations of Genes Marie Lluberes1, Jaime Seguel2 and Jaime Ramírez-Vick3 1, 2 Electrical and Computer Engineering Department, University of Puerto Rico, Mayagüez, Puerto Rico 3 General Engineering Department, University of Puerto Rico, Mayagüez, Puerto Rico or, on contrary, to prevent or to stop an undesirable Abstract - Our goal is to develop an algorithm for the behavior. This “guiding” of the network dynamics is automated study of the dynamics of Probabilistic Boolean referred to as intervention. The power to intervene with the Network (PBN) representation of genes. Model checking is network dynamics has a significant impact in diagnostics an automated method for the verification of properties on and drug design. systems. Continuous Stochastic Logic (CSL), an extension of Biological phenomena manifest in the continuous-time Computation Tree Logic (CTL), is a model-checking tool domain. But, in describing such phenomena we usually that can be used to specify measures for Continuous-time employ a binary language, for instance, expressed or not Markov Chains (CTMC). Thus, as PBNs can be analyzed in expressed; on or off; up or down regulated. Studies the context of Markov theory, the use of CSL as a method for conducted restricting genes expression to only two levels (0 model checking PBNs could be a powerful tool for the or 1) suggested that information retained by these when simulation of gene network dynamics. Particularly, we are binarized is meaningful to the extent that it is remains in a interested in the subject of intervention. This refers to the continuous domain [2].
  • Online Spectral Clustering on Network Streams Yi

    Online Spectral Clustering on Network Streams Yi

    Online Spectral Clustering on Network Streams By Yi Jia Submitted to the graduate degree program in Electrical Engineering and Computer Science and the Graduate Faculty of the University of Kansas in partial fulfillment of the requirements for the degree of Doctor of Philosophy Jun Huan, Chairperson Swapan Chakrabarti Committee members Jerzy Grzymala-Busse Bo Luo Alfred Tat-Kei Ho Date defended: The Dissertation Committee for Yi Jia certifies that this is the approved version of the following dissertation : Online Spectral Clustering on Network Streams Jun Huan, Chairperson Date approved: ii Abstract Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirement cer- tainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the paralleliza- tion of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be pre- determined.
  • Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence

    Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence

    Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology Volume 2007, Article ID 32454, 15 pages doi:10.1155/2007/32454 Research Article Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence Stephen Marshall,1 Le Yu,1 Yufei Xiao,2 and Edward R. Dougherty2, 3, 4 1 Department of Electronic and Electrical Engineering, Faculty of Engineering, University of Strathclyde, Glasgow, G1 1XW, UK 2 Department of Electrical and Computer Engineering, Texas A&M University, College Station, TX 77843-3128, USA 3 Computational Biology Division, Translational Genomics Research Institute, Phoenix, AZ 85004, USA 4 Department of Pathology, University of Texas M. D. Anderson Cancer Center, Houston, TX 77030, USA Received 10 July 2006; Revised 29 January 2007; Accepted 26 February 2007 Recommended by Tatsuya Akutsu The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of proba- bilistic Boolean networks (PBNs) from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be de- termined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all) of the zeros.
  • Boolean Network Control with Ideals

    Boolean Network Control with Ideals

    Portland State University PDXScholar Mathematics and Statistics Faculty Fariborz Maseeh Department of Mathematics Publications and Presentations and Statistics 1-2021 Boolean Network Control with Ideals Ian H. Dinwoodie Portland State University, [email protected] Follow this and additional works at: https://pdxscholar.library.pdx.edu/mth_fac Part of the Physical Sciences and Mathematics Commons Let us know how access to this document benefits ou.y Citation Details Dinwoodie, Ian H., "Boolean Network Control with Ideals" (2021). Mathematics and Statistics Faculty Publications and Presentations. 302. https://pdxscholar.library.pdx.edu/mth_fac/302 This Working Paper is brought to you for free and open access. It has been accepted for inclusion in Mathematics and Statistics Faculty Publications and Presentations by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Boolean Network Control with Ideals I H Dinwoodie Portland State University January 2021 Abstract A method is given for finding controls to transition an initial state x0 to a target set in deterministic or stochastic Boolean network control models. The algorithms use multivariate polynomial algebra. Examples illustrate the application. 1 Introduction A Boolean network is a dynamical system on d nodes (or coordinates) with binary node values, and with transition map F : {0, 1}d → {0, 1}d. The c coordinate maps F = (f1,...,fd) may use binary parameters u ∈ {0, 1} that can be adjusted or controlled at each step, so the image can be writ- ten F (x, u) and F takes {0, 1}d+c → {0, 1}d, usually written in logical nota- tion.
  • Random Boolean Networks As a Toy Model for the Brain

    Random Boolean Networks As a Toy Model for the Brain

    UNIVERSITY OF GENEVA SCIENCE FACULTY VRIJE UNIVERSITEIT OF AMSTERDAM PHYSICS SECTION Random Boolean Networks as a toy model for the brain MASTER THESIS presented at the science faculty of the University of Geneva for obtaining the Master in Theoretical Physics by Chlo´eB´eguin Supervisor (VU): Pr. Greg J Stephens Co-Supervisor (UNIGE): Pr. J´er^ome Kasparian July 2017 Contents Introduction1 1 Biology, physics and the brain4 1.1 Biological description of the brain................4 1.2 Criticality in the brain......................8 1.2.1 Physics reminder..................... 10 1.2.2 Experimental evidences.................. 15 2 Models of neural networks 20 2.1 Classes of models......................... 21 2.1.1 Spiking models...................... 21 2.1.2 Rate-based models.................... 23 2.1.3 Attractor networks.................... 24 2.1.4 Links between the classes of models........... 25 2.2 Random Boolean Networks.................... 28 2.2.1 General definition..................... 28 2.2.2 Kauffman network.................... 30 2.2.3 Hopfield network..................... 31 2.2.4 Towards a RBN for the brain.............. 32 2.2.5 The model......................... 33 3 Characterisation of RBNs 34 3.1 Attractors............................. 34 3.2 Damage spreading........................ 36 3.3 Canonical specific heat...................... 37 4 Results 40 4.1 One population with Gaussian weights............. 40 4.2 Dale's principle and balance of inhibition - excitation..... 46 4.3 Lognormal distribution of the weights.............. 51 4.4 Discussion............................. 55 i 5 Conclusion 58 Bibliography 60 Acknowledgements 66 A Python Code 67 A.1 Dynamics............................. 67 A.2 Attractor search.......................... 69 A.3 Hamming Distance........................ 73 A.4 Canonical specific heat.....................
  • A Random Boolean Network Model and Deterministic Chaos

    A Random Boolean Network Model and Deterministic Chaos

    A Random Boolean Network Model and Deterministic Chaos Mihaela T. Matache* Jack Heidel Department of Mathematics University of Nebraska at Omaha Omaha, NE 68182-0243, USA *[email protected] Abstract This paper considers a simple Boolean network with N nodes, each node’s state at time t being determined by a certain number of parent nodes, which may vary from one node to another. This is an extension of a model studied by Andrecut and Ali ( [5]) who consider the same number of parents for all nodes. We make use of the same Boolean rule as the authors of [5], provide a generalization of the formula for the probability of finding a node in state 1 at a time t and use simulation methods to generate consecutive states of the network for both the real system and the model. The results match well. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed point analysis. We show that the route to chaos is due to a cascade of period- doubling bifurcations which turn into reversed (period - halving) bifurcations for certain combinations of parameter values. 1. Introduction In recent years various studies ( [5], [16], [19], [20], [21], [22], [30], [31]) have shown that a large class of biological networks and cellular automata can be modelled as Boolean networks. These models, besides being easy to understand, are relatively easy to handle. The interest for Boolean networks and their appli- cations in biology and automata networks has actually started much earlier ( [8], [13], [14], [15], [25], [29], [32]), with publications such as the one of Kauffman ( [25]) whose work on the self-organization and adap- tation in complex systems has inspired many other research endeavors.
  • Reward-Driven Training of Random Boolean Network Reservoirs for Model-Free Environments

    Reward-Driven Training of Random Boolean Network Reservoirs for Model-Free Environments

    Portland State University PDXScholar Dissertations and Theses Dissertations and Theses Winter 3-27-2013 Reward-driven Training of Random Boolean Network Reservoirs for Model-Free Environments Padmashri Gargesa Portland State University Follow this and additional works at: https://pdxscholar.library.pdx.edu/open_access_etds Part of the Dynamics and Dynamical Systems Commons, and the Electrical and Computer Engineering Commons Let us know how access to this document benefits ou.y Recommended Citation Gargesa, Padmashri, "Reward-driven Training of Random Boolean Network Reservoirs for Model-Free Environments" (2013). Dissertations and Theses. Paper 669. https://doi.org/10.15760/etd.669 This Thesis is brought to you for free and open access. It has been accepted for inclusion in Dissertations and Theses by an authorized administrator of PDXScholar. Please contact us if we can make this document more accessible: [email protected]. Reward-driven Training of Random Boolean Network Reservoirs for Model-Free Environments by Padmashri Gargesa A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical and Computer Engineering Thesis Committee: Christof Teuscher, Chair Richard P. Tymerski Marek A. Perkowski Portland State University 2013 Abstract Reservoir Computing (RC) is an emerging machine learning paradigm where a fixed kernel, built from a randomly connected "reservoir" with sufficiently rich dynamics, is capable of expanding the problem space in a non-linear fashion to a higher dimensional feature space. These features can then be interpreted by a linear readout layer that is trained by a gradient descent method. In comparison to traditional neural networks, only the output layer needs to be trained, which leads to a significant computational advantage.
  • Solving Satisfiability Problem by Quantum Annealing

    Solving Satisfiability Problem by Quantum Annealing

    UNIVERSITY OF CALIFORNIA Los Angeles Towards Quantum Computing: Solving Satisfiability Problem by Quantum Annealing A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Electrical Engineering by Juexiao Su 2018 c Copyright by Juexiao Su 2018 ABSTRACT OF THE DISSERTATION Towards Quantum Computing: Solving Satisfiability Problem by Quantum Annealing by Juexiao Su Doctor of Philosophy in Electrical Engineering University of California, Los Angeles, 2018 Professor Lei He, Chair To date, conventional computers have never been able to efficiently handle certain tasks, where the number of computation steps is likely to blow up as the problem size increases. As an emerging technology and new computing paradigm, quantum computing has a great potential to tackle those hard tasks efficiently. Among all the existing quantum computation models, quantum annealing has drawn significant attention in recent years due to the real- ization of the commercialized quantum annealer, sparking research interests in developing applications to solve problems that are intractable for classical computers. However, designing and implementing algorithms that manage to harness the enormous computation power from quantum annealer remains a challenging task. Generally, it requires mapping of the given optimization problem into quadratic unconstrained binary optimiza- tion(QUBO) problem and embedding the subsequent QUBO onto the physical architecture of quantum annealer. Additionally, practical quantum annealers are susceptible to errors leading to low probability of the correct solution. In this study, we focus on solving Boolean satisfiability (SAT) problem using quantum annealer while addressing practical limitations. We have proposed a mapping technique that maps SAT problem to QUBO, and we have further devised a tool flow that embeds the QUBO onto the architecture of a quantum annealing device.
  • A Multi-Agent System for Environmental Monitoring Using Boolean Networks and Reinforcement Learning

    A Multi-Agent System for Environmental Monitoring Using Boolean Networks and Reinforcement Learning

    Journal of Cyber Security DOI:10.32604/jcs.2020.010086 Article A Multi-Agent System for Environmental Monitoring Using Boolean Networks and Reinforcement Learning Hanzhong Zheng1 and Dejie Shi2,* 1Department of Computer Science, The University of Pittsburgh, Pittsburgh, PA 15213, USA 2School of Computer and Information Engineering, Hunan University of Technology and Business, Changsha, 410205, China *Corresponding Author: Dejie Shi. Email: [email protected] Received: 10 February 2020; Accepted: 28 June 2020 Abstract: Distributed wireless sensor networks have been shown to be effective for environmental monitoring tasks, in which multiple sensors are deployed in a wide range of the environments to collect information or monitor a particular event, Wireless sensor networks, consisting of a large number of interacting sensors, have been successful in a variety of applications where they are able to share information using different transmission protocols through the communication network. However, the irregular and dynamic environment requires traditional wireless sensor networks to have frequent communications to exchange the most recent information, which can easily generate high communication cost through the collaborative data collection and data transmission. High frequency communication also has high probability of failure because of long distance data transmission. In this paper, we developed a novel approach to multi-sensor environment monitoring network using the idea of distributed system. Its communication network can overcome the difficulties of high communication cost and Single Point of Failure (SPOF) through the decentralized approach, which performs in-network computation. Our approach makes use of Boolean networks that allows for a non-complex method of corroboration and retains meaningful information regarding the dynamics of the communication network.
  • List of Glossary Terms

    List of Glossary Terms

    List of Glossary Terms A Ageofaclusterorfuzzyrule 1054 A correlated equilibrium 3064 Agent 58, 76, 105, 1767, 2578, 3004 Amechanism 1837 Agent architecture 105 Anearestneighbor 790 Agent based models 2940 A social choice function 1837 Agent (or software agent) 2999 A stochastic game 3064 Agent-based computational models 2898 Astrategy 3064 Agent-based model 58 Abelian group 2780 Agent-based modeling 1767 Absolute temperature 940 Agent-based modeling (ABM) 39 Absorbing state 1080 Agent-based simulation 18, 88 Abstract game 675 Aggregation 862 Abstract game of network formation with respect to Aggregation operators 122 irreflexive dominance 2044 Aging 2564, 2611 Abstract game of network formation with respect to path Algebra 2925 dominance 2044 Algebraic models 2898 Accuracy 161, 827 Algorithm 2496 Accuracy (rate) 862 Algorithmic complexity of object x 132 Achievable mate 3235 Algorithmic self-assembly of DNA tiles 1894 Action profile 3023 Allowable set of partners 3234 Action set 3023 Almost equicontinuous CA 914, 3212 Action type 2656 Alphabet of a cellular automaton 1 Activation function 813 ˛-Level set and support 1240 Activator 622 Alternating independent-2-paths 2953 Active membranes 1851 Alternating k-stars 2953 Actors 2029 Alternating k-triangles 2953 Adaptation 39 Amorphous computer 147 Adaptive system 1619 Analog 3187 Additive cellular automata 1 Analog circuit 3260 Additively separable preferences 3235 Ancilla qubits 2478 Adiabatic switching 1998 Anisotropic elements 754 Adjacency matrix 1746, 3114 Annealed law 2564 Adjacent 2864,
  • Introduction to Natural Computation Lecture 18 Random Boolean

    Introduction to Natural Computation Lecture 18 Random Boolean

    Introduction to Natural Computation Lecture 18 Random Boolean Networks Alberto Moraglio 1 / 25 Random Boolean Networks Extension of Cellular Automata. Introduced by Stuart Kauffman (1969) as model for genetic regulatory networks. Uncover fundamental principles of living systems. Hypothesis: living organisms can be constructed from random elements. Simplification: Boolean states for all nodes in the network. 2 / 25 Definition Random Boolean Network (RBN) A random Boolean network consists of N nodes, each with a state 0 or 1 K edges for each node to K different randomly selected nodes a lookup table for each node that determines the next state, according to states of its K neighbours. Last few lectures: fixed graph, random process This time: random graph, deterministic process Note: randomness used to create network, afterwards network remains fixed! 3 / 25 Relation to Cellular Automata http://www.metafysica.nl/boolean.html 4 / 25 Lookup Tables Recall rules from Cellular Automata: RBN: each node has its own random lookup table: inputs at time t state at time t + 1 000 1 001 0 010 0 011 1 100 1 101 0 110 1 111 1 5 / 25 Example of a Simple RBN Gershenson C. Introduction to Random Boolean Networks. ArXiv Nonlinear Sciences e-prints. 2004; 6 / 25 States State space has size 2N . After at most 2N + 1 steps a state will be repeated. 7 / 25 States State space has size 2N . After at most 2N + 1 steps a state will be repeated. Attractors As the system is deterministic, it will get stuck in an attractor. one state → point attractor / steady state two or more states → cycle attractor / state cycle The set of states that flow towards an attractor is called attractor basin.
  • UCLA Samueli Engineering Annoucemente 2019-20

    UCLA Samueli Engineering Annoucemente 2019-20

    ANNOUNCEMENT 2019-20 HENRY SAMUELI SCHOOL OF ENGINEERING AND APPLIED SCIENCE UNIVERSITY OF CALIFORNIA, LOS ANGELES OCTOBER 1, 2019 Contents A Message from the Dean . .3 Exceptional Student Admissions Program . 16 Henry Samueli School of Engineering and Applied Science. 4 Official Publications . 16 Grades . 16 Officers of Administration . 4 Nondiscrimination . 16 The Campus . 4 Harassment . 17 The School . 4 Undergraduate Programs . 19 Endowed Chairs . 4 Admission . 19 The Engineering Profession . 5 Requirements for B.S. Degrees . 22 Calendars. 8 Policies and Regulations . 24 General Information . 9 Honors. 25 Facilities and Services . 9 Graduate Programs . 26 Library Facilities . 9 Master of Science Degrees. 26 Services . 9 Continuing Education . 9 Admission . 27 Career Services . 10 Departments and Programs of the School. 28 Health Services . 10 Bioengineering. 28 Services for Students with Disabilities. 10 Chemical and Biomolecular Engineering. 40 International Student Services . 10 Civil and Environmental Engineering . 50 Fees and Financial Support. 11 Computer Science . 62 Fees and Expenses . 11 Living Accommodations . 11 Electrical and Computer Engineering . 83 Financial Aid . 11 Materials Science and Engineering. 101 Special Programs, Activities, and Awards . 13 Mechanical and Aerospace Engineering . 109 Center for Excellence in Engineering and Diversity (CEED) . 13 Master of Science in Engineering Online Programs . 125 Student Organizations. 15 Schoolwide Programs and Courses. 127 Women in Engineering . 15 Externally Funded Research