Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games
Kant, Gijs; van de Pol, Jan Cornelis; Wijs, A.J.; Bošnački, D.; Edelkamp, S.
Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then
Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games
Directory of Open Access Journals (Sweden)
Gijs Kant
2012-10-01
Full Text Available Parameterised Boolean Equation Systems (PBESs are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal mu-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG, a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.
Boolean reasoning the logic of boolean equations
Brown, Frank Markham
2012-01-01
A systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results. Brown begins with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras. Two concluding chapters deal with applications. 1990 edition.
An Extension of Proof Graphs for Disjunctive Parameterised Boolean Equation Systems
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Yutaro Nagae
2017-01-01
Full Text Available A parameterised Boolean equation system (PBES is a set of equations that defines sets as the least and/or greatest fixed-points that satisfy the equations. This system is regarded as a declarative program defining functions that take a datum and returns a Boolean value. The membership problem of PBESs is a problem to decide whether a given element is in the defined set or not, which corresponds to an execution of the program. This paper introduces reduced proof graphs, and studies a technique to solve the membership problem of PBESs, which is undecidable in general, by transforming it into a reduced proof graph. A vertex X(v in a proof graph represents that the data v is in the set X, if the graph satisfies conditions induced from a given PBES. Proof graphs are, however, infinite in general. Thus we introduce vertices each of which stands for a set of vertices of the original ones, which possibly results in a finite graph. For a subclass of disjunctive PBESs, we clarify some conditions which reduced proof graphs should satisfy. We also show some examples having no finite proof graph except for reduced one. We further propose a reduced dependency space, which contains reduced proof graphs as sub-graphs if a proof graph exists. We provide a procedure to construct finite reduced dependency spaces, and show the soundness and completeness of the procedure.
Boolean Differentiation Equations Applicable in Reconfigurable Computational Medium
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Shidlovskiy Stanislav
2016-01-01
Full Text Available High performance computing environment synthesis with parallel architecture reconstructing throughout the process itself is described. Synthesized computational medium involving Boolean differential equation calculations so as to function in real-time image processing. Automaton imaging was illustrated involving the rearrangement of every processing medium element to calculate the partial differentials of n-th order in respect to Boolean function variables. The method of obtaining setting codes for each element was also described. An example in calculating 2nd -order Boolean derivative to two differentials in respect to Boolean functions, depending on three arguments within the reconstructible computational medium of 8×8 processing elements was given.
Algebraic characteristics and satisfiability threshold of random Boolean equations
Guo, Binghui; Wei, Wei; Sun, Yifan; Zheng, Zhiming
2010-03-01
The satisfiability of a class of random Boolean equations named massive algebraic system septated to linear and nonlinear subproblems is studied in this paper. On one hand, the correlation between the magnetization of generators and the clustering of solutions of the linear subproblem is investigated by analyzing the Gaussian elimination process. On the other hand, the characteristics of maximal elements of solutions of the nonlinear subproblem are studied by introducing the partial order among solutions. Based on the algebraic characteristics of these two subproblems, the upper and lower bounds of satisfiability threshold of massive algebraic system are obtained by unit-clause propagation and leaf-removal process, and coincide as the ratio of nonlinear equations q>0.739 in which analytical values of the satisfiability threshold can be derived. Furthermore, a complete algorithm with heuristic decimation is proposed to observe the approximation of the satisfiability threshold, which performs more efficiently than the classical ones.
Boolean modeling in systems biology: an overview of methodology and applications
International Nuclear Information System (INIS)
Wang, Rui-Sheng; Albert, Réka; Saadatpour, Assieh
2012-01-01
Mathematical modeling of biological processes provides deep insights into complex cellular systems. While quantitative and continuous models such as differential equations have been widely used, their use is obstructed in systems wherein the knowledge of mechanistic details and kinetic parameters is scarce. On the other hand, a wealth of molecular level qualitative data on individual components and interactions can be obtained from the experimental literature and high-throughput technologies, making qualitative approaches such as Boolean network modeling extremely useful. In this paper, we build on our research to provide a methodology overview of Boolean modeling in systems biology, including Boolean dynamic modeling of cellular networks, attractor analysis of Boolean dynamic models, as well as inferring biological regulatory mechanisms from high-throughput data using Boolean models. We finally demonstrate how Boolean models can be applied to perform the structural analysis of cellular networks. This overview aims to acquaint life science researchers with the basic steps of Boolean modeling and its applications in several areas of systems biology. (paper)
Digital clocks: simple Boolean models can quantitatively describe circadian systems.
Akman, Ozgur E; Watterson, Steven; Parton, Andrew; Binns, Nigel; Millar, Andrew J; Ghazal, Peter
2012-09-07
The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day-night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate
Digital clocks: simple Boolean models can quantitatively describe circadian systems
Akman, Ozgur E.; Watterson, Steven; Parton, Andrew; Binns, Nigel; Millar, Andrew J.; Ghazal, Peter
2012-01-01
The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day–night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we
Lavrova, Anastasia I; Postnikov, Eugene B; Zyubin, Andrey Yu; Babak, Svetlana V
2017-04-01
We consider two approaches to modelling the cell metabolism of 6-mercaptopurine, one of the important chemotherapy drugs used for treating acute lymphocytic leukaemia: kinetic ordinary differential equations, and Boolean networks supplied with one controlling node, which takes continual values. We analyse their interplay with respect to taking into account ATP concentration as a key parameter of switching between different pathways. It is shown that the Boolean networks, which allow avoiding the complexity of general kinetic modelling, preserve the possibility of reproducing the principal switching mechanism.
Development of Boolean calculus and its applications. [digital systems design
Tapia, M. A.
1980-01-01
The development of Boolean calculus for its application to developing digital system design methodologies that would reduce system complexity, size, cost, speed, power requirements, etc., is discussed. Synthesis procedures for logic circuits are examined particularly asynchronous circuits using clock triggered flip flops.
Mapping knowledge to boolean dynamic systems in Bateson's epistemology.
Malloy, Thomas E; Jensen, Gary C; Song, Timothy
2005-01-01
Gregory Bateson (1972, 1979) established an epistemology that integrates mind and nature as a necessary unity, a unity in which learning and evolution share fundamental principles and in which criteria for mental process are explicitly specified. E42 is a suite of freely available Java applets that constitute an online research lab for creating and interacting with simulations of the Boolean systems developed by Kauffman (1993) in his study of evolution where he proposed that self-organization and natural selection are co-principles "weaving the tapestry of life." This paper maps Boolean systems, developed in the study of evolution, onto Bateson's epistemology in general and onto his criteria of mental process in particular.
Stötzel, Claudia; Röblitz, Susanna; Siebert, Heike
2015-01-01
In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.
Thakar, Juilee; Albert, Réka
The following sections are included: * Introduction * Boolean Network Concepts and History * Extensions of the Classical Boolean Framework * Boolean Inference Methods and Examples in Biology * Dynamic Boolean Models: Examples in Plant Biology, Developmental Biology and Immunology * Conclusions * References
Caglar, Mehmet Umut; Pal, Ranadip
2011-03-01
Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.
Mechanical system reliability analysis using a combination of graph theory and Boolean function
International Nuclear Information System (INIS)
Tang, J.
2001-01-01
A new method based on graph theory and Boolean function for assessing reliability of mechanical systems is proposed. The procedure for this approach consists of two parts. By using the graph theory, the formula for the reliability of a mechanical system that considers the interrelations of subsystems or components is generated. Use of the Boolean function to examine the failure interactions of two particular elements of the system, followed with demonstrations of how to incorporate such failure dependencies into the analysis of larger systems, a constructive algorithm for quantifying the genuine interconnections between the subsystems or components is provided. The combination of graph theory and Boolean function provides an effective way to evaluate the reliability of a large, complex mechanical system. A numerical example demonstrates that this method an effective approaches in system reliability analysis
Directory of Open Access Journals (Sweden)
Ivana Dragović
2015-01-01
Full Text Available Fuzzy inference systems (FIS enable automated assessment and reasoning in a logically consistent manner akin to the way in which humans reason. However, since no conventional fuzzy set theory is in the Boolean frame, it is proposed that Boolean consistent fuzzy logic should be used in the evaluation of rules. The main distinction of this approach is that it requires the execution of a set of structural transformations before the actual values can be introduced, which can, in certain cases, lead to different results. While a Boolean consistent FIS could be used for establishing the diagnostic criteria for any given disease, in this paper it is applied for determining the likelihood of peritonitis, as the leading complication of peritoneal dialysis (PD. Given that patients could be located far away from healthcare institutions (as peritoneal dialysis is a form of home dialysis the proposed Boolean consistent FIS would enable patients to easily estimate the likelihood of them having peritonitis (where a high likelihood would suggest that prompt treatment is indicated, when medical experts are not close at hand.
CIRCUIT IMPLEMENTATION OF VHDL-DESCRIPTIONS OF SYSTEMS OF PARTIAL BOOLEAN FUNCTIONS
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P. N. Bibilo
2016-01-01
Full Text Available Method for description of incompletely specified (partial Boolean functions in VHDL is proposed. Examples of synthesized VHDL models of partial Boolean functions are presented; and the results of experiments on circuit implementation of VHDL descriptions of systems of partial functions. The realizability of original partial functions in logical circuits was verified by formal verification. The results of the experiments show that the preliminary minimization in DNF class and in the class of BDD representations for pseudo-random systems of completely specified functions does not improve practically (and in the case of BDD sometimes worsens the results of the subsequent synthesis in the basis of FPGA unlike the significant efficiency of these procedures for the synthesis of benchmark circuits taken from the practice of the design.
Goodstein, R L
2007-01-01
This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
Development of Boolean calculus and its application
Tapia, M. A.
1979-01-01
Formal procedures for synthesis of asynchronous sequential system using commercially available edge-sensitive flip-flops are developed. Boolean differential is defined. The exact number of compatible integrals of a Boolean differential were calculated.
Cryptographic Boolean functions and applications
Cusick, Thomas W
2009-01-01
Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research.-Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions -Provides engineers and scient...
Geometric Operators on Boolean Functions
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall; Falster, Peter
In truth-functional propositional logic, any propositional formula represents a Boolean function (according to some valuation of the formula). We describe operators based on Decartes' concept of constructing coordinate systems, for translation of a propositional formula to the image of a Boolean...... function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...
Reliable dynamics in Boolean and continuous networks
International Nuclear Information System (INIS)
Ackermann, Eva; Drossel, Barbara; Peixoto, Tiago P
2012-01-01
We investigate the dynamical behavior of a model of robust gene regulatory networks which possess ‘entirely reliable’ trajectories. In a Boolean representation, these trajectories are characterized by being insensitive to the order in which the nodes are updated, i.e. they always go through the same sequence of states. The Boolean model for gene activity is compared with a continuous description in terms of differential equations for the concentrations of mRNA and proteins. We found that entirely reliable Boolean trajectories can be reproduced perfectly in the continuous model when realistic Hill coefficients are used. We investigate to what extent this high correspondence between Boolean and continuous trajectories depends on the extent of reliability of the Boolean trajectories, and we identify simple criteria that enable the faithful reproduction of the Boolean dynamics in the continuous description. (paper)
Marmarelis, Vasilis Z; Zanos, Theodoros P; Berger, Theodore W
2009-08-01
This paper presents a new modeling approach for neural systems with point-process (spike) inputs and outputs that utilizes Boolean operators (i.e. modulo 2 multiplication and addition that correspond to the logical AND and OR operations respectively, as well as the AND_NOT logical operation representing inhibitory effects). The form of the employed mathematical models is akin to a "Boolean-Volterra" model that contains the product terms of all relevant input lags in a hierarchical order, where terms of order higher than first represent nonlinear interactions among the various lagged values of each input point-process or among lagged values of various inputs (if multiple inputs exist) as they reflect on the output. The coefficients of this Boolean-Volterra model are also binary variables that indicate the presence or absence of the respective term in each specific model/system. Simulations are used to explore the properties of such models and the feasibility of their accurate estimation from short data-records in the presence of noise (i.e. spurious spikes). The results demonstrate the feasibility of obtaining reliable estimates of such models, with excitatory and inhibitory terms, in the presence of considerable noise (spurious spikes) in the outputs and/or the inputs in a computationally efficient manner. A pilot application of this approach to an actual neural system is presented in the companion paper (Part II).
SETS, Boolean Manipulation for Network Analysis and Fault Tree Analysis
International Nuclear Information System (INIS)
Worrell, R.B.
1985-01-01
Description of problem or function - SETS is used for symbolic manipulation of set (or Boolean) equations, particularly the reduction of set equations by the application of set identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze non-coherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. 4. Method of solution - The SETS program is used to read, interpret, and execute the statements of a SETS user program which is an algorithm that specifies the particular manipulations to be performed and the order in which they are to occur. 5. Restrictions on the complexity of the problem - Any properly formed set equation involving the set operations of union, intersection, and complement is acceptable for processing by the SETS program. Restrictions on the size of a set equation that can be processed are not absolute but rather are related to the number of terms in the disjunctive normal form of the equation, the number of literals in the equation, etc. Nevertheless, set equations involving thousands and even hundreds of thousands of terms can be processed successfully
Coded diffraction system in X-ray crystallography using a boolean phase coded aperture approximation
Pinilla, Samuel; Poveda, Juan; Arguello, Henry
2018-03-01
Phase retrieval is a problem present in many applications such as optics, astronomical imaging, computational biology and X-ray crystallography. Recent work has shown that the phase can be better recovered when the acquisition architecture includes a coded aperture, which modulates the signal before diffraction, such that the underlying signal is recovered from coded diffraction patterns. Moreover, this type of modulation effect, before the diffraction operation, can be obtained using a phase coded aperture, just after the sample under study. However, a practical implementation of a phase coded aperture in an X-ray application is not feasible, because it is computationally modeled as a matrix with complex entries which requires changing the phase of the diffracted beams. In fact, changing the phase implies finding a material that allows to deviate the direction of an X-ray beam, which can considerably increase the implementation costs. Hence, this paper describes a low cost coded X-ray diffraction system based on block-unblock coded apertures that enables phase reconstruction. The proposed system approximates the phase coded aperture with a block-unblock coded aperture by using the detour-phase method. Moreover, the SAXS/WAXS X-ray crystallography software was used to simulate the diffraction patterns of a real crystal structure called Rhombic Dodecahedron. Additionally, several simulations were carried out to analyze the performance of block-unblock approximations in recovering the phase, using the simulated diffraction patterns. Furthermore, the quality of the reconstructions was measured in terms of the Peak Signal to Noise Ratio (PSNR). Results show that the performance of the block-unblock phase coded apertures approximation decreases at most 12.5% compared with the phase coded apertures. Moreover, the quality of the reconstructions using the boolean approximations is up to 2.5 dB of PSNR less with respect to the phase coded aperture reconstructions.
Free Boolean Topological Groups
Directory of Open Access Journals (Sweden)
Ol’ga Sipacheva
2015-11-01
Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.
Reverse engineering Boolean networks: from Bernoulli mixture models to rule based systems.
Directory of Open Access Journals (Sweden)
Mehreen Saeed
Full Text Available A Boolean network is a graphical model for representing and analyzing the behavior of gene regulatory networks (GRN. In this context, the accurate and efficient reconstruction of a Boolean network is essential for understanding the gene regulation mechanism and the complex relations that exist therein. In this paper we introduce an elegant and efficient algorithm for the reverse engineering of Boolean networks from a time series of multivariate binary data corresponding to gene expression data. We call our method ReBMM, i.e., reverse engineering based on Bernoulli mixture models. The time complexity of most of the existing reverse engineering techniques is quite high and depends upon the indegree of a node in the network. Due to the high complexity of these methods, they can only be applied to sparsely connected networks of small sizes. ReBMM has a time complexity factor, which is independent of the indegree of a node and is quadratic in the number of nodes in the network, a big improvement over other techniques and yet there is little or no compromise in accuracy. We have tested ReBMM on a number of artificial datasets along with simulated data derived from a plant signaling network. We also used this method to reconstruct a network from real experimental observations of microarray data of the yeast cell cycle. Our method provides a natural framework for generating rules from a probabilistic model. It is simple, intuitive and illustrates excellent empirical results.
Solomon, Alan D
2012-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Boolean Algebra includes set theory, sentential calculus, fundamental ideas of Boolean algebras, lattices, rings and Boolean algebras, the structure of a Boolean algebra, and Boolean
Tucker, Jerry H.; Tapia, Moiez A.; Bennett, A. Wayne
1988-01-01
The concept of Boolean integration is developed, and different Boolean integral operators are introduced. Given the changes in a desired function in terms of the changes in its arguments, the ways of 'integrating' (i.e. realizing) such a function, if it exists, are presented. The necessary and sufficient conditions for integrating, in different senses, the expression specifying the changes are obtained. Boolean calculus has applications in the design of logic circuits and in fault analysis.
Properties of Boolean orthoposets
Tkadlec, Josef
1993-10-01
A Boolean orthoposet is the orthoposet P fulfilling the following condition: If a, b ∈ P and a ∧ b = 0, then a ⊥ b. This condition seems to be a sound generalization of distributivity in orthoposets. Also, the class of (orthomodular) Boolean orthoposets may play an interesting role in quantum logic theory. This class is wide enough and, on the other hand, enjoys some properties of Boolean algebras. In this paper we summarize results on Boolean orthoposets involving distributivity, set representation, properties of the state space, existence of Jauch-Piron states, and results concerning orthocompleteness and completion.
Cordón García, Oscar; Moya Anegón, Félix de; Zarco Fernández, Carmen
2000-01-01
[ES] Although the fuzzy retrieval model constitutes a powerful extension of the boolean one, being able to deal with the imprecision and subjectivity existing in the Information Retrieval process, users are not usually able to express their query requirements in the form of an extended boolean query including weights. To solve this problem, different tools to assist the user in the query formulation have been proposed. In this paper, the genetic algorithm-programming technique is considered t...
The spruce budworm and forest: a qualitative comparison of ODE and Boolean models
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Raina Robeva
2016-01-01
Full Text Available Boolean and polynomial models of biological systems have emerged recently as viable companions to differential equations models. It is not immediately clear however whether such models are capable of capturing the multi-stable behaviour of certain biological systems: this behaviour is often sensitive to changes in the values of the model parameters, while Boolean and polynomial models are qualitative in nature. In the past few years, Boolean models of gene regulatory systems have been shown to capture multi-stability at the molecular level, confirming that such models can be used to obtain information about the system’s qualitative dynamics when precise information regarding its parameters may not be available. In this paper, we examine Boolean approximations of a classical ODE model of budworm outbreaks in a forest and show that these models exhibit a qualitative behaviour consistent with that derived from the ODE models. In particular, we demonstrate that these models can capture the bistable nature of insect population outbreaks, thus showing that Boolean models can be successfully utilized beyond the molecular level.
International Nuclear Information System (INIS)
Piriou, Pierre-Yves; Faure, Jean-Marc; Lesage, Jean-Jacques
2017-01-01
This paper presents a modeling framework that permits to describe in an integrated manner the structure of the critical system to analyze, by using an enriched fault tree, the dysfunctional behavior of its components, by means of Markov processes, and the reconfiguration strategies that have been planned to ensure safety and availability, with Moore machines. This framework has been developed from BDMP (Boolean logic Driven Markov Processes), a previous framework for dynamic repairable systems. First, the contribution is motivated by pinpointing the limitations of BDMP to model complex reconfiguration strategies and the failures of the control of these strategies. The syntax and semantics of GBDMP (Generalized Boolean logic Driven Markov Processes) are then formally defined; in particular, an algorithm to analyze the dynamic behavior of a GBDMP model is developed. The modeling capabilities of this framework are illustrated on three representative examples. Last, qualitative and quantitative analysis of GDBMP models highlight the benefits of the approach.
Optimal stabilization of Boolean networks through collective influence
Wang, Jiannan; Pei, Sen; Wei, Wei; Feng, Xiangnan; Zheng, Zhiming
2018-03-01
Boolean networks have attracted much attention due to their wide applications in describing dynamics of biological systems. During past decades, much effort has been invested in unveiling how network structure and update rules affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. For locally treelike Boolean networks with biased truth tables, we propose a greedy algorithm to identify influential nodes in Boolean networks by minimizing the largest eigenvalue of a modified nonbacktracking matrix. We test the performance of the proposed collective influence algorithm on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes compared with other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying virulence genes that lead to serious diseases.
Algebraic partial Boolean algebras
Smith, D
2003-01-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial...
Algebraic partial Boolean algebras
Smith, Derek
2003-04-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space Script H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E8.
Algebraic partial Boolean algebras
Energy Technology Data Exchange (ETDEWEB)
Smith, Derek [Math Department, Lafayette College, Easton, PA 18042 (United States)
2003-04-04
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A{sub 5} sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E{sub 8}.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Testing Properties of Boolean Functions
2012-01-01
The JUNTATEST algorithm is based on two simple but powerful ideas. The first idea, initially presented by Fischer et al. [52], is that there is a very...Computer and System Sciences, 61(3):428 – 456, 2000. 12 [75] Subhash Khot. On the power of unique 2-prover 1-round games. In Proc. 34th ACM Symposium on...Sharpness of KKL on Schreier graphs, 2009. Manuscript. 6.4 [84] Michal Parnas, Dana Ron, and Alex Samorodnitsky. Testing basic boolean formu- lae . SIAM J
Forced synchronization of autonomous dynamical Boolean networks
International Nuclear Information System (INIS)
Rivera-Durón, R. R.; Campos-Cantón, E.; Campos-Cantón, I.; Gauthier, Daniel J.
2015-01-01
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics
Forced synchronization of autonomous dynamical Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Rivera-Durón, R. R., E-mail: roberto.rivera@ipicyt.edu.mx; Campos-Cantón, E., E-mail: eric.campos@ipicyt.edu.mx [División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A. C., Camino a la Presa San José 2055, Col. Lomas 4 Sección, C.P. 78216, San Luis Potosí, S.L.P. (Mexico); Campos-Cantón, I. [Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, C.P. 78000, San Luis Potosí, S.L.P. (Mexico); Gauthier, Daniel J. [Department of Physics and Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708 (United States)
2015-08-15
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.
An adaptable Boolean net trainable to control a computing robot
International Nuclear Information System (INIS)
Lauria, F. E.; Prevete, R.; Milo, M.; Visco, S.
1999-01-01
We discuss a method to implement in a Boolean neural network a Hebbian rule so to obtain an adaptable universal control system. We start by presenting both the Boolean neural net and the Hebbian rule we have considered. Then we discuss, first, the problems arising when the latter is naively implemented in a Boolean neural net, second, the method consenting us to overcome them and the ensuing adaptable Boolean neural net paradigm. Next, we present the adaptable Boolean neural net as an intelligent control system, actually controlling a writing robot, and discuss how to train it in the execution of the elementary arithmetic operations on operands represented by numerals with an arbitrary number of digits
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Nonlinear integrodifferential equations as discrete systems
Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.
1999-06-01
We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.
Approximate Reasoning with Fuzzy Booleans
van den Broek, P.M.; Noppen, J.A.R.
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp
Linear integral equations and soliton systems
International Nuclear Information System (INIS)
Quispel, G.R.W.
1983-01-01
A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)
A full bayesian approach for boolean genetic network inference.
Directory of Open Access Journals (Sweden)
Shengtong Han
Full Text Available Boolean networks are a simple but efficient model for describing gene regulatory systems. A number of algorithms have been proposed to infer Boolean networks. However, these methods do not take full consideration of the effects of noise and model uncertainty. In this paper, we propose a full Bayesian approach to infer Boolean genetic networks. Markov chain Monte Carlo algorithms are used to obtain the posterior samples of both the network structure and the related parameters. In addition to regular link addition and removal moves, which can guarantee the irreducibility of the Markov chain for traversing the whole network space, carefully constructed mixture proposals are used to improve the Markov chain Monte Carlo convergence. Both simulations and a real application on cell-cycle data show that our method is more powerful than existing methods for the inference of both the topology and logic relations of the Boolean network from observed data.
Logical Attractors: a Boolean Approach to the Dynamics of Psychosis
Kupper, Z.; Hoffmann, H.
A Boolean modeling approach to attractors in the dynamics of psychosis is presented: Kinetic Logic, originating from R. Thomas, describes systems on an intermediate level between a purely verbal, qualitative description and a description using nonlinear differential equations. With this method we may model impact, feedback and temporal evolution, as well as analyze the resulting attractors. In our previous research the method has been applied to general and more specific questions in the dynamics of psychotic disorders. In this paper a model is introduced that describes different dynamical patterns of chronic psychosis in the context of vocational rehabilitation. It also shows to be useful in formulating and exploring possible treatment strategies. Finally, some of the limitations and benefits of Kinetic Logic as a modeling tool for psychology and psychiatry are discussed.
Synchronization in an array of coupled Boolean networks
International Nuclear Information System (INIS)
Li, Rui; Chu, Tianguang
2012-01-01
This Letter presents an analytical study of synchronization in an array of coupled deterministic Boolean networks. A necessary and sufficient criterion for synchronization is established based on algebraic representations of logical dynamics in terms of the semi-tensor product of matrices. Some basic properties of a synchronized array of Boolean networks are then derived for the existence of transient states and the upper bound of the number of fixed points. Particularly, an interesting consequence indicates that a “large” mismatch between two coupled Boolean networks in the array may result in loss of synchrony in the entire system. Examples, including the Boolean model of coupled oscillations in the cell cycle, are given to illustrate the present results. -- Highlights: ► We analytically study synchronization in an array of coupled Boolean networks. ► The study is based on the algebraic representations of logical dynamics. ► A necessary and sufficient algebraic criterion for synchronization is established. ► It reveals some basic properties of a synchronized array of Boolean networks. ► A large mismatch between two coupled networks may result in the loss of synchrony.
A mixed system of equations of elasticity
Shul'ga, M. O.
2010-09-01
A mixed system of six equations of elasticity is represented as a Hamiltonian (canonical) operator system in one of the spatial coordinates. It is shown that this system is the Euler equations for the Hellinger-Reissner principle with an appropriately modified integrand. One more functional with an operator integrand from which the canonical operator system can be derived is set up
On the Computation of Comprehensive Boolean Gröbner Bases
Inoue, Shutaro
We show that a comprehensive Boolean Gröbner basis of an ideal I in a Boolean polynomial ring B (bar A,bar X) with main variables bar X and parameters bar A can be obtained by simply computing a usual Boolean Gröbner basis of I regarding both bar X and bar A as variables with a certain block term order such that bar X ≫ bar A. The result together with a fact that a finite Boolean ring is isomorphic to a direct product of the Galois field mathbb{GF}_2 enables us to compute a comprehensive Boolean Gröbner basis by only computing corresponding Gröbner bases in a polynomial ring over mathbb{GF}_2. Our implementation in a computer algebra system Risa/Asir shows that our method is extremely efficient comparing with existing computation algorithms of comprehensive Boolean Gröbner bases.
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor.
Recent Methodological Advances in Economic Equation Systems.
Theil, Henri; Clements, Kenneth W.
1980-01-01
Examines economic equation systems by describing the simultaneous equation model, its application to the economy as a whole, and a systemwide approach to microeconomics. The systems approach focuses on particular segments of the economy such as consumer spending. (Author/KC)
Lu, Jiao Yang; Zhang, Xin Xing; Huang, Wei Tao; Zhu, Qiu Yan; Ding, Xue Zhi; Xia, Li Qiu; Luo, Hong Qun; Li, Nian Bing
2017-09-19
The most serious and yet unsolved problems of molecular logic computing consist in how to connect molecular events in complex systems into a usable device with specific functions and how to selectively control branchy logic processes from the cascading logic systems. This report demonstrates that a Boolean logic tree is utilized to organize and connect "plug and play" chemical events DNA, nanomaterials, organic dye, biomolecule, and denaturant for developing the dual-signal electrochemical evolution aptasensor system with good resettability for amplification detection of thrombin, controllable and selectable three-state logic computation, and keypad lock security operation. The aptasensor system combines the merits of DNA-functionalized nanoamplification architecture and simple dual-signal electroactive dye brilliant cresyl blue for sensitive and selective detection of thrombin with a wide linear response range of 0.02-100 nM and a detection limit of 1.92 pM. By using these aforementioned chemical events as inputs and the differential pulse voltammetry current changes at different voltages as dual outputs, a resettable three-input biomolecular keypad lock based on sequential logic is established. Moreover, the first example of controllable and selectable three-state molecular logic computation with active-high and active-low logic functions can be implemented and allows the output ports to assume a high impediment or nothing (Z) state in addition to the 0 and 1 logic levels, effectively controlling subsequent branchy logic computation processes. Our approach is helpful in developing the advanced controllable and selectable logic computing and sensing system in large-scale integration circuits for application in biomedical engineering, intelligent sensing, and control.
Boolean-Valued Belief Functions
Czech Academy of Sciences Publication Activity Database
Kramosil, Ivan
2002-01-01
Roč. 31, č. 2 (2002), s. 153-181 ISSN 0308-1079 R&D Projects: GA AV ČR IAA1030803 Institutional research plan: AV0Z1030915 Keywords : Dempster-Schafer theory * Boolean algebra Subject RIV: BA - General Mathematics Impact factor: 0.241, year: 2002
Modular Decomposition of Boolean Functions
J.C. Bioch (Cor)
2002-01-01
textabstractModular decomposition is a thoroughly investigated topic in many areas such as switching theory, reliability theory, game theory and graph theory. Most appli- cations can be formulated in the framework of Boolean functions. In this paper we give a uni_ed treatment of modular
The stability of Boolean network with transmission sensitivity
Wang, Jiannan; Guo, Binghui; Wei, Wei; Mi, Zhilong; Yin, Ziqiao; Zheng, Zhiming
2017-09-01
Boolean network has been widely used in modeling biological systems and one of the key problems is its stability in response to small perturbations. Based on the hypothesis that the states of all nodes are homogenously updated, great progress has been made in previous works. In real biological networks, however, the updates of genes typically show much heterogeneity. To address such conditions, we introduce transmission sensitivity into Boolean network model. By the method of semi-annealed approximation, we illustrate that in a homogenous network, the critical condition of stability has no connection with its transmission sensitivity. As for heterogeneous networks, it reveals that correlations between network topology and transmission sensitivity can have profound effects on the its stability. This result shows a new mechanism that affects the stability of Boolean network, which could be used to control the dynamics in real biological systems.
A comparison of hypertext and Boolean access to biomedical information.
Friedman, C P; Wildemuth, B M; Muriuki, M; Gant, S P; Downs, S M; Twarog, R G; de Bliek, R
1996-01-01
This study explored which of two modes of access to a biomedical database better supported problem solving in bacteriology. Boolean access, which allowed subjects to frame their queries as combinations of keywords, was compared to hypertext access, which allowed subjects to navigate from one database node to another. The accessible biomedical data were identical across systems. Data were collected from 42 first year medical students, each randomized to the Boolean or hypertext system, before and after their bacteriology course. Subjects worked eight clinical case problems, first using only their personal knowledge and, subsequently, with aid from the database. Database retrievals enabled students to answer questions they could not answer based on personal knowledge only. This effect was greater when personal knowledge of bacteriology was lower. The results also suggest that hypertext was superior to Boolean access in helping subjects identify possible infectious agents in these clinical case problems.
Continuous time boolean modeling for biological signaling: application of Gillespie algorithm
Directory of Open Access Journals (Sweden)
Stoll Gautier
2012-08-01
Full Text Available Abstract Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. Background There exist two major types of mathematical modeling approaches: (1 quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2 and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Results Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be
Optimization-Based Approaches to Control of Probabilistic Boolean Networks
Directory of Open Access Journals (Sweden)
Koichi Kobayashi
2017-02-01
Full Text Available Control of gene regulatory networks is one of the fundamental topics in systems biology. In the last decade, control theory of Boolean networks (BNs, which is well known as a model of gene regulatory networks, has been widely studied. In this review paper, our previously proposed methods on optimal control of probabilistic Boolean networks (PBNs are introduced. First, the outline of PBNs is explained. Next, an optimal control method using polynomial optimization is explained. The finite-time optimal control problem is reduced to a polynomial optimization problem. Furthermore, another finite-time optimal control problem, which can be reduced to an integer programming problem, is also explained.
Boolean gates on actin filaments
Energy Technology Data Exchange (ETDEWEB)
Siccardi, Stefano, E-mail: ssiccardi@2ssas.it [The Unconventional Computing Centre, University of the West of England, Bristol (United Kingdom); Tuszynski, Jack A., E-mail: jackt@ualberta.ca [Department of Oncology, University of Alberta, Edmonton, Alberta (Canada); Adamatzky, Andrew, E-mail: andrew.adamatzky@uwe.ac.uk [The Unconventional Computing Centre, University of the West of England, Bristol (United Kingdom)
2016-01-08
Actin is a globular protein which forms long polar filaments in the eukaryotic cytoskeleton. Actin networks play a key role in cell mechanics and cell motility. They have also been implicated in information transmission and processing, memory and learning in neuronal cells. The actin filaments have been shown to support propagation of voltage pulses. Here we apply a coupled nonlinear transmission line model of actin filaments to study interactions between voltage pulses. To represent digital information we assign a logical TRUTH value to the presence of a voltage pulse in a given location of the actin filament, and FALSE to the pulse's absence, so that information flows along the filament with pulse transmission. When two pulses, representing Boolean values of input variables, interact, then they can facilitate or inhibit further propagation of each other. We explore this phenomenon to construct Boolean logical gates and a one-bit half-adder with interacting voltage pulses. We discuss implications of these findings on cellular process and technological applications. - Highlights: • We simulate interaction between voltage pulses using on actin filaments. • We use a coupled nonlinear transmission line model. • We design Boolean logical gates via interactions between the voltage pulses. • We construct one-bit half-adder with interacting voltage pulses.
Particle Systems and Partial Differential Equations I
Gonçalves, Patricia
2014-01-01
This book presents the proceedings of the international conference Particle Systems and Partial Differential Equations I, which took place at the Centre of Mathematics of the University of Minho, Braga, Portugal, from the 5th to the 7th of December, 2012. The purpose of the conference was to bring together world leaders to discuss their topics of expertise and to present some of their latest research developments in those fields. Among the participants were researchers in probability, partial differential equations and kinetics theory. The aim of the meeting was to present to a varied public the subject of interacting particle systems, its motivation from the viewpoint of physics and its relation with partial differential equations or kinetics theory, and to stimulate discussions and possibly new collaborations among researchers with different backgrounds. The book contains lecture notes written by François Golse on the derivation of hydrodynamic equations (compressible and incompressible Euler and Navie...
Dynamic Network-Based Epistasis Analysis: Boolean Examples
Azpeitia, Eugenio; Benítez, Mariana; Padilla-Longoria, Pablo; Espinosa-Soto, Carlos; Alvarez-Buylla, Elena R.
2011-01-01
In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and
Proposed method to construct Boolean functions with maximum possible annihilator immunity
Goyal, Rajni; Panigrahi, Anupama; Bansal, Rohit
2017-07-01
Nonlinearity and Algebraic(annihilator) immunity are two core properties of a Boolean function because optimum values of Annihilator Immunity and nonlinearity are required to resist fast algebraic attack and differential cryptanalysis respectively. For a secure cypher system, Boolean function(S-Boxes) should resist maximum number of attacks. It is possible if a Boolean function has optimal trade-off among its properties. Before constructing Boolean functions, we fixed the criteria of our constructions based on its properties. In present work, our construction is based on annihilator immunity and nonlinearity. While keeping above facts in mind,, we have developed a multi-objective evolutionary approach based on NSGA-II and got the optimum value of annihilator immunity with good bound of nonlinearity. We have constructed balanced Boolean functions having the best trade-off among balancedness, Annihilator immunity and nonlinearity for 5, 6 and 7 variables by the proposed method.
Quantum algorithms for testing Boolean functions
Directory of Open Access Journals (Sweden)
Erika Andersson
2010-06-01
Full Text Available We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the Bernstein-Vazirani quantum algorithm can deterministically identify which one of these Boolean functions we are given using just one single function query. The same quantum algorithm can also be used to learn which input variables other types of Boolean functions depend on, with a success probability that depends on the form of the Boolean function that is tested, but does not depend on the total number of input variables. We also outline a procedure to futher amplify the success probability, based on another quantum algorithm, the Grover search.
Dynamical systems theory for the Gardner equation
Saha, Aparna; Talukdar, B.; Chatterjee, Supriya
2014-02-01
The Gardner equation ut+auux+bu2ux+μuxxx=0 is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation when the effects of higher-order nonlinearity become significant. Using the so-called traveling wave ansatz u (x,t)=φ(ξ), ξ =x-vt (where v is the velocity of the wave) we convert the (1+1)-dimensional partial differential equation to a second-order ordinary differential equation in ϕ with an arbitrary constant and treat the latter equation by the methods of the dynamical systems theory. With some special attention on the equilibrium points of the equation, we derive an analytical constraint for admissible values of the parameters a, b, and μ. From the Hamiltonian form of the system we confirm that, in addition to the usual bright soliton solution, the equation can be used to generate three different varieties of internal waves of which one is a dark soliton recently observed in water [A. Chabchoub et al., Phys. Rev. Lett. 110, 124101 (2013), 10.1103/PhysRevLett.110.124101].
Version Spaces and Generalized Monotone Boolean Functions
J.C. Bioch (Cor); T. Ibaraki
2002-01-01
textabstractWe consider generalized monotone functions f: X --> {0,1} defined for an arbitrary binary relation <= on X by the property x <= y implies f(x) <= f(y). These include the standard monotone (or positive) Boolean functions, regular Boolean functions and other interesting functions as
Boolean gates on actin filaments
Siccardi, Stefano; Tuszynski, Jack A.; Adamatzky, Andrew
2016-01-01
Actin is a globular protein which forms long polar filaments in the eukaryotic cytoskeleton. Actin networks play a key role in cell mechanics and cell motility. They have also been implicated in information transmission and processing, memory and learning in neuronal cells. The actin filaments have been shown to support propagation of voltage pulses. Here we apply a coupled nonlinear transmission line model of actin filaments to study interactions between voltage pulses. To represent digital information we assign a logical TRUTH value to the presence of a voltage pulse in a given location of the actin filament, and FALSE to the pulse's absence, so that information flows along the filament with pulse transmission. When two pulses, representing Boolean values of input variables, interact, then they can facilitate or inhibit further propagation of each other. We explore this phenomenon to construct Boolean logical gates and a one-bit half-adder with interacting voltage pulses. We discuss implications of these findings on cellular process and technological applications.
Bistability and Asynchrony in a Boolean Model of the L-arabinose Operon in Escherichia coli.
Jenkins, Andy; Macauley, Matthew
2017-08-01
The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update and see that the former has several artificial cycles that go away under a general asynchronous update.
Multipath Detection Using Boolean Satisfiability Techniques
Directory of Open Access Journals (Sweden)
Fadi A. Aloul
2011-01-01
Full Text Available A new technique for multipath detection in wideband mobile radio systems is presented. The proposed scheme is based on an intelligent search algorithm using Boolean Satisfiability (SAT techniques to search through the uncertainty region of the multipath delays. The SAT-based scheme utilizes the known structure of the transmitted wideband signal, for example, pseudo-random (PN code, to effectively search through the entire space by eliminating subspaces that do not contain a possible solution. The paper presents a framework for modeling the multipath detection problem as a SAT application. It also provides simulation results that demonstrate the effectiveness of the proposed scheme in detecting the multipath components in frequency-selective Rayleigh fading channels.
Griffin: A Tool for Symbolic Inference of Synchronous Boolean Molecular Networks
Muñoz, Stalin; Carrillo, Miguel; Azpeitia, Eugenio; Rosenblueth, David A.
2018-01-01
Boolean networks are important models of biochemical systems, located at the high end of the abstraction spectrum. A number of Boolean gene networks have been inferred following essentially the same method. Such a method first considers experimental data for a typically underdetermined “regulation” graph. Next, Boolean networks are inferred by using biological constraints to narrow the search space, such as a desired set of (fixed-point or cyclic) attractors. We describe Griffin, a computer tool enhancing this method. Griffin incorporates a number of well-established algorithms, such as Dubrova and Teslenko's algorithm for finding attractors in synchronous Boolean networks. In addition, a formal definition of regulation allows Griffin to employ “symbolic” techniques, able to represent both large sets of network states and Boolean constraints. We observe that when the set of attractors is required to be an exact set, prohibiting additional attractors, a naive Boolean coding of this constraint may be unfeasible. Such cases may be intractable even with symbolic methods, as the number of Boolean constraints may be astronomically large. To overcome this problem, we employ an Artificial Intelligence technique known as “clause learning” considerably increasing Griffin's scalability. Without clause learning only toy examples prohibiting additional attractors are solvable: only one out of seven queries reported here is answered. With clause learning, by contrast, all seven queries are answered. We illustrate Griffin with three case studies drawn from the Arabidopsis thaliana literature. Griffin is available at: http://turing.iimas.unam.mx/griffin. PMID:29559993
Dynamic network-based epistasis analysis: Boolean examples
Directory of Open Access Journals (Sweden)
Eugenio eAzpeitia
2011-12-01
Full Text Available In this review we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the topologies of gene interactions infered. This has been acknowledged in several previous papers and reviews, but here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson (herein, classical epistasis, defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus. Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct gene interaction topologies are hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our review complements previous accounts, not
Integrable systems of partial differential equations determined by structure equations and Lax pair
International Nuclear Information System (INIS)
Bracken, Paul
2010-01-01
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.
Ordinary differential equations and mechanical systems
Awrejcewicz, Jan
2014-01-01
This book applies a step-by-step treatment of the current state-of-the-art of ordinary differential equations used in modeling of engineering systems/processes and beyond. It covers systematically ordered problems, beginning with first and second order ODEs, linear and higher-order ODEs of polynomial form, theory and criteria of similarity, modeling approaches, phase plane and phase space concepts, stability optimization, and ending on chaos and synchronization. Presenting both an overview of the theory of the introductory differential equations in the context of applicability and a systematic treatment of modeling of numerous engineering and physical problems through linear and non-linear ODEs, the volume is self-contained, yet serves both scientific and engineering interests. The presentation relies on a general treatment, analytical and numerical methods, concrete examples, and engineering intuition. The scientific background used is well balanced between elementary and advanced level, making it as a uniqu...
Boolean Dependence Logic and Partially-Ordered Connectives
Ebbing, Johannes; Hella, Lauri; Lohmann, Peter; Virtema, Jonni
2014-01-01
We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\\alpha), where \\alpha is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions. We compare the expressive power of Boolean dependence logic to dependence logic and first-order logic enriched by partially-ordered connec...
Controllability and observability of Boolean networks arising from biology
Li, Rui; Yang, Meng; Chu, Tianguang
2015-02-01
Boolean networks are currently receiving considerable attention as a computational scheme for system level analysis and modeling of biological systems. Studying control-related problems in Boolean networks may reveal new insights into the intrinsic control in complex biological systems and enable us to develop strategies for manipulating biological systems using exogenous inputs. This paper considers controllability and observability of Boolean biological networks. We propose a new approach, which draws from the rich theory of symbolic computation, to solve the problems. Consequently, simple necessary and sufficient conditions for reachability, controllability, and observability are obtained, and algorithmic tests for controllability and observability which are based on the Gröbner basis method are presented. As practical applications, we apply the proposed approach to several different biological systems, namely, the mammalian cell-cycle network, the T-cell activation network, the large granular lymphocyte survival signaling network, and the Drosophila segment polarity network, gaining novel insights into the control and/or monitoring of the specific biological systems.
Solutions of system of P1 equations without use of auxiliary differential equations coupled
International Nuclear Information System (INIS)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos
2000-01-01
The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)
Random networks of Boolean cellular automata
International Nuclear Information System (INIS)
Miranda, Enrique
1990-01-01
Some recent results about random networks of Boolean automata -the Kauffman model- are reviewed. The structure of configuration space is explored. Ultrametricity between cycles is analyzed and the effects of noise in the dynamics are studied. (Author)
Boolean Models of Biological Processes Explain Cascade-Like Behavior
Chen, Hao; Wang, Guanyu; Simha, Rahul; Du, Chenghang; Zeng, Chen
2016-01-01
Biological networks play a key role in determining biological function and therefore, an understanding of their structure and dynamics is of central interest in systems biology. In Boolean models of such networks, the status of each molecule is either “on” or “off” and along with the molecules interact with each other, their individual status changes from “on” to “off” or vice-versa and the system of molecules in the network collectively go through a sequence of changes in state. This sequence of changes is termed a biological process. In this paper, we examine the common perception that events in biomolecular networks occur sequentially, in a cascade-like manner, and ask whether this is likely to be an inherent property. In further investigations of the budding and fission yeast cell-cycle, we identify two generic dynamical rules. A Boolean system that complies with these rules will automatically have a certain robustness. By considering the biological requirements in robustness and designability, we show that those Boolean dynamical systems, compared to an arbitrary dynamical system, statistically present the characteristics of cascadeness and sequentiality, as observed in the budding and fission yeast cell- cycle. These results suggest that cascade-like behavior might be an intrinsic property of biological processes. PMID:26821940
Directory of Open Access Journals (Sweden)
Chao Luo
Full Text Available A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs. In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length[Formula: see text] in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.
Boolean models can explain bistability in the lac operon.
Veliz-Cuba, Alan; Stigler, Brandilyn
2011-06-01
The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is either induced or uninduced. Many dynamical models have been proposed to capture this phenomenon. While most are based on complex mathematical formulations, it has been suggested that for other gene systems network topology is sufficient to produce the desired dynamical behavior. We present a Boolean network as a discrete model for the lac operon. Our model includes the two main glucose control mechanisms of catabolite repression and inducer exclusion. We show that this Boolean model is capable of predicting the ON and OFF steady states and bistability. Further, we present a reduced model which shows that lac mRNA and lactose form the core of the lac operon, and that this reduced model exhibits the same dynamics. This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose.
Numerical analysis of systems of ordinary and stochastic differential equations
Artemiev, S S
1997-01-01
This text deals with numerical analysis of systems of both ordinary and stochastic differential equations. It covers numerical solution problems of the Cauchy problem for stiff ordinary differential equations (ODE) systems by Rosenbrock-type methods (RTMs).
Noisy random Boolean formulae: a statistical physics perspective.
Mozeika, Alexander; Saad, David; Raymond, Jack
2010-10-01
Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.
Stochastic differential equations and a biological system
DEFF Research Database (Denmark)
Wang, Chunyan
1994-01-01
. The simulated results are compared with the experimental data, and it is found that the Euler method is the most simple end efficient method for the stochastic growth model considered. Estimation of the parameters of the growth model is based on the stochastic Kalman filter and a continuous Markov process......The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based...... been developed. Their properties and the relationship between them are discussed. The evolution of a dynamic system or process is usually of great practical interest. In order to simulate the evolution of the process, alternative methods are used to get numerical solutions. In this study, Euler...
Order-to-chaos transition in the hardness of random Boolean satisfiability problems
Varga, Melinda; Sumi, Róbert; Toroczkai, Zoltán; Ercsey-Ravasz, Mária
2016-05-01
Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k -SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ , an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N , the hardness of formulas in random k -SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α , hardness appears through a second-order phase transition at αχ in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ ˜NB |α - αχ|1-γ with 0 <γ <1 . We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased.
A New Calculation for Boolean Derivative Using Cheng Product
Directory of Open Access Journals (Sweden)
Hao Chen
2012-01-01
Full Text Available The matrix expression and relationships among several definitions of Boolean derivatives are given by using the Cheng product. We introduce several definitions of Boolean derivatives. By using the Cheng product, the matrix expressions of Boolean derivative are given, respectively. Furthermore, the relationships among different definitions are presented. The logical calculation is converted into matrix product. This helps to extend the application of Boolean derivative. At last, an example is given to illustrate the main results.
The Permeability of Boolean Sets of Cylinders
Directory of Open Access Journals (Sweden)
Willot F.
2016-07-01
Full Text Available Numerical and analytical results on the permeability of Boolean models of randomly-oriented cylinders with circular cross-section are reported. The present work investigates cylinders of prolate (highly-elongated and oblate (nearly flat types. The fluid flows either inside or outside of the cylinders. The Stokes flow is solved using full-fields Fourier-based computations on 3D binarized microstructures. The permeability is given for varying volume fractions of pores. A new upper-bound is derived for the permeability of the Boolean model of oblate cylinders. The behavior of the permeability in the dilute limit is discussed.
Integrable coupling system of fractional soliton equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-10-05
In this Letter, we consider the derivatives and integrals of fractional order and present a class of the integrable coupling system of the fractional order soliton equations. The fractional order coupled Boussinesq and KdV equations are the special cases of this class. Furthermore, the fractional AKNS soliton equation hierarchy is obtained.
Zohuri, Bahman
2017-01-01
This book provides a technical approach to a Business Resilience System with its Risk Atom and Processing Data Point based on fuzzy logic and cloud computation in real time. Its purpose and objectives define a clear set of expectations for Organizations and Enterprises so their network system and supply chain are totally resilient and protected against cyber-attacks, manmade threats, and natural disasters. These enterprises include financial, organizational, homeland security, and supply chain operations with multi-point manufacturing across the world. Market shares and marketing advantages are expected to result from the implementation of the system. The collected information and defined objectives form the basis to monitor and analyze the data through cloud computation, and will guarantee the success of their survivability's against any unexpected threats. This book will be useful for advanced undergraduate and graduate students in the field of computer engineering, engineers that work for manufacturing com...
Evolutionary Algorithms for Boolean Queries Optimization
Czech Academy of Sciences Publication Activity Database
Húsek, Dušan; Snášel, Václav; Neruda, Roman; Owais, S.S.J.; Krömer, P.
2006-01-01
Roč. 3, č. 1 (2006), s. 15-20 ISSN 1790-0832 R&D Projects: GA AV ČR 1ET100300414 Institutional research plan: CEZ:AV0Z10300504 Keywords : evolutionary algorithms * genetic algorithms * information retrieval * Boolean query Subject RIV: BA - General Mathematics
Boolean Queries Optimization by Genetic Algorithms
Czech Academy of Sciences Publication Activity Database
Húsek, Dušan; Owais, S.S.J.; Krömer, P.; Snášel, Václav
2005-01-01
Roč. 15, - (2005), s. 395-409 ISSN 1210-0552 R&D Projects: GA AV ČR 1ET100300414 Institutional research plan: CEZ:AV0Z10300504 Keywords : evolutionary algorithms * genetic algorithms * genetic programming * information retrieval * Boolean query Subject RIV: BB - Applied Statistics, Operational Research
Directory of Open Access Journals (Sweden)
Mostafa M.A. Khater
Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions
Partial differential equations and systems related to Morrey spaces
Ragusa, Maria Alessandra
2012-01-01
This PhD thesis deals with the study of well posedness, existence and regularity properties of solutions of partial differential equations and systems. Preparatory to the study of partial differential equations is the action of some integral operators, that are extensively used. Such results are very useful to obtain regularity properties of solutions of elliptic, parabolic and ultraparabolic equations of second order with discontinuous coefficients, and later of systems. The thesis consists...
Guo, Wensheng; Yang, Guowu; Wu, Wei; He, Lei; Sun, Mingyu
2014-01-01
In biological systems, the dynamic analysis method has gained increasing attention in the past decade. The Boolean network is the most common model of a genetic regulatory network. The interactions of activation and inhibition in the genetic regulatory network are modeled as a set of functions of the Boolean network, while the state transitions in the Boolean network reflect the dynamic property of a genetic regulatory network. A difficult problem for state transition analysis is the finding of attractors. In this paper, we modeled the genetic regulatory network as a Boolean network and proposed a solving algorithm to tackle the attractor finding problem. In the proposed algorithm, we partitioned the Boolean network into several blocks consisting of the strongly connected components according to their gradients, and defined the connection between blocks as decision node. Based on the solutions calculated on the decision nodes and using a satisfiability solving algorithm, we identified the attractors in the state transition graph of each block. The proposed algorithm is benchmarked on a variety of genetic regulatory networks. Compared with existing algorithms, it achieved similar performance on small test cases, and outperformed it on larger and more complex ones, which happens to be the trend of the modern genetic regulatory network. Furthermore, while the existing satisfiability-based algorithms cannot be parallelized due to their inherent algorithm design, the proposed algorithm exhibits a good scalability on parallel computing architectures.
Robust Satisfiability of Systems of Equations
Czech Academy of Sciences Publication Activity Database
Franek, Peter; Krčál, M.
2015-01-01
Roč. 62, č. 4 (2015), Article 26 ISSN 0004-5411 R&D Projects: GA ČR GBP202/12/G061 Grant - others:GA MŠk(CZ) LL1201 Institutional support: RVO:67985807 Keywords : nonlinear equations * satisfability * undecibility * topological extensions * uncertainty * robustness Subject RIV: IN - Informatics, Computer Science Impact factor: 1.803, year: 2015
Exact solutions for some nonlinear systems of partial differential equations
Energy Technology Data Exchange (ETDEWEB)
Darwish, A.A. [Department of Mathematics, Faculty of Science, Helwan University (Egypt)], E-mail: profdarwish@yahoo.com; Ramady, A. [Department of Mathematics, Faculty of Science, Beni-Suef University (Egypt)], E-mail: aramady@yahoo.com
2009-04-30
A direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear systems of partial differential equations (PDEs) is used and implemented in a computer algebraic system. New solutions for some nonlinear partial differential equations (NLPDEs) are obtained. Graphs of the solutions are displayed.
A New Algorithm for System of Integral Equations
Directory of Open Access Journals (Sweden)
Abdujabar Rasulov
2014-01-01
Full Text Available We develop a new algorithm to solve the system of integral equations. In this new method no need to use matrix weights. Beacause of it, we reduce computational complexity considerable. Using the new algorithm it is also possible to solve an initial boundary value problem for system of parabolic equations. To verify the efficiency, the results of computational experiments are given.
Boolean representations of simplicial complexes and matroids
Rhodes, John
2015-01-01
This self-contained monograph explores a new theory centered around boolean representations of simplicial complexes leading to a new class of complexes featuring matroids as central to the theory. The book illustrates these new tools to study the classical theory of matroids as well as their important geometric connections. Moreover, many geometric and topological features of the theory of matroids find their counterparts in this extended context. Graduate students and researchers working in the areas of combinatorics, geometry, topology, algebra and lattice theory will find this monograph appealing due to the wide range of new problems raised by the theory. Combinatorialists will find this extension of the theory of matroids useful as it opens new lines of research within and beyond matroids. The geometric features and geometric/topological applications will appeal to geometers. Topologists who desire to perform algebraic topology computations will appreciate the algorithmic potential of boolean represent...
Totally optimal decision trees for Boolean functions
Chikalov, Igor
2016-07-28
We study decision trees which are totally optimal relative to different sets of complexity parameters for Boolean functions. A totally optimal tree is an optimal tree relative to each parameter from the set simultaneously. We consider the parameters characterizing both time (in the worst- and average-case) and space complexity of decision trees, i.e., depth, total path length (average depth), and number of nodes. We have created tools based on extensions of dynamic programming to study totally optimal trees. These tools are applicable to both exact and approximate decision trees, and allow us to make multi-stage optimization of decision trees relative to different parameters and to count the number of optimal trees. Based on the experimental results we have formulated the following hypotheses (and subsequently proved): for almost all Boolean functions there exist totally optimal decision trees (i) relative to the depth and number of nodes, and (ii) relative to the depth and average depth.
Evolution of a designless nanoparticle network into reconfigurable Boolean logic.
Bose, S K; Lawrence, C P; Liu, Z; Makarenko, K S; van Damme, R M J; Broersma, H J; van der Wiel, W G
2015-12-01
Natural computers exploit the emergent properties and massive parallelism of interconnected networks of locally active components. Evolution has resulted in systems that compute quickly and that use energy efficiently, utilizing whatever physical properties are exploitable. Man-made computers, on the other hand, are based on circuits of functional units that follow given design rules. Hence, potentially exploitable physical processes, such as capacitive crosstalk, to solve a problem are left out. Until now, designless nanoscale networks of inanimate matter that exhibit robust computational functionality had not been realized. Here we artificially evolve the electrical properties of a disordered nanomaterials system (by optimizing the values of control voltages using a genetic algorithm) to perform computational tasks reconfigurably. We exploit the rich behaviour that emerges from interconnected metal nanoparticles, which act as strongly nonlinear single-electron transistors, and find that this nanoscale architecture can be configured in situ into any Boolean logic gate. This universal, reconfigurable gate would require about ten transistors in a conventional circuit. Our system meets the criteria for the physical realization of (cellular) neural networks: universality (arbitrary Boolean functions), compactness, robustness and evolvability, which implies scalability to perform more advanced tasks. Our evolutionary approach works around device-to-device variations and the accompanying uncertainties in performance. Moreover, it bears a great potential for more energy-efficient computation, and for solving problems that are very hard to tackle in conventional architectures.
Quotients of Boolean algebras and regular subalgebras
Czech Academy of Sciences Publication Activity Database
Balcar, Bohuslav; Pazák, Tomáš
2010-01-01
Roč. 49, č. 3 (2010), s. 329-342 ISSN 1432-0665 R&D Projects: GA AV ČR IAA100190509; GA MŠk MEB060909 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z10750506 Keywords : Boolean algebra * sequential topology * ZFC extension * ideal Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2010 http://link.springer.com/article/10.1007%2Fs00153-010-0174-y
Modulation equations for spatially periodic systems: derivation and solutions
Schielen, R.; Doelman, A.
1996-01-01
We study a class of partial dierential equations in one spatial dimension, which can be seen as model equations for the analysis of pattern formation in physical systems dened on unbounded, weakly oscillating domains. We perform a linear and weakly nonlinear stability analysis for solutions that
Undergraduate Students' Mental Operations in Systems of Differential Equations
Whitehead, Karen; Rasmussen, Chris
2003-01-01
This paper reports on research conducted to understand undergraduate students' ways of reasoning about systems of differential equations (SDEs). As part of a semester long classroom teaching experiment in a first course in differential equations, we conducted task-based interviews with six students after their study of first order differential…
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. ... for the treatment of diffusion, heat conduction, waves, etc., on self-similar fractals [25–28]. Harmonic ... differential equations offer possibilities of modeling dynamical behaviours naturally for which ordinary differential ...
On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations.
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio
2015-01-01
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlevé-I (P[Formula: see text]) equation or its fourth-order analogue P[Formula: see text]. As concrete examples, we discuss nonlinear Schrödinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture.
Unlimited multistability and Boolean logic in microbial signalling
DEFF Research Database (Denmark)
Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca
2015-01-01
reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We...... further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two......-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger...
The Number of Monotone and Self-Dual Boolean Functions
Directory of Open Access Journals (Sweden)
Haviarova L.
2014-12-01
Full Text Available In the present paper we study properties of pre-complete class of Boolean functions - monotone Boolean functions. We discuss interval graph, the abbreviated d.n.f., a minimal d.n.f. and a shortest d.n.f. of this function. Then we present a d.n.f. with the highest number of conjunctionsand we determinate the exact number of them. We count the number of monotone Boolean functions with some special properties. In the end we estimate the number of Boolean functionthat are monotone and self-dual at the same time.
Analysis and control of Boolean networks a semi-tensor product approach
Cheng, Daizhan; Li, Zhiqiang
2010-01-01
This book presents a new approach to the investigation of Boolean control networks, using the semi-tensor product (STP), which can express a logical function as a conventional discrete-time linear system. This makes it possible to analyze basic control problems.
Comparison of Detection and Classification Algorithms Using Boolean and Fuzzy Techniques
Directory of Open Access Journals (Sweden)
Rahul Dixit
2012-01-01
Full Text Available Modern military ranging, tracking, and classification systems are capable of generating large quantities of data. Conventional “brute-force” computational techniques, even with Moore’s law for processors, present a prohibitive computational challenge, and often, the system either fails to “lock onto” a target of interest within the available duty cycle, or the data stream is simply discarded because the system runs out of processing power or time. In searching for high-fidelity convergence, researchers have experimented with various reduction techniques, often using logic diagrams to make inferences from related signal data. Conventional Boolean and fuzzy logic systems generate a very large number of rules, which often are difficult to handle due to limitations in the processors. Published research has shown that reasonable approximations of the target are preferred over incomplete computations. This paper gives a figure of merit for comparing various logic analysis methods and presents results for a hypothetical target classification scenario. Novel multiquantization Boolean approaches also reduce the complexity of these multivariate analyses, making it possible to better use the available data to approximate target classification. This paper shows how such preprocessing can reasonably preserve result confidence and compares the results between Boolean, multi-quantization Boolean, and fuzzy techniques.
Convex solutions of systems arising from Monge-Ampere equations
Directory of Open Access Journals (Sweden)
Haiyan Wang
2009-10-01
Full Text Available We establish two criteria for the existence of convex solutions to a boundary value problem for weakly coupled systems arising from the Monge-Ampère equations. We shall use fixed point theorems in a cone.
Stochastic equations for complex systems theoretical and computational topics
Bessaih, Hakima
2015-01-01
Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations ...
Null controllability of a cascade system of Schrodinger equations
Directory of Open Access Journals (Sweden)
Marcos Lopez-Garcia
2016-03-01
Full Text Available This article presents a control problem for a cascade system of two linear N-dimensional Schrodinger equations. We address the problem of null controllability by means of a control supported in a region not satisfying the classical geometrical control condition. The proof is based on the application of a Carleman estimate with degenerate weights to each one of the equations and a careful analysis of the system in order to prove null controllability with only one control force.
Large Sets in Boolean and Non-Boolean Groups and Topology
Directory of Open Access Journals (Sweden)
Ol’ga V. Sipacheva
2017-10-01
Full Text Available Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely related to vast sets are considered; as a byproduct, interesting relations between vast sets and ultrafilters are revealed.
Multidimensional linearizable system of n-wave-type equations
Zenchuk, A. I.
2017-01-01
We propose a linearizable version of a multidimensional system of n-wave-type nonlinear partial differential equations ( PDEs). We derive this system using the spectral representation of its solution via a procedure similar to the dressing method for nonlinear PDEs integrable by the inverse scattering transform method. We show that the proposed system is completely integrable and construct a particular solution.
Nonlinear analysis of a reaction-diffusion system: Amplitude equations
Energy Technology Data Exchange (ETDEWEB)
Zemskov, E. P., E-mail: zemskov@ccas.ru [Russian Academy of Sciences, Dorodnicyn Computing Center (Russian Federation)
2012-10-15
A reaction-diffusion system with a nonlinear diffusion term is considered. Based on nonlinear analysis, the amplitude equations are obtained in the cases of the Hopf and Turing instabilities in the system. Turing pattern-forming regions in the parameter space are determined for supercritical and subcritical instabilities in a two-component reaction-diffusion system.
A complexity theory based on Boolean algebra
DEFF Research Database (Denmark)
Skyum, Sven; Valiant, Leslie
1985-01-01
A projection of a Boolean function is a function obtained by substituting for each of its variables a variable, the negation of a variable, or a constant. Reducibilities among computational problems under this relation of projection are considered. It is shown that much of what is of everyday rel...... relevance in Turing-machine-based complexity theory can be replicated easily and naturally in this elementary framework. Finer distinctions about the computational relationships among natural problems can be made than in previous formulations and some negative results are proved....
The Boolean algebra and central Galois algebras
Directory of Open Access Journals (Sweden)
George Szeto
2001-01-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb for all x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.
Boolean Factor Analysis by Attractor Neural Network
Czech Academy of Sciences Publication Activity Database
Frolov, A. A.; Húsek, Dušan; Muraviev, I. P.; Polyakov, P.Y.
2007-01-01
Roč. 18, č. 3 (2007), s. 698-707 ISSN 1045-9227 R&D Projects: GA AV ČR 1ET100300419; GA ČR GA201/05/0079 Institutional research plan: CEZ:AV0Z10300504 Keywords : recurrent neural network * Hopfield-like neural network * associative memory * unsupervised learning * neural network architecture * neural network application * statistics * Boolean factor analysis * dimensionality reduction * features clustering * concepts search * information retrieval Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.769, year: 2007
Adiabatically steered open quantum systems: Master equation and optimal phase
International Nuclear Information System (INIS)
Salmilehto, J.; Solinas, P.; Ankerhold, J.; Moettoenen, M.
2010-01-01
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a nonsteered system in the first superadiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.
Methods of mathematical modelling continuous systems and differential equations
Witelski, Thomas
2015-01-01
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such as chemical reactions, population dynamics, mechanical systems, and fluid mechanics. Chapters 1 to 4 cover essential topics in ordinary differential equations, transport equations and the calculus of variations that are important for formulating models. Chapters 5 to 11 then develop more advanced techniques including similarity solutions, matched asymptotic expansions, multiple scale analysis, long-wave models, and fast/slow dynamical systems. Methods of Mathematical Modelling will be useful for advanced undergraduate or beginning graduate students in applied mathematics, engineering and other applied sciences.
Characteristic Equation of the Modified Smith predictor to MIMO Systems
Directory of Open Access Journals (Sweden)
Jorge A. Herrera-Cuartas
2013-11-01
Full Text Available The delay in control systems is a feature frequently in real systems due to the transport of objects or information, a series connection of multiple systems or own processing and sensors delay, among others. Recently there have been several studies to identify the external delay MIMO systems, these works are focused on identification and on-line control of MIMO systems and use a multimodel structure based on modified Smith predictor using different search method. It is clear that for the implementation of the algorithm, and to obtain the convergence and stability analysis, it is necessary to have closed-loop equations of modified Smith predictor. However, in these works is not presented the analytical procedure, not be the main object, displaying only the closed loop equations without the procedure for obtaining it. Therefore, to respond, in this paper, we present an analytical way to derive the closed-loop equations of a modified Smith predictor.
Bethe-Salpeter equation for a four fermion system I
Energy Technology Data Exchange (ETDEWEB)
Kim, S.K.; Muller, B.; Greiner, W.
1988-08-01
The authors derive the Bethe-Salpeter equation for bound states of a four-body system. They treat only two-body interaction kernels in the ladder approximation. The equations should be applicable for the description of exotic meson states (q qq-barq-bar states) and the ''poly-positronium'' states discussed in connection with the interpretation of the narrow coincidence peaks in the spectra of electrons and positrons observed in heavy ion collisions.
Selected equation of state in the acentric factor system
International Nuclear Information System (INIS)
Schreiber, D.R.; Pitzer, K.S.
1988-06-01
A new equation of state in the acentric factor system is developed on the basis of high-precision data. The region in critical temperature T/sub r/, critical density P/sub r/ space is identified where there is good agreement as well as the regions of significant departures. The equation fits very well in the critical region. 10 refs., 6 figs., 3 tabs
GBL-2D Version 1.0: a 2D geometry boolean library.
Energy Technology Data Exchange (ETDEWEB)
McBride, Cory L. (Elemental Technologies, American Fort, UT); Schmidt, Rodney Cannon; Yarberry, Victor R.; Meyers, Ray J. (Elemental Technologies, American Fort, UT)
2006-11-01
This report describes version 1.0 of GBL-2D, a geometric Boolean library for 2D objects. The library is written in C++ and consists of a set of classes and routines. The classes primarily represent geometric data and relationships. Classes are provided for 2D points, lines, arcs, edge uses, loops, surfaces and mask sets. The routines contain algorithms for geometric Boolean operations and utility functions. Routines are provided that incorporate the Boolean operations: Union(OR), XOR, Intersection and Difference. A variety of additional analytical geometry routines and routines for importing and exporting the data in various file formats are also provided. The GBL-2D library was originally developed as a geometric modeling engine for use with a separate software tool, called SummitView [1], that manipulates the 2D mask sets created by designers of Micro-Electro-Mechanical Systems (MEMS). However, many other practical applications for this type of software can be envisioned because the need to perform 2D Boolean operations can arise in many contexts.
An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks
Zheng, Desheng; Yang, Guowu; Li, Xiaoyu; Wang, Zhicai; Liu, Feng; He, Lei
2013-01-01
Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems. Availability The software package is available at https://sites.google.com/site/desheng619/download. PMID:23585840
Boolean orthoposets and two-valued states on them
Tkadlec, Josef
1992-06-01
A Boolean orthoposet (see e.g. [2]) is the orthoposet P fulfilling the following condition: If a, b ∈ P and a ∧ b = 0 then a⊥ b. This condition seems to be a sound generalization of distributivity in orthoposets (see e.g. [8]). Also, the class of (orthomodular) Boolean orthoposets may play an interesting role in quantum logic theory. This class is wide enough (see [4,3]) and on the other hand, enjoys some properties of Boolean algebras [4,8,5]. In quantum logic theory an important role is played by so-called Jauch-Piron states [1,6,7]. In this paper we clarify the connection between Boolean orthoposets and orthoposets with "enough" two-valued Jauch-Piron states. Further, we obtain a characterization of Boolean orthoposets in terms of two-valued states.
On the stability of some systems of exponential difference equations
Directory of Open Access Journals (Sweden)
N. Psarros
2018-01-01
Full Text Available In this paper we prove the stability of the zero equilibria of two systems of difference equations of exponential type, which are some extensions of an one-dimensional biological model. The stability of these systems is investigated in the special case when one of the eigenvalues is equal to -1 and the other eigenvalue has absolute value less than 1, using centre manifold theory. In addition, we study the existence and uniqueness of positive equilibria, the attractivity and the global asymptotic stability of these equilibria of some related systems of difference equations.
Lyapunov equation for infinite-dimensional discrete bilinear systems
International Nuclear Information System (INIS)
Costa, O.L.V.; Kubrusly, C.S.
1991-03-01
Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)
How to build master equations for complex systems
Breuer, Heinz-Peter; Petruccione, Francesco
1995-12-01
Typical complex systems, e. g., complex chemical reactions, reaction-diffusion systems, and turbulent fluids are described on a macroscopic level, that is, neglecting fluctuations, with the help of deterministic equations for corresponding variables. In this article it is shown on a phenomenological level, that these systems can be described in terms of integer- or real-valued Markov processes as well, which are governed by master equations. The latter are constructed such that the macroscopic law and the fluctuations around it are reproduced correctly. Stochastic processes defined through master equations can easily be simulated. The efficiency, the stability and the parallelization of the algorithms for stochastic simulations are discussed for some examples. In the last part of the paper it is shown that the same phenomenological approach can be successfully applied to open quantum systems. The wave function is assumed to be a complex valued stochastic process in Hilbert space and the quantum master equation for the statistical operator is regarded as the equation of motion for the two-point correlation function.
Nonlocal Symmetries to Systems of Nonlinear Diffusion Equations
International Nuclear Information System (INIS)
Qu Changzheng; Kang Jing
2008-01-01
In this paper, we study potential symmetries to certain systems of nonlinear diffusion equations. Those systems have physical applications in soil science, mathematical biology, and invariant curve flows in R 3 . Lie point symmetries of the potential system, which cannot be projected to vector fields of the given dependent and independent variables, yield potential symmetries. The class of the system that admits potential symmetries is expanded.
Simulating Quantitative Cellular Responses Using Asynchronous Threshold Boolean Network Ensembles
Directory of Open Access Journals (Sweden)
Shah Imran
2011-07-01
Full Text Available Abstract Background With increasing knowledge about the potential mechanisms underlying cellular functions, it is becoming feasible to predict the response of biological systems to genetic and environmental perturbations. Due to the lack of homogeneity in living tissues it is difficult to estimate the physiological effect of chemicals, including potential toxicity. Here we investigate a biologically motivated model for estimating tissue level responses by aggregating the behavior of a cell population. We assume that the molecular state of individual cells is independently governed by discrete non-deterministic signaling mechanisms. This results in noisy but highly reproducible aggregate level responses that are consistent with experimental data. Results We developed an asynchronous threshold Boolean network simulation algorithm to model signal transduction in a single cell, and then used an ensemble of these models to estimate the aggregate response across a cell population. Using published data, we derived a putative crosstalk network involving growth factors and cytokines - i.e., Epidermal Growth Factor, Insulin, Insulin like Growth Factor Type 1, and Tumor Necrosis Factor α - to describe early signaling events in cell proliferation signal transduction. Reproducibility of the modeling technique across ensembles of Boolean networks representing cell populations is investigated. Furthermore, we compare our simulation results to experimental observations of hepatocytes reported in the literature. Conclusion A systematic analysis of the results following differential stimulation of this model by growth factors and cytokines suggests that: (a using Boolean network ensembles with asynchronous updating provides biologically plausible noisy individual cellular responses with reproducible mean behavior for large cell populations, and (b with sufficient data our model can estimate the response to different concentrations of extracellular ligands. Our
Solving Systems of Equations with Techniques from Artificial Intelligence
Directory of Open Access Journals (Sweden)
Irina Maria Terfaloaga
2015-07-01
Full Text Available A frequent problem in numerical analysis is solving the systems of equations. That problem has generated in time a great interest among mathematicians and computer scientists, as evidenced by the large number of numerical methods developed. Besides the classical numerical methods, in the last years were proposed methods inspired by techniques from artificial intelligence. Hybrid methods have been also proposed along the time [15, 19]. The goal of this study is to make a survey of methods inspired from artificial intelligence for solving systems of equations
Multiparameter extrapolation and deflation methods for solving equation systems
Directory of Open Access Journals (Sweden)
A. J. Hughes Hallett
1984-01-01
Full Text Available Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.
Refined Fuchs inequalities for systems of linear differential equations
International Nuclear Information System (INIS)
Gontsov, R R
2004-01-01
We refine the Fuchs inequalities obtained by Corel for systems of linear meromorphic differential equations given on the Riemann sphere. Fuchs inequalities enable one to estimate the sum of exponents of the system over all its singular points. We refine these well-known inequalities by considering the Jordan structure of the leading coefficient of the Laurent series for the matrix of the right-hand side of the system in the neighbourhood of a singular point
Some overdetermined systems of complex partial differential equations
International Nuclear Information System (INIS)
Le Hung Son.
1990-01-01
In this paper we extend some properties of analytic functions on several complex variables to solutions of overdetermined systems of complex partial differential equations. It is proved that many global properties of analytic functions are true for solutions of the Vekua system in special cases. The relation between analytic functions and solutions of quasi-linear systems is discussed in the paper. (author). 8 refs
Existence of a coupled system of fractional differential equations
Energy Technology Data Exchange (ETDEWEB)
Ibrahim, Rabha W. [Multimedia unit, Department of Computer System and Technology Faculty of Computer Science & IT, University of Malaya, 50603 Kuala Lumpur (Malaysia); Siri, Zailan [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-10-22
We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.
Evolutionary Algorithms for Boolean Functions in Diverse Domains of Cryptography.
Picek, Stjepan; Carlet, Claude; Guilley, Sylvain; Miller, Julian F; Jakobovic, Domagoj
2016-01-01
The role of Boolean functions is prominent in several areas including cryptography, sequences, and coding theory. Therefore, various methods for the construction of Boolean functions with desired properties are of direct interest. New motivations on the role of Boolean functions in cryptography with attendant new properties have emerged over the years. There are still many combinations of design criteria left unexplored and in this matter evolutionary computation can play a distinct role. This article concentrates on two scenarios for the use of Boolean functions in cryptography. The first uses Boolean functions as the source of the nonlinearity in filter and combiner generators. Although relatively well explored using evolutionary algorithms, it still presents an interesting goal in terms of the practical sizes of Boolean functions. The second scenario appeared rather recently where the objective is to find Boolean functions that have various orders of the correlation immunity and minimal Hamming weight. In both these scenarios we see that evolutionary algorithms are able to find high-quality solutions where genetic programming performs the best.
Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited
Directory of Open Access Journals (Sweden)
Faryabi Babak
2009-01-01
Full Text Available An approximate representation for the state space of a context-sensitive probabilistic Boolean network has previously been proposed and utilized to devise therapeutic intervention strategies. Whereas the full state of a context-sensitive probabilistic Boolean network is specified by an ordered pair composed of a network context and a gene-activity profile, this approximate representation collapses the state space onto the gene-activity profiles alone. This reduction yields an approximate transition probability matrix, absent of context, for the Markov chain associated with the context-sensitive probabilistic Boolean network. As with many approximation methods, a price must be paid for using a reduced model representation, namely, some loss of optimality relative to using the full state space. This paper examines the effects on intervention performance caused by the reduction with respect to various values of the model parameters. This task is performed using a new derivation for the transition probability matrix of the context-sensitive probabilistic Boolean network. This expression of transition probability distributions is in concert with the original definition of context-sensitive probabilistic Boolean network. The performance of optimal and approximate therapeutic strategies is compared for both synthetic networks and a real case study. It is observed that the approximate representation describes the dynamics of the context-sensitive probabilistic Boolean network through the instantaneously random probabilistic Boolean network with similar parameters.
Boolean networks with robust and reliable trajectories
International Nuclear Information System (INIS)
Schmal, Christoph; Peixoto, Tiago P; Drossel, Barbara
2010-01-01
We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule and which is also robust against noise. Robustness is quantified as the probability that the dynamics return to the reliable trajectory after a perturbation of the state of a single node. In order to achieve high robustness, we navigate through the space of possible update functions by using an evolutionary algorithm. We constrain the networks to those having the minimum number of connections required to obtain the reliable trajectory. Surprisingly, we find that robustness always reaches values close to 100% during the evolutionary optimization process. The set of update functions can be evolved such that it differs only slightly from that of networks that were not optimized with respect to robustness. The state space of the optimized networks is dominated by the basin of attraction of the reliable trajectory.
The Boolean algebra of Galois algebras
Directory of Open Access Journals (Sweden)
Lianyong Xue
2003-02-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={bÃ¢ÂˆÂˆB|bx=g(xbÃ¢Â€Â‰for allÃ¢Â€Â‰xÃ¢ÂˆÂˆB} for each gÃ¢ÂˆÂˆG, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|gÃ¢ÂˆÂˆG}, e a nonzero element in Ba, and He={gÃ¢ÂˆÂˆG|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.
Theory reduction and non-Boolean theories.
Primas, H
1977-07-19
It is suggested that biological theories should be embedded into the family of non-Boolean theories based on an orthomodular propositional calculus. The structure of universal theories that include quantal phenomena is investigated and it is shown that their subtheories form a directed set which cannot be totally orders. A precise definition of theory reduction is given; it turns out that hierarchically different descriptive levels are not related by a homomorphic map. A subtheory that is reducible to a more general theory can be associated with the emergence of novel concepts and is in general subject to a wider empirical clissification scheme than the reducing theory. The implications of these results for reductionism, holism, emergence, and their conceptual unification are discussed.
Representing Boolean Functions by Decision Trees
Chikalov, Igor
2011-01-01
A Boolean or discrete function can be represented by a decision tree. A compact form of decision tree named binary decision diagram or branching program is widely known in logic design [2, 40]. This representation is equivalent to other forms, and in some cases it is more compact than values table or even the formula [44]. Representing a function in the form of decision tree allows applying graph algorithms for various transformations [10]. Decision trees and branching programs are used for effective hardware [15] and software [5] implementation of functions. For the implementation to be effective, the function representation should have minimal time and space complexity. The average depth of decision tree characterizes the expected computing time, and the number of nodes in branching program characterizes the number of functional elements required for implementation. Often these two criteria are incompatible, i.e. there is no solution that is optimal on both time and space complexity. © Springer-Verlag Berlin Heidelberg 2011.
RESOLUTION DE SYSTEMES D'EQUATIONS DE DISTANCE AVEC INCERTITUDES.
GRANDON, CARLOS; GRANDON, CARLOS
2007-01-01
In this thesis we are interested in a particular class of problems which frequently appear in robotics (and many other areas as chemistry, molecular biology, Computer-Aided Design (CAD), and aeronautics). They are systems of distance equations with uncert 190p.
Local first integrals for systems of differential equations
International Nuclear Information System (INIS)
Zhang Xiang
2003-01-01
The main purpose of this paper is to provide some sufficient conditions for a system of differential equations to have local first integrals in a certain neighbourhood of a singularity. Our results generalize those given in Kwek et al (2003 Z. Angew. Math. Phys. 54 26) and Li et al (2003 Z. Angew. Math. Phys. 54 235)
On Coupled System of Navier-Stokes Equations and Temperature
African Journals Online (AJOL)
Dr. Anthony Peter
ABSTRACT. This paper deals with the coupled system of Navier-Stokes equations and temperature (Thermohydraulics) in a strip in the class of spatially non-decaying (infinite-energy) solutions belonging to the properly chosen uniformly local Sobolev spaces. The global well-posedness and dissipativity of the Navier- ...
Projective geometry of systems of second-order differential equations
International Nuclear Information System (INIS)
Aminova, A V; Aminov, N A
2006-01-01
It is proved that every projective connection on an n-dimensional manifold M is locally defined by a system S of n-1 second-order ordinary differential equations resolved with respect to the second derivatives and with right-hand sides cubic in the first derivatives, and that every differential system S defines a projective connection on M. The notion of equivalent differential systems is introduced and necessary and sufficient conditions are found for a system S to be reducible by a change of variables to a system whose integral curves are straight lines. It is proved that the symmetry group of a differential system S is a group of projective transformations in n-dimensional space with the associated projective connection and has dimension ≤n 2 +2n. Necessary and sufficient conditions are found for a system to admit the maximal symmetry group; basis vector fields and structure equations of the maximal symmetry Lie algebra are produced. As an application a classification is given of the systems S of two second-order differential equations admitting three-dimensional soluble symmetry groups.
Equivalence Checking of Combinational Circuits using Boolean Expression Diagrams
DEFF Research Database (Denmark)
Hulgaard, Henrik; Williams, Poul Frederick; Andersen, Henrik Reif
1999-01-01
The combinational logic-level equivalence problem is to determine whether two given combinational circuits implement the same Boolean function. This problem arises in a number of CAD applications, for example when checking the correctness of incremental design changes (performed either manually...... or by a design automation tool).This paper introduces a data structure called Boolean Expression Diagrams (BEDs) and two algorithms for transforming a BED into a Reduced Ordered Binary Decision Diagram (OBDD). BEDs are capable of representing any Boolean circuit in linear space and can exploit structural...
An equations of motion approach for open shell systems
International Nuclear Information System (INIS)
Yeager, D.L.; McKoy, V.
1975-01-01
A straightforward scheme is developed for extending the equations of motion formalism to systems with simple open shell ground states. Equations for open shell random phase approximation (RPA) are given for the cases of one electron outside of a closed shell in a nondegenerate molecular orbital and for the triplet ground state with two electrons outside of a closed shell in degenerate molecular orbitals. Applications to other open shells and extension of the open shell EOM to higher orders are both straightforward. Results for the open shell RPA for lithium atom and oxygen molecule are given
Periodic solutions to systems of reaction-diffusion equations
Rosen, G.
1976-01-01
Necessary and sufficient conditions are derived for the existence of temporally periodic 'dissipative structure' solutions in weak diffusion with the reaction rate terms dominant in a generic system of reaction-diffusion differential equations. The enumerator index i of the equations denotes the density or concentration of the ith participating molecular or biological species, and D sub i is the diffusivity constant for the ith species while Q sub i (c), an algebraic function of the n-tuple c, expresses the local rate of production of the ith species due to chemical reactions or biological interactions.
The Neumann Type Systems and Algebro-Geometric Solutions of a System of Coupled Integrable Equations
International Nuclear Information System (INIS)
Chen Jinbing; Qiao Zhijun
2011-01-01
A system of (1+1)-dimensional coupled integrable equations is decomposed into a pair of new Neumann type systems that separate the spatial and temporal variables for this system over a symplectic submanifold. Then, the Neumann type flows associated with the coupled integrable equations are integrated on the complex tour of a Riemann surface. Finally, the algebro-geometric solutions expressed by Riemann theta functions of the system of coupled integrable equations are obtained by means of the Jacobi inversion.
Fully Digital Chaotic Differential Equation-based Systems And Methods
Radwan, Ahmed Gomaa Ahmed
2012-09-06
Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.
Application of the Bayes equation to predicting reactor system reliability
International Nuclear Information System (INIS)
Fullwood, R.R.; Erdmann, R.C.; Rumble, E.T.; Lellouche, G.S.
1977-01-01
Reliability predictions for systems exhibiting few, if any, failures require the use of all available information. The Bayes equation incorporates prior engineering information with test data to provide statistically improved posterior estimates. Classical results agree with those obtained from the Bayes equation by using no prior information. For the case of failure-on-demand, this is equivalent to assuming a 50% mean failure probability for the prior information--hardly an appropriate estimate for a reliable system such as a reactor scram system. The method of Bayes conjugates applied to the cases of aging failure and failure-on-demand yields formulas for calculating mean, standard deviation, and confidence values. Various methods for incorporating prior information are possible. For example, calculating scram failure probabilities by incorporating prior information obtained from fault tree analysis of a scram system with historical test data indicates a mean scram failure probability of approx. 8 x 10 -6 per demand
MINPACK-1, Subroutine Library for Nonlinear Equation System
International Nuclear Information System (INIS)
Garbow, Burton S.
1984-01-01
1 - Description of problem or function: MINPACK1 is a package of FORTRAN subprograms for the numerical solution of systems of non- linear equations and nonlinear least-squares problems. The individual programs are: Identification/Description: - CHKDER: Check gradients for consistency with functions, - DOGLEG: Determine combination of Gauss-Newton and gradient directions, - DPMPAR: Provide double precision machine parameters, - ENORM: Calculate Euclidean norm of vector, - FDJAC1: Calculate difference approximation to Jacobian (nonlinear equations), - FDJAC2: Calculate difference approximation to Jacobian (least squares), - HYBRD: Solve system of nonlinear equations (approximate Jacobian), - HYBRD1: Easy-to-use driver for HYBRD, - HYBRJ: Solve system of nonlinear equations (analytic Jacobian), - HYBRJ1: Easy-to-use driver for HYBRJ, - LMDER: Solve nonlinear least squares problem (analytic Jacobian), - LMDER1: Easy-to-use driver for LMDER, - LMDIF: Solve nonlinear least squares problem (approximate Jacobian), - LMDIF1: Easy-to-use driver for LMDIF, - LMPAR: Determine Levenberg-Marquardt parameter - LMSTR: Solve nonlinear least squares problem (analytic Jacobian, storage conserving), - LMSTR1: Easy-to-use driver for LMSTR, - QFORM: Accumulate orthogonal matrix from QR factorization QRFAC Compute QR factorization of rectangular matrix, - QRSOLV: Complete solution of least squares problem, - RWUPDT: Update QR factorization after row addition, - R1MPYQ: Apply orthogonal transformations from QR factorization, - R1UPDT: Update QR factorization after rank-1 addition, - SPMPAR: Provide single precision machine parameters. 4. Method of solution - MINPACK1 uses the modified Powell hybrid method and the Levenberg-Marquardt algorithm
Modelling biochemical reaction systems by stochastic differential equations with reflection.
Niu, Yuanling; Burrage, Kevin; Chen, Luonan
2016-05-07
In this paper, we gave a new framework for modelling and simulating biochemical reaction systems by stochastic differential equations with reflection not in a heuristic way but in a mathematical way. The model is computationally efficient compared with the discrete-state Markov chain approach, and it ensures that both analytic and numerical solutions remain in a biologically plausible region. Specifically, our model mathematically ensures that species numbers lie in the domain D, which is a physical constraint for biochemical reactions, in contrast to the previous models. The domain D is actually obtained according to the structure of the corresponding chemical Langevin equations, i.e., the boundary is inherent in the biochemical reaction system. A variant of projection method was employed to solve the reflected stochastic differential equation model, and it includes three simple steps, i.e., Euler-Maruyama method was applied to the equations first, and then check whether or not the point lies within the domain D, and if not perform an orthogonal projection. It is found that the projection onto the closure D¯ is the solution to a convex quadratic programming problem. Thus, existing methods for the convex quadratic programming problem can be employed for the orthogonal projection map. Numerical tests on several important problems in biological systems confirmed the efficiency and accuracy of this approach. Copyright © 2016 Elsevier Ltd. All rights reserved.
Differential equations, dynamical systems, and an introduction to chaos
Smale, Stephen; Devaney, Robert L
2003-01-01
Thirty years in the making, this revised text by three of the world''s leading mathematicians covers the dynamical aspects of ordinary differential equations. it explores the relations between dynamical systems and certain fields outside pure mathematics, and has become the standard textbook for graduate courses in this area. The Second Edition now brings students to the brink of contemporary research, starting from a background that includes only calculus and elementary linear algebra.The authors are tops in the field of advanced mathematics, including Steve Smale who is a recipient of the Field''s Medal for his work in dynamical systems.* Developed by award-winning researchers and authors* Provides a rigorous yet accessible introduction to differential equations and dynamical systems* Includes bifurcation theory throughout* Contains numerous explorations for students to embark uponNEW IN THIS EDITION* New contemporary material and updated applications* Revisions throughout the text, including simplification...
Attractor Transformation by Impulsive Control in Boolean Control Network
Directory of Open Access Journals (Sweden)
Bo Gao
2013-01-01
Full Text Available Boolean control networks have recently been attracting considerable interests as computational models for genetic regulatory networks. In this paper, we present an approach of impulsive control for attractor transitions in Boolean control networks based on the recent developed matrix semitensor product theory. The reachability of attractors is estimated, and the controller is also obtained. The general derivation proposed here is exemplified with a kind of gene model, which is the protein-nucleic acid interactions network, on numerical simulations.
Mohammed, K. Elboree
2015-10-01
In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.
Experimental quantum computing to solve systems of linear equations.
Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei
2013-06-07
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.
PATHLOGIC-S: a scalable Boolean framework for modelling cellular signalling.
Directory of Open Access Journals (Sweden)
Liam G Fearnley
Full Text Available Curated databases of signal transduction have grown to describe several thousand reactions, and efficient use of these data requires the development of modelling tools to elucidate and explore system properties. We present PATHLOGIC-S, a Boolean specification for a signalling model, with its associated GPL-licensed implementation using integer programming techniques. The PATHLOGIC-S specification has been designed to function on current desktop workstations, and is capable of providing analyses on some of the largest currently available datasets through use of Boolean modelling techniques to generate predictions of stable and semi-stable network states from data in community file formats. PATHLOGIC-S also addresses major problems associated with the presence and modelling of inhibition in Boolean systems, and reduces logical incoherence due to common inhibitory mechanisms in signalling systems. We apply this approach to signal transduction networks including Reactome and two pathways from the Panther Pathways database, and present the results of computations on each along with a discussion of execution time. A software implementation of the framework and model is freely available under a GPL license.
Resummed memory kernels in generalized system-bath master equations
Mavros, Michael G.; Van Voorhis, Troy
2014-08-01
Generalized master equations provide a concise formalism for studying reduced population dynamics. Usually, these master equations require a perturbative expansion of the memory kernels governing the dynamics; in order to prevent divergences, these expansions must be resummed. Resummation techniques of perturbation series are ubiquitous in physics, but they have not been readily studied for the time-dependent memory kernels used in generalized master equations. In this paper, we present a comparison of different resummation techniques for such memory kernels up to fourth order. We study specifically the spin-boson Hamiltonian as a model system bath Hamiltonian, treating the diabatic coupling between the two states as a perturbation. A novel derivation of the fourth-order memory kernel for the spin-boson problem is presented; then, the second- and fourth-order kernels are evaluated numerically for a variety of spin-boson parameter regimes. We find that resumming the kernels through fourth order using a Padé approximant results in divergent populations in the strong electronic coupling regime due to a singularity introduced by the nature of the resummation, and thus recommend a non-divergent exponential resummation (the "Landau-Zener resummation" of previous work). The inclusion of fourth-order effects in a Landau-Zener-resummed kernel is shown to improve both the dephasing rate and the obedience of detailed balance over simpler prescriptions like the non-interacting blip approximation, showing a relatively quick convergence on the exact answer. The results suggest that including higher-order contributions to the memory kernel of a generalized master equation and performing an appropriate resummation can provide a numerically-exact solution to system-bath dynamics for a general spectral density, opening the way to a new class of methods for treating system-bath dynamics.
Boolean network model of the Pseudomonas aeruginosa quorum sensing circuits.
Dallidis, Stylianos E; Karafyllidis, Ioannis G
2014-09-01
To coordinate their behavior and virulence and to synchronize attacks against their hosts, bacteria communicate by continuously producing signaling molecules (called autoinducers) and continuously monitoring the concentration of these molecules. This communication is controlled by biological circuits called quorum sensing (QS) circuits. Recently QS circuits and have been recognized as an alternative target for controlling bacterial virulence and infections without the use of antibiotics. Pseudomonas aeruginosa is a Gram-negative bacterium that infects insects, plants, animals and humans and can cause acute infections. This bacterium has three interconnected QS circuits that form a very complex and versatile QS system, the operation of which is still under investigation. Here we use Boolean networks to model the complete QS system of Pseudomonas aeruginosa and we simulate and analyze its operation in both synchronous and asynchronous modes. The state space of the QS system is constructed and it turned out to be very large, hierarchical, modular and scale-free. Furthermore, we developed a simulation tool that can simulate gene knock-outs and study their effect on the regulons controlled by the three QS circuits. The model and tools we developed will give to life scientists a deeper insight to this complex QS system.
Fractional Euler-Lagrange Equations Applied to Oscillatory Systems
Directory of Open Access Journals (Sweden)
Sergio Adriani David
2015-04-01
Full Text Available In this paper, we applied the Riemann-Liouville approach and the fractional Euler-Lagrange equations in order to obtain the fractional nonlinear dynamic equations involving two classical physical applications: “Simple Pendulum” and the “Spring-Mass-Damper System” to both integer order calculus (IOC and fractional order calculus (FOC approaches. The numerical simulations were conducted and the time histories and pseudo-phase portraits presented. Both systems, the one that already had a damping behavior (Spring-Mass-Damper and the system that did not present any sort of damping behavior (Simple Pendulum, showed signs indicating a possible better capacity of attenuation of their respective oscillation amplitudes. This implication could mean that if the selection of the order of the derivative is conveniently made, systems that need greater intensities of damping or vibrating absorbers may benefit from using fractional order in dynamics and possibly in control of the aforementioned systems. Thereafter, we believe that the results described in this paper may offer greater insights into the complex behavior of these systems, and thus instigate more research efforts in this direction.
Equation-free model reduction for complex dynamical systems
International Nuclear Information System (INIS)
Le Maitre, O. P.; Mathelin, L.; Le Maitre, O. P.
2010-01-01
This paper presents a reduced model strategy for simulation of complex physical systems. A classical reduced basis is first constructed relying on proper orthogonal decomposition of the system. Then, unlike the alternative approaches, such as Galerkin projection schemes for instance, an equation-free reduced model is constructed. It consists in the determination of an explicit transformation, or mapping, for the evolution over a coarse time-step of the projection coefficients of the system state on the reduced basis. The mapping is expressed as an explicit polynomial transformation of the projection coefficients and is computed once and for all in a pre-processing stage using the detailed model equation of the system. The reduced system can then be advanced in time by successive applications of the mapping. The CPU cost of the method lies essentially in the mapping approximation which is performed offline, in a parallel fashion, and only once. Subsequent application of the mapping to perform a time-integration is carried out at a low cost thanks to its explicit character. Application of the method is considered for the 2-D flow around a circular cylinder. We investigate the effectiveness of the reduced model in rendering the dynamics for both asymptotic state and transient stages. It is shown that the method leads to a stable and accurate time-integration for only a fraction of the cost of a detailed simulation, provided that the mapping is properly approximated and the reduced basis remains relevant for the dynamics investigated. (authors)
Unlimited multistability and Boolean logic in microbial signalling.
Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S
2015-07-06
The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.
Modelling adversary actions against a nuclear material accounting system
International Nuclear Information System (INIS)
Lim, J.J.; Huebel, J.G.
1979-01-01
A typical nuclear material accounting system employing double-entry bookkeeping is described. A logic diagram is used to model the interactions of the accounting system and the adversary when he attempts to thwart it. Boolean equations are derived from the logic diagram; solution of these equations yields the accounts and records through which the adversary may disguise a SSNM theft and the collusion requirements needed to accomplish this feat. Some technical highlights of the logic diagram are also discussed
Analytical solutions for systems of partial differential-algebraic equations.
Benhammouda, Brahim; Vazquez-Leal, Hector
2014-01-01
This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.
A Generalized Representation Formula for Systems of Tensor Wave Equations
Shao, Arick
2011-08-01
In this paper, we generalize the Kirchhoff-Sobolev parametrix of Klainerman and Rodnianski (Hyperbolic Equ. 4(3):401-433, 2007) to systems of tensor wave equations with additional first-order terms. We also present a different derivation, which better highlights that such representation formulas are supported entirely on past null cones. This generalization of (Hyperbolic Equ. 4(3):401-433, 2007) is a key component for extending Klainerman and Rodnianski's breakdown criterion result for Einstein-vacuum spacetimes in (J. Amer. Math. Soc. 23(2):345-382, 2009) to Einstein-Maxwell and Einstein-Yang-Mills spacetimes.
Ferroelectric-antiferroelectric mixed systems. Equation of state, thermodynamic functions
Directory of Open Access Journals (Sweden)
N.A.Korynevskii
2006-01-01
Full Text Available The problem of equation of state for ferroelectric-antiferroelectric mixed systems in the whole region of a concentration change (0≤n≤1 is discussed. The main peculiarity of the presented model turns out to be the possibility for the site dipole momentum to be oriented ferroelectrically in z-direction and antiferroelectrically in x-direction. Such a situation takes place in mixed compounds of KDP type. The different phases (ferro-, antiferro-, paraelectric, dipole glass and some combinations of them have been found and analyzed.
Integrability of a system of two nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Zhukhunashvili, V.Z.
1989-01-01
In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants
Iterative solution of large sparse systems of equations
Hackbusch, Wolfgang
2016-01-01
In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature. The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms. The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.
Dissipation equation of motion approach to open quantum systems
Yan, YiJing; Jin, Jinshuang; Xu, Rui-Xue; Zheng, Xiao
2016-08-01
This paper presents a comprehensive account of the dissipaton-equation-of-motion (DEOM) theory for open quantum systems. This newly developed theory treats not only the quantum dissipative systems of primary interest, but also the hybrid environment dynamics that are also experimentally measurable. Despite the fact that DEOM recovers the celebrated hierarchical-equations-of-motion (HEOM) formalism, these two approaches have some fundamental differences. To show these differences, we also scrutinize the HEOM construction via its root at the influence functional path integral formalism. We conclude that many unique features of DEOM are beyond the reach of the HEOM framework. The new DEOM approach renders a statistical quasi-particle picture to account for the environment, which can be either bosonic or fermionic. The review covers the DEOM construction, the physical meanings of dynamical variables, the underlying theorems and dissipaton algebra, and recent numerical advancements for efficient DEOM evaluations of various problems. We also address the issue of high-order many-dissipaton truncations with respect to the invariance principle of quantum mechanics of Schrödinger versus Heisenberg prescriptions. DEOM serves as a universal tool for characterizing of stationary and dynamic properties of system-and-bath interferences, as highlighted with its real-time evaluation of both linear and nonlinear current noise spectra of nonequilibrium electronic transport.
Discrete Painlevé equations from Y-systems
International Nuclear Information System (INIS)
Hone, Andrew N W; Inoue, Rei
2014-01-01
We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlevé equations can arise from this construction. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
Continuous monitoring of dynamical systems and master equations
Energy Technology Data Exchange (ETDEWEB)
Lopes Oliveira, L.F. [Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais, 30510-000, Belo Horizonte, MG (Brazil); Rossi, R., E-mail: romeu_rossi@hotmail.com [Universidade Federal de Viçosa, Campus Florestal, 35690-000, Florestal, MG (Brazil); Bosco de Magalhães, A.R.; Peixoto de Faria, J.G. [Programa de Pós-Graduação em Modelagem Matemática e Computacional, Centro Federal de Educação Tecnológica de Minas Gerais, 30510-000, Belo Horizonte, MG (Brazil); Departamento de Física e Matemática, Centro Federal de Educação Tecnológica de Minas Gerais, 30510-000, Belo Horizonte, MG (Brazil); Nemes, M.C. [Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, CP 702, 30161-970, Belo Horizonte, MG (Brazil)
2012-04-30
We illustrate the equivalence between the non-unitary evolution of an open quantum system governed by a Markovian master equation and a process of continuous measurements involving this system. We investigate a system of two coupled modes, only one of them interacting with external degrees of freedom, represented, in the first case, by a finite number of harmonic oscillators, and, in the second, by a sequence of atoms where each one interacts with a single mode during a limited time. Two distinct regimes appear, one of them corresponding to a Zeno-like behavior in the limit of large dissipation. -- Highlights: ► We illustrate the conjecture that non-unitary evolution can be simulated by continuous measurements. ► The relation between unitary and non-unitary couplings define distinct dynamical regimes. ► One regime with large “dissipation constant” is a Zeno-like behavior.
INTERVAL STATE ESTIMATION FOR SINGULAR DIFFERENTIAL EQUATION SYSTEMS WITH DELAYS
Directory of Open Access Journals (Sweden)
T. A. Kharkovskaia
2016-07-01
Full Text Available The paper deals with linear differential equation systems with algebraic restrictions (singular systems and a method of interval observer design for this kind of systems. The systems contain constant time delay, measurement noise and disturbances. Interval observer synthesis is based on monotone and cooperative systems technique, linear matrix inequations, Lyapunov function theory and interval arithmetic. The set of conditions that gives the possibility for interval observer synthesis is proposed. Results of synthesized observer operation are shown on the example of dynamical interindustry balance model. The advantages of proposed method are that it is adapted to observer design for uncertain systems, if the intervals of admissible values for uncertain parameters are given. The designed observer is capable to provide asymptotically definite limits on the estimation accuracy, since the interval of admissible values for the object state is defined at every instant. The obtained result provides an opportunity to develop the interval estimation theory for complex systems that contain parametric uncertainty, varying delay and nonlinear elements. Interval observers increasingly find applications in economics, electrical engineering, mechanical systems with constraints and optimal flow control.
Solving Systems of Linear Equations with a Superconducting Quantum Processor.
Zheng, Yarui; Song, Chao; Chen, Ming-Cheng; Xia, Benxiang; Liu, Wuxin; Guo, Qiujiang; Zhang, Libo; Xu, Da; Deng, Hui; Huang, Keqiang; Wu, Yulin; Yan, Zhiguang; Zheng, Dongning; Lu, Li; Pan, Jian-Wei; Wang, H; Lu, Chao-Yang; Zhu, Xiaobo
2017-05-26
Superconducting quantum circuits are a promising candidate for building scalable quantum computers. Here, we use a four-qubit superconducting quantum processor to solve a two-dimensional system of linear equations based on a quantum algorithm proposed by Harrow, Hassidim, and Lloyd [Phys. Rev. Lett. 103, 150502 (2009)PRLTAO0031-900710.1103/PhysRevLett.103.150502], which promises an exponential speedup over classical algorithms under certain circumstances. We benchmark the solver with quantum inputs and outputs, and characterize it by nontrace-preserving quantum process tomography, which yields a process fidelity of 0.837±0.006. Our results highlight the potential of superconducting quantum circuits for applications in solving large-scale linear systems, a ubiquitous task in science and engineering.
Refinement monoids, equidecomposability types, and boolean inverse semigroups
Wehrung, Friedrich
2017-01-01
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Equivalence Checking of Combinational Circuits using Boolean Expression Diagrams
DEFF Research Database (Denmark)
Hulgaard, Henrik; Williams, Poul Frederick; Andersen, Henrik Reif
1999-01-01
or by a design automation tool).This paper introduces a data structure called Boolean Expression Diagrams (BEDs) and two algorithms for transforming a BED into a Reduced Ordered Binary Decision Diagram (OBDD). BEDs are capable of representing any Boolean circuit in linear space and can exploit structural...... similarities between the two circuits that are compared. These properties make BEDs suitable for verifying the equivalence of combinational circuits. BEDs can be seen as an intermediate representation between circuits (which are compact) and OBDDs (which are canonical).Based on a large number of combinational...
A Boolean Approach to Airline Business Model Innovation
DEFF Research Database (Denmark)
Hvass, Kristian Anders
Research in business model innovation has identified its significance in creating a sustainable competitive advantage for a firm, yet there are few empirical studies identifying which combination of business model activities lead to success and therefore deserve innovative attention. This study...... analyzes the business models of North America low-cost carriers from 2001 to 2010 using a Boolean minimization algorithm to identify which combinations of business model activities lead to operational profitability. The research aim is threefold: complement airline literature in the realm of business model...... innovation, introduce Boolean minimization methods to the field, and propose alternative business model activities to North American carriers striving for positive operating results....
On Kolmogorov's superpositions and Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Beiu, V.
1998-12-31
The paper overviews results dealing with the approximation capabilities of neural networks, as well as bounds on the size of threshold gate circuits. Based on an explicit numerical (i.e., constructive) algorithm for Kolmogorov's superpositions they will show that for obtaining minimum size neutral networks for implementing any Boolean function, the activation function of the neurons is the identity function. Because classical AND-OR implementations, as well as threshold gate implementations require exponential size (in the worst case), it will follow that size-optimal solutions for implementing arbitrary Boolean functions require analog circuitry. Conclusions and several comments on the required precision are ending the paper.
Constant-Overhead Secure Computation of Boolean Circuits using Preprocessing
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Zakarias, Sarah Nouhad Haddad
We present a protocol for securely computing a Boolean circuit $C$ in presence of a dishonest and malicious majority. The protocol is unconditionally secure, assuming access to a preprocessing functionality that is not given the inputs to compute on. For a large number of players the work done by...... with an additional multiplication property. We also show a new algorithm for verifying the product of Boolean matrices in quadratic time with exponentially small error probability, where previous methods would only give a constant error....
Petersson, K J F; Friberg, L E; Karlsson, M O
2010-10-01
Computer models of biological systems grow more complex as computing power increase. Often these models are defined as differential equations and no analytical solutions exist. Numerical integration is used to approximate the solution; this can be computationally intensive, time consuming and be a large proportion of the total computer runtime. The performance of different integration methods depend on the mathematical properties of the differential equations system at hand. In this paper we investigate the possibility of runtime gains by calculating parts of or the whole differential equations system at given time intervals, outside of the differential equations solver. This approach was tested on nine models defined as differential equations with the goal to reduce runtime while maintaining model fit, based on the objective function value. The software used was NONMEM. In four models the computational runtime was successfully reduced (by 59-96%). The differences in parameter estimates, compared to using only the differential equations solver were less than 12% for all fixed effects parameters. For the variance parameters, estimates were within 10% for the majority of the parameters. Population and individual predictions were similar and the differences in OFV were between 1 and -14 units. When computational runtime seriously affects the usefulness of a model we suggest evaluating this approach for repetitive elements of model building and evaluation such as covariate inclusions or bootstraps.
An efficient algorithm for solving nonlinear system of differential equations and applications
Directory of Open Access Journals (Sweden)
Mustafa GÜLSU
2015-10-01
Full Text Available In this article, we apply Chebyshev collocation method to obtain the numerical solutions of nonlinear systems of differential equations. This method transforms the nonlinear systems of differential equation to nonlinear systems of algebraic equations. The convergence of the numerical method are given and their applicability is illustrated with some examples.
System of adjoint P1 equations for neutron moderation
International Nuclear Information System (INIS)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos
2000-01-01
In some applications of perturbation theory, it is necessary know the adjoint neutron flux, which is obtained by the solution of adjoint neutron diffusion equation. However, the multigroup constants used for this are weighted in only the direct neutron flux, from the solution of direct P1 equations. In this work, this procedure is questioned and the adjoint P1 equations are derived by the neutron transport equation, the reversion operators rules and analogies between direct and adjoint parameters. (author)
Assessment of Electronic Circuits Reliability Using Boolean Truth Table Modeling Method
International Nuclear Information System (INIS)
EI-Shanshoury, A.I.
2011-01-01
This paper explores the use of Boolean Truth Table modeling Method (BTTM) in the analysis of qualitative data. It is widely used in certain fields especially in the fields of electrical and electronic engineering. Our work focuses on the evaluation of power supply circuit reliability using (BTTM) which involves systematic attempts to falsify and identify hypotheses on the basis of truth tables constructed from qualitative data. Reliability parameters such as the system's failure rates for the power supply case study are estimated. All possible state combinations (operating and failed states) of the major components in the circuit were listed and their effects on overall system were studied
Document Ranking in E-Extended Boolean Logic
Czech Academy of Sciences Publication Activity Database
Holub, M.; Húsek, Dušan; Pokorný, J.
1996-01-01
Roč. 4, č. 7 (1996), s. 3-17 ISSN 1310-0513. [Annual Colloquium on IR Research /19./. Aberdeen, 08.04.1997-09.04.1997] R&D Projects: GA ČR GA102/94/0728 Keywords : information retrieval * document ranking * extended Boolean logic
On the Road to Genetic Boolean Matrix Factorization
Czech Academy of Sciences Publication Activity Database
Snášel, V.; Platoš, J.; Krömer, P.; Húsek, Dušan; Frolov, A.
2007-01-01
Roč. 17, č. 6 (2007), s. 675-688 ISSN 1210-0552 Institutional research plan: CEZ:AV0Z10300504 Keywords : data mining * genetic algorithms * Boolean factorization * binary data * machine learning * feature extraction Subject RIV: IN - Informatics, Computer Science Impact factor: 0.280, year: 2007
Free Boolean algebras over unions of two well orderings
Czech Academy of Sciences Publication Activity Database
Bonnet, R.; Faouzi, L.; Kubiś, Wieslaw
2009-01-01
Roč. 156, č. 7 (2009), s. 1177-1185 ISSN 0166-8641 Institutional research plan: CEZ:AV0Z10190503 Keywords : Well quasi orderings * Poset algebras * Superatomic Boolean algebras * Compact distributive lattices Subject RIV: BA - General Mathematics Impact factor: 0.441, year: 2009
Complexity of Identification and Dualization of Positive Boolean Functions
J.C. Bioch (Cor); T. Ibaraki
1995-01-01
textabstractWe consider in this paper the problem of identifying min T(f{hook}) and max F(f{hook}) of a positive (i.e., monotone) Boolean function f{hook}, by using membership queries only, where min T(f{hook}) (max F(f{hook})) denotes the set of minimal true vectors (maximal false vectors) of
Learning restricted Boolean network model by time-series data.
Ouyang, Hongjia; Fang, Jie; Shen, Liangzhong; Dougherty, Edward R; Liu, Wenbin
2014-01-01
Restricted Boolean networks are simplified Boolean networks that are required for either negative or positive regulations between genes. Higa et al. (BMC Proc 5:S5, 2011) proposed a three-rule algorithm to infer a restricted Boolean network from time-series data. However, the algorithm suffers from a major drawback, namely, it is very sensitive to noise. In this paper, we systematically analyze the regulatory relationships between genes based on the state switch of the target gene and propose an algorithm with which restricted Boolean networks may be inferred from time-series data. We compare the proposed algorithm with the three-rule algorithm and the best-fit algorithm based on both synthetic networks and a well-studied budding yeast cell cycle network. The performance of the algorithms is evaluated by three distance metrics: the normalized-edge Hamming distance [Formula: see text], the normalized Hamming distance of state transition [Formula: see text], and the steady-state distribution distance μ (ssd). Results show that the proposed algorithm outperforms the others according to both [Formula: see text] and [Formula: see text], whereas its performance according to μ (ssd) is intermediate between best-fit and the three-rule algorithms. Thus, our new algorithm is more appropriate for inferring interactions between genes from time-series data.
Exact traveling wave solutions for system of nonlinear evolution equations.
Khan, Kamruzzaman; Akbar, M Ali; Arnous, Ahmed H
2016-01-01
In this work, recently deduced generalized Kudryashov method is applied to the variant Boussinesq equations, and the (2 + 1)-dimensional breaking soliton equations. As a result a range of qualitative explicit exact traveling wave solutions are deduced for these equations, which motivates us to develop, in the near future, a new approach to obtain unsteady solutions of autonomous nonlinear evolution equations those arise in mathematical physics and engineering fields. It is uncomplicated to extend this method to higher-order nonlinear evolution equations in mathematical physics. And it should be possible to apply the same method to nonlinear evolution equations having more general forms of nonlinearities by utilizing the traveling wave hypothesis.
Modeling integrated cellular machinery using hybrid Petri-Boolean networks.
Directory of Open Access Journals (Sweden)
Natalie Berestovsky
Full Text Available The behavior and phenotypic changes of cells are governed by a cellular circuitry that represents a set of biochemical reactions. Based on biological functions, this circuitry is divided into three types of networks, each encoding for a major biological process: signal transduction, transcription regulation, and metabolism. This division has generally enabled taming computational complexity dealing with the entire system, allowed for using modeling techniques that are specific to each of the components, and achieved separation of the different time scales at which reactions in each of the three networks occur. Nonetheless, with this division comes loss of information and power needed to elucidate certain cellular phenomena. Within the cell, these three types of networks work in tandem, and each produces signals and/or substances that are used by the others to process information and operate normally. Therefore, computational techniques for modeling integrated cellular machinery are needed. In this work, we propose an integrated hybrid model (IHM that combines Petri nets and Boolean networks to model integrated cellular networks. Coupled with a stochastic simulation mechanism, the model simulates the dynamics of the integrated network, and can be perturbed to generate testable hypotheses. Our model is qualitative and is mostly built upon knowledge from the literature and requires fine-tuning of very few parameters. We validated our model on two systems: the transcriptional regulation of glucose metabolism in human cells, and cellular osmoregulation in S. cerevisiae. The model produced results that are in very good agreement with experimental data, and produces valid hypotheses. The abstract nature of our model and the ease of its construction makes it a very good candidate for modeling integrated networks from qualitative data. The results it produces can guide the practitioner to zoom into components and interconnections and investigate them
Solving differential–algebraic equation systems by means of index reduction methodology
DEFF Research Database (Denmark)
Sørensen, Kim; Houbak, Niels; Condra, Thomas
2006-01-01
of a number of differential equations and algebraic equations — a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of ordinary differential equations — ODEs....... stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper...
Solving differential-algebraic equation systems by means of index reduction methodology
DEFF Research Database (Denmark)
Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph
2006-01-01
of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper...
Maxwell-Vlasov equations as a continuous Hamiltonian system
International Nuclear Information System (INIS)
Morrison, P.J.
1980-09-01
The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion
Maxwell-Vlasov equations as a continuous Hamiltonian system
International Nuclear Information System (INIS)
Morrison, P.J.
1980-11-01
The well-known Maxwell-Vlasov equations that describe a collisionless plasma are cast into Hamiltonian form. The dynamical variables are the physical although noncanonical variables E, B, and f. We present a Poisson bracket which acts on these variables and the energy functional to produce the equations of motion
Modeling systems containing alkanolamines with the CPA equation of state
DEFF Research Database (Denmark)
Avlund, Ane Søgaard; Kontogeorgis, Georgios; Michelsen, Michael Locht
2008-01-01
An association model, the cubic-plus-association (CPA) equation of state (EoS), is applied for the first time to a class of multifunctional compounds (alkanolamines). Three alkanolamines of practical and scientific significance are considered; monoethanolamine (MEA), diethanolamine (DEA...... studied using the CPA equation of state (alcohols, amines, and glycols)....
Variances as order parameter and complexity measure for random Boolean networks
International Nuclear Information System (INIS)
Luque, Bartolo; Ballesteros, Fernando J; Fernandez, Manuel
2005-01-01
Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems
A quantum speedup in machine learning: finding an N-bit Boolean function for a classification
International Nuclear Information System (INIS)
Yoo, Seokwon; Lee, Jinhyoung; Bang, Jeongho; Lee, Changhyoup
2014-01-01
We compare quantum and classical machines designed for learning an N-bit Boolean function in order to address how a quantum system improves the machine learning behavior. The machines of the two types consist of the same number of operations and control parameters, but only the quantum machines utilize the quantum coherence naturally induced by unitary operators. We show that quantum superposition enables quantum learning that is faster than classical learning by expanding the approximate solution regions, i.e., the acceptable regions. This is also demonstrated by means of numerical simulations with a standard feedback model, namely random search, and a practical model, namely differential evolution. (paper)
Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras
Andrade, Jefferson O.; Kameyama, Yukiyoshi
2012-01-01
Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In thi...
Construction of a fuzzy and all Boolean logic gates based on DNA
DEFF Research Database (Denmark)
M. Zadegan, Reza; Jepsen, Mette D E; Hildebrandt, Lasse
2015-01-01
to the operation of the six Boolean logic gates AND, NAND, OR, NOR, XOR, and XNOR. The logic gate complex is shown to work also when implemented in a three-dimensional DNA origami box structure, where it controlled the position of the lid in a closed or open position. Implementation of multiple microRNA sensitive...... DNA locks on one DNA origami box structure enabled fuzzy logical operation that allows biosensing of complex molecular signals. Integrating logic gates with DNA origami systems opens a vast avenue to applications in the fields of nanomedicine for diagnostics and therapeutics....
Variances as order parameter and complexity measure for random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Luque, Bartolo [Departamento de Matematica Aplicada y EstadIstica, Escuela Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, Madrid 28040 (Spain); Ballesteros, Fernando J [Observatori Astronomic, Universitat de Valencia, Ed. Instituts d' Investigacio, Pol. La Coma s/n, E-46980 Paterna, Valencia (Spain); Fernandez, Manuel [Departamento de Matematica Aplicada y EstadIstica, Escuela Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, Plaza Cardenal Cisneros 3, Madrid 28040 (Spain)
2005-02-04
Several order parameters have been considered to predict and characterize the transition between ordered and disordered phases in random Boolean networks, such as the Hamming distance between replicas or the stable core, which have been successfully used. In this work, we propose a natural and clear new order parameter: the temporal variance. We compute its value analytically and compare it with the results of numerical experiments. Finally, we propose a complexity measure based on the compromise between temporal and spatial variances. This new order parameter and its related complexity measure can be easily applied to other complex systems.
International Nuclear Information System (INIS)
Brett, Tobias; Galla, Tobias
2014-01-01
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period
Brett, Tobias; Galla, Tobias
2014-03-28
We present a heuristic derivation of Gaussian approximations for stochastic chemical reaction systems with distributed delay. In particular, we derive the corresponding chemical Langevin equation. Due to the non-Markovian character of the underlying dynamics, these equations are integro-differential equations, and the noise in the Gaussian approximation is coloured. Following on from the chemical Langevin equation, a further reduction leads to the linear-noise approximation. We apply the formalism to a delay variant of the celebrated Brusselator model, and show how it can be used to characterise noise-driven quasi-cycles, as well as noise-triggered spiking. We find surprisingly intricate dependence of the typical frequency of quasi-cycles on the delay period.
A system of abstract measure delay differential equations
Directory of Open Access Journals (Sweden)
Bapurao Dhage
2003-01-01
Full Text Available In this paper existence and uniqueness results for an abstract measure delay differential equation are proved, by using Leray-Schauder nonlinear alternative, under Carathéodory conditions.
Hong, Changki; Hwang, Jeewon; Cho, Kwang-Hyun; Shin, Insik
2015-01-01
Boolean networks have been widely used to model biological processes lacking detailed kinetic information. Despite their simplicity, Boolean network dynamics can still capture some important features of biological systems such as stable cell phenotypes represented by steady states. For small models, steady states can be determined through exhaustive enumeration of all state transitions. As the number of nodes increases, however, the state space grows exponentially thus making it difficult to find steady states. Over the last several decades, many studies have addressed how to handle such a state space explosion. Recently, increasing attention has been paid to a satisfiability solving algorithm due to its potential scalability to handle large networks. Meanwhile, there still lies a problem in the case of large models with high maximum node connectivity where the satisfiability solving algorithm is known to be computationally intractable. To address the problem, this paper presents a new partitioning-based method that breaks down a given network into smaller subnetworks. Steady states of each subnetworks are identified by independently applying the satisfiability solving algorithm. Then, they are combined to construct the steady states of the overall network. To efficiently apply the satisfiability solving algorithm to each subnetwork, it is crucial to find the best partition of the network. In this paper, we propose a method that divides each subnetwork to be smallest in size and lowest in maximum node connectivity. This minimizes the total cost of finding all steady states in entire subnetworks. The proposed algorithm is compared with others for steady states identification through a number of simulations on both published small models and randomly generated large models with differing maximum node connectivities. The simulation results show that our method can scale up to several hundreds of nodes even for Boolean networks with high maximum node connectivity. The
Discrete systems related to the sixth Painleve equation
International Nuclear Information System (INIS)
Ramani, A; Ohta, Y; Grammaticos, B
2006-01-01
We present discrete Painleve equations which can be obtained as contiguity relations of the solutions of the continuous Painleve VI. The derivation is based on the geometry of the affine Weyl group D (1) 4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau-Ablowitz-Fokas equation, which is a Miura transformed, 'modified', P VI
A model for closing the inviscid form of the average-passage equation system
Adamczyk, J. J.; Mulac, R. A.; Celestina, M. L.
1986-01-01
A mathematical model is proposed for closing or mathematically completing the system of equations which describes the time average flow field through the blade passages of multistage turbomachinery. These equations referred to as the average passage equation system govern a conceptual model which has proven useful in turbomachinery aerodynamic design and analysis. The closure model is developed so as to insure a consistency between these equations and the axisymmetric through flow equations. The closure model was incorporated into a computer code for use in simulating the flow field about a high speed counter rotating propeller and a high speed fan stage. Results from these simulations are presented.
Solution of systems of linear algebraic equations by the method of summation of divergent series
International Nuclear Information System (INIS)
Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.
2015-01-01
A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru
Susuki, Yoshihiko; Hikihara Takashi; Chiang, HD
2004-01-01
This paper discusses stability boundaries in an electric power system with dc transmission based on a differential-algebraic equation (DAE) system. The DAE system is derived to analyze transient stability of the ac/dc power system: the differential equation represents the dynamics of the generator and the dc transmission, and the algebraic equation the active and reactive power relationship between the ac system and the dc transmission. In this paper complete characterization of stability bou...
High Quality Test Pattern Generation and Boolean Satisfiability
Eggersglüß, Stephan
2012-01-01
This book provides an overview of automatic test pattern generation (ATPG) and introduces novel techniques to complement classical ATPG, based on Boolean Satisfiability (SAT). A fast and highly fault efficient SAT-based ATPG framework is presented which is also able to generate high-quality delay tests such as robust path delay tests, as well as tests with long propagation paths to detect small delay defects. The aim of the techniques and methodologies presented in this book is to improve SAT-based ATPG, in order to make it applicable in industrial practice. Readers will learn to improve the performance and robustness of the overall test generation process, so that the ATPG algorithm reliably will generate test patterns for most targeted faults in acceptable run time to meet the high fault coverage demands of industry. The techniques and improvements presented in this book provide the following advantages: Provides a comprehensive introduction to test generation and Boolean Satisfiability (SAT); Describes a...
New approach to solve fully fuzzy system of linear equations using ...
Indian Academy of Sciences (India)
This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied ...
New approach to solve fully fuzzy system of linear equations using ...
Indian Academy of Sciences (India)
Abstract. This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and.
Boolean Functions with a Simple Certificate for CNF Complexity
Czech Academy of Sciences Publication Activity Database
Čepek, O.; Kučera, P.; Savický, Petr
2012-01-01
Roč. 160, 4-5 (2012), s. 365-382 ISSN 0166-218X R&D Projects: GA MŠk(CZ) 1M0545 Grant - others:GA ČR(CZ) GP201/07/P168; GA ČR(CZ) GAP202/10/1188 Institutional research plan: CEZ:AV0Z10300504 Keywords : Boolean functions * CNF representations Subject RIV: BA - General Mathematics Impact factor: 0.718, year: 2012
Elements of Boolean-Valued Dempster-Shafer Theory
Czech Academy of Sciences Publication Activity Database
Kramosil, Ivan
2000-01-01
Roč. 10, č. 5 (2000), s. 825-835 ISSN 1210-0552. [SOFSEM 2000 Workshop on Soft Computing. Milovy, 27.11.2000-28.11.2000] R&D Projects: GA ČR GA201/00/1489 Institutional research plan: AV0Z1030915 Keywords : Boolean algebra * belief function * Dempster-Shafer theory * Dempster combination rule * nonspecifity degree Subject RIV: BA - General Mathematics
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Approximating attractors of Boolean networks by iterative CTL model checking
Directory of Open Access Journals (Sweden)
Hannes eKlarner
2015-09-01
Full Text Available This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: faithfulness which requires that the oscillating variables of all attractors in a trapspace correspond to their dimensions, univocality which requires that there is a unique attractor in each trap space and completeness which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal and complete which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Binary higher order neural networks for realizing Boolean functions.
Zhang, Chao; Yang, Jie; Wu, Wei
2011-05-01
In order to more efficiently realize Boolean functions by using neural networks, we propose a binary product-unit neural network (BPUNN) and a binary π-ς neural network (BPSNN). The network weights can be determined by one-step training. It is shown that the addition " σ," the multiplication " π," and two kinds of special weighting operations in BPUNN and BPSNN can implement the logical operators " ∨," " ∧," and " ¬" on Boolean algebra 〈Z(2),∨,∧,¬,0,1〉 (Z(2)={0,1}), respectively. The proposed two neural networks enjoy the following advantages over the existing networks: 1) for a complete truth table of N variables with both truth and false assignments, the corresponding Boolean function can be realized by accordingly choosing a BPUNN or a BPSNN such that at most 2(N-1) hidden nodes are needed, while O(2(N)), precisely 2(N) or at most 2(N), hidden nodes are needed by existing networks; 2) a new network BPUPS based on a collaboration of BPUNN and BPSNN can be defined to deal with incomplete truth tables, while the existing networks can only deal with complete truth tables; and 3) the values of the weights are all simply -1 or 1, while the weights of all the existing networks are real numbers. Supporting numerical experiments are provided as well. Finally, we present the risk bounds of BPUNN, BPSNN, and BPUPS, and then analyze their probably approximately correct learnability.
The Schroedinger-Newton equation as model of self-gravitating quantum systems
International Nuclear Information System (INIS)
Grossardt, Andre
2013-01-01
The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem
Boolean network model for cancer pathways: predicting carcinogenesis and targeted therapy outcomes.
Directory of Open Access Journals (Sweden)
Herman F Fumiã
Full Text Available A Boolean dynamical system integrating the main signaling pathways involved in cancer is constructed based on the currently known protein-protein interaction network. This system exhibits stationary protein activation patterns--attractors--dependent on the cell's microenvironment. These dynamical attractors were determined through simulations and their stabilities against mutations were tested. In a higher hierarchical level, it was possible to group the network attractors into distinct cell phenotypes and determine driver mutations that promote phenotypic transitions. We find that driver nodes are not necessarily central in the network topology, but at least they are direct regulators of central components towards which converge or through which crosstalk distinct cancer signaling pathways. The predicted drivers are in agreement with those pointed out by diverse census of cancer genes recently performed for several human cancers. Furthermore, our results demonstrate that cell phenotypes can evolve towards full malignancy through distinct sequences of accumulated mutations. In particular, the network model supports routes of carcinogenesis known for some tumor types. Finally, the Boolean network model is employed to evaluate the outcome of molecularly targeted cancer therapies. The major find is that monotherapies were additive in their effects and that the association of targeted drugs is necessary for cancer eradication.
International Nuclear Information System (INIS)
Kudryavtsev, L D
2006-01-01
The problem under consideration concerns when a system of ordinary differential equations reducible to a weakly non-linear system has solutions with the same asymptotic behaviour as solutions of the corresponding homogeneous system. The existence and uniqueness of global solutions to the inhomogeneous system is established in the form of a solution to a homogeneous system of differential equations, in the case when asymptotic initial data is prescribed at the singular points of these systems.
International Nuclear Information System (INIS)
Lofgren, E.V.
1985-08-01
This course in System Reliability and Analysis Techniques focuses on the probabilistic quantification of accident sequences and the link between accident sequences and consequences. Other sessions in this series focus on the quantification of system reliability and the development of event trees and fault trees. This course takes the viewpoint that event tree sequences or combinations of system failures and success are available and that Boolean equations for system fault trees have been developed and are available. 93 figs., 11 tabs
Adams Predictor-Corrector Systems for Solving Fuzzy Differential Equations
Directory of Open Access Journals (Sweden)
Dequan Shang
2013-01-01
Full Text Available A predictor-corrector algorithm and an improved predictor-corrector (IPC algorithm based on Adams method are proposed to solve first-order differential equations with fuzzy initial condition. These algorithms are generated by updating the Adams predictor-corrector method and their convergence is also analyzed. Finally, the proposed methods are illustrated by solving an example.
An integrated approach to determine phenomenological equations in metallic systems
Ghamarian, Iman
It is highly desirable to be able to make predictions of properties in metallic materials based upon the composition of the material and the microstructure. Unfortunately, the complexity of real, multi-component, multi-phase engineering alloys makes the provision of constituent-based (i.e., composition or microstructure) phenomenological equations extremely difficult. Due to these difficulties, qualitative predictions are frequently used to study the influence of microstructure or composition on the properties. Neural networks were used as a tool to get a quantitative model from a database. However, the developed model is not a phenomenological model. In this study, a new method based upon the integration of three separate modeling approaches, specifically artificial neural networks, genetic algorithms, and monte carlo was proposed. These three methods, when coupled in the manner described in this study, allows for the extraction of phenomenological equations with a concurrent analysis of uncertainty. This approach has been applied to a multi-component, multi-phase microstructure exhibiting phases with varying spatial and morphological distributions. Specifically, this approach has been applied to derive a phenomenological equation for the prediction of yield strength in alpha+beta processed Ti-6-4. The equation is consistent with not only the current dataset but also, where available, the limited information regarding certain parameters such as intrinsic yield strength of pure hexagonal close-packed alpha titanium.
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
These sections are written in more intuitive fashion avoiding the jargon as far as possible. In §3, we discuss some examples of Fα-differential equations. ..... We emphasize the appearance of intersection F ∩ I in the definition of M and m, and also the use of (Sα. F (xi+1) − Sα. F (xi)) as in a Riemann–Stieltjes sum instead.
On the Equational Definition of the Least Prefixed Point
DEFF Research Database (Denmark)
Santocanale, Luigi
2003-01-01
We propose a method to axiomatize by equations the least prefixed point of an order preserving function. We discuss its domain of application and show that the Boolean modal μ-calculus has a complete equational axiomatization. The method relies on the existence of a “closed structure” and its...
Dynamics of open quantum spin systems : An assessment of the quantum master equation approach
Zhao, P.; De Raedt, H.; Miyashita, S.; Jin, F.; Michielsen, K.
2016-01-01
Data of the numerical solution of the time-dependent Schrodinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of
A model for closing the inviscid form of the average passage equation system
Adamczyk, John J.; Mulac, R. A.; Celestina, M. L.
1996-01-01
A mathematical model for closing or mathematically completing the system of equations is proposed. The model describes the time average flow field through the blade passages of multistage turbomachinery. These average-passage equation systems govern a conceptual model useful in turbomachinery aerodynamic design and analysis. The closure model was developed to insure a consistency between these equations and the axisymmetric through-flow equations. The closure model was incorporated into a calculation code for use in the simulation of the flow field about a high-speed counter rotating propeller and a high-speed fan stage.
Directory of Open Access Journals (Sweden)
Fayyaz Ahmad
2017-01-01
Full Text Available A modification to an existing iterative method for computing zeros with unknown multiplicities of nonlinear equations or a system of nonlinear equations is presented. We introduce preconditioners to nonlinear equations or a system of nonlinear equations and their corresponding Jacobians. The inclusion of preconditioners provides numerical stability and accuracy. The different selection of preconditioner offers a family of iterative methods. We modified an existing method in a way that we do not alter its inherited quadratic convergence. Numerical simulations confirm the quadratic convergence of the preconditioned iterative method. The influence of preconditioners is clearly reflected in the numerically achieved accuracy of computed solutions.
International Nuclear Information System (INIS)
Rawajfeh, M. K.; Al-Matar, A.
2000-01-01
A generalized equation relating equilibrium data, phase ratio and fractional recovery is developed. The use of this equation reduces the presentation of these data to a single dimensionless curve independent of the system and the operating conditions. The validity of this equation is tested using experimental data for different liquid - liquid systems at various condition. a reasonable agreement between experimental results and predicated ones was obtained. The use of this equation in investigating the effect of phase ratio on the fractional recovery is illustrated. (authors). 6 refs., 4 figs., 3 tabs
Tanışlı, Murat; Kansu, Mustafa Emre; Demir, Süleyman
2014-05-01
In this paper, the real, complex octonion algebra and their properties are defined. The electromagnetic and gravito-electromagnetic equations with monopoles in terms of S and reference systems are presented in vector notations. Additionally, the duality transformations of gravito-electromagnetic situation for two reference systems are also represented. Besides, it is explained that Maxwell-like equations for gravito-electromagnetism are also invariant under Lorentz transformations. By introducing complex octonionic differential operator, a new generalized complex octonionic field term consisting of electromagnetic and gravito-electromagnetic components has been firstly suggested for Lorentz system. Afterwards, a complex octonionic source equation is obtained as in basic way, more compact and elegant notation. By defining a new complex octonionic general potential term, the field equation is attained once again. The components of complex octonionic field and wave equations are written in detailed for S and reference systems.
Global existence and decay of solutions of a nonlinear system of wave equations
Said-Houari, Belkacem
2012-03-01
This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.
Lyapunov stability and its application to systems of ordinary differential equations
Kennedy, E. W.
1979-01-01
An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.
An analogy between macroscopic and microscopic systems for Maxwell's equations in higher dimensions
Emre Kansu, Mustafa
2013-12-01
In this study, Maxwell's equations are discussed for macroscopic and microscopic systems by obtaining them from free and bound charge and current densities. In addition to electric and magnetic fields, the polarization and magnetization vectors are defined by the hyperbolic octonion basis. Finally, by introducing the hyperbolic octonionic field equation, for the first time, the hyperbolic octonionic source equation is represented in a simple, useful and elegant manner in terms of free charge, free and bound current densities.
A 'User-Friendly' Approach to the Dynamical Equations of Non-Holonomic Systems
Directory of Open Access Journals (Sweden)
Sergio Benenti
2007-03-01
Full Text Available Two effective methods for writing the dynamical equations for non-holonomic systems are illustrated. They are based on the two types of representation of the constraints: by parametric equations or by implicit equations. They can be applied to linear as well as to non-linear constraints. Only the basic notions of vector calculus on Euclidean 3-space and on tangent bundles are needed. Elementary examples are illustrated.
Directory of Open Access Journals (Sweden)
Heinz Toparkus
2014-04-01
Full Text Available In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial value problems in appropriate basic areas, and you can try to achieve a solution of these problems by means of transform methods.
Periodic Solutions of a System of Delay Differential Equations for a Small Delay
Directory of Open Access Journals (Sweden)
Adu A.M. Wasike
2002-06-01
Full Text Available We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system. This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem.
An Association Rule Mining Algorithm Based on a Boolean Matrix
Directory of Open Access Journals (Sweden)
Hanbing Liu
2007-09-01
Full Text Available Association rule mining is a very important research topic in the field of data mining. Discovering frequent itemsets is the key process in association rule mining. Traditional association rule algorithms adopt an iterative method to discovery, which requires very large calculations and a complicated transaction process. Because of this, a new association rule algorithm called ABBM is proposed in this paper. This new algorithm adopts a Boolean vector "relational calculus" method to discovering frequent itemsets. Experimental results show that this algorithm can quickly discover frequent itemsets and effectively mine potential association rules.
A Construction of Boolean Functions with Good Cryptographic Properties
2014-01-01
over Fn2 defined by Wf (u) = ∑ x∈Fn2 (−1)f(x)+u·x, where u ∈ Fn2 and u · x is an inner product , for instance, u · x = u1x1 + u2x3 + · · · + unxn, where u...later on for all these classes. We mention also the paper of Pasalic [27], which introduces the notion of high degree product (HDP) to mea- sure the...2008, LNCS 5350, Springer–Verlag, 2008, pp. 425–440. [10] C. Carlet and K. Feng, “An Infinite Class of Balanced Vectorial Boolean Functions with Optimum
A Boolean Approach to Airline Business Model Innovation
DEFF Research Database (Denmark)
Hvass, Kristian Anders
Research in business model innovation has identified its significance in creating a sustainable competitive advantage for a firm, yet there are few empirical studies identifying which combination of business model activities lead to success and therefore deserve innovative attention. This study...... analyzes the business models of North America low-cost carriers from 2001 to 2010 using a Boolean minimization algorithm to identify which combinations of business model activities lead to operational profitability. The research aim is threefold: complement airline literature in the realm of business model...
Bebop to the Boolean boogie an unconventional guide to electronics
Maxfield, Clive
2003-01-01
From reviews of the first edition:""If you want to be reminded of the joy of electronics, take a look at Clive (Max) Maxfield's book Bebop to the Boolean Boogie.""--Computer Design ""Lives up to its title as a useful and entertaining technical guide....well-suited for students, technical writers, technicians, and sales and marketing people.""--Electronic Design""Writing a book like this one takes audacity! ... Maxfield writes lucidly on a variety of complex topics without 'writing down' to his audience."" --EDN""A highly readable, well-illustrated guided tour
Two Expectation-Maximization Algorithms for Boolean Factor Analysis
Czech Academy of Sciences Publication Activity Database
Frolov, A. A.; Húsek, Dušan; Polyakov, P.Y.
2014-01-01
Roč. 130, 23 April (2014), s. 83-97 ISSN 0925-2312 R&D Projects: GA ČR GAP202/10/0262 Grant - others:GA MŠk(CZ) ED1.1.00/02.0070; GA MŠk(CZ) EE.2.3.20.0073 Program:ED Institutional research plan: CEZ:AV0Z10300504 Keywords : Boolean Factor analysis * Binary Matrix factorization * Neural networks * Binary data model * Dimension reduction * Bars problem Subject RIV: IN - Informatics, Computer Science Impact factor: 2.083, year: 2014
Ket-Bra entangled state method for solving master equation of finite-level system
Ren, Yi-Chong; Wang, Shu; Fan, Hong-Yi; Chen, Feng
2017-11-01
In this paper, we first introduce Ket-Bra entangled state method to solve master equation of finite-level system, which can convert master equation into Schrödinger-like equation and solve it with the mature methodology of Schrödinger equation. Then, several physical models include a radioactivity damped 2-level atom driven by classical field, a J- C model with cavity damping, a V-type qutrit under amplitude damping and N-qubits open Heisenberg chain have been solved with KBES method. Furthermore, the dynamic evolution and decoherence process of these models are investigated.
Description of Five-Nucleon Systems Using Faddeev-Yakubovsky Equations
Lazauskas, Rimantas
2018-03-01
A brief overview of Faddeev-Yakubovsky equations is presented before deriving 5-body ones. Numerical formalism, enabling to solve these equations in configuration space for a system of five nucleons is described. Microscopic calculations are realized to determine phaseshifts of low energy neutron scattering on ^4He and 1/2^+ resonance position of ^5H, employing phenomenological MT I-III potential.
Directory of Open Access Journals (Sweden)
Berenguer MI
2010-01-01
Full Text Available This paper deals with obtaining a numerical method in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach, a sequence of functions which approximate the solution of this type of equation, due to some properties of certain biorthogonal systems for the Banach spaces and .
Tsai, Tien-Lung; Shau, Wen-Yi; Hu, Fu-Chang
2006-01-01
This article generalizes linear path analysis (PA) and simultaneous equations models (SiEM) to deal with mixed responses of different types in a recursive or triangular system. An efficient instrumental variable (IV) method for estimating the structural coefficients of a 2-equation partially recursive generalized path analysis (GPA) model and…
Directory of Open Access Journals (Sweden)
Pål Johan From
2012-04-01
Full Text Available This paper presents the explicit dynamic equations of multibody mechanical systems. This is the second paper on this topic. In the first paper the dynamics of a single rigid body from the Boltzmann--Hamel equations were derived. In this paper these results are extended to also include multibody systems. We show that when quasi-velocities are used, the part of the dynamic equations that appear from the partial derivatives of the system kinematics are identical to the single rigid body case, but in addition we get terms that come from the partial derivatives of the inertia matrix, which are not present in the single rigid body case. We present for the first time the complete and correct derivation of multibody systems based on the Boltzmann--Hamel formulation of the dynamics in Lagrangian form where local position and velocity variables are used in the derivation to obtain the singularity-free dynamic equations. The final equations are written in global variables for both position and velocity. The main motivation of these papers is to allow practitioners not familiar with differential geometry to implement the dynamic equations of rigid bodies without the presence of singularities. Presenting the explicit dynamic equations also allows for more insight into the dynamic structure of the system. Another motivation is to correct some errors commonly found in the literature. Unfortunately, the formulation of the Boltzmann-Hamel equations used here are presented incorrectly. This has been corrected by the authors, but we present here, for the first time, the detailed mathematical details on how to arrive at the correct equations. We also show through examples that using the equations presented here, the dynamics of a single rigid body is reduced to the standard equations on a Lagrangian form, for example Euler's equations for rotational motion and Euler--Lagrange equations for free motion.
Reduced equations of motion for quantum systems driven by diffusive Markov processes.
Sarovar, Mohan; Grace, Matthew D
2012-09-28
The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.
Rosenbaum, J. S.
1971-01-01
Systems of ordinary differential equations in which the magnitudes of the eigenvalues (or time constants) vary greatly are commonly called stiff. Such systems of equations arise in nuclear reactor kinetics, the flow of chemically reacting gas, dynamics, control theory, circuit analysis and other fields. The research reported develops an A-stable numerical integration technique for solving stiff systems of ordinary differential equations. The method, which is called the generalized trapezoidal rule, is a modification of the trapezoidal rule. However, the method is computationally more efficient than the trapezoidal rule when the solution of the almost-discontinuous segments is being calculated.
Effective methods of solving of model equations of certain class of thermal systems
International Nuclear Information System (INIS)
Lach, J.
1985-01-01
A number of topics connected with solving of model equations of certain class of thermal systems by the method of successive approximations is touched. A system of partial differential equations of the first degree, appearing most frequently in practical applications of heat and mass transfer theory is reduced to an equivalent system of Volterra integral equations of the second kind. Among a few sample applications the thermal processes appearing in the fuel channel of nuclear reactor are solved. The theoretical analysis is illustrated by the results of numerical calculations given in tables and diagrams. 111 refs., 17 figs., 16 tabs. (author)
New soliton solutions of the system of equations for the ion sound and Langmuir waves
Directory of Open Access Journals (Sweden)
Seyma Tuluce Demiray
2016-11-01
Full Text Available This study is based on new soliton solutions of the system of equations for the ion sound wave under the action of the ponderomotive force due to high-frequency field and for the Langmuir wave. The generalized Kudryashov method (GKM, which is one of the analytical methods, has been tackled for finding exact solutions of the system of equations for the ion sound wave and the Langmuir wave. By using this method, dark soliton solutions of this system of equations have been obtained. Also, by using Mathematica Release 9, some graphical simulations were designed to see the behavior of these solutions.
Parametric Borel summability for some semilinear system of partial differential equations
Directory of Open Access Journals (Sweden)
Hiroshi Yamazawa
2015-01-01
Full Text Available In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with \\(n\\ independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002, 313-322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singular perturbation parameter for a linear equation with one independent variable. We shall extend their results to a semilinear system of equations with general independent variables.
Complexity classifications for different equivalence and audit problems for Boolean circuits
BÃ¶hler, Elmar; Creignou, Nadia; Galota, Matthias; Reith, Steffen; Schnoor, Henning; Vollmer, Heribert
2010-01-01
We study Boolean circuits as a representation of Boolean functions and conskier different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all other gate types we show these problems are at least NP-hard.
Ones and zeros understanding Boolean algebra digital circuits and the logic of sets
Gregg, John
1998-01-01
"Ones and Zeros explains, in lay terms, Boolean algebra, the suprisingly simple system of mathematical logic used in digital computer circuitry. Ones and Zeros follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. Readers will learn about the interesting history of the development of symbolic logic in particular, and the often misunderstood process of mathematical invention and scientific discovery, in general. Ones and Zeros also features practical exercises with answers, real-world examples of digital circuit design, and a reading list." "Ones and Zeros will be of particular interest to software engineers who want to gain a comprehensive understanding of computer hardware." "Outstanding features include: a history of mathematical logic, an explanation of the logic of digital circuits, and hands-on exercises and examples."--Jacket.
On extension of solutions of a simultaneous system of iterative functional equations
Directory of Open Access Journals (Sweden)
Janusz Matkowski
2009-01-01
Full Text Available Some sufficient conditions which allow to extend every local solution of a simultaneous system of equations in a single variable of the form \\[ \\varphi(x = h (x, \\varphi[f_1(x],\\ldots,\\varphi[f_m(x],\\] \\[\\varphi(x = H (x, \\varphi[F_1(x],\\ldots,\\varphi[F_m(x],\\] to a global one are presented. Extensions of solutions of functional equations, both in single and in several variables, play important role (cf. for instance [M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warsaw, 1968, M. Kuczma, B. Choczewski, R. Ger, Iterative functional equations, Encyclopedia of Mathematics and Its Applications v. 32, Cambridge, 1990, J. Matkowski, Iteration groups, commuting functions and simultaneous systems of linear functional equations, Opuscula Math. 28 (2008 4, 531-541].
On the complexities of ionospheric current systems equator ward of ...
African Journals Online (AJOL)
Therefore the complexities of the diurnal profiles of Sq(H) and SPMF(H), even on a very quiet day after correcting for Dst, are caused by the interactions of the magnetic fields of the following current systems; the EEJ current system periodically modulated by the lunar current system in accordance with lunar phases and ...
Chemical Visualization of Boolean Functions: A Simple Chemical Computer
Blittersdorf, R.; Müller, J.; Schneider, F. W.
1995-08-01
We present a chemical realization of the Boolean functions AND, OR, NAND, and NOR with a neutralization reaction carried out in three coupled continuous flow stirred tank reactors (CSTR). Two of these CSTR's are used as input reactors, the third reactor marks the output. The chemical reaction is the neutralization of hydrochloric acid (HCl) with sodium hydroxide (NaOH) in the presence of phenolphtalein as an indicator, which is red in alkaline solutions and colorless in acidic solutions representing the two binary states 1 and 0, respectively. The time required for a "chemical computation" is determined by the flow rate of reactant solutions into the reactors since the neutralization reaction itself is very fast. While the acid flow to all reactors is equal and constant, the flow rate of NaOH solution controls the states of the input reactors. The connectivities between the input and output reactors determine the flow rate of NaOH solution into the output reactor, according to the chosen Boolean function. Thus the state of the output reactor depends on the states of the input reactors.
Boolean models of biosurfactants production in Pseudomonas fluorescens.
Directory of Open Access Journals (Sweden)
Adrien Richard
Full Text Available Cyclolipopeptides (CLPs are biosurfactants produced by numerous Pseudomonas fluorescens strains. CLP production is known to be regulated at least by the GacA/GacS two-component pathway, but the full regulatory network is yet largely unknown. In the clinical strain MFN1032, CLP production is abolished by a mutation in the phospholipase C gene (plcC and not restored by plcC complementation. Their production is also subject to phenotypic variation. We used a modelling approach with Boolean networks, which takes into account all these observations concerning CLP production without any assumption on the topology of the considered network. Intensive computation yielded numerous models that satisfy these properties. All models minimizing the number of components point to a bistability in CLP production, which requires the presence of a yet unknown key self-inducible regulator. Furthermore, all suggest that a set of yet unexplained phenotypic variants might also be due to this epigenetic switch. The simplest of these Boolean networks was used to propose a biological regulatory network for CLP production. This modelling approach has allowed a possible regulation to be unravelled and an unusual behaviour of CLP production in P. fluorescens to be explained.
Synchronization Analysis of Master-Slave Probabilistic Boolean Networks.
Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W C; Cao, Jinde
2015-08-28
In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results.
Assanova, Anar T.; Bakirova, Elmira A.; Kadirbayeva, Zhazira M.
2017-09-01
The periodic problem for a system of integro-differential equations of hyperbolic type with impulse effects is considered. This problem is reduced to an equivalent problem, consisting of a family of periodic boundary value problems for system of ordinary differential equations with parameter and impulse effects and integral relations by method of introducing additional functions. Sufficient conditions for existence of unique solution to the family of periodic boundary value problem with the impulse effects for system of the ordinary differential equations are received by parametrization method. Conditions for the unique solvability of periodic problem for system of integro - differential equations of hyperbolic type with impulse effects are established in the term of initial data.
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I. A. Pugachev
2013-01-01
Full Text Available A process of heat transfer in continuous casting mould is considered. The substantiated equations predict shell growth, temperature distributions, solidification rates and can be used for continuous casters control systems.
National Research Council Canada - National Science Library
Lucke, Robert
2002-01-01
.... Design equations are presented to allow quick assessment of the hardware parameters required for a notional system, most notably optical aperture sizes and the laser's power, chirp, and pulse rate capabilities...
Riccati and Ermakov Equations in Time-Dependent and Time-Independent Quantum Systems
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Dieter Schuch
2008-05-01
Full Text Available The time-evolution of the maximum and the width of exact analytic wave packet (WP solutions of the time-dependent Schrödinger equation (SE represents the particle and wave aspects, respectively, of the quantum system. The dynamics of the maximum, located at the mean value of position, is governed by the Newtonian equation of the corresponding classical problem. The width, which is directly proportional to the position uncertainty, obeys a complex nonlinear Riccati equation which can be transformed into a real nonlinear Ermakov equation. The coupled pair of these equations yields a dynamical invariant which plays a key role in our investigation. It can be expressed in terms of a complex variable that linearizes the Riccati equation. This variable also provides the time-dependent parameters that characterize the Green's function, or Feynman kernel, of the corresponding problem. From there, also the relation between the classical and quantum dynamics of the systems can be obtained. Furthermore, the close connection between the Ermakov invariant and the Wigner function will be shown. Factorization of the dynamical invariant allows for comparison with creation/annihilation operators and supersymmetry where the partner potentials fulfil (real Riccati equations. This provides the link to a nonlinear formulation of time-independent quantum mechanics in terms of an Ermakov equation for the amplitude of the stationary state wave functions combined with a conservation law. Comparison with SUSY and the time-dependent problems concludes our analysis.
Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations
Aliyu, MDS
2011-01-01
A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter
A Direct Derivation of the Equations of Motion for 3D-Flexible Mechanical Systems
DEFF Research Database (Denmark)
Pedersen, Niels Leergaard; Pedersen, Mads Leergaard
1998-01-01
Equations of motion for rigid bodies with the body-fixed co-ordinate system placed at or away from the centre of mass are derived in a clear and direct way by making use of the two basic equations of mechanics (Newton's second law and the corresponding law of angular momentum). The dynamic...... equations for flexible mechanical systems are derived using the principle of virtual work, which introduces inertia in a straightforward manner, because this principle treats inertia as a force. The flexible formulation is exemplified by the use of circular beam elements and some basic matrices are derived...
Computer programs for the solution of systems of linear algebraic equations
Sequi, W. T.
1973-01-01
FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.
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Musa Danjuma SHEHU
2008-06-01
Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.
The national fire-danger rating system: basic equations
Jack D. Cohen; John E. Deeming
1985-01-01
Updating the National Fire-Danger Rating System (NFDRS) was completed in 1977, and operational use of it was begun the next year. The System provides a guide to wildfire control and suppression by its indexes that measure the relative potential of initiating fires. Such fires do not behave erraticallyâthey spread without spotting through continuous ground fuels....
Implicit Lagrangian equations and the mathematical modeling of physical systems
Moreau, Luc; van der Schaft, Arjan
2002-01-01
We introduce a class of optimal control problems on manifolds which gives rise (via the Pontryagin maximum principle) to a class of implicit Lagrangian systems (a notion which is introduced in the paper). We apply this to the mathematical modeling of interconnected mechanical systems and mechanical
Exact non-Markovian master equations for multiple qubit systems: Quantum-trajectory approach
Chen, Yusui; You, J. Q.; Yu, Ting
2014-11-01
A wide class of exact master equations for a multiple qubit system can be explicitly constructed by using the corresponding exact non-Markovian quantum-state diffusion equations. These exact master equations arise naturally from the quantum decoherence dynamics of qubit system as a quantum memory coupled to a collective colored noisy source. The exact master equations are also important in optimal quantum control, quantum dissipation, and quantum thermodynamics. In this paper, we show that the exact non-Markovian master equation for a dissipative N -qubit system can be derived explicitly from the statistical average of the corresponding non-Markovian quantum trajectories. We illustrated our general formulation by an explicit construction of a three-qubit system coupled to a non-Markovian bosonic environment. This multiple qubit master equation offers an accurate time evolution of quantum systems in various domains, and paves the way to investigate the memory effect of an open system in a non-Markovian regime without any approximation.
Super-transient scaling in time-delay autonomous Boolean network motifs
Energy Technology Data Exchange (ETDEWEB)
D' Huys, Otti, E-mail: otti.dhuys@phy.duke.edu; Haynes, Nicholas D. [Department of Physics, Duke University, Durham, North Carolina 27708 (United States); Lohmann, Johannes [Department of Physics, Duke University, Durham, North Carolina 27708 (United States); Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin (Germany); Gauthier, Daniel J. [Department of Physics, Duke University, Durham, North Carolina 27708 (United States); Department of Physics, The Ohio State University, Columbus, Ohio 43210 (United States)
2016-09-15
Autonomous Boolean networks are commonly used to model the dynamics of gene regulatory networks and allow for the prediction of stable dynamical attractors. However, most models do not account for time delays along the network links and noise, which are crucial features of real biological systems. Concentrating on two paradigmatic motifs, the toggle switch and the repressilator, we develop an experimental testbed that explicitly includes both inter-node time delays and noise using digital logic elements on field-programmable gate arrays. We observe transients that last millions to billions of characteristic time scales and scale exponentially with the amount of time delays between nodes, a phenomenon known as super-transient scaling. We develop a hybrid model that includes time delays along network links and allows for stochastic variation in the delays. Using this model, we explain the observed super-transient scaling of both motifs and recreate the experimentally measured transient distributions.
Solution of degenerate hypergeometric system of Horn consisting of three equations
Tasmambetov, Zhaksylyk N.; Zhakhina, Ryskul U.
2017-09-01
The possibilities of constructing normal-regular solutions of a system consisting of three partial differential equations of the second order are studied by the Frobenius-Latysheva method. The method of determining unknown coefficients is shown and the relationship of the studied system with the system, which solution is Laguerre's polynomial of three variables is indicated. The generalization of the Frobenius-Latysheva method to the case of a system consisting of three equations makes it possible to clarify the relationship of such systems, which solutions are special functions of three variables. These systems include the functions of Whittaker and Bessel, 205 special functions of three variables from the list of M. Srivastava and P.W. Carlsson, as well as orthogonal polynomials of three variables. All this contributes to the further development of the analytic theory of systems consisting of three partial differential equations of the second order.
Latella, Ivan; Pérez-Madrid, Agustín
2013-10-01
The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.
3rd International Conference on Particle Systems and Partial Differential Equations
Soares, Ana
2016-01-01
The main focus of this book is on different topics in probability theory, partial differential equations and kinetic theory, presenting some of the latest developments in these fields. It addresses mathematical problems concerning applications in physics, engineering, chemistry and biology that were presented at the Third International Conference on Particle Systems and Partial Differential Equations, held at the University of Minho, Braga, Portugal in December 2014. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, providing a venue for them to present their latest findings and discuss their areas of expertise. Further, it was intended to introduce a vast and varied public, including young researchers, to the subject of interacting particle systems, its underlying motivation, and its relation to partial differential equations. This book will appeal to probabilists, analysts and those mathematicians whose wor...
Method for solving logical loops in system reliability analysis
International Nuclear Information System (INIS)
Matsuoka, Takeshi
2010-01-01
The procedure for solving Boolean equations with unknown element(s) is presented. Discussions are made for operation of typical engineering systems with loop structure. It is revealed that components are necessary to be classified into three types. Time-dependent expression of a component's state is given and operating states of loop structures are identified by Boolean algebraic procedure. The procedure proposed in this paper is applicable to the condition that components can start at any time in system operational sequence, and each component has multiple chances to be started. A sample system was analyzed and the result was confirmed by a step by step analysis. The procedure shown in this paper is very useful in evaluating engineering systems which have logical loop structure(s), and also useful in effectively designing high reliable systems. (author)
Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra
International Nuclear Information System (INIS)
Gerdt, V.P.; Kostov, N.A.
1989-01-01
In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs
Interacting multiagent systems kinetic equations and Monte Carlo methods
Pareschi, Lorenzo
2014-01-01
The description of emerging collective phenomena and self-organization in systems composed of large numbers of individuals has gained increasing interest from various research communities in biology, ecology, robotics and control theory, as well as sociology and economics. Applied mathematics is concerned with the construction, analysis and interpretation of mathematical models that can shed light on significant problems of the natural sciences as well as our daily lives. To this set of problems belongs the description of the collective behaviours of complex systems composed by a large enough number of individuals. Examples of such systems are interacting agents in a financial market, potential voters during political elections, or groups of animals with a tendency to flock or herd. Among other possible approaches, this book provides a step-by-step introduction to the mathematical modelling based on a mesoscopic description and the construction of efficient simulation algorithms by Monte Carlo methods. The ar...
Adapted Boolean network models for extracellular matrix formation
Directory of Open Access Journals (Sweden)
Wollbold Johannes
2009-07-01
Full Text Available Abstract Background Due to the rapid data accumulation on pathogenesis and progression of chronic inflammation, there is an increasing demand for approaches to analyse the underlying regulatory networks. For example, rheumatoid arthritis (RA is a chronic inflammatory disease, characterised by joint destruction and perpetuated by activated synovial fibroblasts (SFB. These abnormally express and/or secrete pro-inflammatory cytokines, collagens causing joint fibrosis, or tissue-degrading enzymes resulting in destruction of the extra-cellular matrix (ECM. We applied three methods to analyse ECM regulation: data discretisation to filter out noise and to reduce complexity, Boolean network construction to implement logic relationships, and formal concept analysis (FCA for the formation of minimal, but complete rule sets from the data. Results First, we extracted literature information to develop an interaction network containing 18 genes representing ECM formation and destruction. Subsequently, we constructed an asynchronous Boolean network with biologically plausible time intervals for mRNA and protein production, secretion, and inactivation. Experimental gene expression data was obtained from SFB stimulated by TGFβ1 or by TNFα and discretised thereafter. The Boolean functions of the initial network were improved iteratively by the comparison of the simulation runs to the experimental data and by exploitation of expert knowledge. This resulted in adapted networks for both cytokine stimulation conditions. The simulations were further analysed by the attribute exploration algorithm of FCA, integrating the observed time series in a fine-tuned and automated manner. The resulting temporal rules yielded new contributions to controversially discussed aspects of fibroblast biology (e.g., considerable expression of TNF and MMP9 by fibroblasts stimulation and corroborated previously known facts (e.g., co-expression of collagens and MMPs after TNF
Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations
Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der
Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general
Directory of Open Access Journals (Sweden)
Kushnir V.
2017-12-01
Full Text Available The problem of constructing quadratic equations and systems of equations with parameters using Maple-technology is studied. Today, the "learning tasks of reverse thinking" (V.A. Krutetsky or simply "inverse problems" (P.M.Erdniev are increasingly being introduced into the educational process. The tasks of constructing mathematical tasks in advance of a certain type and certain properties are inverse problems that unfold another aspect of the learning situation and thereby create a "surplus of its vision" (M.M. Bakhtin. The solution of inverse problems develops students’ thinking, imagination and other higher mental functions. However, their introduction into the educational process is still insufficient. One of the reasons for this situation is the insufficient number of benefits with a sufficient number of variants of the same type of tasks. Especially it concerns the construction of problems with parameters. Designing in "manual mode" requires significant temporary cognitive, physical and other efforts, carries the risks of allowing technical and computational errors. In the days of the information society and the digital economy, there are all the possibilities to perform the chain of design actions in a certain ICT environment (we have a Maple-environment. It solves the resulted difficulties of construction, creates a new educational and information environment, allows to produce automatically a sufficient number of different versions of the same type of tasks. Tasks with parameters require creativity from the students, non-standard approaches to the solution. Each task with parameters requires the creation of its own method and algorithm for solving and productive learning. The article is devoted to solving of the above problems.
The Sylvester equation and the elliptic Korteweg-de Vries system
Sun, Ying-ying; Zhang, Da-jun; Nijhoff, Frank W.
2017-03-01
The elliptic potential Korteweg-de Vries lattice system is a multi-component extension of the lattice potential Korteweg-de Vries equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper we generalize the class of solutions by allowing the spectral parameter to be a full matrix obeying a matrix version of the equation of the elliptic curve, and for the Cauchy matrix to be a solution of a Sylvester type matrix equation subject to this matrix elliptic curve equation. The construction involves solving the matrix elliptic curve equation by using Toeplitz matrix techniques, and analysing the solution of the Sylvester equation in terms of Jordan normal forms. Furthermore, we consider the continuum limit system associated with the elliptic potential Korteweg-de Vries system, and analyse the dynamics of the soliton solutions, which reveals some new features of the elliptic system in comparison to the non-elliptic case.
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
International Nuclear Information System (INIS)
Maccari, A.
1997-01-01
Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio endash temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a open-quotes universalclose quotes character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. copyright 1997 American Institute of Physics
Equation-free modeling unravels the behavior of complex ecological systems
DeAngelis, Donald L.; Yurek, Simeon
2015-01-01
Ye et al. (1) address a critical problem confronting the management of natural ecosystems: How can we make forecasts of possible future changes in populations to help guide management actions? This problem is especially acute for marine and anadromous fisheries, where the large interannual fluctuations of populations, arising from complex nonlinear interactions among species and with varying environmental factors, have defied prediction over even short time scales. The empirical dynamic modeling (EDM) described in Ye et al.’s report, the latest in a series of papers by Sugihara and his colleagues, offers a promising quantitative approach to building models using time series to successfully project dynamics into the future. With the term “equation-free” in the article title, Ye et al. (1) are suggesting broader implications of their approach, considering the centrality of equations in modern science. From the 1700s on, nature has been increasingly described by mathematical equations, with differential or difference equations forming the basic framework for describing dynamics. The use of mathematical equations for ecological systems came much later, pioneered by Lotka and Volterra, who showed that population cycles might be described in terms of simple coupled nonlinear differential equations. It took decades for Lotka–Volterra-type models to become established, but the development of appropriate differential equations is now routine in modeling ecological dynamics. There is no question that the injection of mathematical equations, by forcing “clarity and precision into conjecture” (2), has led to increased understanding of population and community dynamics. As in science in general, in ecology equations are a key method of communication and of framing hypotheses. These equations serve as compact representations of an enormous amount of empirical data and can be analyzed by the powerful methods of mathematics.
Reconfigurable Boolean logic using magnetic single-electron transistors.
Directory of Open Access Journals (Sweden)
M Fernando Gonzalez-Zalba
Full Text Available We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET. The device consists of an aluminium single-electron transistor with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer, which induces a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network.
Reconfigurable Boolean Logic Using Magnetic Single-Electron Transistors
Gonzalez-Zalba, M. Fernando; Ciccarelli, Chiara; Zarbo, Liviu P.; Irvine, Andrew C.; Campion, Richard C.; Gallagher, Bryan L.; Jungwirth, Tomas; Ferguson, Andrew J.; Wunderlich, Joerg
2015-01-01
We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET). The device consists of an aluminium single-electron transistor with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer, which induces a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network. PMID:25923789
Identification of Boolean Networks Using Premined Network Topology Information.
Zhang, Xiaohua; Han, Huaxiang; Zhang, Weidong
2017-02-01
This brief aims to reduce the data requirement for the identification of Boolean networks (BNs) by using the premined network topology information. First, a matching table is created and used for sifting the true from the false dependences among the nodes in the BNs. Then, a dynamic extension to matching table is developed to enable the dynamic locating of matching pairs to start as soon as possible. Next, based on the pseudocommutative property of the semitensor product, a position-transform mining is carried out to further improve data utilization. Combining the above, the topology of the BNs can be premined for the subsequent identification. Examples are given to illustrate the efficiency of reducing the data requirement. Some excellent features, such as the online and parallel processing ability, are also demonstrated.
ZKBoo: Faster Zero-Knowledge for Boolean Circuits
DEFF Research Database (Denmark)
Giacomelli, Irene; Madsen, Jesper; Orlandi, Claudio
2016-01-01
variants of IKOS, which highlights their pros and cons for practically rele- vant soundness parameters; ◦ A generalization and simplification of their approach, which leads to faster Σ-protocols (that can be made non-interactive using the Fiat-Shamir heuristic) for state- ments of the form “I know x...... such that y = φ (x)” (where φ is a circuit and y a public value); ◦ A case study, where we provide explicit protocols, implementations and benchmarking of zero-knowledge protocols for the SHA-1 and SHA-256 circuits.......In this paper we describe ZKBoo, a proposal for practically efficient zero-knowledge arguments especially tailored for Boolean circuits and report on a proof-of- concept implementation. As an highlight, we can generate (resp. verify) a non-interactive proof for the SHA-1 circuit in approximately 13...
Boolean Algebra Application in Analysis of Flight Accidents
Directory of Open Access Journals (Sweden)
Casandra Venera BALAN
2015-12-01
Full Text Available Fault tree analysis is a deductive approach for resolving an undesired event into its causes, identifying the causes of a failure and providing a framework for a qualitative and quantitative evaluation of the top event. An alternative approach to fault tree analysis methods calculus goes to logical expressions and it is based on a graphical representation of the data structure for a logic - based binary decision diagram representation. In this analysis, such sites will be reduced to a minimal size and arranged in the sense that the variables appear in the same order in each path. An event can be defined as a statement that can be true or false. Therefore, Boolean algebra rules allow restructuring of a Fault Tree into one equivalent to it, but simpler.
New Quasi-Newton Method for Solving Systems of Nonlinear Equations
Czech Academy of Sciences Publication Activity Database
Lukšan, Ladislav; Vlček, Jan
2017-01-01
Roč. 62, č. 2 (2017), s. 121-134 ISSN 0862-7940 R&D Projects: GA ČR GA13-06684S Institutional support: RVO:67985807 Keywords : nonlinear equations * systems of equations * trust-region methods * quasi- Newton methods * adjoint Broyden methods * numerical algorithms * numerical experiments Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 0.618, year: 2016 http://hdl.handle.net/10338.dmlcz/146699
International Nuclear Information System (INIS)
Mikami, T.
2000-01-01
R. Jordan, D. Kinderlehrer, and F. Otto proposed the discrete-time approximation of the Fokker-Planck equation by the variational formulation. It is determined by the Wasserstein metric, an energy functional, and the Gibbs-Boltzmann entropy functional. In this paper we study the asymptotic behavior of the dynamical systems which describe their approximation of the Fokker-Planck equation and characterize the limit as a solution to a class of variational problems
A New Block Solver for Large, Full, Unsymmetric, Complex Systems of Linear Algebraic Equations.
1988-02-01
THE COEFFICIENT C MATRIX IN THAT ORDER. ON OUTPUT, UTI CONTAINS THE SOLUTION C MATRIX. C C THE NASTRAN DMAP INSTRUCTIONS TO INTERFACE WITH ’OCSOLVE...developed. Although OCSOLVE was developed for use with the finite element program NASTRAN , it is designed t,) be easily adapted for other applications...solve such a system of 500 equations with complex- valued coefficients to about 5% of the time required by the equation solver in NASTRAN . The solver
Iu. Caraus
1997-01-01
This article generalizes the results which were obtained in the paper [1], written together with my scientific-adviser, doctor-habilitat, professor Zolotarevschi V. Theoretical foundation of the collocation method and of mechanical quadrature method for singular integro-differential equations systems (SIDE) in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle, is given below. Let $\\Gamma $ be a s...
Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system
Directory of Open Access Journals (Sweden)
Boris V. Kapitonov
2010-02-01
Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.
Asymptotic behavior of a system of micropolar equations
Directory of Open Access Journals (Sweden)
Pedro Marin-Rubio
2016-03-01
Full Text Available This work is concerned with three-dimensional micropolar fluids flows in a bounded domain with boundary of class $C^{\\infty}.$ Based on the theory of dissipative systems, we prove the existence of a restricted global attractors for local semiflows on suitable fractional phase spaces $\\mathbf{Z}^{\\alpha}_{p},$ namely for $p\\in (3,+\\infty$ and $\\alpha\\in [1/2,1$. Moreover, we prove that all these attractors are in fact the same set. Previously, it is shown that the Lamé operator is a sectorial operator in each $L_{p}(\\Omega$ with $1
Entire positive solution to the system of nonlinear elliptic equations
Directory of Open Access Journals (Sweden)
Miaoxin Yao
2006-09-01
Full Text Available The second-order nonlinear elliptic system Ã¢ÂˆÂ’ÃŽÂ”u=f1(xuÃŽÂ±+g1(xuÃ¢ÂˆÂ’ÃŽÂ²+h1(xuÃŽÂ³P(v, Ã¢ÂˆÂ’ÃŽÂ”v=f2(xvÃŽÂ±+g2(xvÃ¢ÂˆÂ’ÃŽÂ²+h2(xvÃŽÂ³P(u with 0<ÃŽÂ±,ÃŽÂ²,ÃŽÂ³<1, is considered in Ã¢Â„ÂN. Under suitable hypotheses on functions fi, gi, hi(i=1,2, and P, it is shown that this system possesses an entire positive solution (u,vÃ¢ÂˆÂˆÃ¢Â„Â‚loc2,ÃŽÂ¸(Ã¢Â„ÂNÃƒÂ—Ã¢Â„Â‚loc2,ÃŽÂ¸(Ã¢Â„ÂN(0<ÃŽÂ¸<1 such that both u and v are bounded below and above by positive constant multiples of |x|2Ã¢ÂˆÂ’N for all |x|Ã¢Â‰Â¥1.
Exact solutions and conservation laws of the system of two-dimensional viscous Burgers equations
Abdulwahhab, Muhammad Alim
2016-10-01
Fluid turbulence is one of the phenomena that has been studied extensively for many decades. Due to its huge practical importance in fluid dynamics, various models have been developed to capture both the indispensable physical quality and the mathematical structure of turbulent fluid flow. Among the prominent equations used for gaining in-depth insight of fluid turbulence is the two-dimensional Burgers equations. Its solutions have been studied by researchers through various methods, most of which are numerical. Being a simplified form of the two-dimensional Navier-Stokes equations and its wide range of applicability in various fields of science and engineering, development of computationally efficient methods for the solution of the two-dimensional Burgers equations is still an active field of research. In this study, Lie symmetry method is used to perform detailed analysis on the system of two-dimensional Burgers equations. Optimal system of one-dimensional subalgebras up to conjugacy is derived and used to obtain distinct exact solutions. These solutions not only help in understanding the physical effects of the model problem but also, can serve as benchmarks for constructing algorithms and validation of numerical solutions of the system of Burgers equations under consideration at finite Reynolds numbers. Independent and nontrivial conserved vectors are also constructed.
On the economical solution method for a system of linear algebraic equations
Directory of Open Access Journals (Sweden)
Awrejcewicz Jan
2004-01-01
Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ 3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O( h x 1 2 + h x 2 2 . The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.
On the economical solution method for a system of linear algebraic equations
Directory of Open Access Journals (Sweden)
Jan Awrejcewicz
2004-01-01
Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.
Asymptotic Analysis of a System of Algebraic Equations Arising in Dislocation Theory
Hall, Cameron L.
2010-01-01
The system of algebraic equations given by σn j=0, j≠=i sgn(xi-xj )|xi-xj|a = 1, i = 1, 2, ⋯ , n, x0 = 0, appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole. We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n→∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment, but, up to corrections of logarithmic order, it also leads to a differential equation. The continuum approximation is valid only for i neither too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem. © 2010 Society for Industrial and Applied Mathematics.
A finite difference treatment of differential equation systems with widely differing time constants
International Nuclear Information System (INIS)
Dalton, G.R.; Gamble, M.T.
1983-01-01
A consistent method of solving systems of coupled time-dependent differential equations with vastly divergent time constants has been developed. This method is directly applicable to finite difference techniques of solutions using matrix algebra. Application to systems of isotope burnup and buildup equations with time constants ranging from minutes to millions of years demonstrates the utility of the method. Similarity to the prompt jump method of reactor kinetics indicates applicability to a wider range of positive as well as negative time constant systems
International Nuclear Information System (INIS)
Adamova, D.; Ulehla, I.; Horejsi, J.
1984-01-01
The matrix generalization of the Pruefer transformation introduced by Atkinson is applied to a coupled system of the radial Schroedinger equations. It is shown that the phase functions corresponding to the matrix case exhibit properties analogous to those of the Pruefer phase function encountered in the scalar case. Rigorous theorems are established which allow one to determine the eigenvalues of the original Schroedinger system with an arbitrary accuracy provided that the asymptotic behaviour of the phase functions is known. The possibility of obtaining the phase functions by means of the integration of an appropriate system of nonlinear 1st order differential equations is briefly discussed
Solution of the Lyapunov matrix equation for a system with a time-dependent stiffness matrix
DEFF Research Database (Denmark)
Pommer, Christian; Kliem, Wolfhard
2004-01-01
The stability of the linearized model of a rotor system with non-symmetric strain and axial loads is investigated. Since we are using a fixed reference system, the differential equations have the advantage to be free of Coriolis and centrifugal forces. A disadvantage is nevertheless the occurrenc...... of time-dependent periodic terms in the stiffness matrix. However, by solving the Lyapunov matrix equation we can formulate several stability conditions for the rotor system. Hereby the positive definiteness of a certain averaged stiffness matrix plays a crucial role....
International Nuclear Information System (INIS)
Rosenfeld, M.; Kwak, D.; Vinokur, M.
1988-01-01
A solution method based on a fractional step approach is developed for obtaining time-dependent solutions of the three-dimensional, incompressible Navier-Stokes equations in generalized coordinate systems. The governing equations are discretized conservatively by finite volumes using a staggered mesh system. The primitive variable formulation uses the volume fluxes across the faces of each computational cell as dependent variables. This procedure, combined with accurate and consistent approximations of geometric parameters, is done to satisfy the discretized mass conservation equation to machine accuracy as well as to gain favorable convergence properties of the Poisson solver. The discretized equations are second-order-accurate in time and space and no smoothing terms are added. An approximate-factorization scheme is implemented in solving the momentum equations. A novel ZEBRA scheme with four-color ordering is devised for the efficient solution of the Poisson equation. Several two and three-dimensional solutions are compared with other numerical and experimental results to validate the present method. 23 references
Numerical simulation of stochastic point kinetic equation in the dynamical system of nuclear reactor
International Nuclear Information System (INIS)
Saha Ray, S.
2012-01-01
Highlights: ► In this paper stochastic neutron point kinetic equations have been analyzed. ► Euler–Maruyama method and Strong Taylor 1.5 order method have been discussed. ► These methods are applied for the solution of stochastic point kinetic equations. ► Comparison between the results of these methods and others are presented in tables. ► Graphs for neutron and precursor sample paths are also presented. -- Abstract: In the present paper, the numerical approximation methods, applied to efficiently calculate the solution for stochastic point kinetic equations () in nuclear reactor dynamics, are investigated. A system of Itô stochastic differential equations has been analyzed to model the neutron density and the delayed neutron precursors in a point nuclear reactor. The resulting system of Itô stochastic differential equations are solved over each time-step size. The methods are verified by considering different initial conditions, experimental data and over constant reactivities. The computational results indicate that the methods are simple and suitable for solving stochastic point kinetic equations. In this article, a numerical investigation is made in order to observe the random oscillations in neutron and precursor population dynamics in subcritical and critical reactors.
Chicurel-Uziel, Enrique
2007-08-01
A pair of closed parametric equations are proposed to represent the Heaviside unit step function. Differentiating the step equations results in two additional parametric equations, that are also hereby proposed, to represent the Dirac delta function. These equations are expressed in algebraic terms and are handled by means of elementary algebra and elementary calculus. The proposed delta representation complies exactly with the values of the definition. It complies also with the sifting property and the requisite unit area and its Laplace transform coincides with the most general form given in the tables. Furthermore, it leads to a very simple method of solution of impulsive vibrating systems either linear or belonging to a large class of nonlinear problems. Two example solutions are presented.
New approach to solve fully fuzzy system of linear equations using ...
Indian Academy of Sciences (India)
... double parametric form of fuzzy numbers converts the n×n fully fuzzy system of linear equations to a crisp system of same order. Triangular and trapezoidal convex normalized fuzzy sets are used for the present analysis. Known example problems are solved to illustrate the efficacy and reliability of the proposed methods.
On existence of soliton solutions of arbitrary-order system of nonlinear Schrodinger equations
International Nuclear Information System (INIS)
Zhestkov, S.V.
2003-01-01
The soliton solutions are constructed for the system of arbitrary-order coupled nonlinear Schrodinger equations . The necessary and sufficient conditions of existence of these solutions are obtained. It is shown that the maximum number of solitons in nondegenerate case is 4L, where L is order of the system. (author)
On Solving Systems of Equations by Successive Reduction Using 2×2 Matrices
Carley, Holly
2014-01-01
Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available The method of generalized quasilinearization for the system of nonlinear impulsive differential equations with periodic boundary conditions is studied. As a byproduct, the result for the system without impulses can be obtained, which is a new result as well.
Energy Technology Data Exchange (ETDEWEB)
Nolte, Roman
2009-11-20
Discovered in 1997, the Jarzynski equation is one of several new theorems of nonequilibrium thermodynamics. Not only this equation makes a more severe statement than the second law of thermodynamics, it does also relate process quantities from processes far from equilibrium to equilibrium quantities. In particular during the investigation of very small systems there has been drawn much attention to this equation and the related fluctuation theorems during the last years. Something similar applies for the description of microbiological processes which take place often stationary but rarely in thermodynamical equilibrium. However, especially according to small systems the question of the validity of the equation in the quantum case emerges. Though meanwhile quite comprehensive proofs concerning classical systems have been found, for that case uncertainty and contradictory statements exist, founding on different definitions and interpretations of the quantum analogon of expressions of the equation. Simple examples on which the different approaches can be tested, are so far missing. In this work two such examples are investigated and it is examined, how the results differ from their classical counterparts and which properties of quantum systems influence the result. (orig.)
Conservation laws for certain time fractional nonlinear systems of partial differential equations
Singla, Komal; Gupta, R. K.
2017-12-01
In this study, an extension of the concept of nonlinear self-adjointness and Noether operators is proposed for calculating conserved vectors of the time fractional nonlinear systems of partial differential equations. In our recent work (J Math Phys 2016; 57: 101504), by proposing the symmetry approach for time fractional systems, the Lie symmetries for some fractional nonlinear systems have been derived. In this paper, the obtained infinitesimal generators are used to find conservation laws for the corresponding fractional systems.
Discovering governing equations from data by sparse identification of nonlinear dynamical systems.
Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan
2016-04-12
Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.
Boolean and advanced searching for EDGAR data on www.sec.gov
Securities and Exchange Commission — This search allows users to enter complex boolean queries to access all but the most recent day's EDGAR filings on www.sec.gov. Filings are from 1994 to present.
Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem
Directory of Open Access Journals (Sweden)
Vladimir A. Emelichev
2002-11-01
Full Text Available We consider a multiple criterion Boolean programming problem with MINMAX partial criteria. The extreme level of independent perturbations of partial criteria parameters such that efficient (Pareto optimal solution preserves optimality was obtained.
A SAT-based algorithm for finding attractors in synchronous Boolean networks.
Dubrova, Elena; Teslenko, Maxim
2011-01-01
This paper addresses the problem of finding attractors in synchronous Boolean networks. The existing Boolean decision diagram-based algorithms have limited capacity due to the excessive memory requirements of decision diagrams. The simulation-based algorithms can be applied to larger networks, however, they are incomplete. We present an algorithm, which uses a SAT-based bounded model checking to find all attractors in a Boolean network. The efficiency of the presented algorithm is evaluated by analyzing seven networks models of real biological processes, as well as 150,000 randomly generated Boolean networks of sizes between 100 and 7,000. The results show that our approach has a potential to handle an order of magnitude larger models than currently possible.
Constructivizability of the Boolean algebra B(ω) with a distinguished automorphism
Czech Academy of Sciences Publication Activity Database
Bazhenov, N. A.; Tukhbatullina, Regina
2012-01-01
Roč. 51, č. 5 (2012), s. 384-403 ISSN 0002-5232 Institutional support: PRVOUK-P23 Keywords : Boolean algebra * constructivizability * degree spectra of structures Subject RIV: AH - Economics Impact factor: 0.493, year: 2012
A novel generalized design methodology and realization of Boolean operations using DNA.
Zoraida, B S E; Arock, Michael; Ronald, B S M; Ponalagusamy, R
2009-09-01
The biological deoxyribonucleic acid (DNA) strand has been increasingly seen as a promising computing unit. A new algorithm is formulated in this paper to design any DNA Boolean operator with molecular beacons (MBs) as its input. Boolean operators realized using the proposed design methodology is presented. The developed operators adopt a uniform representation for logical 0 and 1 for any Boolean operator. The Boolean operators designed in this work employ only a hybridization operation at each stage. Further, this paper for the first time brings out the realization of a binary adder and subtractor using molecular beacons. Simulation results of the DNA-based binary adder and subtractor are given to validate the design.
Multilevel solvers of first-order system least-squares for Stokes equations
Energy Technology Data Exchange (ETDEWEB)
Lai, Chen-Yao G. [National Chung Cheng Univ., Chia-Yi (Taiwan, Province of China)
1996-12-31
Recently, The use of first-order system least squares principle for the approximate solution of Stokes problems has been extensively studied by Cai, Manteuffel, and McCormick. In this paper, we study multilevel solvers of first-order system least-squares method for the generalized Stokes equations based on the velocity-vorticity-pressure formulation in three dimensions. The least-squares functionals is defined to be the sum of the L{sup 2}-norms of the residuals, which is weighted appropriately by the Reynolds number. We develop convergence analysis for additive and multiplicative multilevel methods applied to the resulting discrete equations.
Rosenbaum, J. S.
1976-01-01
If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.
Geometric methods of global attraction in systems of delay differential equations
El-Morshedy, Hassan A.; Ruiz-Herrera, Alfonso
2017-11-01
In this paper we deduce criteria of global attraction in systems of delay differential equations. Our methodology is new and consists in "dominating" the nonlinear terms of the system by a scalar function and then studying some dynamical properties of that function. One of the crucial benefits of our approach is that we obtain delay-dependent results of global attraction that cover the best delay-independent conditions. We apply our results in a gene regulatory model and the classical Nicholson's blowfly equation with patch structure.
Solving the Coupled System Improves Computational Efficiency of the Bidomain Equations
Southern, J.A.
2009-10-01
The bidomain equations are frequently used to model the propagation of cardiac action potentials across cardiac tissue. At the whole organ level, the size of the computational mesh required makes their solution a significant computational challenge. As the accuracy of the numerical solution cannot be compromised, efficiency of the solution technique is important to ensure that the results of the simulation can be obtained in a reasonable time while still encapsulating the complexities of the system. In an attempt to increase efficiency of the solver, the bidomain equations are often decoupled into one parabolic equation that is computationally very cheap to solve and an elliptic equation that is much more expensive to solve. In this study, the performance of this uncoupled solution method is compared with an alternative strategy in which the bidomain equations are solved as a coupled system. This seems counterintuitive as the alternative method requires the solution of a much larger linear system at each time step. However, in tests on two 3-D rabbit ventricle benchmarks, it is shown that the coupled method is up to 80% faster than the conventional uncoupled method-and that parallel performance is better for the larger coupled problem.
Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables
Chikalov, Igor
2013-01-01
In this paper, we present the empirical results for relationships between time (depth) and space (number of nodes) complexity of decision trees computing monotone Boolean functions, with at most five variables. We use Dagger (a tool for optimization of decision trees and decision rules) to conduct experiments. We show that, for each monotone Boolean function with at most five variables, there exists a totally optimal decision tree which is optimal with respect to both depth and number of nodes.
Interpolation of the discrete logarithm in a finite field of characteristic two by Boolean functions
DEFF Research Database (Denmark)
Brandstaetter, Nina; Lange, Tanja; Winterhof, Arne
2005-01-01
We obtain bounds on degree, weight, and the maximal Fourier coefficient of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic.......We obtain bounds on degree, weight, and the maximal Fourier coefficient of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic....
2017-09-01
duties due to Sailors, across the globe, who stand the watch. As Winston Churchill once said, “we sleep safely at night because rough men stand ready...Chapter 2 contains definitions and preliminary generalized Boolean function material. This is followed by Chapters 3–5, which contain the bulk of the...Generalized Boolean Functions Sic Parvis Magna Sir Francis DrakeA In this chapter we begin by covering some basic definitions and properties which we will make
An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks
Cabessa, Jérémie; Villa, Alessandro E. P.
2014-01-01
We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of -automata, and then translating the most refined classification of -automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits. PMID:24727866
UNIFIED MODELS OF ELEMENTS OF POWER SUPPLY SYSTEMS BASED ON EQUATIONS IN PHASE COORDINATES
Directory of Open Access Journals (Sweden)
Yu.N. Vepryk
2015-12-01
Full Text Available Purpose. The models of electrical machines in the phase coordinates, the universal algorithm for the simulation of separate elements in a d-q coordinates system and in a phase-coordinates system are proposed. Methodology. Computer methods of investigation of transients in electrical systems are based on a compilation of systems of differential equations and their numerical integration solution methods. To solve differential equations an implicit method of numerical integration was chosen. Because it provides to complete structural simulation possibility: firstly developing models of separate elements and then forming a model of the complex system. For the mathematical simulation of electromagnetic transients in the elements of the electrical systems has been accepted the implicit Euler-Cauchy method, because it provides a higher precision and stability of the computing processes. Results. In developing the model elements identified two groups of elements: - Static elements and electrical machines in the d-q coordinates; - Rotating electrical machines in phase coordinates. As an example, the paper provides a model of synchronous and asynchronous electric machines in the d-q coordinates system and the phase coordinate system. The generalization algorithm and the unified notation form of equations of elements of an electrical system are obtained. It provides the possibility of using structural methods to develop a mathematical model of power systems under transient conditions. Practical value. In addition, the using of a computer model allows to implement multivariant calculations for research and study of factors affecting the quantitative characteristics of the transients.
Forward-backward equations for nonlinear propagation in axially invariant optical systems
International Nuclear Information System (INIS)
Ferrando, Albert; Zacares, Mario; Fernandez de Cordoba, Pedro; Binosi, Daniele; Montero, Alvaro
2005-01-01
We present a general framework to deal with forward and backward components of the electromagnetic field in axially invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse inhomogeneities. With a minimum amount of approximations, we obtain a system of two first-order equations for forward and backward components, explicitly showing the nonlinear couplings among them. The modal approach used allows for an effective reduction of the dimensionality of the original problem from 3+1 (three spatial dimensions plus one time dimension) to 1+1 (one spatial dimension plus one frequency dimension). The new equations can be written in a spinor Dirac-like form, out of which conserved quantities can be calculated in an elegant manner. Finally, these equations inherently incorporate spatiotemporal couplings, so that they can be easily particularized to deal with purely temporal or purely spatial effects. Nonlinear forward pulse propagation and nonparaxial evolution of spatial structures are analyzed as examples
Cortés, Juan-C; Sánchez-Sánchez, Almudena; Santonja, Francisco-J; Villanueva, Rafael-J
2011-11-01
In this paper we describe epiModel, a code developed in Mathematica that facilitates the building of systems of differential equations corresponding to type-epidemiological linear or quadratic models whose characteristics are defined in text files following an easy syntax. It includes the possibility of obtaining the equations of models involving age and/or sex groups. Copyright © 2011. Published by Elsevier Ltd.
On global asymptotic stability of solutions of a system of ordinary differential equations
Filimonov, M. Yu.
2017-12-01
To investigate global asymptotic stability in general of an equilibrium position of an autonomous system of ordinary differential equations, considered by V.A. Pliss, a function different from the Lyapunov functions is applied. V.A. Pliss proved that for this system it is impossible to construct the Lyapunov function as a sum of a quadratic form and an integral of some nonlinear function defined by the right-hand side of the system.
Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations
International Nuclear Information System (INIS)
Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.
2003-01-01
We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations
Continuous limits for an integrable coupling system of Toda equation hierarchy
Energy Technology Data Exchange (ETDEWEB)
Li Li [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China); Yu Fajun, E-mail: yfajun@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2009-09-21
In this Letter, we present an integrable coupling system of lattice hierarchy and its continuous limits by using of Lie algebra sl(4). By introducing a complex discrete spectral problem, the integrable coupling system of Toda lattice hierarchy is derived. It is shown that a new complex lattice spectral problem converges to the integrable couplings of discrete soliton equation hierarchy, which has the integrable coupling system of C-KdV hierarchy as a new kind of continuous limit.
On the uniform boundedness of the solutions of systems of reaction-diffusion equations
Directory of Open Access Journals (Sweden)
L. Melkemi
2005-12-01
Full Text Available We consider a system of reaction-diffusion equations for which the uniform boundedness of the solutions can not be derived by existing methods. The system may represent, in particular, an epidemic model describing the spread of an infection disease within a population. We present an $L^{p}$ argument allowing to establish the global existence and the uniform boundedness of the solutions of the considered system.
New form of the Euler-Bernoulli rod equation applied to robotic systems
Directory of Open Access Journals (Sweden)
Filipović Mirjana
2008-01-01
Full Text Available This paper presents a theoretical background and an example of extending the Euler-Bernoulli equation from several aspects. Euler-Bernoulli equation (based on the known laws of dynamics should be supplemented with all the forces that are participating in the formation of the bending moment of the considered mode. The stiffness matrix is a full matrix. Damping is an omnipresent elasticity characteristic of real systems, so that it is naturally included in the Euler-Bernoulli equation. It is shown that Daniel Bernoulli's particular integral is just one component of the total elastic deformation of the tip of any mode to which we have to add a component of the elastic deformation of a stationary regime in accordance with the complexity requirements of motion of an elastic robot system. The elastic line equation mode of link of a complex elastic robot system is defined based on the so-called 'Euler-Bernoulli Approach' (EBA. It is shown that the equation of equilibrium of all forces present at mode tip point ('Lumped-mass approach' (LMA follows directly from the elastic line equation for specified boundary conditions. This, in turn, proves the essential relationship between LMA and EBA approaches. In the defined mathematical model of a robotic system with multiple DOF (degree of freedom in the presence of the second mode, the phenomenon of elasticity of both links and joints are considered simultaneously with the presence of the environment dynamics - all based on the previously presented theoretical premises. Simulation results are presented. .
Multipoint Singular Boundary-Value Problem for Systems of Nonlinear Differential Equations
Directory of Open Access Journals (Sweden)
Zdeněk Šmarda
2009-01-01
Full Text Available A singular Cauchy-Nicoletti problem for a system of nonlinear ordinary differential equations is considered. With the aid of combination of Ważewski's topological method and Schauder's principle, the theorem concerning the existence of a solution of this problem (having the graph in a prescribed domain is proved.
Existence and uniqueness of solution for a system of equations of ...
African Journals Online (AJOL)
The existence and uniqueness of solution for a system of equations of microwave heating of biologic issue is discussed. Using the Green function approach we establish the existence and uniqueness of solution. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 177-180 ...
Maat, Siti Mistima; Zakaria, Effandi
2011-01-01
Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…
DEFF Research Database (Denmark)
Folas, Georgios; Derawi, Samer; Michelsen, Michael Locht
2005-01-01
The cubic-plus-association equation of state (CPA EoS) has been extended to phase equilibria of industrially important binary mixtures of alcohol-hydrocarbon, alcohol/glycol-water systems and mixtures with organic acids. The ability of the model to predict different types of equilibria was tested...
Application of the cubic-plus-association (CPA) equation of state to cross-associating systems
DEFF Research Database (Denmark)
Folas, Georgios; Gabrielsen, Jostein; Michelsen, Michael Locht
2005-01-01
The cubic-plus-association (CPA) equation of state (EoS) is applied, using different combining rules, to vapor-liquid equilibria (VLE) and liquid-liquid equilibria (LLE) of alcohol-water systems. It is demonstrated that the Elliott combining rule (ECR) with a common temperature...
New approach to solve fully fuzzy system of linear equations using ...
Indian Academy of Sciences (India)
Otadi & Mosleh (2012) have applied a linear programming approach to find the non-negative solution of a fully fuzzy matrix equation whose elements of the coefficient matrix are considered as arbitrary triangular fuzzy numbers. There are no restrictions about the elements of the coefficient matrix of the corresponding system ...
Tonisson, Eno
2015-01-01
Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…
Simplified Equations to Estimate Flushline Diameter for Subsurface Drip Irrigation Systems
A formulation of the Hazen-Williams equation is typically used to determine the diameter of the common flushline that is often used at the distal end of subsurface drip irrigation systems to aid in joint flushing of a group of driplines. Although this method is accurate, its usage is not intuitive a...
Winkel, Brian
2012-01-01
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)
Directory of Open Access Journals (Sweden)
Azizollah Babakhani
2010-01-01
Full Text Available We investigate the existence and uniqueness of positive solution for system of nonlinear fractional differential equations in two dimensions with delay. Our analysis relies on a nonlinear alternative of Leray-Schauder type and Krasnoselskii's fixed point theorem in a cone.
Computing Gröbner and Involutive Bases for Linear Systems of Difference Equations
Yanovich, Denis
2018-02-01
The computation of involutive bases and Gröbner bases for linear systems of difference equations is solved and its importance for physical and mathematical problems is discussed. The algorithm and issues concerning its implementation in C are presented and calculation times are compared with the competing programs. The paper ends with consideration on the parallel version of this implementation and its scalability.
Optimal Homotopy Asymptotic Method for Solving System of Fredholm Integral Equations
Directory of Open Access Journals (Sweden)
Bahman Ghazanfari
2013-08-01
Full Text Available In this paper, optimal homotopy asymptotic method (OHAM is applied to solve system of Fredholm integral equations. The effectiveness of optimal homotopy asymptotic method is presented. This method provides easy tools to control the convergence region of approximating solution series wherever necessary. The results of OHAM are compared with homotopy perturbation method (HPM and Taylor series expansion method (TSEM.
Graphene-based non-Boolean logic circuits
Liu, Guanxiong; Ahsan, Sonia; Khitun, Alexander G.; Lake, Roger K.; Balandin, Alexander A.
2013-10-01
Graphene revealed a number of unique properties beneficial for electronics. However, graphene does not have an energy band-gap, which presents a serious hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. Here we show that the negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gapless graphene. The negative differential resistance—observed under certain biasing schemes—is an intrinsic property of graphene, resulting from its symmetric band structure. Our atomistic modeling shows that the negative differential resistance appears not only in the drift-diffusion regime but also in the ballistic regime at the nanometer-scale—although the physics changes. The obtained results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.
Approximate solution to the Kolmogorov equation for a fission chain-reacting system
International Nuclear Information System (INIS)
Ruby, L.; McSwine, T.L.
1986-01-01
An approximate solution has been obtained for the Kolmogorov equation describing a fission chain-reacting system. The method considers the population of neutrons, delayed-neutron precursors, and detector counts. The effect of the detector is separated from the statistics of the chain reaction by a weak coupling assumption that predicts that the detector responds to the average rather than to the instantaneous neutron population. An approximate solution to the remaining equation, involving the populations of neutrons and precursors, predicts a negative-binomial behaviour for the neutron probability distribution
Directory of Open Access Journals (Sweden)
C. Ünlü
2013-01-01
Full Text Available A modification of the variational iteration method (VIM for solving systems of nonlinear fractional-order differential equations is proposed. The fractional derivatives are described in the Caputo sense. The solutions of fractional differential equations (FDE obtained using the traditional variational iteration method give good approximations in the neighborhood of the initial position. The main advantage of the present method is that it can accelerate the convergence of the iterative approximate solutions relative to the approximate solutions obtained using the traditional variational iteration method. Illustrative examples are presented to show the validity of this modification.
An efficient parallel algorithm for the solution of a tridiagonal linear system of equations
Stone, H. S.
1971-01-01
Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.
Wazwaz, Abdul-Majid
2012-06-01
In this work, we explore a variety of solitary wave ansatze and periodic wave ansatze to some nonlinear equations. Three complex systems of nonlinear equations that appear in mathematical physics are investigated. We derive abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota-Maccari system. The results obtained show that these three coupled equations exhibit the richness of explicit solutions: solitons, periodic and rational wave solutions.
Diffuse optical tomography through solving a system of quadratic equations: theory and simulations.
Kanmani, B; Vasu, R M
2006-02-21
This paper discusses the iterative solution of the nonlinear problem of optical tomography. In the established forward model-based iterative image reconstruction (MOBIIR) method a linear perturbation equation containing the first derivative of the forward operator is solved to obtain the update vector for the optical properties. In MOBIIR, the perturbation equation is updated by recomputing the first derivative after each update of the optical properties. In the method presented here a nonlinear perturbation equation, containing terms up to the second derivative, is used to iteratively solve for the optical property updates. Through this modification, reconstructions with reasonable contrast recovery and accuracy are obtained without the need for updating the perturbation equation and therefore eliminating the outer iteration of the usual MOBIIR algorithm. To improve the performance of the algorithm the outer iteration is reintroduced in which the perturbation equation is recomputed without re-estimating the derivatives and with only updated computed data. The system of quadratic equations is solved using either a modified conjugate gradient descent scheme or a two-step linearized predictor-corrector scheme. A quick method employing the adjoint of the forward operator is used to estimate the derivatives. By solving the nonlinear perturbation equation it is shown that the iterative scheme is able to recover large contrast variations in absorption coefficient with improved noise tolerance in data. This ability has not been possible so far with linear algorithms. This is demonstrated by presenting results of numerical simulations from objects with inhomogeneous inclusions in absorption coefficient with different contrasts and shapes.
Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems
Skinner, Thomas E.
2018-01-01
The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which
Numerical Treatment of the Boltzmann Equation for Self-Propelled Particle Systems
Directory of Open Access Journals (Sweden)
Florian Thüroff
2014-11-01
Full Text Available Kinetic theories constitute one of the most promising tools to decipher the characteristic spatiotemporal dynamics in systems of actively propelled particles. In this context, the Boltzmann equation plays a pivotal role, since it provides a natural translation between a particle-level description of the system’s dynamics and the corresponding hydrodynamic fields. Yet, the intricate mathematical structure of the Boltzmann equation substantially limits the progress toward a full understanding of this equation by solely analytical means. Here, we propose a general framework to numerically solve the Boltzmann equation for self-propelled particle systems in two spatial dimensions and with arbitrary boundary conditions. We discuss potential applications of this numerical framework to active matter systems and use the algorithm to give a detailed analysis to a model system of self-propelled particles with polar interactions. In accordance with previous studies, we find that spatially homogeneous isotropic and broken-symmetry states populate two distinct regions in parameter space, which are separated by a narrow region of spatially inhomogeneous, density-segregated moving patterns. We find clear evidence that these three regions in parameter space are connected by first-order phase transitions and that the transition between the spatially homogeneous isotropic and polar ordered phases bears striking similarities to liquid-gas phase transitions in equilibrium systems. Within the density-segregated parameter regime, we find a novel stable limit-cycle solution of the Boltzmann equation, which consists of parallel lanes of polar clusters moving in opposite directions, so as to render the overall symmetry of the system’s ordered state nematic, despite purely polar interactions on the level of single particles.
Directory of Open Access Journals (Sweden)
Yongquan Zhou
2013-01-01
Full Text Available In view of the traditional numerical method to solve the nonlinear equations exist is sensitive to initial value and the higher accuracy of defects. This paper presents an invasive weed optimization (IWO algorithm which has population diversity with the heuristic global search of differential evolution (DE algorithm. In the iterative process, the global exploration ability of invasive weed optimization algorithm provides effective search area for differential evolution; at the same time, the heuristic search ability of differential evolution algorithm provides a reliable guide for invasive weed optimization. Based on the test of several typical nonlinear equations and a circle packing problem, the results show that the differential evolution invasive weed optimization (DEIWO algorithm has a higher accuracy and speed of convergence, which is an efficient and feasible algorithm for solving nonlinear systems of equations.
Vrettas, Michail D; Opper, Manfred; Cornford, Dan
2015-01-01
This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.
One-Dimensional Optimal System and Similarity Reductions of Wu—Zhang Equation
Xiong, Na; Li, Yu-Qi; Chen, Jun-Chao; Chen, Yong
2016-07-01
The one-dimensional optimal system for the Lie symmetry group of the (2+1)-dimensional Wu—Zhang equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlevé integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady case of the Wu-Zhang equation. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11375090, 11275072 and 11435005, Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Functional Integral Approach to the Solution of a System of Stochastic Differential Equations
Directory of Open Access Journals (Sweden)
Ayryan Edik
2018-01-01
Full Text Available A new method for the evaluation of the characteristics of the solution of a system of stochastic differential equations is presented. This method is based on the representation of a probability density function p through a functional integral. The functional integral representation is obtained by means of the Onsager-Machlup functional technique for a special case when the diffusion matrix for the SDE system defines a Riemannian space with zero curvature.
International Nuclear Information System (INIS)
Brandt, F.
1993-01-01
It is shown that Baecklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs. (orig.)
Directory of Open Access Journals (Sweden)
Hajnalka Péics
2016-08-01
Full Text Available The asymptotic behavior of solutions of the system of difference equations with continuous time and lag function between two known real functions is studied. The cases when the lag function is between two linear delay functions, between two power delay functions and between two constant delay functions are observed and illustrated by examples. The asymptotic estimates of solutions of the considered system are obtained.
Rebenda, Josef; Šmarda, Zdeněk
2017-07-01
In the paper, we propose a correct and efficient semi-analytical approach to solve initial value problem for systems of functional differential equations with delay. The idea is to combine the method of steps and differential transformation method (DTM). In the latter, formulas for proportional arguments and nonlinear terms are used. An example of using this technique for a system with constant and proportional delays is presented.
Yousef, Hamood. M.; Ismail, A. I. B. MD.
2017-08-01
Many attempts have been presented to solve the system of Delay Differential Equations (DDE) with Initial Value Problem. As a result, it has shown difficulties when getting the solution or cannot be solved. In this paper, a Variational Iteration Method is employed to find out an approximate solution for the system of DDE with initial value problems. The example illustrates convenient and an efficiency comparison with the exact solution.
Analysis of a quadratic system obtained from a scalar third order differential equation
Directory of Open Access Journals (Sweden)
Fabio Scalco Dias
2010-11-01
Full Text Available In this article, we study the nonlinear dynamics of a quadratic system in the three dimensional space which can be obtained from a scalar third order differential equation. More precisely, we study the stability and bifurcations which occur in a parameter dependent quadratic system in the three dimensional space. We present an analytical study of codimension one, two and three Hopf bifurcations, generic Bogdanov-Takens and fold-Hopf bifurcations.
On the solution of a class of fuzzy system of linear equations
Indian Academy of Sciences (India)
Abstract. Inthis paper, we consider the system of linear equations A˜x = ˜b, where. A ∈ Rn×n is a crisp H-matrix and ˜b is a fuzzy n-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices.
Functional Integral Approach to the Solution of a System of Stochastic Differential Equations
Ayryan, Edik; Egorov, Alexander; Kulyabov, Dmitri; Malyutin, Victor; Sevastianov, Leonid
2018-02-01
A new method for the evaluation of the characteristics of the solution of a system of stochastic differential equations is presented. This method is based on the representation of a probability density function p through a functional integral. The functional integral representation is obtained by means of the Onsager-Machlup functional technique for a special case when the diffusion matrix for the SDE system defines a Riemannian space with zero curvature.
He's homotopy perturbation method for systems of integro-differential equations
International Nuclear Information System (INIS)
Biazar, J.; Ghazvini, H.; Eslami, M.
2009-01-01
In this article, the homotopy perturbation method [He JH. Homotopy perturbation technique. Comput Meth Appl Mech Eng 1999;178:257-62; He JH. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int J Non-Linear Mech 2000;35(1):37-43; He JH. Comparison of homotopy perturbation method and homotopy analysis method. Appl Math Comput 2004;156:527-39; He JH. Homotopy perturbation method: a new nonlinear analytical technique. Appl Math Comput 2003;135:73-79; He JH. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl Math Comput 2004;151:287-92; He JH. Application of homotopy perturbation method to nonlinear wave equations Chaos, Solitons and Fractals 2005;26:695-700] is applied to solve linear and nonlinear systems of integro-differential equations. Some nonlinear examples are presented to illustrate the ability of the method for such system. Examples for linear system are so easy that has been ignored.
Finite-dimensional attractor for a composite system of wave/plate equations with localized damping
International Nuclear Information System (INIS)
Bucci, Francesca; Toundykov, Daniel
2010-01-01
The long-term behaviour of solutions to a model for acoustic–structure interactions is addressed; the system consists of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of interest are the existence of a global attractor for the dynamics generated by this composite system as well as dimensionality and regularity of the attractor. A distinct and challenging feature of the problem is the geometrically restricted dissipation on the wave component of the system. It is shown that the existence of a global attractor of finite fractal dimension—established in a previous work by Bucci et al (2007 Commun. Pure Appl. Anal. 6 113–40) only in the presence of full-interior acoustic damping—holds even in the case of localized dissipation. This nontrivial generalization is inspired by, and consistent with, the recent advances in the study of wave equations with nonlinear localized damping
Energy Technology Data Exchange (ETDEWEB)
Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)
1996-12-31
Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.
Discretized partial differential equations - Examples of control systems defined on modules
Brockett, R. W.; Willems, J. L.
1974-01-01
The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.
Fermion propagator in an out of equilibrium quantum-field system and the Boltzmann equation
International Nuclear Information System (INIS)
Niegawa, A.
2002-01-01
We aim to construct from first principles a perturbative framework for studying nonequilibrium quantum-field systems that include massless Dirac fermions. The system of our concern is a quasiuniform system near equilibrium or a nonequilibrium quasistationary system. We employ the closed-time-path formalism and use the so-called gradient approximation. Essentially no further approximation is introduced. We construct a fermion propagator, with which a well-defined perturbative framework is formulated. In the course of the construction of the framework, we obtain the generalized Boltzmann equation that describes the evolution of the number-density functions of (anti)fermionic quasiparticles
Tensor-GMRES method for large sparse systems of nonlinear equations
Feng, Dan; Pulliam, Thomas H.
1994-01-01
This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.
Directory of Open Access Journals (Sweden)
Sara Cruz y Cruz
2013-01-01
Full Text Available We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the Hamiltonian for this system and find the modifications required in the Euler-Lagrange and Hamilton's equations to reproduce the appropriate Newton's dynamical law. Since the Hamiltonian is not time invariant, we get a constant of motion suited to write the dynamical equations in the form of the Hamilton's ones. The time-dependent first integrals of motion are then obtained from the factorization of such a constant. A canonical transformation is found to map the variable mass equations to those of a constant mass. As particular cases, we recover some recent results for which the dependence of the mass on the position was already unnoticed, and find new solvable potentials of the Pöschl-Teller form which seem to be new. The latter are associated to either the su(1,1 or the su(2 Lie algebras depending on the sign of the Hamiltonian.
Equations for Hereditary Substitution in Leivant's Predicative System F: A Case Study
Directory of Open Access Journals (Sweden)
Cyprien Mangin
2015-07-01
Full Text Available This paper presents a case study of formalizing a normalization proof for Leivant's Predicative System F using the Equations package. Leivant's Predicative System F is a stratified version of System F, where type quantification is annotated with kinds representing universe levels. A weaker variant of this system was studied by Stump & Eades, employing the hereditary substitution method to show normalization. We improve on this result by showing normalization for Leivant's original system using hereditary substitutions and a novel multiset ordering on types. Our development is done in the Coq proof assistant using the Equations package, which provides an interface to define dependently-typed programs with well-founded recursion and full dependent pattern- matching. Equations allows us to define explicitly the hereditary substitution function, clarifying its algorithmic behavior in presence of term and type substitutions. From this definition, consistency can easily be derived. The algorithmic nature of our development is crucial to reflect languages with type quantification, enlarging the class of languages on which reflection methods can be used in the proof assistant.
Damage Spreading in Spatial and Small-world Random Boolean Networks
Energy Technology Data Exchange (ETDEWEB)
Lu, Qiming [Fermilab; Teuscher, Christof [Portland State U.
2014-02-18
The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ($\\bar{K} \\ll 1$) and that the critical connectivity of stability $K_s$ changes compared to random networks. At higher $\\bar{K}$, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.
The boolean algebra with restricted variables as a tool for fault tree modularization
International Nuclear Information System (INIS)
Caldarola, L.; Wickenhaeuser, A.
1981-08-01
The number of minimal cut sets (m.c.s.) of very complex and highly interconnected fault trees can become extremely large (e.g. more than 10 7 ). In this case the usual analytical approach of dissecting the fault tree TOP variable into m.c.s. is not only computationally prohibitively expensive, but also meaningless because it does not offer any synthetic overview of system behavior. The method proposed in this paper overcomes the deficiencies of the analytical method. It is shown that, by applying boolean algebra with restricted variables (b.a.w.r.v.), the concept of fault tree modularization can be straightforwardly extended from a single gate to a set of gates. Thus, large fault trees are divided into smaller fault trees (modules), which are connected to each other according to a simple scheme. This scheme is represented by a block diagram in which each block is a module. The modules are analyzed separately by the m.c.s. method, and the results are combined according of the TOP event. The method allows the calculation of very large fault trees in a short time and offers a synthetic overview of systems behavior through the block diagram. Numerical examples are also included. Calculations have been carried out by using the computer code MUSTAMO, which is based on the theory developed in this paper. (orig.) [de
Construction of a fuzzy and Boolean logic gates based on DNA.
Zadegan, Reza M; Jepsen, Mette D E; Hildebrandt, Lasse L; Birkedal, Victoria; Kjems, Jørgen
2015-04-17
Logic gates are devices that can perform logical operations by transforming a set of inputs into a predictable single detectable output. The hybridization properties, structure, and function of nucleic acids can be used to make DNA-based logic gates. These devices are important modules in molecular computing and biosensing. The ideal logic gate system should provide a wide selection of logical operations, and be integrable in multiple copies into more complex structures. Here we show the successful construction of a small DNA-based logic gate complex that produces fluorescent outputs corresponding to the operation of the six Boolean logic gates AND, NAND, OR, NOR, XOR, and XNOR. The logic gate complex is shown to work also when implemented in a three-dimensional DNA origami box structure, where it controlled the position of the lid in a closed or open position. Implementation of multiple microRNA sensitive DNA locks on one DNA origami box structure enabled fuzzy logical operation that allows biosensing of complex molecular signals. Integrating logic gates with DNA origami systems opens a vast avenue to applications in the fields of nanomedicine for diagnostics and therapeutics. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Structures and Boolean Dynamics in Gene Regulatory Networks
Szedlak, Anthony
This dissertation discusses the topological and dynamical properties of GRNs in cancer, and is divided into four main chapters. First, the basic tools of modern complex network theory are introduced. These traditional tools as well as those developed by myself (set efficiency, interset efficiency, and nested communities) are crucial for understanding the intricate topological properties of GRNs, and later chapters recall these concepts. Second, the biology of gene regulation is discussed, and a method for disease-specific GRN reconstruction developed by our collaboration is presented. This complements the traditional exhaustive experimental approach of building GRNs edge-by-edge by quickly inferring the existence of as of yet undiscovered edges using correlations across sets of gene expression data. This method also provides insight into the distribution of common mutations across GRNs. Third, I demonstrate that the structures present in these reconstructed networks are strongly related to the evolutionary histories of their constituent genes. Investigation of how the forces of evolution shaped the topology of GRNs in multicellular organisms by growing outward from a core of ancient, conserved genes can shed light upon the ''reverse evolution'' of normal cells into unicellular-like cancer states. Next, I simulate the dynamics of the GRNs of cancer cells using the Hopfield model, an infinite range spin-glass model designed with the ability to encode Boolean data as attractor states. This attractor-driven approach facilitates the integration of gene expression data into predictive mathematical models. Perturbations representing therapeutic interventions are applied to sets of genes, and the resulting deviations from their attractor states are recorded, suggesting new potential drug targets for experimentation. Finally, I extend the Hopfield model to modular networks, cyclic attractors, and complex attractors, and apply these concepts to simulations of the cell cycle
Neutron stars in compact binary systems: From the equation of state to gravitational radiation
Read, Jocelyn S.
Neutron stars are incredibly dense astrophysical objects that give a unique glimpse of physics at extreme scales. This thesis examines computational and mathematical methods of translating our theoretical understanding of neutron star physics, from the properties of matter to the relativistic behaviour of binary systems, into observable characteristics of astrophysical neutron stars. The properties of neutron star matter are encoded in the equation of state, which has substantial uncertainty. Many equations of state have been proposed based on different models of the underlying physics. These predict various quantities, such as the maximum stable mass, which allow them to be ruled out by astronomical measurements. This thesis presents a natural way to write a general equation of state that can approximate many different candidate equations of state with a few parameters. Astronomical observations are then used to systematically constrain parameter values, instead of ruling out models on a case-by-case basis. Orbiting pairs of neutron stars will release gravitational radiation and spiral in toward each other. The radiation may be observable with ground-based detectors. Until the stars get very close to each other the rate of inspiral is slow, and the orbits are approximately circular. One can numerically find spacetime solutions that satisfy the full set of Einstein equations by imposing an exact helical symmetry. However, we find that the helically-symmetric solution must be matched to a waveless boundary region to achieve convergence. Work with toy models suggests this lack of convergence is intractable, but the agreement of waveless and helical codes validates the use of either approximation to construct state-of-the-art initial data for fully dynamic binary neutron star simulations. The parameterized equation of state can be used with such numerical simulations to systematically explore how the emitted gravitational waves depend on the properties of neutron star
Directory of Open Access Journals (Sweden)
Gao Guo-Ping
2016-01-01
Full Text Available In this article, we investigate the local fractional 3-D compressible Navier-Stokes equation via local fractional derivative. We use the Cantor-type cylindrical co-ordinate method to transfer 3-D compressible Navier-Stokes equation from the Cantorian co-ordinate system to the Cantor-type cylindrical co-ordinate system.
Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.
Maybank, Philip J; Whiteley, Jonathan P
2014-02-01
Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.
DEFF Research Database (Denmark)
Mikkelsen, Frederik Vissing
Broadly speaking, this thesis is devoted to model selection applied to ordinary dierential equations and risk estimation under model selection. A model selection framework was developed for modelling time course data by ordinary dierential equations. The framework is accompanied by the R software...... eective computational tools for estimating unknown structures in dynamical systems, such as gene regulatory networks, which may be used to predict downstream eects of interventions in the system. A recommended algorithm based on the computational tools is presented and thoroughly tested in various...... simulation studies and applications. The second part of the thesis also concerns model selection, but focuses on risk estimation, i.e., estimating the error of mean estimators involving model selection. An extension of Stein's unbiased risk estimate (SURE), which applies to a class of estimators with model...
Recent symbolic summation methods to solve coupled systems of differential and difference equations
International Nuclear Information System (INIS)
Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de
2014-07-01
We outline a new algorithm to solve coupled systems of differential equations in one continuous variable x (resp. coupled difference equations in one discrete variable N) depending on a small parameter ε: given such a system and given sufficiently many initial values, we can determine the first coefficients of the Laurent-series solutions in ε if they are expressible in terms of indefinite nested sums and products. This systematic approach is based on symbolic summation algorithms in the context of difference rings/fields and uncoupling algorithms. The proposed method gives rise to new interesting applications in connection with integration by parts (IBP) methods. As an illustrative example, we will demonstrate how one can calculate the ε-expansion of a ladder graph with 6 massive fermion lines.
Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved.......Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....
Cellular ion channel-pump system modeling using switched stochastic differential equations.
Weaver, Jeffrey
2007-01-01
This paper identifies a multidimensional random switched process model of a neuron with embedded Ca++ ion channel and pump molecules adiabatically interacting based on local ion concentrations near the cell membrane. The model interprets known physiology of the channels as a coupled set of switched random processes and derives mechanical equations based on concentration flow among different states of the system. Rapid changes to channel barrier energies occurring during channel opening and closing transitions are modeled as another degree of freedom commutating the state of the overall system. An ion reservoir model is used as the primary tool to incorporate stochastic effects in channel operation. The complete model is analyzed numerically and then the equations are used to motivate a stochastic model for closed state dwell times. The result is compared against expected results of a leaky-integrator and known single-channel histograms.
Sweilam, N. H.; Abou Hasan, M. M.
2017-05-01
In this paper, the weighted-average non-standard finite-difference (WANSFD) method is used to study numerically the general time-fractional nonlinear, one-dimensional problem of thermoelasticity. This model contains the standard system arising in thermoelasticity as a special case. The stability of the proposed method is analyzed by a procedure akin to the standard John von Neumann technique. Moreover, the accuracy of the proposed scheme is proved. Numerical results are presented graphically, which reveal that the WANSFD method is easy to implement, effective and convenient for solving the proposed system. The proposed method could also be easily extended to solve other systems of fractional partial differential equations.
Open quantum system model of the one-dimensional Burgers equation with tunable shear viscosity
International Nuclear Information System (INIS)
Yepez, Jeffrey
2006-01-01
Presented is an analysis of an open quantum model of the time-dependent evolution of a flow field governed by the nonlinear Burgers equation in one spatial dimension. The quantum model is a system of qubits where there exists a minimum time interval in the time-dependent dynamics. Each temporally discrete unitary quantum-mechanical evolution is followed by state reduction of the quantum state. The mesoscopic behavior of this quantum model is described by a quantum Boltzmann equation with a naturally emergent entropy function and H theorem and the model obeys the detailed balance principle. The macroscopic-scale effective field theory for the quantum model is derived using a perturbative Chapman-Enskog expansion applied to the linearized quantum Boltzmann equation. The entropy function is consistent with the quantum-mechanical collision process and a Fermi-Dirac single-particle distribution function for the occupation probabilities of the qubit's energy eigenstates. Comparisons are presented between analytical predictions and numerical predictions and the agreement is excellent, indicating that the nonlinear Burgers equation with a tunable shear viscosity is the operative macroscopic scale effective field theory
Blow-up analysis for a system of heat equations coupled through a nonlinear boundary condition
DEFF Research Database (Denmark)
Pedersen, M.; Lin, Zhigui
2001-01-01
Consider the system of heat equations uit - Δui = 0 (i = 1 , . . . , k, uk+i := u1) in Ω x (0, T) coupled through nonlinear boundary conditions ∂ui/∂η = up1i+1 on ∂Ω x [0, T). The upper and lower bounds of the blow-up rate is derived. © 2000 Elsevier Science Ltd. All rights reserved....
A vanishing diffusion limit in a nonstandard system of phase field equations
Czech Academy of Sciences Publication Activity Database
Colli, P.; Gilardi, G.; Krejčí, Pavel; Sprekels, J.
2014-01-01
Roč. 3, č. 2 (2014), s. 257-275 ISSN 2163-2480 R&D Projects: GA ČR GAP201/10/2315 Institutional support: RVO:67985840 Keywords : nonstandard phase field system * nonlinear partial differential equations * asympotic limit Subject RIV: BA - General Mathematics Impact factor: 0.373, year: 2014 http://aimsciences.org/journals/displayArticlesnew.jsp?paperID=9918
A combined modification of Newton`s method for systems of nonlinear equations
Energy Technology Data Exchange (ETDEWEB)
Monteiro, M.T.; Fernandes, E.M.G.P. [Universidade do Minho, Braga (Portugal)
1996-12-31
To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.
Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations
International Nuclear Information System (INIS)
Sczaniecki, L.
1981-02-01
A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)
Linear Response in Complex Systems: CTRW and the Fractional Fokker-Planck Equations
Sokolov, I. M.; Blumen, A.; Klafter, J.
2001-01-01
We consider the linear response of systems modelled by continuous-time random walks (CTRW) and by fractional Fokker-Planck equations under the influence of time-dependent external fields. We calculate the corresponding response functions explicitely. The CTRW curve exhibits aging, i.e. it is not translationally invariant in the time-domain. This is different from what happens under fractional Fokker-Planck conditions.
On a New Method for Computing the Numerical Solution of Systems of Nonlinear Equations
Directory of Open Access Journals (Sweden)
H. Montazeri
2012-01-01
Full Text Available We consider a system of nonlinear equations F(x=0. A new iterative method for solving this problem numerically is suggested. The analytical discussions of the method are provided to reveal its sixth order of convergence. A discussion on the efficiency index of the contribution with comparison to the other iterative methods is also given. Finally, numerical tests illustrate the theoretical aspects using the programming package Mathematica.
New version of the RADUGA system for solving transport equations in the R-Z geometry
International Nuclear Information System (INIS)
Bass, L.P.; Germogenova, T.A.; Goncharov, A.N.; Petrulevich, A.A.; Khmylev, A.N.
1987-01-01
The RADUGA-3 version of the RADUGA modular program used to solve the multigroup system of equations of radiation transport with anisotropic scattering by the discrete ordinate method in two-dimensional R-Z-geometry, is described. Modules, introduced into the new version, broaden the program possibilities and allow to improve calculational accuracy and to reduce essentially (by 2-5 times) calculation time
On Landweber–Kaczmarz methods for regularizing systems of ill-posed equations in Banach spaces
International Nuclear Information System (INIS)
Leitão, A; Alves, M Marques
2012-01-01
In this paper, iterative regularization methods of Landweber–Kaczmarz type are considered for solving systems of ill-posed equations modeled (finitely many) by operators acting between Banach spaces. Using assumptions of uniform convexity and smoothness on the parameter space, we are able to prove a monotony result for the proposed method, as well as to establish convergence (for exact data) and stability results (in the noisy data case). (paper)
Directory of Open Access Journals (Sweden)
Ahmad Bashir
2010-01-01
Full Text Available We study an initial value problem for a coupled Caputo type nonlinear fractional differential system of higher order. As a first problem, the nonhomogeneous terms in the coupled fractional differential system depend on the fractional derivatives of lower orders only. Then the nonhomogeneous terms in the fractional differential system are allowed to depend on the unknown functions together with the fractional derivative of lower orders. Our method of analysis is based on the reduction of the given system to an equivalent system of integral equations. Applying the nonlinear alternative of Leray-Schauder, we prove the existence of solutions of the fractional differential system. The uniqueness of solutions of the fractional differential system is established by using the Banach contraction principle. An illustrative example is also presented.
An Improvement to a Multi-Client Searchable Encryption Scheme for Boolean Queries.
Jiang, Han; Li, Xue; Xu, Qiuliang
2016-12-01
The migration of e-health systems to the cloud computing brings huge benefits, as same as some security risks. Searchable Encryption(SE) is a cryptography encryption scheme that can protect the confidentiality of data and utilize the encrypted data at the same time. The SE scheme proposed by Cash et al. in Crypto2013 and its follow-up work in CCS2013 are most practical SE Scheme that support Boolean queries at present. In their scheme, the data user has to generate the search tokens by the counter number one by one and interact with server repeatedly, until he meets the correct one, or goes through plenty of tokens to illustrate that there is no search result. In this paper, we make an improvement to their scheme. We allow server to send back some information and help the user to generate exact search token in the search phase. In our scheme, there are only two round interaction between server and user, and the search token has [Formula: see text] elements, where n is the keywords number in query expression, and [Formula: see text] is the minimum documents number that contains one of keyword in query expression, and the computation cost of server is [Formula: see text] modular exponentiation operation.
Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras
Andrade, Jefferson O.; Kameyama, Yukiyoshi
Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In this paper, we propose a novel, efficient algorithm for multi-valued bounded model checking. A notable feature of our algorithm is that it is not based on reduction of multi-values into two-values; instead, it generates a single formula which represents multi-valuedness by a suitable encoding, and asks a standard SAT solver to check its satisfiability. Our experimental results show a significant improvement in the number of variables and clauses and also in execution time compared with the reduction-based one.
Directory of Open Access Journals (Sweden)
Tomáš Mrkvička
2011-03-01
Full Text Available Methods for testing the Boolean model assumption from binary images are briefly reviewed. Two hundred binary images of mammary cancer tissue and 200 images of mastopathic tissue were tested individually on the Boolean model assumption. In a previous paper, it had been found that a Monte Carlo method based on the approximation of the envelopes by a multi-normal distribution with the normalized intrinsic volume densities of parallel sets as a summary statistics had the highest power for this purpose. Hence, this method was used here as its first application to real biomedical data. It was found that mastopathic tissue deviates from the Boolean model significantly more strongly than mammary cancer tissue does.
Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks
Directory of Open Access Journals (Sweden)
Koichi Kobayashi
2010-01-01
Full Text Available In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.
Energy Technology Data Exchange (ETDEWEB)
Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos [Universidade Federal, Rio de Janeiro, RJ (Brazil). Coordenacao dos Programas de Pos-graduacao de Engenharia. Programa de Engenharia Nuclear
2000-07-01
The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)
Nursyahidah, F.; Saputro, B. A.; Rubowo, M. R.
2018-03-01
The aim of this research is to know the students’ understanding of linear equation system in two variables using Ethnomathematics and to acquire learning trajectory of linear equation system in two variables for the second grade of lower secondary school students. This research used methodology of design research that consists of three phases, there are preliminary design, teaching experiment, and retrospective analysis. Subject of this study is 28 second grade students of Sekolah Menengah Pertama (SMP) 37 Semarang. The result of this research shows that the students’ understanding in linear equation system in two variables can be stimulated by using Ethnomathematics in selling buying tradition in Peterongan traditional market in Central Java as a context. All of strategies and model that was applied by students and also their result discussion shows how construction and contribution of students can help them to understand concept of linear equation system in two variables. All the activities that were done by students produce learning trajectory to gain the goal of learning. Each steps of learning trajectory of students have an important role in understanding the concept from informal to the formal level. Learning trajectory using Ethnomathematics that is produced consist of watching video of selling buying activity in Peterongan traditional market to construct linear equation in two variables, determine the solution of linear equation in two variables, construct model of linear equation system in two variables from contextual problem, and solving a contextual problem related to linear equation system in two variables.
Sotiropoulos, Vassilios; Kaznessis, Yiannis N
2008-01-07
Models involving stochastic differential equations (SDEs) play a prominent role in a wide range of applications where systems are not at the thermodynamic limit, for example, biological population dynamics. Therefore there is a need for numerical schemes that are capable of accurately and efficiently integrating systems of SDEs. In this work we introduce a variable size step algorithm and apply it to systems of stiff SDEs with multiple multiplicative noise. The algorithm is validated using a subclass of SDEs called chemical Langevin equations that appear in the description of dilute chemical kinetics models, with important applications mainly in biology. Three representative examples are used to test and report on the behavior of the proposed scheme. We demonstrate the advantages and disadvantages over fixed time step integration schemes of the proposed method, showing that the adaptive time step method is considerably more stable than fixed step methods with no excessive additional computational overhead.
DEFF Research Database (Denmark)
Maia, Filipa Meireles; Tsivintzelis, Ioannis; Rodriguez, Oscar
2012-01-01
and their interactions with other components is still needed. In this work, we made a review of literature studies on modelling systems with ionic liquids using equation of state models. Furthermore, we applied the Cubic Plus Association (CPA) equation of state to describe the phase behaviour of two ionic liquids, 1...... is in progress for improving the modelling of LLE with the CPA equation of state....
Gomez-Cabrero, David
2017-05-09
The rise and growth of Systems Biology following the sequencing of the human genome has been astounding. Early on, an iterative wet-dry methodology was formulated which turned out as a successful approach in deciphering biological complexity. Such type of analysis effectively identified and associated molecular network signatures operative in biological processes across different systems. Yet, it has proven difficult to distinguish between causes and consequences, thus making it challenging to attack medical questions where we require precise causative drug targets and disease mechanisms beyond a web of associated markers. Here we review principal advances with regard to identification of structure, dynamics, control, and design of biological systems, following the structure in the visionary review from 2002 by Dr. Kitano. Yet, here we find that the underlying challenge of finding the governing mechanistic system equations enabling precision medicine remains open thus rendering clinical translation of systems biology arduous. However, stunning advances in raw computational power, generation of high-precision multi-faceted biological data, combined with powerful algorithms hold promise to set the stage for data-driven identification of equations implicating a fundamental understanding of living systems during health and disease.
Field theory and weak Euler-Lagrange equation for classical particle-field systems.
Qin, Hong; Burby, Joshua W; Davidson, Ronald C
2014-10-01
It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.
Utility rate equations of group population dynamics in biological and social systems.
Yukalov, Vyacheslav I; Yukalova, Elizaveta P; Sornette, Didier
2013-01-01
We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate equations, whose parameters are characterized by the utility of each group with respect to the society as a whole and by the mutual utilities of groups with respect to each other. We analyze in detail the cases of two groups (cooperators and defectors) and of three groups (cooperators, defectors, and regulators) and find that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about [Formula: see text] each. This is in agreement with the data for bee and ant colonies. The classification of societies by their distance from equilibrium is proposed. We apply the formalism to rank the countries according to the introduced metric quantifying their relative stability, which depends on the cost of defectors and regulators as well as their respective population fractions. We find a remarkable concordance with more standard economic ranking based, for instance, on GDP per capita.
Equivalent Quantum Equations in a System Inspired by Bouncing Droplets Experiments
Borghesi, Christian
2017-07-01
In this paper we study a classical and theoretical system which consists of an elastic medium carrying transverse waves and one point-like high elastic medium density, called concretion. We compute the equation of motion for the concretion as well as the wave equation of this system. Afterwards we always consider the case where the concretion is not the wave source any longer. Then the concretion obeys a general and covariant guidance formula, which leads in low-velocity approximation to an equivalent de Broglie-Bohm guidance formula. The concretion moves then as if exists an equivalent quantum potential. A strictly equivalent free Schrödinger equation is retrieved, as well as the quantum stationary states in a linear or spherical cavity. We compute the energy (and momentum) of the concretion, naturally defined from the energy (and momentum) density of the vibrating elastic medium. Provided one condition about the amplitude of oscillation is fulfilled, it strikingly appears that the energy and momentum of the concretion not only are written in the same form as in quantum mechanics, but also encapsulate equivalent relativistic formulas.
Master equation for open two-band systems and its applications to Hall conductance
Shen, H. Z.; Zhang, S. S.; Dai, C. M.; Yi, X. X.
2018-02-01
Hall conductivity in the presence of a dephasing environment has recently been investigated with a dissipative term introduced phenomenologically. In this paper, we study the dissipative topological insulator (TI) and its topological transition in the presence of quantized electromagnetic environments. A Lindblad-type equation is derived to determine the dynamics of a two-band system. When the two-band model describes TIs, the environment may be the fluctuations of radiation that surround the TIs. We find the dependence of decay rates in the master equation on Bloch vectors in the two-band system, which leads to a mixing of the band occupations. Hence the environment-induced current is in general not perfectly topological in the presence of coupling to the environment, although deviations are small in the weak limit. As an illustration, we apply the Bloch-vector-dependent master equation to TIs and calculate the Hall conductance of tight-binding electrons in a two-dimensional lattice. The influence of environments on the Hall conductance is presented and discussed. The calculations show that the phase transition points of the TIs are robust against the quantized electromagnetic environment. The results might bridge the gap between quantum optics and topological photonic materials.
Equation of material balance for systems of double porosity with layer of initial gas
International Nuclear Information System (INIS)
Niz, Eider; Hidrobo, Eduardo A; Penuela, Gherson; Ordonez, Anibal; Calderon, Zuly H
2004-01-01
The physical complexity associated to naturally fractured reservoirs calls for the use of more robust formulations of the Material-Balance Equation (MBE) for determining the initial hydrocarbon in place and predicting reservoir performance. In this paper, we present an improved version of the dual-porosity MBE for naturally fractured reservoirs, published by Penuela et al. (2001), including the existence of an initial gas phase in the reservoir. Considering that a fractured reservoir may be modeled either using different properties for each porous medium or with average values for the total system, two solution techniques based on each of these assumptions are proposed. Convenient arrangements of the equation allow us to estimate not only the original oil and gas volumes but also the relative storage capacity of the porous media (fractures and matrix) and the compressibility for the fractured and total systems. The new equation can be applied to a broader range of reservoirs due to its more general character. The consistency of the expression proposed has been tested with a set of synthetic models exhibiting different storage capacity in the fractures
A two-qubit photonic quantum processor and its application to solving systems of linear equations
Barz, Stefanie; Kassal, Ivan; Ringbauer, Martin; Lipp, Yannick Ole; Dakić, Borivoje; Aspuru-Guzik, Alán; Walther, Philip
2014-01-01
Large-scale quantum computers will require the ability to apply long sequences of entangling gates to many qubits. In a photonic architecture, where single-qubit gates can be performed easily and precisely, the application of consecutive two-qubit entangling gates has been a significant obstacle. Here, we demonstrate a two-qubit photonic quantum processor that implements two consecutive CNOT gates on the same pair of polarisation-encoded qubits. To demonstrate the flexibility of our system, we implement various instances of the quantum algorithm for solving of systems of linear equations. PMID:25135432
Modeling Water Containing Systems with the Simplified PC-SAFT and CPA Equations of State
DEFF Research Database (Denmark)
Liang, Xiaodong; Tsivintzelis, Ioannis; Kontogeorgis, Georgios M.
2014-01-01
Numerous studies have been presented for modeling of water containing systems with the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state (EOS), and more than 20 water parameter sets have been published with emphasis on different applications. In this work, eight...... pressure and saturated liquid density of water. For the aforementioned aqueous systems, the PC-SAFT correlations using the newly developed parameters are compared with the corresponding correlations of the cubic plus association EOS. The two models show comparable results for phase equilibria, and both...
Directory of Open Access Journals (Sweden)
Qi Wang
2012-01-01
Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.
Weak KAM theory for a weakly coupled system of Hamilton–Jacobi equations
Figalli, Alessio
2016-06-23
Here, we extend the weak KAM and Aubry–Mather theories to optimal switching problems. We consider three issues: the analysis of the calculus of variations problem, the study of a generalized weak KAM theorem for solutions of weakly coupled systems of Hamilton–Jacobi equations, and the long-time behavior of time-dependent systems. We prove the existence and regularity of action minimizers, obtain necessary conditions for minimality, extend Fathi’s weak KAM theorem, and describe the asymptotic limit of the generalized Lax–Oleinik semigroup. © 2016, Springer-Verlag Berlin Heidelberg.
Improving the quantum cost of reversible Boolean functions using reorder algorithm
Ahmed, Taghreed; Younes, Ahmed; Elsayed, Ashraf
2018-05-01
This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed-Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decrease the quantum cost of the reversible circuit. The paper achieves a decrease in the quantum cost and/or the circuit length, on average, when compared with relevant work in the literature.
Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence
Directory of Open Access Journals (Sweden)
Le Yu
2007-05-01
Full Text Available The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic 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 determined 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. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1 separate the data sequence into Ã‚Â“pureÃ‚Â” subsequences corresponding to constituent Boolean networks; (2 given a subsequence, infer a Boolean network; and (3 infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm
Boolean Matching Filters Based on Row and Column Weights of Reed–Muller Polarity Coefficient Matrix
Directory of Open Access Journals (Sweden)
Chip-Hong Chang
2002-01-01
Full Text Available In this article, we have shown, by means of the EXOR Ternary Decision Diagram that the number of literals and product terms of the Fixed Polarity Reed–Muller (FPRM expansions can be used to fully classify all Boolean functions in NP equivalent class and NPN equivalent class, respectively. Efficient graph based algorithms to compute the complete weight vectors have been presented. The proof and computation method has led to the derivation of a set of characteristic signatures that has low probability of aliasing when used as the Boolean matching filters in library mapping.
Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence
Directory of Open Access Journals (Sweden)
Xiao Yufei
2007-01-01
Full Text Available The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic 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 determined 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. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1 separate the data sequence into "pure" subsequences corresponding to constituent Boolean networks; (2 given a subsequence, infer a Boolean network; and (3 infer the probabilities of perturbation, the probability of there being a switch between constituent Boolean networks, and the selection probabilities governing which network is to be selected given a switch. Capturing the full dynamic behavior of probabilistic Boolean networks, be they binary or multivalued, will require the use of temporal data, and a great deal of it. This should not be surprising given the complexity of the model and the number of parameters, both transitional and static, that must be estimated. In addition to providing an inference algorithm, this paper
Directory of Open Access Journals (Sweden)
Iu. Caraus
1997-08-01
Full Text Available This article generalizes the results which were obtained in the paper [1], written together with my scientific-adviser, doctor-habilitat, professor Zolotarevschi V. Theoretical foundation of the collocation method and of mechanical quadrature method for singular integro-differential equations systems (SIDE in the case when the equations are given on a closed contour satisfying some conditions of smoothness, without their reduction to the unit circle, is given below. Let $\\Gamma $ be a smooth Jordan border limiting the one-spanned area $F^{+}$, containing a point $ t=0$, $ F^{-}= C \\setminus \\{ F^{+}\\cup \\Gamma \\}$, $C $ is a full complex plane. Let $z= \\psi (w-$ be a function, mapping comformally and single-valuedly the surface $\\Gamma_{0}=\\{|w| >1 \\} $ on $F^{-} $ so that $ \\psi (\\infty = \\infty ,\\psi^{ (\\prime }(\\infty >0$. We shall assume that the function $ z= \\psi (w$ has its second derivative, satisfying on $\\Gamma_{0} $ the H\\"older condition with some parameter $ \
General decay of solutions of a nonlinear system of viscoelastic wave equations
Said-Houari, Belkacem
2011-04-16
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
A relativistic extended Fermi-Thomas-like equation for a self-gravitating system of fermions
International Nuclear Information System (INIS)
Merloni, A.; Ruffini, R.; Torroni, V.
1998-01-01
The authors extend previous results of a Fermi-Thomas model, describing self-gravitating fermions in their ground state, to a relativistic gravitational theory in Minkowski space. In such a theory the source term of the gravitational potential depends both on the pressure and the density of the fluid. It is shown that, in correspondence of this relativistic treatment, still a Fermi-Thomas-like equation can be derived for the self-gravitating system, though the non-linearities are much more complex. No Fermi-Thomas-like equation can be obtained in the General Relativistic treatment. The canonical results for neutron stars and white dwarfs are recovered and also some erroneous statements in the scientific literature are corrected
Mechanical Analogy-based Iterative Method for Solving a System of Linear Equations
Directory of Open Access Journals (Sweden)
Yu. V. Berchun
2015-01-01
Full Text Available The paper reviews prerequisites to creating a variety of the iterative methods to solve a system of linear equations (SLE. It considers the splitting methods, variation-type methods, projection-type methods, and the methods of relaxation.A new iterative method based on mechanical analogy (the movement without resistance of a material point, that is connected by ideal elastically-linear constraints with unending guides defined by equations of solved SLE. The mechanical system has the unique position of stable equilibrium, the coordinates of which correspond to the solution of linear algebraic equation. The model of the mechanical system is a system of ordinary differential equations of the second order, integration of which allows you to define the point trajectory. In contrast to the classical methods of relaxation the proposed method does not ensure a trajectory passage through the equilibrium position. Thus the convergence of the method is achieved through the iterative stop of a material point at the moment it passes through the next (from the beginning of the given iteration minimum of potential energy. After that the next iteration (with changed initial coordinates starts.A resource-intensive process of numerical integration of differential equations in order to obtain a precise law of motion (at each iteration is replaced by defining its approximation. The coefficients of the approximating polynomial of the fourth order are calculated from the initial conditions, including higher-order derivatives. The resulting approximation enables you to evaluate the kinetic energy of a material point to calculate approximately the moment of time to reach the maximum kinetic energy (and minimum of the potential one, i.e. the end of the iteration.The software implementation is done. The problems with symmetric positive definite matrix, generated as a result of using finite element method, allowed us to examine a convergence rate of the proposed method
Students’ Decisions to Use an eLearning System: A Structural Equation Modelling Analysis
Directory of Open Access Journals (Sweden)
Muneer Abbad
2009-12-01
Full Text Available This research investigates and identifies some of the major factors affecting students’ adoption of an e-learning system at Arab Open University in Jordan. E-learning adoption is approached from the information systems acceptance point of view. An extended version of the Technology Acceptance Model (TAM was developed to investigate the underlying factors that influence students’ decisions to use an e-learning system. The proposed model uses the actual use of an e-learning system. It is different from most of the prior TAM studies, which only used a single dependent variable (intention to use. The model was estimated using Structural Equation Modelling (SEM. The final models derived from this study indicated that beliefs of usefulness and ease of use partially mediate the relationship between external factors and intention to use and actual use of e-learning systems.
Fu, Wei; Nijhoff, Frank W
2017-07-01
A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearizing transform, which establishes a general class of integral transforms between solutions. As a particular application, novel soliton-type solutions for the lattice CKP equation are obtained.
FEQinput—An editor for the full equations (FEQ) hydraulic modeling system
Ancalle, David S.; Ancalle, Pablo J.; Domanski, Marian M.
2017-10-30
IntroductionThe Full Equations Model (FEQ) is a computer program that solves the full, dynamic equations of motion for one-dimensional unsteady hydraulic flow in open channels and through control structures. As a result, hydrologists have used FEQ to design and operate flood-control structures, delineate inundation maps, and analyze peak-flow impacts. To aid in fighting floods, hydrologists are using the software to develop a system that uses flood-plain models to simulate real-time streamflow.Input files for FEQ are composed of text files that contain large amounts of parameters, data, and instructions that are written in a format exclusive to FEQ. Although documentation exists that can aid in the creation and editing of these input files, new users face a steep learning curve in order to understand the specific format and language of the files.FEQinput provides a set of tools to help a new user overcome the steep learning curve associated with creating and modifying input files for the FEQ hydraulic model and the related utility tool, Full Equations Utilities (FEQUTL).
A Dynamic System of Growth and Yield Equations for Pinus patula
Directory of Open Access Journals (Sweden)
Wenceslao Santiago-García
2017-11-01
Full Text Available Sustainable forest management needs tools that can predict how silvicultural treatments will affect cutting stands. Growth and yield systems are an example of these tools because they can represent periods of growth and yield of a stand in numerical terms. The aim of this research was to develop a dynamic growth and yield timber system with the stand-level models approach for Pinus patula in even-aged forests of Ixtlán de Juárez, Oaxaca, Mexico. The data was obtained from two consecutive remeasurements of 66 permanent 400 m2 plots. With this information, prediction and projection equations in the algebraic difference approach for mean diameter at breast height (DBH, basal area and total volume per hectare were fitted through the seemingly unrelated regression technique. Mortality was fitted by the non-linear least squares method. A model of dominant height and site index (Levakovic II with polymorphism was related to basal area, DBH, total volume ha−1 and mortality equations. The growth system generated an average optimal age rotation of 32 years when the current annual increment (CAI was the same as the mean annual increment (MAI for the mean site index and a density of 1500 trees ha−1 at five years. The growth and yield system developed is an important tool for planning forest management of even-aged P. patula forests.
International Nuclear Information System (INIS)
Guth, M.A.S.
1987-01-01
This paper applies the method of assigning probability in Dempster-Shafer Theory (DST) to the components of rule-based expert systems used in the control of nuclear reactors. Probabilities are assigned to premises, consequences, and rules themselves. This paper considers how uncertainty can propagate through a system of Boolean equations, such as fault trees or expert systems. The probability masses assigned to primary initiating events in the expert system can be derived from observing a nuclear reactor in operation or based on engineering knowledge of the reactor parts. Use of DST mass assignments offers greater flexibility to the construction of expert systems
Multifractal chaotic attractors in a system of delay-differential equations modeling road traffic.
Safonov, Leonid A.; Tomer, Elad; Strygin, Vadim V.; Ashkenazy, Yosef; Havlin, Shlomo
2002-12-01
We study a system of delay-differential equations modeling single-lane road traffic. The cars move in a closed circuit and the system's variables are each car's velocity and the distance to the car ahead. For low and high values of traffic density the system has a stable equilibrium solution, corresponding to the uniform flow. Gradually decreasing the density from high to intermediate values we observe a sequence of supercritical Hopf bifurcations forming multistable limit cycles, corresponding to flow regimes with periodically moving traffic jams. Using an asymptotic technique we find approximately small limit cycles born at Hopf bifurcations and numerically preform their global continuations with decreasing density. For sufficiently large delay the system passes to chaos following the Ruelle-Takens-Newhouse scenario (limit cycles-two-tori-three-tori-chaotic attractors). We find that chaotic and nonchaotic attractors coexist for the same parameter values and that chaotic attractors have a broad multifractal spectrum. (c) 2002 American Institute of Physics.
lowast-SDYM fields and heavenly spaces: I. lowast-SDYM equations as an integrable system
Formanski, Sebastian; Przanowski, Maciej
2005-05-01
It is shown that the self-dual Yang-Mills (SDYM) equations for the lowast-bracket Lie algebra on a heavenly space can be reduced to one equation (the master equation). Two hierarchies of conservation laws for this equation are constructed. Then the twistor transform and a solution to the Riemann-Hilbert problem are given.
Towards a General Equation for the Survival of Microbes Transferred between Solar System Bodies
Fries, M.; Steele, A.
2014-01-01
It should be possible to construct a general equation describing the survival of microbes transferred between Solar System bodies. Such an equation will be useful for constraining the likelihood of transfer of viable organisms between bodies throughout the lifetime of the Solar System, and for refining Planetary Protection constraints placed on future missions. We will discuss the construction of such an equation, present a plan for definition of pertinent factors, and will describe what research will be necessary to quantify those factors. Description: We will examine the case of microbes transferred between Solar System bodies as residents in meteorite material ejected from one body (the "intial body") and deposited on another (the "target body"). Any microbes transferred in this fashion will experience four distinct phases between their initial state on the initial body, up to the point where they colonize the target body. Each of these phases features phenomena capable of reducing or exterminating the initial microbial population. They are: 1) Ejection: Material is ejected from the initial body, imparting shock followed by rapid desiccation and cooling. 2) Transport: Material travels through interplanetary space to the target body, exposing a hypothetical microbial population to extended desiccation, irradiation, and temperature extremes. 3) Infall: Material is deposited on the target body, diminishing the microbial population through shock, mass loss, and heating. 4) Adaptation: Any microbes which survive the previous three phases must then adapt to new chemophysical conditions of the target body. Differences in habitability between the initial and target bodies dominate this phase. A suitable general-form equation can be assembled from the above factors by defining the initial number of microbes in an ejected mass and applying multiplicitive factors based on the physical phenomena inherent to each phase. It should be possible to present the resulting equation
Peng, NaiFu; Guan, Hui; Wu, ChuiJie
2016-04-01
In this paper, the theory of constructing optimal dynamical systems based on weighted residual presented by Wu & Sha is applied to three-dimensional Navier-Stokes equations, and the optimal dynamical system modeling equations are derived. Then the multiscale global optimization method based on coarse graining analysis is presented, by which a set of approximate global optimal bases is directly obtained from Navier-Stokes equations and the construction of optimal dynamical systems is realized. The optimal bases show good properties, such as showing the physical properties of complex flows and the turbulent vortex structures, being intrinsic to real physical problem and dynamical systems, and having scaling symmetry in mathematics, etc.. In conclusion, using fewer terms of optimal bases will approach the exact solutions of Navier-Stokes equations, and the dynamical systems based on them show the most optimal behavior.
Zieniuk, Eugeniusz; Kapturczak, Marta
2017-07-01
In recent studies of parametric integral equations system (PIES), the input data, necessary to define the shape of boundary, was defined in precise way. However, it is just assumption for further calculations. In practice even the most accurate measurement instruments generate errors. Therefore, in this paper we decide to propose the method for modelling and solving the boundary value problems with uncertainly defined shape of boundary. In view of advantages in precisely defined problems, we decide to generalize PIES method. To define the uncertainty of the input data we propose the modification of directed interval arithmetic.
International Nuclear Information System (INIS)
Dehghan, Mehdi; Shakourifar, Mohammad; Hamidi, Asgar
2009-01-01
The purpose of this study is to implement Adomian-Pade (Modified Adomian-Pade) technique, which is a combination of Adomian decomposition method (Modified Adomian decomposition method) and Pade approximation, for solving linear and nonlinear systems of Volterra functional equations. The results obtained by using Adomian-Pade (Modified Adomian-Pade) technique, are compared to those obtained by using Adomian decomposition method (Modified Adomian decomposition method) alone. The numerical results, demonstrate that ADM-PADE (MADM-PADE) technique, gives the approximate solution with faster convergence rate and higher accuracy than using the standard ADM (MADM).
Bagci, Hakan
2014-11-11
We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
Aydogmus, F.
2015-02-01
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the "Heisenberg dream." In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented.
Stella, L.; Lorenz, C. D.; Kantorovich, L.
2014-04-01
The generalized Langevin equation (GLE) has been recently suggested to simulate the time evolution of classical solid and molecular systems when considering general nonequilibrium processes. In this approach, a part of the whole system (an open system), which interacts and exchanges energy with its dissipative environment, is studied. Because the GLE is derived by projecting out exactly the harmonic environment, the coupling to it is realistic, while the equations of motion are non-Markovian. Although the GLE formalism has already found promising applications, e.g., in nanotribology and as a powerful thermostat for equilibration in classical molecular dynamics simulations, efficient algorithms to solve the GLE for realistic memory kernels are highly nontrivial, especially if the memory kernels decay nonexponentially. This is due to the fact that one has to generate a colored noise and take account of the memory effects in a consistent manner. In this paper, we present a simple, yet efficient, algorithm for solving the GLE for practical memory kernels and we demonstrate its capability for the exactly solvable case of a harmonic oscillator coupled to a Debye bath.
4th International Conference on Particle Systems and Partial Differential Equations
Soares, Ana
2017-01-01
'This book addresses mathematical problems motivated by various applications in physics, engineering, chemistry and biology. It gathers the lecture notes from the mini-course presented by Jean-Christophe Mourrat on the construction of the various stochastic “basic” terms involved in the formulation of the dynamic Ö4 theory in three space dimensions, as well as selected contributions presented at the fourth meeting on Particle Systems and PDEs, which was held at the University of Minho’s Centre of Mathematics in December 2015. The purpose of the conference was to bring together prominent researchers working in the fields of particle systems and partial differential equations, offering them a forum to present their recent results and discuss their topics of expertise. The meeting was also intended to present to a vast and varied public, including young researchers, the area of interacting particle systems, its underlying motivation, and its relation to partial differential equations. The book w...
Energy Technology Data Exchange (ETDEWEB)
Clemens, M.; Weiland, T. [Technische Hochschule Darmstadt (Germany)
1996-12-31
In the field of computational electrodynamics the discretization of Maxwell`s equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extended to a whole class of methods for complex-symmetric algorithms SCBiCG(T, n), which only require one matrix vector multiplication per iteration step. In this class the well-known conjugate orthogonal conjugate gradient (COCG) method for complex-symmetric systems corresponds to the case n = 0. The case n = 1 yields the BiCGCR method which corresponds to the conjugate residual algorithm for the real-valued case. These methods in combination with a minimal residual smoothing process are applied separately to practical 3D electro-quasistatical and eddy-current problems in electrodynamics. The practical performance of the SCBiCG methods is compared with other methods such as QMR and TFQMR.
Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann
Czech Academy of Sciences Publication Activity Database
Balcar, Bohuslav; Jech, Thomas; Pazák, Tomáš
2005-01-01
Roč. 37, č. 6 (2005), s. 885-898 ISSN 0024-6093 Institutional research plan: CEZ:AV0Z10750506; CEZ:AV0Z10190503 Keywords : Boolean algebras * Maharam submeasure * weak distributivity * independent reals Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2005
The objective of this work is to elucidate biological networks underlying cellular tipping points using time-course data. We discretized the high-content imaging (HCI) data and inferred Boolean networks (BNs) that could accurately predict dynamic cellular trajectories. We found t...
Characterization of Boolean Algebras in Terms of Certain States of Jauch-Piron Type
Matoušek, Milan; Pták, Pavel
2015-12-01
Suppose that L is an orthomodular lattice (a quantum logic). We show that L is Boolean exactly if L possesses a strongly unital set of weakly Jauch-Piron states, or if L possesses a unital set of weakly positive states. We also discuss some general properties of Jauch-Piron-like states.
Yes/No/Maybe: A Boolean attempt at feedback | Louw | Journal for ...
African Journals Online (AJOL)
This paper describes an experiment in which Boolean feedback (a kind of checklist) was used to provide feedback on the paragraph structures of first year students in an Academic Literacy course. We begin by introducing the major problems with feedback on L2 writing and establishing why a focus on paragraph structures ...
The Concept of the "Imploded Boolean Search": A Case Study with Undergraduate Chemistry Students
Tomaszewski, Robert
2016-01-01
Critical thinking and analytical problem-solving skills in research involves using different search strategies. A proposed concept for an "Imploded Boolean Search" combines three unique identifiable field types to perform a search: keyword(s), numerical value(s), and a chemical structure or reaction. The object of this type of search is…
Computable categoricity of the Boolean algebra B(omega) with a distinguished automorphism
Czech Academy of Sciences Publication Activity Database
Bazhenov, N. A.; Tukhbatullina, Regina
2013-01-01
Roč. 52, č. 2 (2013), s. 89-97 ISSN 0002-5232 Institutional support: PRVOUK-P23 Keywords : Boolean algebra with distinguished automorphism * computable categoricity * categoricity spectrum Subject RIV: BA - General Mathematics Impact factor: 0.488, year: 2013
The second hyperpolarizability of systems described by the space-fractional Schrödinger equation
Dawson, Nathan J.; Nottage, Onassis; Kounta, Moussa
2018-01-01
The static second hyperpolarizability is derived from the space-fractional Schrödinger equation in the particle-centric view. The Thomas-Reiche-Kuhn sum rule matrix elements and the three-level ansatz determines the maximum second hyperpolarizability for a space-fractional quantum system. The total oscillator strength is shown to decrease as the space-fractional parameter α decreases, which reduces the optical response of a quantum system in the presence of an external field. This damped response is caused by the wavefunction dependent position and momentum commutation relation. Although the maximum response is damped, we show that the one-dimensional quantum harmonic oscillator is no longer a linear system for α ≠ 1, where the second hyperpolarizability becomes negative before ultimately damping to zero at the lower fractional limit of α → 1 / 2.
Diagnostic models of intelligent tutor system for teaching skills to solve algebraic equations
Directory of Open Access Journals (Sweden)
Andrey Grigoriyevich Chukhray
2007-10-01
Full Text Available In this paper one solution for teaching skills to solve n-power algebraic equation by Lobachevsky-Greffe-Dandelen method is described. StudentÃ¢Â€Â™s mistakes are discovered and classified. Based on signal-parametric approach to fault diagnosis in dynamic systems mathematical diagnostic models which allow detecting mistake classes by comparing student calculated results and system calculated results are created. Features of proposed diagnostic models application are presented. Intelligent tutor system is developed and used on Ã¢Â€ÂœAutomatic Control TheoryÃ¢Â€Â practical training by third year students of National Aerospace University.
Energy Technology Data Exchange (ETDEWEB)
Gene Golub; Kwok Ko
2009-03-30
The solutions of sparse eigenvalue problems and linear systems constitute one of the key computational kernels in the discretization of partial differential equations for the modeling of linear accelerators. The computational challenges faced by existing techniques for solving those sparse eigenvalue problems and linear systems call for continuing research to improve on the algorithms so that ever increasing problem size as required by the physics application can be tackled. Under the support of this award, the filter algorithm for solving large sparse eigenvalue problems was developed at Stanford to address the computational difficulties in the previous methods with the goal to enable accelerator simulations on then the world largest unclassified supercomputer at NERSC for this class of problems. Specifically, a new method, the Hemitian skew-Hemitian splitting method, was proposed and researched as an improved method for solving linear systems with non-Hermitian positive definite and semidefinite matrices.
Boundary Equations and Regularity Theory for Geometric Variational Systems with Neumann Data
Schikorra, Armin
2018-02-01
We study boundary regularity of maps from two-dimensional domains into manifolds which are critical with respect to a generic conformally invariant variational functional and which, at the boundary, intersect perpendicularly with a support manifold. For example, harmonic maps, or H-surfaces, with a partially free boundary condition. In the interior it is known, by the celebrated work of Rivière, that these maps satisfy a system with an antisymmetric potential, from which one can derive the interior regularity of the solution. Avoiding a reflection argument, we show that these maps satisfy along the boundary a system of equations which also exhibits a (nonlocal) antisymmetric potential that combines information from the interior potential and the geometric Neumann boundary condition. We then proceed to show boundary regularity for solutions to such systems.
Contribution to the minimization of time for the solution of algebraic differential equations system
International Nuclear Information System (INIS)
Michael, Samir.
1982-11-01
This note deals with the solution of large algebraic-differential systems involved in physical sciences specially in electronics and nuclear physics. The theoretical aspects for the stability of multistep methods is presented in detail. The stability condition is developed and we present our own conditions of stability. These conditions give rise to many new formulae that have very small truncation error. However for a real time simulation, it is necessary to obtain a very high computation speed. For this purpose, we have considered a multiprocessor machine and we have investigated the parallelization of the algorithm of generalized GEAR method. For a linear system, the method of GAUSS-JORDAN is used with some modifications. A new algorithm is presented for parallel matrix multiplication. This research work has been applied to the resolution of a system of equations corresponding to an experiment of gamma thermometry in a nuclear reactor (four thermometers in this case) [fr
Majeed, Muhammad Usman
2017-07-19
Steady-state elliptic partial differential equations (PDEs) are frequently used to model a diverse range of physical phenomena. The source and boundary data estimation problems for such PDE systems are of prime interest in various engineering disciplines including biomedical engineering, mechanics of materials and earth sciences. Almost all existing solution strategies for such problems can be broadly classified as optimization-based techniques, which are computationally heavy especially when the problems are formulated on higher dimensional space domains. However, in this dissertation, feedback based state estimation algorithms, known as state observers, are developed to solve such steady-state problems using one of the space variables as time-like. In this regard, first, an iterative observer algorithm is developed that sweeps over regular-shaped domains and solves boundary estimation problems for steady-state Laplace equation. It is well-known that source and boundary estimation problems for the elliptic PDEs are highly sensitive to noise in the data. For this, an optimal iterative observer algorithm, which is a robust counterpart of the iterative observer, is presented to tackle the ill-posedness due to noise. The iterative observer algorithm and the optimal iterative algorithm are then used to solve source localization and estimation problems for Poisson equation for noise-free and noisy data cases respectively. Next, a divide and conquer approach is developed for three-dimensional domains with two congruent parallel surfaces to solve the boundary and the source data estimation problems for the steady-state Laplace and Poisson kind of systems respectively. Theoretical results are shown using a functional analysis framework, and consistent numerical simulation results are presented for several test cases using finite difference discretization schemes.
Ding, Lei; Xiao, Lin; Liao, Bolin; Lu, Rongbo; Peng, Hua
2017-01-01
To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.
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M. Eshaghi Gordji
2011-01-01
Full Text Available We prove the generalized Hyers-Ulam-Rassias stability of a general system of Euler-Lagrange-type quadratic functional equations in non-Archimedean 2-normed spaces and Menger probabilistic non-Archimedean-normed spaces.
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Jaroslav Jaroš
2015-01-01
Full Text Available We consider \\(n\\-dimensional cyclic systems of second order differential equations \\[(p_i(t|x_{i}'|^{\\alpha_i -1}x_{i}'' = q_{i}(t|x_{i+1}|^{\\beta_i-1}x_{i+1},\\] \\[\\quad i = 1,\\ldots,n, \\quad (x_{n+1} = x_1 \\tag{\\(\\ast\\}\\] under the assumption that the positive constants \\(\\alpha_i\\ and \\(\\beta_i\\ satisfy \\(\\alpha_1{\\ldots}\\alpha_n \\gt \\beta_1{\\ldots}\\beta_n\\ and \\(p_i(t\\ and \\(q_i(t\\ are regularly varying functions, and analyze positive strongly increasing solutions of system (\\(\\ast\\ in the framework of regular variation. We show that the situation for the existence of regularly varying solutions of positive indices for (\\(\\ast\\ can be characterized completely, and moreover that the asymptotic behavior of such solutions is governed by the unique formula describing their order of growth precisely. We give examples demonstrating that the main results for (\\(\\ast\\ can be applied to some classes of partial differential equations with radial symmetry to acquire accurate information about the existence and the asymptotic behavior of their radial positive strongly increasing solutions.
The Use of BBC (Box, Board, and Comics Media in The Systems of Linear Equation
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P D Widyastuti
2017-12-01
Full Text Available Mathematics is one of the lessons in school. Starting from elementary school, junior high school, senior high school, even college. Mathematics is abstract and identic with numbers, so the author guessed that maybe this is the reason why students consider that mathematics is a difficult lesson. In fact, the learners deliver the material step by step. First, the teacher introduced something concrete to the students (related to the surrounding environment. After that, teacher introduced something more abstract to the students. Sometimes, the transition from concrete to abstract become the problem in the learning process. One of the materials that convert concrete to abstract is systems of linear equations in 8th grade because in this stage students are introduced to more coefficients and variables. This article will discuss how to use media in the form of BBC (Box, Board, and Comics on systems of linear equations. This research is about Research and Development (R &D. The procedures of comics followed the ADDIE model which included analysis, design, development, implementation, and evaluation. This research aims to create a valid media based on the validation by the and students’ responses which can be proven that BBC (Box, Board, and Comics media are interesting and worthy to use in the classroom.
Generating rate equations for complex enzyme systems by a computer-assisted systematic method
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Beard Daniel A
2009-08-01
Full Text Available Abstract Background While the theory of enzyme kinetics is fundamental to analyzing and simulating biochemical systems, the derivation of rate equations for complex mechanisms for enzyme-catalyzed reactions is cumbersome and error prone. Therefore, a number of algorithms and related computer programs have been developed to assist in such derivations. Yet although a number of algorithms, programs, and software packages are reported in the literature, one or more significant limitation is associated with each of these tools. Furthermore, none is freely available for download and use by the community. Results We have implemented an algorithm based on the schematic method of King and Altman (KA that employs the topological theory of linear graphs for systematic generation of valid reaction patterns in a GUI-based stand-alone computer program called KAPattern. The underlying algorithm allows for the assumption steady-state, rapid equilibrium-binding, and/or irreversibility for individual steps in catalytic mechanisms. The program can automatically generate MathML and MATLAB output files that users can easily incorporate into simulation programs. Conclusion A computer program, called KAPattern, for generating rate equations for complex enzyme system is a freely available and can be accessed at http://www.biocoda.org.
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Shohag Barman
Full Text Available Inferring a gene regulatory network from time-series gene expression data in systems biology is a challenging problem. Many methods have been suggested, most of which have a scalability limitation due to the combinatorial cost of searching a regulatory set of genes. In addition, they have focused on the accurate inference of a network structure only. Therefore, there is a pressing need to develop a network inference method to search regulatory genes efficiently and to predict the network dynamics accurately.In this study, we employed a Boolean network model with a restricted update rule scheme to capture coarse-grained dynamics, and propose a novel mutual information-based Boolean network inference (MIBNI method. Given time-series gene expression data as an input, the method first identifies a set of initial regulatory genes using mutual information-based feature selection, and then improves the dynamics prediction accuracy by iteratively swapping a pair of genes between sets of the selected regulatory genes and the other genes. Through extensive simulations with artificial datasets, MIBNI showed consistently better performance than six well-known existing methods, REVEAL, Best-Fit, RelNet, CST, CLR, and BIBN in terms of both structural and dynamics prediction accuracy. We further tested the proposed method with two real gene expression datasets for an Escherichia coli gene regulatory network and a fission yeast cell cycle network, and also observed better results using MIBNI compared to the six other methods.Taken together, MIBNI is a promising tool for predicting both the structure and the dynamics of a gene regulatory network.
Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I
International Nuclear Information System (INIS)
Tsuchida, Takayuki; Wolf, Thomas
2005-01-01
We perform a classification of integrable systems of mixed scalar and vector evolution equations with respect to higher symmetries. We consider polynomial systems that are homogeneous under a suitable weighting of variables. This paper deals with the KdV weighting, the Burgers (or potential KdV or modified KdV) weighting, the Ibragimov-Shabat weighting and two unfamiliar weightings. The case of other weightings will be studied in a subsequent paper. Making an ansatz for undetermined coefficients and using a computer package for solving bilinear algebraic systems, we give the complete lists of second-order systems with a third-order or a fourth-order symmetry and third-order systems with a fifth-order symmetry. For all but a few systems in the lists, we show that the system (or, at least a subsystem of it) admits either a Lax representation or a linearizing transformation. A thorough comparison with recent work of Foursov and Olver is made
A Coupled System of Integrodifferential Equations Arising in Liquidity Risk Model
International Nuclear Information System (INIS)
Pham, Huyen; Tankov, Peter
2009-01-01
We study the mathematical aspects of the portfolio/consumption choice problem in a market model with liquidity risk introduced in (Pham and Tankov, Math. Finance, 2006, to appear). In this model, the investor can trade and observe stock prices only at exogenous Poisson arrival times. He may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous time stochastic control problem, nonstandard in the literature. We show how the dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we prove an analytic characterization of this control problem by adapting the concept of viscosity solutions. This coupled system of IDE may be numerically solved by a decoupling algorithm, and this is the topic of a companion paper (Pham and Tankov, Math. Finance, 2006, to appear)
PARALLEL SMAC ALGORITHMS TO SOLVE SHALLOW WATER EQUATION WITH UNSTRUCTURED COLLOCATED GRID SYSTEM
Yamashita, Haruka; Ushijima, Satoru
A computational method to solve shallow water equations has been investigated with an SMAC method which is usually employed in the simulation for incompressible fluids. In particular, this numerical method is implemented in the unstructured collocated grid system with the distributed memory system to increase the parallel efficiency. The developed computational method was applied to the 1D dam-break problem and the free-surface flows in a meandering open channel. As a result of the 1D dam-break simulations, it was confirmed that this method improve the numerical stability. While, in the case of the meandering open channel, it was confirmed that the predicted water depth and depth-averaged velocity distributions are qualitatively in good agreement with the experimental results and that the reasonable parallel efficiencies are attained by parallel computations.
On a Third-Order System of Difference Equations with Variable Coefficients
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Stevo Stević
2012-01-01
Full Text Available We show that the system of three difference equations xn+1=an(1xn-2/(bn(1ynzn-1xn-2+cn(1, yn+1=an(2yn-2/(bn(2znxn-1yn-2+cn(2, and zn+1=an(3zn-2/(bn(3xnyn-1zn-2+cn(3, n∈N0, where all elements of the sequences an(i, bn(i, cn(i, n∈N0, i∈{1,2,3}, and initial values x-j, y-j, z-j, j∈{0,1,2}, are real numbers, can be solved. Explicit formulae for solutions of the system are derived, and some consequences on asymptotic behavior of solutions for the case when coefficients are periodic with period three are deduced.
Effect of mesoscopic fluctuations on equation of state in cluster-forming systems
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A. Ciach
2012-06-01
Full Text Available Equation of state for systems with particles self-assembling into aggregates is derived within a mesoscopic theory combining density functional and field-theoretic approaches. We focus on the effect of mesoscopic fluctuations in the disordered phase. The pressure - volume fraction isotherms are calculated explicitly for two forms of the short-range attraction long-range repulsion potential. Mesoscopic fluctuations lead to an increased pressure in each case, except for very small volume fractions. When large clusters are formed, the mechanical instability of the system is present at much higher temperature than found in mean-field approximation. In this case phase separation competes with the formation of periodic phases (colloidal crystals. In the case of small clusters, no mechanical instability associated with separation into dilute and dense phases appears.
Time evolution of many-body localized systems with the flow equation approach
Thomson, S. J.; Schiró, M.
2018-02-01
The interplay between interactions and quenched disorder can result in rich dynamical quantum phenomena far from equilibrium, particularly when many-body localization prevents the system from full thermalization. With the aim of tackling this interesting regime, here we develop a semianalytical flow equation approach to study the time evolution of strongly disordered interacting quantum systems. We apply this technique to a prototype model of interacting spinless fermions in a random on-site potential in both one and two dimensions. Key results include (i) an explicit construction of the local integrals of motion that characterize the many-body localized phase in one dimension, ultimately connecting the microscopic model to phenomenological descriptions, (ii) calculation of these quantities in two dimensions, and (iii) an investigation of the real-time dynamics in the localized phase which reveals the crucial role of l -bit interactions for enhancing dephasing and relaxation.
Radiometer uncertainty equation research of 2D planar scanning PMMW imaging system
Hu, Taiyang; Xu, Jianzhong; Xiao, Zelong
2009-07-01
With advances in millimeter-wave technology, passive millimeter-wave (PMMW) imaging technology has received considerable concerns, and it has established itself in a wide range of military and civil practical applications, such as in the areas of remote sensing, blind landing, precision guidance and security inspection. Both the high transparency of clothing at millimeter wavelengths and the spatial resolution required to generate adequate images combine to make imaging at millimeter wavelengths a natural approach of screening people for concealed contraband detection. And at the same time, the passive operation mode does not present a safety hazard to the person who is under inspection. Based on the description to the design and engineering implementation of a W-band two-dimensional (2D) planar scanning imaging system, a series of scanning methods utilized in PMMW imaging are generally compared and analyzed, followed by a discussion on the operational principle of the mode of 2D planar scanning particularly. Furthermore, it is found that the traditional radiometer uncertainty equation, which is derived from a moving platform, does not hold under this 2D planar scanning mode due to the fact that there is no absolute connection between the scanning rates in horizontal direction and vertical direction. Consequently, an improved radiometer uncertainty equation is carried out in this paper, by means of taking the total time spent on scanning and imaging into consideration, with the purpose of solving the problem mentioned above. In addition, the related factors which affect the quality of radiometric images are further investigated under the improved radiometer uncertainty equation, and ultimately some original results are presented and analyzed to demonstrate the significance and validity of this new methodology.
Hasegawa, Chihiro; Duffull, Stephen B
2018-02-01
Pharmacokinetic-pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge-Kutta) which need to be matched to the characteristics of the problem at hand. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear pharmacokinetic model with Michaelis-Menten elimination (E1), an integrated glucose-insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched time-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.
Derivative free Davidon-Fletcher-Powell (DFP) for solving symmetric systems of nonlinear equations
Mamat, M.; Dauda, M. K.; Mohamed, M. A. bin; Waziri, M. Y.; Mohamad, F. S.; Abdullah, H.
2018-03-01
Research from the work of engineers, economist, modelling, industry, computing, and scientist are mostly nonlinear equations in nature. Numerical solution to such systems is widely applied in those areas of mathematics. Over the years, there has been significant theoretical study to develop methods for solving such systems, despite these efforts, unfortunately the methods developed do have deficiency. In a contribution to solve systems of the form F(x) = 0, x ∈ Rn , a derivative free method via the classical Davidon-Fletcher-Powell (DFP) update is presented. This is achieved by simply approximating the inverse Hessian matrix with {Q}k+1-1 to θkI. The modified method satisfied the descent condition and possess local superlinear convergence properties. Interestingly, without computing any derivative, the proposed method never fail to converge throughout the numerical experiments. The output is based on number of iterations and CPU time, different initial starting points were used on a solve 40 benchmark test problems. With the aid of the squared norm merit function and derivative-free line search technique, the approach yield a method of solving symmetric systems of nonlinear equations that is capable of significantly reducing the CPU time and number of iteration, as compared to its counterparts. A comparison between the proposed method and classical DFP update were made and found that the proposed methodis the top performer and outperformed the existing method in almost all the cases. In terms of number of iterations, out of the 40 problems solved, the proposed method solved 38 successfully, (95%) while classical DFP solved 2 problems (i.e. 05%). In terms of CPU time, the proposed method solved 29 out of the 40 problems given, (i.e.72.5%) successfully whereas classical DFP solves 11 (27.5%). The method is valid in terms of derivation, reliable in terms of number of iterations and accurate in terms of CPU time. Thus, suitable and achived the objective.
Extended sine-Gordon Equation Method and Its Application to Maccari's System
International Nuclear Information System (INIS)
Song Lina; Zhang Hongqing
2005-01-01
An extended sine-Gordon equation method is proposed to construct exact travelling wave solutions to Maccari's equation based upon a generalized sine-Gordon equation. It is shown that more new travelling wave solutions can be found by this new method, which include bell-shaped soliton solutions, kink-shaped soliton solutions, periodic wave solution, and new travelling waves.
International Nuclear Information System (INIS)
Zagrebnov, V.A.
1980-01-01
Using resolvents for Kirkwood-Zalburg, Kirkwood-Ruelle and Meier-Montroll operators, solutions of the finite-volume correlation equations for tempered boundary conditions are obtained explicity. The uniqueness theorem is proved. A connection of the correlation equations with the Dobrushin-Landford-Ruelle equations for the Gibbs probability measure is discussed
Solving the Bateman equations in CASMO5 using implicit ode numerical methods for stiff systems
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Hykes, J. M.; Ferrer, R. M. [Studsvik Scandpower, Inc., 504 Shoup Avenue, Idaho Falls, ID (United States)
2013-07-01
The Bateman equations, which describe the transmutation of nuclides over time as a result of radioactive decay, absorption, and fission, are often numerically stiff. This is especially true if short-lived nuclides are included in the system. This paper describes the use of implicit numerical methods for o D Es applied to the stiff Bateman equations, specifically employing the Backward Differentiation Formulas (BDF) form of the linear multistep method. As is true in other domains, using an implicit method removes or lessens the (sometimes severe) step-length constraints by which explicit methods must abide. To gauge its accuracy and speed, the BDF method is compared to a variety of other solution methods, including Runge-Kutta explicit methods and matrix exponential methods such as the Chebyshev Rational Approximation Method (CRAM). A preliminary test case was chosen as representative of a PWR lattice depletion step and was solved with numerical libraries called from a Python front-end. The Figure of Merit (a combined measure of accuracy and efficiency) for the BDF method was nearly identical to that for CRAM, while explicit methods and other matrix exponential approximations trailed behind. The test case includes 319 nuclides, in which the shortest-lived nuclide is {sup 98}Nb with a half-life of 2.86 seconds. Finally, the BDF and CRAM methods were compared within CASMO5, where CRAM had a FOM about four times better than BDF, although the BDF implementation was not fully optimized. (authors)
A toolbox to solve coupled systems of differential and difference equations
International Nuclear Information System (INIS)
Ablinger, Jakob; Schneider, Carsten; Bluemlein, Johannes; Freitas, Abilio de
2016-01-01
We present algorithms to solve coupled systems of linear differential equations, arising in the calculation of massive Feynman diagrams with local operator insertions at 3-loop order, which do not request special choices of bases. Here we assume that the desired solution has a power series representation and we seek for the coefficients in closed form. In particular, if the coefficients depend on a small parameter ε (the dimensional parameter), we assume that the coefficients themselves can be expanded in formal Laurent series w.r.t. ε and we try to compute the first terms in closed form. More precisely, we have a decision algorithm which solves the following problem: if the terms can be represented by an indefinite nested hypergeometric sum expression (covering as special cases the harmonic sums, cyclotomic sums, generalized harmonic sums or nested binomial sums), then we can calculate them. If the algorithm fails, we obtain a proof that the terms cannot be represented by the class of indefinite nested hypergeometric sum expressions. Internally, this problem is reduced by holonomic closure properties to solving a coupled system of linear difference equations. The underlying method in this setting relies on decoupling algorithms, difference ring algorithms and recurrence solving. We demonstrate by a concrete example how this algorithm can be applied with the new Mathematica package SolveCoupledSystem which is based on the packages Sigma, HarmonicSums and OreSys. In all applications the representation in x-space is obtained as an iterated integral representation over general alphabets, generalizing Poincare iterated integrals.
Global dynamics for switching systems and their extensions by linear differential equations
Huttinga, Zane; Cummins, Bree; Gedeon, Tomáš; Mischaikow, Konstantin
2018-03-01
Switching systems use piecewise constant nonlinearities to model gene regulatory networks. This choice provides advantages in the analysis of behavior and allows the global description of dynamics in terms of Morse graphs associated to nodes of a parameter graph. The parameter graph captures spatial characteristics of a decomposition of parameter space into domains with identical Morse graphs. However, there are many cellular processes that do not exhibit threshold-like behavior and thus are not well described by a switching system. We consider a class of extensions of switching systems formed by a mixture of switching interactions and chains of variables governed by linear differential equations. We show that the parameter graphs associated to the switching system and any of its extensions are identical. For each parameter graph node, there is an order-preserving map from the Morse graph of the switching system to the Morse graph of any of its extensions. We provide counterexamples that show why possible stronger relationships between the Morse graphs are not valid.
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Michelsen, Michael Locht; Folas, Georgios
2006-01-01
In this second article of the review on the applications of the CPA (Cubic-Plus-Association) equation of state, the focus is placed on cross-associating systems. Various such mixtures are investigated, including (i) systems with two self-associating compounds ( e. g., water-alcohol systems...
International Nuclear Information System (INIS)
Ignat'yev, A O
2003-01-01
A system of ordinary differential equations with impulse action at fixed moments of time is considered. The system is assumed to have the zero solution. It is shown that the existence of a corresponding Lyapunov function is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of differential equations and impulse actions are obtained under which the uniform asymptotic stability of the zero solution of the 'unperturbed' system implies the uniform asymptotic stability of the zero solution of the 'perturbed' system
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A. Sakabekov
2016-01-01
Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.
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Sawicki Dominik
2015-09-01
Full Text Available One of the most popular applications of high power lasers is heating of the surface layer of a material, in order to change its properties. Numerical methods allow an easy and fast way to simulate the heating process inside of the material. The most popular numerical methods FEM and BEM, used to simulate this kind of processes have one fundamental defect, which is the necessity of discretization of the boundary or the domain. An alternative to avoid the mentioned problem are parametric integral equations systems (PIES, which do not require classical discretization of the boundary and the domain while being numerically solved. PIES method was previously used with success to solve steady-state problems, as well as transient heat transfer problems. The purpose of this paper is to test the efficacy of the PIES method with time discretization in solving problem of laser heating of a material, with different pulse shape approximation functions.
Regularity theory for quasilinear elliptic systems and Monge—Ampère equations in two dimensions
Schulz, Friedmar
1990-01-01
These lecture notes have been written as an introduction to the characteristic theory for two-dimensional Monge-Ampère equations, a theory largely developed by H. Lewy and E. Heinz which has never been presented in book form. An exposition of the Heinz-Lewy theory requires auxiliary material which can be found in various monographs, but which is presented here, in part because the focus is different, and also because these notes have an introductory character. Self-contained introductions to the regularity theory of elliptic systems, the theory of pseudoanalytic functions and the theory of conformal mappings are included. These notes grew out of a seminar given at the University of Kentucky in the fall of 1988 and are intended for graduate students and researchers interested in this area.
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Josefa Caballero
2014-01-01
Full Text Available We study an existence result for the following coupled system of nonlinear fractional hybrid differential equations with homogeneous boundary conditions D0+α[x(t/f(t,x(t,y(t]=g(t,x(t,y(t,D0+αy(t/f(t,y(t,x(t=g(t,y(t,x(t, 0
Aguila-Camacho, Norelys; Duarte-Mermoud, Manuel A
2016-01-01
This paper presents the analysis of three classes of fractional differential equations appearing in the field of fractional adaptive systems, for the case when the fractional order is in the interval α ∈(0,1] and the Caputo definition for fractional derivatives is used. The boundedness of the solutions is proved for all three cases, and the convergence to zero of the mean value of one of the variables is also proved. Applications of the obtained results to fractional adaptive schemes in the context of identification and control problems are presented at the end of the paper, including numerical simulations which support the analytical results. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Dynamics of excited instantons in the system of forced Gursey nonlinear differential equations
International Nuclear Information System (INIS)
Aydogmus, F.
2015-01-01
The Gursey model is a 4D conformally invariant pure fermionic model with a nonlinear spinor self-coupled term. Gursey proposed his model as a possible basis for a unitary description of elementary particles following the “Heisenberg dream.” In this paper, we consider the system of Gursey nonlinear differential equations (GNDEs) formed by using the Heisenberg ansatz. We use it to understand how the behavior of spinor-type Gursey instantons can be affected by excitations. For this, the regular and chaotic numerical solutions of forced GNDEs are investigated by constructing their Poincaré sections in phase space. A hierarchical cluster analysis method for investigating the forced GNDEs is also presented
Energy Technology Data Exchange (ETDEWEB)
Valat, J. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1960-12-15
Universal stability diagrams have been calculated and experimentally checked for Hill-Meissner type equations with square-wave coefficients. The study of these equations in the phase-plane has then made it possible to extend the periodic solution calculations to the case of non-linear differential equations with periodic square-wave coefficients. This theory has been checked experimentally. For non-linear coupled systems with constant coefficients, a search was first made for solutions giving an algebraic motion. The elliptical and Fuchs's functions solve such motions. The study of non-algebraic motions is more delicate, apart from the study of nonlinear Lissajous's motions. A functional analysis shows that it is possible however in certain cases to decouple the system and to find general solutions. For non-linear coupled systems with periodic square-wave coefficients it is then possible to calculate the conditions leading to periodic solutions, if the two non-linear associated systems with constant coefficients fall into one of the categories of the above paragraph. (author) [French] Pour les equations du genre de Hill-Meissner a coefficients creneles, on a calcule des diagrammes universels de stabilite et ceux-ci ont ete verifies experimentalement. L'etude de ces equations dans le plan de phase a permis ensuite d'etendre le calcul des solutions periodiques au cas des equations differentielles non lineaires a coefficients periodiques creneles. Cette theorie a ete verifiee experimentalement. Pour Jes systemes couples non lineaires a coefficients constants, on a d'abord cherche les solutions menant a des mouvements algebriques. Les fonctions elliptiques et fuchsiennes uniformisent de tels mouvements. L'etude de mouvements non algebriques est plus delicate, a part l'etude des mouvements de Lissajous non lineaires. Une analyse fonctionnelle montre qu'il est toutefois possible dans certains cas de decoupler le systeme et de
Parumasur, N.; Willie, R.
2008-09-01
We consider a simple HIV/AIDs finite dimensional mathematical model on interactions of the blood cells, the HIV/AIDs virus and the immune system for consistence of the equations to the real biomedical situation that they model. A better understanding to a cure solution to the illness modeled by the finite dimensional equations is given. This is accomplished through rigorous mathematical analysis and is reinforced by numerical analysis of models developed for real life cases.
On the Equational Definition of the Least Prefixed Point
DEFF Research Database (Denmark)
Santocanale, Luigi
2001-01-01
We show how to axiomatize by equations the least prexed point of an order preserving function and discuss the domain of application of the proposed method. Thus, we generalize the well known equational axiomatization of Propositional Dynamic Logic to a complete equational axiomatization of the Bo......We show how to axiomatize by equations the least prexed point of an order preserving function and discuss the domain of application of the proposed method. Thus, we generalize the well known equational axiomatization of Propositional Dynamic Logic to a complete equational axiomatization...... of the Boolean Modal -Calculus. We show on the other hand that the existence of a term which does not preserve the order is an essential condition for the least prexed point to be denable by equations....
Korayem, M H; Nekoo, S R
2015-07-01
This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Singhatanadgid, Pairod; Jommalai, Panupan
2016-01-01
The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.
Energy Technology Data Exchange (ETDEWEB)
Singhatanadgid, Pairod; Jommalai, Panupan [Chulalongkorn University, Bangkok (Thailand)
2016-05-15
The extended Kantorovich method using multi-term displacement functions is applied to the buckling problem of laminated plates with various boundary conditions. The out-of-plane displacement of the buckled plate is written as a series of products of functions of parameter x and functions of parameter y. With known functions in parameter x or parameter y, a set of governing equations and a set of boundary conditions are obtained after applying the variational principle to the total potential energy of the system. The higher order differential equations are then transformed into a set of first-order differential equations and solved for the buckling load and mode. Since the governing equations are first-order differential equations, solutions can be obtained analytically with the out-of-plane displacement written in the form of an exponential function. The solutions from the proposed technique are verified with solutions from the literature and FEM solutions. The bucking loads correspond very well to other available solutions in most of the comparisons. The buckling modes also compare very well with the finite element solutions. The proposed solution technique transforms higher-order differential equations to first-order differential equations, and they are analytically solved for out-of-plane displacement in the form of an exponential function. Therefore, the proposed solution technique yields a solution which can be considered as an analytical solution.
Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods
Directory of Open Access Journals (Sweden)
F. M. Mahomed
2011-01-01
Full Text Available In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied semi-invariants for systems of two linear hyperbolic PDEs in two independent variables. Separately, by splitting a complex scalar ordinary differential equation (ODE into its real and imaginary parts PDEs for two functions of two variables were obtained and their symmetry structure studied. In this work we revisit semi-invariants under equivalence transformations of the dependent variables for systems of two linear hyperbolic PDEs in two independent variables when such systems correspond to scalar complex linear hyperbolic equations in two independent variables, using the above-mentioned splitting procedure. The semi-invariants under linear changes of the dependent variables deduced for this class of hyperbolic linear systems correspond to the complex semi-invariants of the complex scalar linear (1+1 hyperbolic equation. We show that the adjoint factorization corresponds precisely to the complex splitting. We also study the reductions and the inverse problem when such systems of two linear hyperbolic PDEs arise from a linear complex hyperbolic PDE. Examples are given to show the application of this approach.
A Linear System of Differential Equations Related to Vector-Valued Jack Polynomials on the Torus
Dunkl, Charles F.
2017-06-01
For each irreducible module of the symmetric group S_{N} there is a set of parametrized nonsymmetric Jack polynomials in N variables taking values in the module. These polynomials are simultaneous eigenfunctions of a commutative set of operators, self-adjoint with respect to two Hermitian forms, one called the contravariant form and the other is with respect to a matrix-valued measure on the N-torus. The latter is valid for the parameter lying in an interval about zero which depends on the module. The author in a previous paper [SIGMA 12 (2016), 033, 27 pages] proved the existence of the measure and that its absolutely continuous part satisfies a system of linear differential equations. In this paper the system is analyzed in detail. The N-torus is divided into (N-1)! connected components by the hyperplanes x_{i}=x_{j}, i
Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier width
DEFF Research Database (Denmark)
Gutin, Gregory; Yeo, Anders
2012-01-01
A function f: -1,1n→R is called pseudo-Boolean. It is well-known that each pseudo-Boolean function f can be written as f(x)=∑ I∈Ff̂(I) χI(x), where F⊆I:I⊆[n], [n]=1,2,...,n, χI(x)= ∏ i∈I xi and f̂(I) are non-zero reals. The degree of f is max|I|:I∈F and the width of f is the minimum integer ρ suc...... for each q>papplications, we prove a stronger inequality: || f||4≤( 2ρ+1)14|| f||2....
The trajectory-coherent approximation and the system of moments for the Hartree type equation
Directory of Open Access Journals (Sweden)
V. V. Belov
2002-01-01
Full Text Available The general construction of semiclassically concentrated solutions to the Hartree type equation, based on the complex WKB-Maslov method, is presented. The formal solutions of the Cauchy problem for this equation, asymptotic in small parameter ℏ (ℏ→0, are constructed with a power accuracy of O(ℏ N/2, where N is any natural number. In constructing the semiclassically concentrated solutions, a set of Hamilton-Ehrenfest equations (equations for centered moments is essentially used. The nonlinear superposition principle has been formulated for the class of semiclassically concentrated solutions of Hartree type equations. The results obtained are exemplified by a one-dimensional Hartree type equation with a Gaussian potential.
Complete CCC Boolean Algebras, the order Sequential Topology, and a Problem of von Neumann
Czech Academy of Sciences Publication Activity Database
Balcar, Bohuslav; Jech, Thomas; Pazák, Tomáš
2005-01-01
Roč. 37, č. 6 (2005), s. 885-898 ISSN 0024-6093 R&D Projects: GA ČR(CZ) GA201/02/0857; GA ČR(CZ) GA201/03/0933 Institutional research plan: CEZ:AV0Z10190503 Keywords : Boolean algebra * Maharam submeasure * weak distributivity Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2005
Rates of Minimization of Error Functionals over Boolean Variable-Basis Functions
Czech Academy of Sciences Publication Activity Database
Kainen, P.C.; Kůrková, Věra; Sanguineti, M.
2005-01-01
Roč. 4, č. 4 (2005), s. 355-368 ISSN 1570-1166 R&D Projects: GA ČR GA201/02/0428; GA ČR GA201/05/0557 Grant - others:Area MC 6(EU) Project 22 Institutional research plan: CEZ:AV0Z10300504 Keywords : high-dimensional optimization * minimizing sequences * Boolean decision functions * decision tree Subject RIV: BA - General Mathematics
Recurrent Neural Network Based Boolean Factor Analysis and its Application to Word Clustering
Czech Academy of Sciences Publication Activity Database
Frolov, A. A.; Húsek, Dušan; Polyakov, P.Y.
2009-01-01
Roč. 20, č. 7 (2009), s. 1073-1086 ISSN 1045-9227 R&D Projects: GA MŠk(CZ) 1M0567 Institutional research plan: CEZ:AV0Z10300504 Keywords : recurrent neural network * Hopfield-like neural network * associative memory * unsupervised learning * neural network architecture * neural network application * statistics * Boolean factor analysis * concepts search * information retrieval Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.889, year: 2009
Comparison of Seven Methods for Boolean Factor Analysis and Their Evaluation by Information Gain
Czech Academy of Sciences Publication Activity Database
Frolov, A.; Húsek, Dušan; Polyakov, P.Y.
2016-01-01
Roč. 27, č. 3 (2016), s. 538-550 ISSN 2162-237X R&D Projects: GA MŠk ED1.1.00/02.0070 Institutional support: RVO:67985807 Keywords : associative memory * bars problem (BP) * Boolean factor analysis (BFA) * data mining * dimension reduction * Hebbian learning rule * information gain * likelihood maximization (LM) * neural network application * recurrent neural network * statistics Subject RIV: IN - Informatics, Computer Science Impact factor: 6.108, year: 2016
Representations and Rates of Approximation of Real-Valued Boolean Functions by Neural Networks
Czech Academy of Sciences Publication Activity Database
Kůrková, Věra; Savický, Petr; Hlaváčková, Kateřina
1998-01-01
Roč. 11, č. 4 (1998), s. 651-659 ISSN 0893-6080 R&D Projects: GA AV ČR IAA2030602; GA AV ČR IAA2075606; GA ČR GA201/95/0976 Keywords : real-valued Boolean function * percepron network * rate of approximation * variation with respect to half-spaces * decision tree * Hadamard communication matrix Subject RIV: BA - General Mathematics Impact factor: 1.017, year: 1998
Completely positive matrices over Boolean algebras and their CP-rank
Directory of Open Access Journals (Sweden)
Mohindru Preeti
2015-04-01
Full Text Available Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite. In addition,we formulate various CP-rank inequalities of completely positive matrices over special semirings using semiring homomorphisms.
Energy Technology Data Exchange (ETDEWEB)
Abhyankar, Shrirang [Argonne National Lab. (ANL), Argonne, IL (United States); Anitescu, Mihai [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil [Argonne National Lab. (ANL), Argonne, IL (United States); Zhang, Hong [Argonne National Lab. (ANL), Argonne, IL (United States)
2016-03-31
Sensitivity analysis is an important tool to describe power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this work, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as DC exciters, by deriving and implementing the adjoint jump conditions that arise from state and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.
Directory of Open Access Journals (Sweden)
Aleksandr Alekseev
2015-07-01
Full Text Available We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.
Harris, Daniel R.; Henderson, Darren W.; Kavuluru, Ramakanth; Stromberg, Arnold J.; Johnson, Todd R.
2015-01-01
We present a custom, Boolean query generator utilizing common-table expressions (CTEs) that is capable of scaling with big datasets. The generator maps user-defined Boolean queries, such as those interactively created in clinical-research and general-purpose healthcare tools, into SQL. We demonstrate the effectiveness of this generator by integrating our work into the Informatics for Integrating Biology and the Bedside (i2b2) query tool and show that it is capable of scaling. Our custom generator replaces and outperforms the default query generator found within the Clinical Research Chart (CRC) cell of i2b2. In our experiments, sixteen different types of i2b2 queries were identified by varying four constraints: date, frequency, exclusion criteria, and whether selected concepts occurred in the same encounter. We generated non-trivial, random Boolean queries based on these 16 types; the corresponding SQL queries produced by both generators were compared by execution times. The CTE-based solution significantly outperformed the default query generator and provided a much more consistent response time across all query types (M=2.03, SD=6.64 vs. M=75.82, SD=238.88 seconds). Without costly hardware upgrades, we provide a scalable solution based on CTEs with very promising empirical results centered on performance gains. The evaluation methodology used for this provides a means of profiling clinical data warehouse performance. PMID:25192572
PARAMETER ESTIMATION IN NON-HOMOGENEOUS BOOLEAN MODELS: AN APPLICATION TO PLANT DEFENSE RESPONSE
Directory of Open Access Journals (Sweden)
Maria Angeles Gallego
2014-11-01
Full Text Available Many medical and biological problems require to extract information from microscopical images. Boolean models have been extensively used to analyze binary images of random clumps in many scientific fields. In this paper, a particular type of Boolean model with an underlying non-stationary point process is considered. The intensity of the underlying point process is formulated as a fixed function of the distance to a region of interest. A method to estimate the parameters of this Boolean model is introduced, and its performance is checked in two different settings. Firstly, a comparative study with other existent methods is done using simulated data. Secondly, the method is applied to analyze the longleaf data set, which is a very popular data set in the context of point processes included in the R package spatstat. Obtained results show that the new method provides as accurate estimates as those obtained with more complex methods developed for the general case. Finally, to illustrate the application of this model and this method, a particular type of phytopathological images are analyzed. These images show callose depositions in leaves of Arabidopsis plants. The analysis of callose depositions, is very popular in the phytopathological literature to quantify activity of plant immunity.
Exploring candidate biological functions by Boolean Function Networks for Saccharomyces cerevisiae.
Directory of Open Access Journals (Sweden)
Maria Simak
Full Text Available The great amount of gene expression data has brought a big challenge for the discovery of Gene Regulatory Network (GRN. For network reconstruction and the investigation of regulatory relations, it is desirable to ensure directness of links between genes on a map, infer their directionality and explore candidate biological functions from high-throughput transcriptomic data. To address these problems, we introduce a Boolean Function Network (BFN model based on techniques of hidden Markov model (HMM, likelihood ratio test and Boolean logic functions. BFN consists of two consecutive tests to establish links between pairs of genes and check their directness. We evaluate the performance of BFN through the application to S. cerevisiae time course data. BFN produces regulatory relations which show consistency with succession of cell cycle phases. Furthermore, it also improves sensitivity and specificity when compared with alternative methods of genetic network reverse engineering. Moreover, we demonstrate that BFN can provide proper resolution for GO enrichment of gene sets. Finally, the Boolean functions discovered by BFN can provide useful insights for the identification of control mechanisms of regulatory processes, which is the special advantage of the proposed approach. In combination with low computational complexity, BFN can serve as an efficient screening tool to reconstruct genes relations on the whole genome level. In addition, the BFN approach is also feasible to a wide range of time course datasets.
Chemical potential in active systems: predicting phase equilibrium from bulk equations of state?
Paliwal, Siddharth; Rodenburg, Jeroen; van Roij, René; Dijkstra, Marjolein
2018-01-01
We derive a microscopic expression for a quantity μ that plays the role of chemical potential of active Brownian particles (ABPs) in a steady state in the absence of vortices. We show that μ consists of (i) an intrinsic chemical potential similar to passive systems, which depends on density and self-propulsion speed, but not on the external potential, (ii) the external potential, and (iii) a newly derived one-body swim potential due to the activity of the particles. Our simulations on ABPs show good agreement with our Fokker–Planck calculations, and confirm that μ (z) is spatially constant for several inhomogeneous active fluids in their steady states in a planar geometry. Finally, we show that phase coexistence of ABPs with a planar interface satisfies not only mechanical but also diffusive equilibrium. The coexistence can be well-described by equating the bulk chemical potential and bulk pressure obtained from bulk simulations for systems with low activity but requires explicit evaluation of the interfacial contributions at high activity.
Classical integrable systems and soliton equations related to eleven-vertex R-matrix
Energy Technology Data Exchange (ETDEWEB)
Levin, A., E-mail: alevin@hse.ru [NRU HSE, Department of Mathematics, Myasnitskaya str. 20, Moscow, 101000 (Russian Federation); ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); Olshanetsky, M., E-mail: olshanet@itep.ru [ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); MIPT, Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 (Russian Federation); Zotov, A., E-mail: zotov@mi.ras.ru [Steklov Mathematical Institute RAS, Gubkina str. 8, Moscow, 119991 (Russian Federation); ITEP, B. Cheremushkinskaya str. 25, Moscow, 117218 (Russian Federation); MIPT, Institutskii per. 9, Dolgoprudny, Moscow Region, 141700 (Russian Federation)
2014-10-15
In our recent paper we suggested a natural construction of the classical relativistic integrable tops in terms of the quantum R-matrices. Here we study the simplest case – the 11-vertex R-matrix and related gl{sub 2} rational models. The corresponding top is equivalent to the 2-body Ruijsenaars–Schneider (RS) or the 2-body Calogero–Moser (CM) model depending on its description. We give different descriptions of the integrable tops and use them as building blocks for construction of more complicated integrable systems such as Gaudin models and classical spin chains (periodic and with boundaries). The known relation between the top and CM (or RS) models allows to rewrite the Gaudin models (or the spin chains) in the canonical variables. Then they assume the form of n-particle integrable systems with 2n constants. We also describe the generalization of the top to 1+1 field theories. It allows us to get the Landau–Lifshitz type equation. The latter can be treated as non-trivial deformation of the classical continuous Heisenberg model. In a similar way the deformation of the principal chiral model is described.