Modelling Techniques for Biomolecular Networks
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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 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
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
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
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 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
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
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. -
Conjunctively Polynomial–Like Boolean Functions and the Maximal Closed Classes
Annales Univ. Sci. Budapest., Sect. Comp. 32 (2010) 49-61 CONJUNCTIVELY POLYNOMIAL{LIKE BOOLEAN FUNCTIONS AND THE MAXIMAL CLOSED CLASSES J. Gonda (Budapest, Hungary) Abstract. In [7] it was introduced the notion of the conjunctively polynomial like Boolean functions. In this article it is investigated how these functions are related to the maximal closed classes of the Boolean functions and it is pointed out that there are bases of the Boolean functions containing only conjunctively polynomial-like Boolean functions. In this article disjunction and logical sum, conjunction and logical product, exclusive or and modulo two sum, as well as complementation and negation are used in the same sense and they are denoted respectively by +; ¢ (or simply without any operation sign), © and ¹. The elements of the ¯eld with two elements and the elements of the Boolean algebra with two elements are denoted by the same signs, namely by 0 and 1; N denotes the non-negative integers, and N+ the positive ones. 1. Introduction Logical functions and especially the two-valued ones have important roles in our everyday life, so it is easy to understand why they are widely investigated. A scope of investigations is the representations of these functions and the transforms from one representation to another ([3], [4], [5], [8]). Another area of the examinations is the search of special classes of the set of the functions. Post determined the closed classes of the switching functions [9], but there are a lot of another classes of the Boolean functions invariant with respect to some Mathematics Subject Classi¯cation: 06E30, 94C10, 15A18 50 J. -
Composition of Post Classes and Normal Forms of Boolean Functions Miguel Couceiroa,1, Stephan Foldesb, Erkko Lehtonenb,∗
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Discrete Mathematics 306 (2006) 3223–3243 www.elsevier.com/locate/disc Composition of Post classes and normal forms of Boolean functions Miguel Couceiroa,1, Stephan Foldesb, Erkko Lehtonenb,∗ aDepartment of Mathematics, Statistics and Philosophy, University of Tampere, FI-33014 Tampereen yliopisto, Finland bInstitute of Mathematics, Tampere University of Technology, P.O. Box 553, FI-33101 Tampere, Finland Received 23 March 2005; received in revised form 12 May 2006; accepted 25 June 2006 Available online 6 September 2006 Abstract The class composition C◦K of Boolean clones, being the set of composite functions f(g1,...,gn) with f ∈ C, g1,...,gn ∈ K, is investigated. This composition C ◦ K is either the join C ∨ K in the Post Lattice or it is not a clone, and all pairs of clones C, K are classified accordingly. Factorizations of the clone of all Boolean functions as a composition of minimal clones are described and seen to correspond to normal form representations of Boolean functions. The median normal form, arising from the factorization of with the clone SM of self-dual monotone functions as the leftmost composition factor, is compared in terms of complexity with the well-known DNF, CNF, and Zhegalkin (Reed–Muller) polynomial representations, and it is shown to provide a more efficient normal form representation. © 2006 Elsevier B.V. All rights reserved. MSC: 06E30; 08A70 Keywords: Function class composition; Clones; Boolean functions; Post classes; Class factorization; Normal forms; DNF; CNF; Zhegalkin polynomial; Reed–Muller polynomial; Formulas; Efficient representations; Complexity; Median; Ternary majority 1. -
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 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,