Energy Technology Data Exchange (ETDEWEB)
Korshunov, A D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2003-10-31
Monotone Boolean functions are an important object in discrete mathematics and mathematical cybernetics. Topics related to these functions have been actively studied for several decades. Many results have been obtained, and many papers published. However, until now there has been no sufficiently complete monograph or survey of results of investigations concerning monotone Boolean functions. The object of this survey is to present the main results on monotone Boolean functions obtained during the last 50 years.
Canteaut, Anne; Videau, Marion
2005-01-01
http://www.ieee.org/; We present an extensive study of symmetric Boolean functions, especially of their cryptographic properties. Our main result establishes the link between the periodicity of the simplified value vector of a symmetric Boolean function and its degree. Besides the reduction of the amount of memory required for representing a symmetric function, this property has some consequences from a cryptographic point of view. For instance, it leads to a new general bound on the order of...
Computational complexity of Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Korshunov, Aleksei D [Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2012-02-28
Boolean functions are among the fundamental objects of discrete mathematics, especially in those of its subdisciplines which fall under mathematical logic and mathematical cybernetics. The language of Boolean functions is convenient for describing the operation of many discrete systems such as contact networks, Boolean circuits, branching programs, and some others. An important parameter of discrete systems of this kind is their complexity. This characteristic has been actively investigated starting from Shannon's works. There is a large body of scientific literature presenting many fundamental results. The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching. Bibliography: 165 titles.
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...
Quantum algorithms for testing Boolean functions
Erika Andersson; Floess, Dominik F.; Mark Hillery
2010-01-01
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...
Geometric Operators on Boolean Functions
DEFF Research Database (Denmark)
Frisvad, Jeppe Revall; Falster, Peter
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...... independent of representation such that we no longer need to be much concerned with the form of the Boolean functions. Knowing that the operators can easily be implemented (as they have been in array-based logic), shows the advantage they give with respect to automated reasoning....
Evolutionary Design of Boolean Functions
Institute of Scientific and Technical Information of China (English)
WANG Zhang-yi; ZHANG Huan-guo; QIN Zhong-ping; MENG Qing-shu
2005-01-01
We use evolutionary computing to synthesize Boolean functions randomly. By using specific crossover and mutation operator in evolving process and modifying search space and fitness function, we get some high non-linearity functions which have other good cryptography characteristics such as autocorrelation etc. Comparing to other heuristic search techniques, evolutionary computing approach is more effective because of global search strategy and implicit parallelism.
Construction of optimized Boolean functions
Institute of Scientific and Technical Information of China (English)
CHEN Wei; YANG Yi-xian; NIU Xin-xin
2006-01-01
Considering connections of characteristics,this paper is aimed at the construction of optimized Boolean functions.A new method based on the Bent function,discrete Walsh spectrum and characteristics matrices are presented by concatenating,breaking,and revising output sequences conditionally.This new construction can be used to construct different kinds of functions satisfying different design criteria.
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 decompositio
Boolean networks with veto functions
Ebadi, Haleh; Klemm, Konstantin
2014-08-01
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expressions for the sensitivity of these functions and provide evidence for their role in natural systems. In an intracellular signal transduction network [Helikar et al., Proc. Natl. Acad. Sci. USA 105, 1913 (2008), 10.1073/pnas.0705088105], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. In Boolean networks for control of the yeast cell cycle [Li et al., Proc. Natl. Acad. Sci. USA 101, 4781 (2004), 10.1073/pnas.0305937101; Davidich et al., PLoS ONE 3, e1672 (2008), 10.1371/journal.pone.0001672], no or minimal changes to the wiring diagrams are necessary to formulate their dynamics in terms of the veto functions introduced here.
Progress in Applications of Boolean Functions
Sasao, Tsutomu
2010-01-01
This book brings together five topics on the application of Boolean functions. They are 1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with their own distinct merit. 2. Boolean functions for cryptography: The process of encrypting/decrypting plain text messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks.
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.
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 speci
Polynomial threshold functions and Boolean threshold circuits
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2013-01-01
We study the complexity of computing Boolean functions on general Boolean domains by polynomial threshold functions (PTFs). A typical example of a general Boolean domain is 12n . We are mainly interested in the length (the number of monomials) of PTFs, with their degree and weight being...... of secondary interest. We show that PTFs on general Boolean domains are tightly connected to depth two threshold circuits. Our main results in regard to this connection are: PTFs of polynomial length and polynomial degree compute exactly the functions computed by THRMAJ circuits. An exponential length lower...
Local Correction of Boolean Functions
Alon, Noga
2011-01-01
A Boolean function f over n variables is said to be q-locally correctable if, given a black-box access to a function g which is "close" to an isomorphism f_sigma of f, we can compute f_sigma(x) for any x in Z_2^n with good probability using q queries to g. We observe that any k-junta, that is, any function which depends only on k of its input variables, is O(2^k)-locally correctable. Moreover, we show that there are examples where this is essentially best possible, and locally correcting some k-juntas requires a number of queries which is exponential in k. These examples, however, are far from being typical, and indeed we prove that for almost every k-junta, O(k log k) queries suffice.
Adiabatic quantum gates and Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Andrecut, M; Ali, M K [Department of Physics, University of Lethbridge, Lethbridge, AB, T1K 3M4 (Canada)
2004-06-25
We discuss the logical implementation of quantum gates and Boolean functions in the framework of quantum adiabatic method, which uses the language of ground states, spectral gaps and Hamiltonians instead of the standard unitary transformation language. (letter to the editor)
Boolean nested canalizing functions: a comprehensive analysis
Li, Yuan; Murrugarra, David; Aguilar, Boris; Laubenbacher, Reinhard
2012-01-01
Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being nested canalizing, a property inspired by the concept of canalization in evolutionary biology. It has been shown that networks comprised of nested canalizing functions have dynamic properties that make them suitable for modeling molecular regulatory networks, namely a small number of (large) attractors, as well as relatively short limit cycles. This paper contains a detailed analysis of this class of functions, based on a novel normal form as polynomial functions over the Boolean field. The concept of layer is introduced that stratifies variables into different classes depending on their level of dominance. Using this layer concept a closed form formula is derived for the number of nested canalizing functions with a given number of variables. Additional metrics analyzed in...
Analysis of affinely equivalent Boolean functions
Institute of Scientific and Technical Information of China (English)
MENG QingShu; ZHANG HuanGuo; YANG Min; WANG ZhangYi
2007-01-01
By some basic transforms and invariant theory, we give two results: 1) an algorithm,which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent. This is useful in studying Boolean functions and in engineering. For example, we classify all 8-variable homogeneous bent functions of degree 3 into two classes; 2) Reed-Muller codes R(4,6)/R(1,6), R(3,7)/R(1,7) are classified efficiently.
On the average sensitivity of laced Boolean functions
jiyou, Li
2011-01-01
In this paper we obtain the average sensitivity of the laced Boolean functions. This confirms a conjecture of Shparlinski. We also compute the weights of the laced Boolean functions and show that they are almost balanced.
Information encryption systems based on Boolean functions
Directory of Open Access Journals (Sweden)
Aureliu Zgureanu
2011-02-01
Full Text Available An information encryption system based on Boolean functions is proposed. Information processing is done using multidimensional matrices, performing logical operations with these matrices. At the basis of ensuring high level security of the system the complexity of solving the problem of building systems of Boolean functions that depend on many variables (tens and hundreds is set. Such systems represent the private key. It varies both during the encryption and decryption of information, and during the transition from one message to another.
Competitive learning of monotone Boolean functions
2014-01-01
We apply competitive analysis onto the problem of minimizing the number of queries to an oracle to completely reconstruct a given monotone Boolean function. Besides lower and upper bounds on the competitivity we determine optimal deterministic online algorithms for the smallest problem instances.
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.
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.
Stratification and enumeration of Boolean functions by canalizing depth
He, Qijun
2015-01-01
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively picked off, until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. This generalizes recent work on the algebraic structure of nested canalizing functions, and it yields a stratification of all Boolean functions by their canalizing depth. As a result, we obtain closed formulas for the number of n-variable Boolean functions with depth k, which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions.
Stratification and enumeration of Boolean functions by canalizing depth
He, Qijun; Macauley, Matthew
2016-01-01
Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively "picked off", until a non-canalizing function remains. In this paper, we show how every Boolean function has a unique algebraic form involving extended monomial layers and a well-defined core polynomial. This generalizes recent work on the algebraic structure of nested canalizing functions, and it yields a stratification of all Boolean functions by their canalizing depth. As a result, we obtain closed formulas for the number of n-variable Boolean functions with depth k, which simultaneously generalizes enumeration formulas for canalizing, and nested canalizing functions.
Constructions of vector output Boolean functions with high generalized nonlinearity
Institute of Scientific and Technical Information of China (English)
KE Pin-hui; ZHANG Sheng-yuan
2008-01-01
Carlet et al. recently introduced generalized nonlinearity to measure the ability to resist the improved correlation attack of a vector output Boolean function. This article presents a construction of vector output Boolean functions with high generalized nonlinearity using the sample space. The relation between the resilient order and generalized nonlinearity is also 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.
Polynomial threshold functions and Boolean threshold circuits
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.
2013-01-01
of secondary interest. We show that PTFs on general Boolean domains are tightly connected to depth two threshold circuits. Our main results in regard to this connection are: PTFs of polynomial length and polynomial degree compute exactly the functions computed by THRMAJ circuits. An exponential length lower...... bound for PTFs that holds regardless of degree, thereby extending known lower bounds for THRMAJ circuits. We generalize two-party unbounded error communication complexity to the multi-party number-on-the-forehead setting, and show that communication lower bounds for 3-player protocols would yield size...... lower bounds for THRTHR circuits. We obtain several other results about PTFs. These include relationships between weight and degree of PTFs, and a degree lower bound for PTFs of constant length. We also consider a variant of PTFs over the max-plus algebra. We show that they are connected to PTFs over...
Construction and enumeration of Boolean functions with maximum algebraic immunity
Institute of Scientific and Technical Information of China (English)
ZHANG WenYing; WU ChuanKun; LIU XiangZhong
2009-01-01
Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents two main results to find balanced Boolean functions with maximum algebraic immunity. Through swapping the values of two bits, and then generalizing the result to swap some pairs of bits of the symmetric Boolean function constructed by Dalai, a new class of Boolean functions with maximum algebraic immunity are constructed. Enumeration of such functions is also given. For a given function p(x) with deg(p(x)) < [n/2], we give a method to construct functions in the form p(x)+q(x) which achieve the maximum algebraic immunity, where every term with nonzero coefficient in the ANF of q(x) has degree no less than [n/2].
A fast quantum algorithm for the affine Boolean function identification
Younes, Ahmed
2015-02-01
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean function is affine, then one more query to the oracle (the two-query algorithm) is required to identify the affinity of the function with certainty. The second aim of the paper is to show that if the provided Boolean function is incompletely defined, then the one-query and the two-query algorithms can be used as bounded-error quantum polynomial algorithms to identify certain classes of incompletely defined linear and affine Boolean functions respectively with probability of success at least 2/3.
Control of random Boolean networks via average sensitivity of Boolean functions
Institute of Scientific and Technical Information of China (English)
Chen Shi-Jian; Hong Yi-Guang
2011-01-01
In this paper, we discuss how to transform the disordered phase into an ordered phase in random Boolean networks. To increase the effectiveness, a control scheme is proposed, which periodically freezes a fraction of the network based on the average sensitivity of Boolean functions of the nodes. Theoretical analysis is carried out to estimate the expected critical value of the fraction, and shows that the critical value is reduced using this scheme compared to that of randomly freezing a fraction of the nodes. Finally, the simulation is given for illustrating the effectiveness of the proposed method.
QBF-Based Boolean Function Bi-Decomposition
Chen, Huan; Marques-Silva, Joao
2011-01-01
Boolean function bi-decomposition is ubiquitous in logic synthesis. It entails the decomposition of a Boolean function using two-input simple logic gates. Existing solutions for bi-decomposition are often based on BDDs and, more recently, on Boolean Satisfiability. In addition, the partition of the input set of variables is either assumed, or heuristic solutions are considered for finding good partitions. In contrast to earlier work, this paper proposes the use of Quantified Boolean Formulas (QBF) for computing bi- decompositions. These bi-decompositions are optimal in terms of the achieved disjointness and balancedness of the input set of variables. Experimental results, obtained on representative benchmarks, demonstrate clear improvements in the quality of computed decompositions, but also the practical feasibility of QBF-based bi-decomposition.
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.
Superatomic Boolean algebras constructed from strongly unbounded functions
Martinez, Juan Carlos
2010-01-01
Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that $\\kappa,\\lambda$ are infinite cardinals such that $\\kappa^{+++} \\leq \\lambda$, $\\kappa^{_{{\\omega}_1}\\concatenation \\$ and $\\_{{\\omega}_2}\\concatenation \\$ can be cardinal sequences of superatomic Boolean algebras.
New Considerations for Spectral Classification of Boolean Switching Functions
Directory of Open Access Journals (Sweden)
J. E. Rice
2011-01-01
Full Text Available This paper presents some new considerations for spectral techniques for classification of Boolean functions. These considerations incorporate discussions of the feasibility of extending this classification technique beyond n=5. A new implementation is presented along with a basic analysis of the complexity of the problem. We also note a correction to results in this area that were reported in previous work.
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 f{hoo
Characterization of Linearly Separable Boolean Functions: A Graph-Theoretic Perspective.
Rao, Yanyi; Zhang, Xianda
2016-04-05
In this paper, we present a novel approach for studying Boolean function in a graph-theoretic perspective. In particular, we first transform a Boolean function f of n variables into an induced subgraph Hf of the n-dimensional hypercube, and then, we show the properties of linearly separable Boolean functions on the basis of the analysis of the structure of Hf. We define a new class of graphs, called hyperstar, and prove that the induced subgraph Hf of any linearly separable Boolean function f is a hyperstar. The proposal of hyperstar helps us uncover a number of fundamental properties of linearly separable Boolean functions in this paper.
The Nonlinearity of Sum and Product for Boolean Functions
Directory of Open Access Journals (Sweden)
Huang Jinglian
2016-01-01
Full Text Available In this paper, we study the relationship between the nonlinearity of Boolean function and the nonlinearity of the sum and product of Boolean function, while derivative and e-derivative are used to study the problem further. We obtain that the sum of two functions’ nonlinearity is not less than the nonlinearity of the sum of two functions. The relationship between the nonlinearity of function and the nonlinearity of the sum and product of two functions are also obtained. Furthermore, we also get the relationship between the nonlinearity of the product of functions, and the derivative and e-derivative of function. Moreover, we also deduced some important applications on the basis of the above work.
On the parity complexity measures of Boolean functions
Zhang,Zhiqiang; Shi, Yaoyun
2010-01-01
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its complement. We also show that they are polynomially related to an analogue of the block sensitivity. We further study parity decision trees in their relations with an intermediate variant of the decisi...
On designated-weight Boolean functions with highest algebraic immunity
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Algebraic immunity has been considered as one of cryptographically significant properties for Boolean functions. In this paper, we study ∑d-1 i=0 (ni)-weight Boolean functions with algebraic immunity achiev-ing the minimum of d and n - d + 1, which is highest for the functions. We present a simpler sufficient and necessary condition for these functions to achieve highest algebraic immunity. In addition, we prove that their algebraic degrees are not less than the maximum of d and n - d + 1, and for d = n1 +2 their nonlinearities equalthe minimum of ∑d-1 i=0 (ni) and ∑ d-1 i=0 (ni). Lastly, we identify two classes of such functions, one having algebraic degree of n or n-1.
Global Avalanche Characteristics of Boolean Functions by Concatenation
Institute of Scientific and Technical Information of China (English)
Mingsheng Ren
2016-01-01
In order to measure the correlation propeties of two Boolean functions, the global avalanche characteristics of Boolean functions constructed by concatenation are discussed, i.e., f1‖f2 and f1‖f2‖f3‖f4. Firstly, for the function f = f1‖f2 , the cross⁃correlation function of f1 , f2 in the special condition are studied. In this case, f, f1 , f2 must be in desired form. By computing their sum⁃of⁃squares indicators, the cross⁃correlation function between f1 , f2 is obtained. Secondly, for the function g = f1‖f2‖f3‖f4 , by analyzing the relation among their auto⁃correlation functions, their sum⁃of⁃squares indicators are investigated. Based on them, the sum⁃of⁃squares indicators of functions obtained by Canteaut et al. are investigated. The results show that the correlation property of g is good when the correlation properties of Boolean functions f1 , f2 , f3 , f4 are good.
On K-wise Independent Distributions and Boolean Functions
Benjamini, Itai; Peled, Ron
2012-01-01
We pursue a systematic study of the following problem. Let f:{0,1}^n -> {0,1} be a (usually monotone) Boolean function whose behaviour is well understood when the input bits are identically independently distributed. What can be said about the behaviour of the function when the input bits are not completely independent, but only k-wise independent, i.e. every subset of k bits is independent? more precisely, how high should k be so that any k-wise independent distribution "fools" the function, i.e. causes it to behave nearly the same as when the bits are completely independent? We analyze several well known Boolean functions (including AND, Majority, Tribes and Percolation among others), some of which turn out to have surprising properties. In some of our results we use tools from the theory of the classical moment problem, seemingly for the first time in this subject, to shed light on these questions.
Improved Decomposition for a System of Completely Specified Boolean Functions
Directory of Open Access Journals (Sweden)
Saeid Taghavi Afshord
2013-12-01
Full Text Available Functional decomposition is an important and powerful technique in the logic synthesis. The ternary matrix cover approach is one of the existing methods of this type. This method is also used in decomposition of a system of completely specified Boolean functions. Before constructing the desired superposition, it needs to encode a table. There is a trivial encoding method. But to find a better solution, it is important to use a special approach, because the result of the encoding has a direct influence on the obtained functions. In this paper, an efficient algorithm to encode this table is presented. It uses the approach connected with the assembling Boolean hyper cube method. The proposed algorithm is explained in details with an example. The benefits and impacts of the suggested technique are also discussed.
Complexity of Propositional Abduction for Restricted Sets of Boolean Functions
Creignou, Nadia; Thomas, Michael
2009-01-01
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional abduction, where the knowledge base and the manifestation are represented by propositional formulae. The problem of deciding whether there exists an explanation has been shown to be SigmaP2-complete in general. We consider variants obtained by restricting the allowed connectives in the formulae to certain sets of Boolean functions. We give a complete classification of the complexity for all considerable sets of Boolean functions. In this way, we identify easier cases, namely NP-complete and polynomial cases; and we highlight sources of intractability. Further, we address the problem of counting the explanations and draw a complete picture for the counting complexity.
On Third-Order Nonlinearity of Biquadratic Monomial Boolean Functions
Directory of Open Access Journals (Sweden)
Brajesh Kumar Singh
2014-01-01
Full Text Available The rth-order nonlinearity of Boolean function plays a central role against several known attacks on stream and block ciphers. Because of the fact that its maximum equals the covering radius of the rth-order Reed-Muller code, it also plays an important role in coding theory. The computation of exact value or high lower bound on the rth-order nonlinearity of a Boolean function is very complicated problem, especially when r>1. This paper is concerned with the computation of the lower bounds for third-order nonlinearities of two classes of Boolean functions of the form Tr1nλxd for all x∈2n, λ∈2n*, where a d=2i+2j+2k+1, where i, j, and k are integers such that i>j>k≥1 and n>2i, and b d=23ℓ+22ℓ+2ℓ+1, where ℓ is a positive integer such that gcdℓ,=1 and n>6.
On the parity complexity measures of Boolean functions
Zhang, Zhiqiang; 10.1016/j.tcs.2010.03.027
2010-01-01
The parity decision tree model extends the decision tree model by allowing the computation of a parity function in one step. We prove that the deterministic parity decision tree complexity of any Boolean function is polynomially related to the non-deterministic complexity of the function or its complement. We also show that they are polynomially related to an analogue of the block sensitivity. We further study parity decision trees in their relations with an intermediate variant of the decision trees, as well as with communication complexity.
Graph-based algorithms for Boolean function manipulation
Energy Technology Data Exchange (ETDEWEB)
Bryant, R.E.
1986-08-01
In this paper the authors present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. The algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. The authors present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of the approach.
On Various Nonlinearity Measures for Boolean Functions.
Boyar, Joan; Find, Magnus Gausdal; Peralta, René
2016-07-01
A necessary condition for the security of cryptographic functions is to be "sufficiently distant" from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that six common measures, nonlinearity, algebraic degree, annihilator immunity, algebraic thickness, normality, and multiplicative complexity, are incomparable in the sense that for each pair of measures, μ1, μ2, there exist functions f1, f2 with f1 being more nonlinear than f2 according to μ1, but less nonlinear according to μ2. We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions.
From Exact Learning to Computing Boolean Functions and Back Again
Goschin, Sergiu
2012-01-01
The goal of the paper is to relate complexity measures associated with the evaluation of Boolean functions (certificate complexity, decision tree complexity) and learning dimensions used to characterize exact learning (teaching dimension, extended teaching dimension). The high level motivation is to discover non-trivial relations between exact learning of an unknown concept and testing whether an unknown concept is part of a concept class or not. Concretely, the goal is to provide lower and upper bounds of complexity measures for one problem type in terms of the other.
Three New Construction Methods of the Highly Nonlinear Balanced Boolean Function
Institute of Scientific and Technical Information of China (English)
TANXinglie; SHEKun; JIQingbing; ZHOUMingtian; SHENChangxiang
2003-01-01
Nonlinearity is a nonlinear criterion of Boolean function. In this paper, some useful definitions and theorems are introduced, and then three new ways to construct the highly nonlinear balanced boolean function are given by ways of concatenating, dividing, modifying and alternating, which are proven to be very effective.
On the 2m-variable symmetric Boolean functions with maximum algebraic immunity
Institute of Scientific and Technical Information of China (English)
QU LongJiang; LI Chao
2008-01-01
The properties of the 2m-variable symmetric Boolean functions with maximum al-gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced.
On the construction of cryptographically strong Boolean functions with desirable trade-off
Institute of Scientific and Technical Information of China (English)
REN Kui; PARK Jaemin; KIM Kwangjo
2005-01-01
This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2)n→GF(2))with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties: nl(f)=22k-1-2k+2k-2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k+23k-2 and the absolute avalanche characteristic of △f satisfying △f=2k+1. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions.
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 functions of an odd number of variables with maximum algebraic immunity
Institute of Scientific and Technical Information of China (English)
LI Na; QI WenFeng
2007-01-01
In this paper, we study Boolean functions of an odd number of variables with maximum algebraic immunity, We identify three classes of such functions, and give some necessary conditions of such functions, which help to examine whether a Boolean function of an odd number of variables has the maximum algebraic immunity. Further, some necessary conditions for such functions to have also higher nonlinearity are proposed, and a class of these functions are also obtained. Finally,we present a sufficient and necessary condition for Boolean functions of an odd number of variables to achieve maximum algebraic immunity and to be also 1-resilient.
Characterizing short-term stability for Boolean networks over any distribution of transfer functions
Seshadhri, C.; Smith, Andrew M.; Vorobeychik, Yevgeniy; Mayo, Jackson R.; Armstrong, Robert C.
2016-07-01
We present a characterization of short-term stability of Kauffman's N K (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of this formula is the Fourier analysis of Boolean functions, which describes such functions as multilinear polynomials over the inputs. Numerical simulations on mixtures of threshold functions and nested canalyzing functions demonstrate the formula's correctness.
Realization of Functional Complete Stateful Boolean Logic in Memristive Crossbar.
Li, Yi; Zhou, Ya-Xiong; Xu, Lei; Lu, Ke; Wang, Zhuo-Rui; Duan, Nian; Jiang, Lei; Cheng, Long; Chang, Ting-Chang; Chang, Kuan-Chang; Sun, Hua-Jun; Xue, Kan-Hao; Miao, Xiang-Shui
2016-12-21
Nonvolatile stateful logic computing in memristors is a promising paradigm with which to realize the unity of information storage and processing in the same physical location that has shown great feasibility for breaking the von Neumann bottleneck in traditional computing architecture. How to reduce the computational complexity of memristor-based logic functions is a matter of concern. Here, based on a general logic expression, we proposed a method to implement the arbitrary logic of complete 16 Boolean logic in two steps with one memristor in the crossbar architecture. A representative functional complete NAND logic is successfully experimentally demonstrated in the filamentary Ag-AgGeTe-Ta memristors to prove the validity of our method. We believe our work may promote the development of the revolutionary logic in memory architectures.
On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions
Zertuche, Federico
2009-04-01
NK-Kauffman networks LKN are a subset of the Boolean functions on N Boolean variables to themselves, ΛN={ξ :Z2N→Z2N}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function Ψ :LKN→ΛN. The probability PK that Ψ(f )=Ψ(f'), when f' is obtained through f by a change in one of its K-Boolean functions (bK:Z2K→Z2), and/or connections, is calculated. The leading term of the asymptotic expansion of PK, for N ≫1, turns out to depend on the probability to extract the tautology and contradiction Boolean functions, and in the average value of the distribution of probability of the Boolean functions, the other terms decay as O(1/N). In order to accomplish this, a classification of the Boolean functions in terms of what I have called their irreducible degree of connectivity is established. The mathematical findings are discussed in the biological context, where Ψ is used to model the genotype-phenotype map.
Vectorial Resilient PC(l) of Order k Boolean Functions from AG-Codes
Institute of Scientific and Technical Information of China (English)
Hao CHEN; Liang MA; Jianhua LI
2011-01-01
Propagation criteria and resiliency of vectorial Boolean functions are important for cryptographic purpose (see [1- 4, 7, 8, 10, 11, 16]). Kurosawa, Stoh [8] and Carlet [1]gave a construction of Boolean functions satisfying PC(l) of order k from binary linear or nonlinear codes. In this paper, the algebraic-geometric codes over GF(2m) are used to modify the Carlet and Kurosawa-Satoh's construction for giving vectorial resilient Boolean functions satisfying PC(l) of order k criterion. This new construction is compared with previously known results.
The Properties of 2-Summable Boolean Function and 3-Summable Boolean Function%可求和布尔函数的性质
Institute of Scientific and Technical Information of China (English)
曾利全; 许道云
2016-01-01
可求和布尔函数是临界布尔函数判定理论中比较重要的内容之一。该类函数有一个参数k , k表示布尔函数存在k个成真点X1,X2,…Xk和k个成假点Y1,Y2,…Yk ,并且它们的和相等。本文主要研究了n元2-可求和布尔函数和n元3-可求和布尔函数的基本性质。%One of the most important theorem in recognition of threshold function is the k- asummable Boolean function for all k≥2, where k is the number of true point of the Boolean function, say X1,X2,…Xk , and the number of false point of the Boolean function, say, Y1,Y2,…Yk ,such that∑ki=1Xi =∑ki=1Yi . It is shown that the basic properties of 2-summable Boolean function and 3-summable Boolean function.
Institute of Scientific and Technical Information of China (English)
闵应骅; 李忠诚; 赵著行
1997-01-01
Boolean algebra successfully describes the logical behavior of a digital circuit, and has been widely used in electronic circuit design and test With the development of high speed VLSIs it is a drawback for Boolean algebra to be unable to describe circuit timing behavior. Therefore a Boolean process is defined as a family of Boolean van ables relevant to the time parameter t. A real-valued sample of a Boolean process is a waveform. Waveform functions can be manipulated formally by using mathematical tools. The distance, difference and limit of a waveform polynomial are defined, and a sufficient and necessary condition of the limit existence is presented. Based on this, the concept of sensitization is redefined precisely to demonstrate the potential and wide application possibility The new definition is very different from the traditional one, and has an impact on determining the sensitizable paths with maximum or minimum length, and false paths, and then designing and testing high performance circuits
Optimal computation of symmetric Boolean functions in Tree networks
Kowshik, Hemant
2010-01-01
In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a function of two nodes with integer measurements. We allow for block computation to enhance data fusion efficiency, and determine the minimum worst-case total number of bits to be exchanged to perform the desired computation. We establish lower bounds using fooling sets, and provide a novel scheme which attains the lower bounds, using information theoretic tools. For a class of functions called sum-threshold functions, this scheme is shown to be optimal. We then turn to tree networks and derive a lower bound for the number of bits exchanged on each link by viewing it as a two node problem. We show that the protocol of recursive innetwork aggregation achieves this lower bound in the case of sumthreshold functions. Thus we have provided a communication and in-network computation stra...
A transition calculus for Boolean functions. [logic circuit analysis
Tucker, J. H.; Bennett, A. W.
1974-01-01
A transition calculus is presented for analyzing the effect of input changes on the output of logic circuits. The method is closely related to the Boolean difference, but it is more powerful. Both differentiation and integration are considered.
Affine Equivalence of Quartic Monomial Rotation Symmetric Boolean Functions in Prime Power Dimension
2015-01-27
Odd Number of Variables, International Work- shop on Boolean Functions : Cryptography and Applications (BFCA 2005), University of Rouen, France (2005...Affine Equivalence of Quartic Monomial Rotation Symmetric Boolean Functions in Prime Power Dimension Pantelimon Stănică Naval Postgraduate School... Department of Applied Mathematics, Monterey, CA 93943–5216, USA; pstanica@nps.edu Abstract In this paper we analyze and exactly compute the number of
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.
On $2k$-Variable Symmetric Boolean Functions with Maximum Algebraic Immunity $k$
Wang, Hui; Li, Yuan; Kan, Haibin
2011-01-01
Given a positive even integer $n$, it is found that the weight distribution of any $n$-variable symmetric Boolean function with maximum algebraic immunity $\\frac{n}{2}$ is determined by the binary expansion of $n$. Based on that, all $n$-variable symmetric Boolean functions with maximum algebraic immunity are constructed. The amount is $(2\\wt(n)+1)2^{\\lfloor \\log_2 n \\rfloor}$.
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....
Exact quantum algorithm to distinguish Boolean functions of different weights
Energy Technology Data Exchange (ETDEWEB)
Braunstein, Samuel L [Computer Science, University of York, York YO10 5DD (United Kingdom); Choi, Byung-Soo [Computer Science, University of York, York YO10 5DD (United Kingdom); Ghosh, Subhroshekhar [Indian Statistical Institute, Kolkata 700 108 (India); Maitra, Subhamoy [Applied Statistics Unit, Indian Statistical Institute, Kolkata 700 108 (India)
2007-07-20
In this work, we exploit the Grover operator for the weight analysis of a Boolean function, specifically to solve the weight-decision problem. The weight w is the fraction of all possible inputs for which the output is 1. The goal of the weight-decision problem is to find the exact weight w from the given two weights w{sub 1} and w{sub 2} satisfying a general weight condition as w{sub 1} + w{sub 2} = 1 and 0 < w{sub 1} < w{sub 2} < 1. First, we propose a limited weight-decision algorithm where the function has another constraint: a weight is in {l_brace} W{sub 1} = sin{sup 2}(k/(2k+1) {pi}/2), w{sub 2} = cos{sup 2}(k/(2k+1) {pi}/2){r_brace} for integer k. Second, by changing the phases in the last two Grover iterations, we propose a general weight-decision algorithm which is free from the above constraint. Finally, we show that when our algorithm requires O(k) queries to find w with a unit success probability, any classical algorithm requires at least {omega}(k{sup 2}) queries for a unit success probability. In addition, we show that our algorithm requires fewer queries to solve this problem compared with the quantum counting algorithm.
Leont'ev, V. K.
2015-11-01
A pseudo-Boolean function is an arbitrary mapping of the set of binary n-tuples to the real line. Such functions are a natural generalization of classical Boolean functions and find numerous applications in various applied studies. Specifically, the Fourier transform of a Boolean function is a pseudo-Boolean function. A number of facts associated with pseudo-Boolean polynomials are presented, and their applications to well-known discrete optimization problems are described.
Li, Yuan; Kan, Haibin
2011-01-01
In this paper, we explicitly construct a large class of symmetric Boolean functions on $2k$ variables with algebraic immunity not less than $d$, where integer $k$ is given arbitrarily and $d$ is a given suffix of $k$ in binary representation. If let $d = k$, our constructed functions achieve the maximum algebraic immunity. Remarkably, $2^{\\lfloor \\log_2{k} \\rfloor + 2}$ symmetric Boolean functions on $2k$ variables with maximum algebraic immunity are constructed, which is much more than the previous constructions. Based on our construction, a lower bound of symmetric Boolean functions with algebraic immunity not less than $d$ is derived, which is $2^{\\lfloor \\log_2{d} \\rfloor + 2(k-d+1)}$. As far as we know, this is the first lower bound of this kind.
Influence and interaction indexes for pseudo-Boolean functions: a unified least squares approach
Marichal, Jean-Luc
2012-01-01
The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified degree. We first observe that this property still holds if we consider approximations by pseudo-Boolean functions depending only on specified variables. We then show that the Banzhaf influence index can also be obtained from the latter approximation problem. Considering certain weighted versions of this approximation problem, we introduce a class of weighted Banzhaf influence indexes, analyze their most important properties, and point out similarities between the weighted Banzhaf influence index and the corresponding weighted Banzhaf interaction index.
Mechanical system reliability analysis using a combination of graph theory and Boolean function
Energy Technology Data Exchange (ETDEWEB)
Tang, J
2001-04-01
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.
On （2m + 1）-variable symmetric Boolean functions with submaximum algebraic immunity 2m-1
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
All (2m +1)-variable symmetric Boolean functions with submaximal algebraic immunity 2m-1 are described and constructed. The total number of such Boolean functions is 32 ·22m-3 +3m-2 · 24 - 2 for m≥2.
Computing Symmetric Boolean Functions by Circuits with Few Exact Threshold Gates
DEFF Research Database (Denmark)
Hansen, Kristoffer Arnsfelt
2007-01-01
We consider constant depth circuits augmented with few exact threshold gates with arbitrary weights. We prove strong (up to exponential) size lower bounds for such circuits computing symmetric Boolean functions. Our lower bound is expressed in terms of a natural parameter, the balance, of symmetric...
Directory of Open Access Journals (Sweden)
V. Rusan
2012-01-01
Full Text Available The paper considers calculation methods for reliability of agricultural distribution power networks while using Boolean algebra functions and analytical method. Reliability of 10 kV overhead line circuits with automatic sectionalization points and automatic standby activation has been investigated in the paper.
Simple Max-Min Ant Systems and the Optimization of Linear Pseudo-Boolean Functions
Kötzing, Timo; Sudholt, Dirk; Wagner, Markus
2010-01-01
With this paper, we contribute to the understanding of ant colony optimization (ACO) algorithms by formally analyzing their runtime behavior. We study simple MAX-MIN ant systems on the class of linear pseudo-Boolean functions defined on binary strings of length 'n'. Our investigations point out how the progress according to function values is stored in pheromone. We provide a general upper bound of O((n^3 \\log n)/ \\rho) for two ACO variants on all linear functions, where (\\rho) determines the pheromone update strength. Furthermore, we show improved bounds for two well-known linear pseudo-Boolean functions called OneMax and BinVal and give additional insights using an experimental study.
A Note on "On the Construction of Boolean Functions with Optimal Algebraic Immunity"
Li, Yuan; Kokichi, Futatsugi
2011-01-01
In this note, we go further on the "basis exchange" idea presented in \\cite{LiNa1} by using Mobious inversion. We show that the matrix $S_1(f)S_0(f)^{-1}$ has a nice form when $f$ is chosen to be the majority function, where $S_1(f)$ is the matrix with row vectors $\\upsilon_k(\\alpha)$ for all $\\alpha \\in 1_f$ and $S_0(f)=S_1(f\\oplus1)$. And an exact counting for Boolean functions with maximum algebraic immunity by exchanging one point in on-set with one point in off-set of the majority function is given. Furthermore, we present a necessary condition according to weight distribution for Boolean functions to achieve algebraic immunity not less than a given number.
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.
Gardy, Danièle
2005-01-01
International audience; We examine how we can define several probability distributions on the set of Boolean functions on a fixed number of variables, starting from a representation of Boolean expressions by trees. Analytic tools give us a systematic way to prove the existence of probability distributions, the main challenge being the actual computation of the distributions. We finally consider the relations between the probability of a Boolean function and its complexity.
On the Complexity of the Evaluation of Transient Extensions of Boolean Functions
Directory of Open Access Journals (Sweden)
Janusz Brzozowski
2010-08-01
Full Text Available Transient algebra is a multi-valued algebra for hazard detection in gate circuits. Sequences of alternating 0's and 1's, called transients, represent signal values, and gates are modeled by extensions of boolean functions to transients. Formulas for computing the output transient of a gate from the input transients are known for NOT, AND, OR} and XOR gates and their complements, but, in general, even the problem of deciding whether the length of the output transient exceeds a given bound is NP-complete. We propose a method of evaluating extensions of general boolean functions. We introduce and study a class of functions with the following property: Instead of evaluating an extension of a boolean function on a given set of transients, it is possible to get the same value by using transients derived from the given ones, but having length at most 3. We prove that all functions of three variables, as well as certain other functions, have this property, and can be efficiently evaluated.
The phase diagram of random Boolean networks with nested canalizing functions
Peixoto, Tiago P
2010-01-01
We obtain the phase diagram of random Boolean networks with nested canalizing functions. Using the annealed approximation, we obtain the evolution of the number $b_t$ of nodes with value one, and the network sensitivity $\\lambda$, and we compare with numerical simulations of quenched networks. We find that, contrary to what was reported by Kauffman et al. [Proc. Natl. Acad. Sci. 2004 101 49 17102-7], these networks have a rich phase diagram, were both the "chaotic" and frozen phases are present, as well as an oscillatory regime of the value of $b_t$. We argue that the presence of only the frozen phase in the work of Kauffman et al. was due simply to the specific parametrization used, and is not an inherent feature of this class of functions. However, these networks are significantly more stable than the variants where all possible Boolean functions are allowed.
Generalization of Boolean Functions Properties to Functions Defined over GF(p
Directory of Open Access Journals (Sweden)
Saad Elmansori
2012-01-01
Full Text Available Problem statement: Traditionally, cryptographic applications designed on hardware have always tried to take advantage of the simplicity of implementation functions over GF(p, p = 2, to reduce costs and improve performance. On the contrast, functions defined over GF(p; p > 2, possess far better cryptographic properties than GF(2 functions. Approach: We generalize some of the previous results on cryptographic Boolean functions to functions defined over GF(p; p > 2. Results: We generalize Siegenthalers construction to functions defined over finite field. We characterize the linear structures of functions over GF(p in terms of their Walsh transform values. We then investigate the relation between the autocorrelation coefficients of functions over GF(p and their Walsh spectrum. We also derive an upper bound for the dimension of the linear space of the functions defined over GF(p. Finally, we present a method to construct a bent function from semi-bent functions. Conclusion: Functions defined over GF(p can achieve better cryptographic bounds than GF(2 functions. In this paper we gave a generalization of several of the GF(2 cryptographic properties to functions defined over GF(p, where p is an odd prime.
Universal asynchronous RSFQ gate for realization of Boolean functions of dual-rail binary variables
Energy Technology Data Exchange (ETDEWEB)
Dimov, B [University of Technology Ilmenau, Institute for Information Technology, PO Box 100565, D-98684 Ilmenau (Germany); Khabipov, M [Physikalisch-Technische Bundesanstalt, Division 2.42, Bundesallee 100, D-38116 Braunschweig (Germany); Balashov, D [Physikalisch-Technische Bundesanstalt, Division 2.42, Bundesallee 100, D-38116 Braunschweig (Germany); Brandt, C M [Physikalisch-Technische Bundesanstalt, Division 2.42, Bundesallee 100, D-38116 Braunschweig (Germany); Ortlepp, Th [University of Technology Ilmenau, Institute for Information Technology, PO Box 100565, D-98684 Ilmenau (Germany); Hagedorn, D [Physikalisch-Technische Bundesanstalt, Division 2.42, Bundesallee 100, D-38116 Braunschweig (Germany); Buchholz, F-Im [Physikalisch-Technische Bundesanstalt, Division 2.42, Bundesallee 100, D-38116 Braunschweig (Germany); Niemeyer, J [Physikalisch-Technische Bundesanstalt, Division 2.42, Bundesallee 100, D-38116 Braunschweig (Germany); Uhlmann, F H [University of Technology Ilmenau, Institute for Information Technology, PO Box 100565, D-98684 Ilmenau (Germany)
2006-06-01
We report on the design, optimization, fabrication, and successful testing of an universal asynchronous RSFQ logic gate based on the dual-rail data coding. Properly connecting its inputs and outputs, one can perform most of the basic Boolean functions over a pair of dual-rail input variables. Therefore, this gate is fundamental component for the development of high-speed complex asynchronous RSFQ digital devices.
Zhan, Qiqin; Chen, Xiaojun
2016-01-01
This paper proposes an interactive method of model clipping for computer-assisted surgical planning. The model is separated by a data filter that is defined by the implicit function of the clipping path. Being interactive to surgeons, the clipping path that is composed of the plane widgets can be manually repositioned along the desirable presurgical path, which means that surgeons can produce any accurate shape of the clipped model. The implicit function is acquired through a recursive algorithm based on the Boolean combinations (including Boolean union and Boolean intersection) of a series of plane widgets' implicit functions. The algorithm is evaluated as highly efficient because the best time performance of the algorithm is linear, which applies to most of the cases in the computer-assisted surgical planning. Based on the above stated algorithm, a user-friendly module named SmartModelClip is developed on the basis of Slicer platform and VTK. A number of arbitrary clipping paths have been tested. Experimental results of presurgical planning for three types of Le Fort fractures and for tumor removal demonstrate the high reliability and efficiency of our recursive algorithm and robustness of the module.
Efficient Minimization of Higher Order Submodular Functions using Monotonic Boolean Functions
Ramalingam, Srikumar; Ladicky, Lubor; Torr, Philip H S
2011-01-01
Submodular function minimization is a key problem in a wide variety of applications in machine learning, economics, game theory, computer vision and many others. The general solver has a complexity of $O(n^6+n^5L)$ where $L$ is the time required to evaluate the function and $n$ is the number of variables \\cite{orlin09}. On the other hand, many useful applications in computer vision and machine learning applications are defined over a special subclasses of submodular functions in which that can be written as the sum of many submodular cost functions defined over cliques containing few variables. In such functions, the pseudo-Boolean (or polynomial) representation \\cite{BorosH02} of these subclasses are of degree (or order, or clique size) $k$ where $k<
Detecting small attractors of large Boolean networks by function-reduction-based strategy.
Zheng, Qiben; Shen, Liangzhong; Shang, Xuequn; Liu, Wenbin
2016-04-01
Boolean networks (BNs) are widely used to model gene regulatory networks and to design therapeutic intervention strategies to affect the long-term behaviour of systems. A central aim of Boolean-network analysis is to find attractors that correspond to various cellular states, such as cell types or the stage of cell differentiation. This problem is NP-hard and various algorithms have been used to tackle it with considerable success. The idea is that a singleton attractor corresponds to n consistent subsequences in the truth table. To find these subsequences, the authors gradually reduce the entire truth table of Boolean functions by extending a partial gene activity profile (GAP). Not only does this process delete inconsistent subsequences in truth tables, it also directly determines values for some nodes not extended, which means it can abandon the partial GAPs that cannot lead to an attractor as early as possible. The results of simulation show that the proposed algorithm can detect small attractors with length p = 4 in BNs of up to 200 nodes with average indegree K = 2.
How Low Can Approximate Degree and Quantum Query Complexity be for Total Boolean Functions?
Ambainis, Andris
2012-01-01
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / log log n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Monotone Boolean approximation
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1982-12-01
This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application for the analysis of noncoherent fault trees and event tree sequences.
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Hulgaard, Henrik
2002-01-01
This paper presents a new data structure called boolean expression diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of binary decision diagrams (BDDs) which can represent any Boolean circuit in linear space. Two algorithms are described for transforming...... a BED into a reduced ordered BDD. One is a generalized version of the BDD apply-operator while the other can exploit the structural information of the Boolean expression. This ability is demonstrated by verifying that two different circuit implementations of a 16-bit multiplier implement the same...... Boolean function. Using BEDs, this verification problem is solved efficiently, while using standard BDD techniques this problem is infeasible. Generally, BEDs are useful in applications, for example tautology checking, where the end-result as a reduced ordered BDD is small. Moreover, using operators...
DEFF Research Database (Denmark)
Andersen, Henrik Reif; Hulgaard, Henrik
1997-01-01
This paper presents a new data structure called Boolean Expression Diagrams (BEDs) for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) which can represent any Boolean circuit in linear space and still maintain many of the desirable...... properties of BDDs. Two algorithms are described for transforming a BED into a reduced ordered BDD. One closely mimics the BDD apply-operator while the other can exploit the structural information of the Boolean expression. The efficacy of the BED representation is demonstrated by verifying...... that the redundant and non-redundant versions of the ISCAS 85 benchmark circuits are identical. In particular, it is verified that the two 16-bit multiplication circuits (c6288 and c6288nr) implement the same Boolean functions. Using BEDs, this verification problem is solved in less than a second, while using...
Walsh Spectrum Properties of Rotation Symmetric Boolean Function
Institute of Scientific and Technical Information of China (English)
WANG Yongjuan; HAN Wenbao; LI Shiqu
2006-01-01
Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric(RotS) function is special. For a RotS n variables function f(x1,x2,...,xn) we have f(ρkn(x1,x2,...xn))=f(x1,x2,...,xn) for k=0,1,...,n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.
Forcing functions in Kauffman's random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Stauffer, D.
1987-02-01
The phase transition between frozen and chaotic behavior in Kauffman's cellular automata on a nearest neighbor square lattice does not agree with the percolation threshold of the forcing functions.
A Note on a Conjecture for Balanced Elementary Symmetric Boolean Functions
Su, Wei; Pott, Alexander
2012-01-01
Cusick {\\it et al.} conjectured that the elementary symmetric Boolean functions of the form $\\sigma_{2^{t+1}l-1, 2^t}$ are the only balanced ones in 2008. In this note, by analyzing the weight of $\\sigma_{n, 2^t}$ and $\\sigma_{n, d}$, we prove that ${\\rm wt}(\\sigma_{n, d})<2^{n-1}$ holds in most cases. According to the remainder of modulo 4, we consider the weight of $\\sigma_{n, d}$ from two aspects: $n\\equiv 3({\\rm mod\\}4)$ and $n\
A technology mapping of boolean functions for CPLDs
Kania, Dariusz
2014-10-01
The effective technology mapping for PAL-based Complex PLDs is presented. The aim of this approach is to cover a multiple-output function by a minimal number of PAL-based logic blocks. Proposed algorithm, implemented within the PALDec system, has been used for synthesizing the benchmarks. The obtained results are compared with the classical technology mapping.
Trinh, Hung-Cuong; Kwon, Yung-Keun
2015-11-01
Efficiently identifying functionally important genes in order to understand the minimal requirements of normal cellular development is challenging. To this end, a variety of structural measures have been proposed and their effectiveness has been investigated in recent literature; however, few studies have shown the effectiveness of dynamics-based measures. This led us to investigate a dynamic measure to identify functionally important genes, and the effectiveness of which was verified through application on two large-scale human signaling networks. We specifically consider Boolean sensitivity-based dynamics against an update-rule perturbation (BSU) as a dynamic measure. Through investigations on two large-scale human signaling networks, we found that genes with relatively high BSU values show slower evolutionary rate and higher proportions of essential genes and drug targets than other genes. Gene-ontology analysis showed clear differences between the former and latter groups of genes. Furthermore, we compare the identification accuracies of essential genes and drug targets via BSU and five well-known structural measures. Although BSU did not always show the best performance, it effectively identified the putative set of genes, which is significantly different from the results obtained via the structural measures. Most interestingly, BSU showed the highest synergy effect in identifying the functionally important genes in conjunction with other measures. Our results imply that Boolean-sensitive dynamics can be used as a measure to effectively identify functionally important genes in signaling networks.
Boolean differential equations
Steinbach, Bernd
2013-01-01
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the structure of a Boolean Algebra significantly. Based on a small number of definitions, many theorems have been proven. The available operations have been efficiently implemented in several software packages. There is a very wide field of applications. While a Boolean Algebra is focused on values of logic functions, the BDC allows the evaluation of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. Due to the same basic data structures, the BDC can
Boolean complexes and boolean numbers
Tenner, Bridget Eileen
2017-01-01
International audience; The Bruhat order gives a poset structure to any Coxeter group. The ideal of elements in this poset having boolean principal order ideals forms a simplicial poset. This simplicial poset defines the boolean complex for the group. In a Coxeter system of rank n, we show that the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres. The number of these spheres is the boolean number, which can be computed inductively from the unlabeled Coxeter syste...
Quantum tests for the linearity and permutation invariance of Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Hillery, Mark [Department of Physics, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10021 (United States); Andersson, Erika [SUPA, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)
2011-12-15
The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is {epsilon}-far from having that property. The performance of the algorithm is judged by how many calls need to be made to the black box in order to determine, with high probability, which of the two alternatives is the case. Here we present two quantum algorithms, the first to determine whether the function is linear and the second to determine whether it is symmetric (invariant under permutations of the arguments). Both require order {epsilon}{sup -2/3} calls to the oracle, which is better than known classical algorithms. In addition, in the case of linearity testing, if the function is linear, the quantum algorithm identifies which linear function it is. The linearity test combines the Bernstein-Vazirani algorithm and amplitude amplification, while the test to determine whether a function is symmetric uses projective measurements and amplitude amplification.
2014-01-01
Background An algebraic method for information fusion based on nonadditive set functions is used to assess the joint contribution of Boolean network attributes to the sensitivity of the network to individual node mutations. The node attributes or characteristics under consideration are: in-degree, out-degree, minimum and average path lengths, bias, average sensitivity of Boolean functions, and canalizing degrees. The impact of node mutations is assessed using as target measure the average Hamming distance between a non-mutated/wild-type network and a mutated network. Results We find that for a biochemical signal transduction network consisting of several main signaling pathways whose nodes represent signaling molecules (mainly proteins), the algebraic method provides a robust classification of attribute contributions. This method indicates that for the biochemical network, the most significant impact is generated mainly by the combined effects of two attributes: out-degree, and average sensitivity of nodes. Conclusions The results support the idea that both topological and dynamical properties of the nodes need to be under consideration. The algebraic method is robust against the choice of initial conditions and partition of data sets in training and testing sets for estimation of the nonadditive set functions of the information fusion procedure. PMID:25189194
Boolean logic functions of a synthetic peptide network.
Ashkenasy, Gonen; Ghadiri, M Reza
2004-09-15
Living cells can process rapidly and simultaneously multiple extracellular input signals through the complex networks of evolutionary selected biomolecular interactions and chemical transformations. Recent approaches to molecular computation have increasingly sought to mimic or exploit various aspects of biology. A number of studies have adapted nucleic acids and proteins to the design of molecular logic gates and computational systems, while other works have affected computation in living cells via biochemical pathway engineering. Here we report that de novo designed synthetic peptide networks can also mimic some of the basic logic functions of the more complex biological networks. We show that segments of a small network whose graph structure is composed of five nodes and 15 directed edges can express OR, NOR, and NOTIF logic.
Implementation of Complete Boolean Logic Functions in Single Complementary Resistive Switch.
Gao, Shuang; Zeng, Fei; Wang, Minjuan; Wang, Guangyue; Song, Cheng; Pan, Feng
2015-01-01
The unique complementary switching behaviour of complementary resistive switches (CRSs) makes them very attractive for logic applications. The implementation of complete Boolean logic functions in a single CRS cell is certainly an extremely important step towards the commercialisation of related logic circuits, but it has not been accomplished to date. Here, we report two methods for the implementation of complete Boolean logic functions in a single CRS cell. The first method is based on the intrinsic switchable diode of a peculiar CRS cell that is composed of two anti-serial bipolar resistive switches with a rectifying high resistance state, while the second method is based directly on the complementary switching behaviour itself of any single CRS cell. The feasibilities of both methods have been theoretically predicted and then experimentally demonstrated on the basis of a Ta/Ta2O5/Pt/Ta2O5/Ta CRS cell. Therefore, these two methods-in particular the complementary switching behaviour itself-based method, which has natural immunity to the sneak-path issue of crossbar logic circuits-are believed to be capable of significantly advancing both our understanding and commercialization of related logic circuits. Moreover, peculiar CRS cells have been demonstrated to be feasible for tri-level storage, which can serve as an alternative method of realising ultra-high-density data storage.
Boolean operations with implicit and parametric representation of primitives using R-functions.
Fougerolle, Yohan D; Gribok, Andrei; Foufou, Sebti; Truchetet, Frédéric; Abidi, Mongi A
2005-01-01
We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a Constructive Solid Geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.
Directory of Open Access Journals (Sweden)
Huang Jinglian
2016-01-01
Full Text Available We put forward an efficient method to study the algebraic immunity of H Boolean functions with Hamming weight of 2n-1 + 2n-2, getting the existence of the higher-order algebraic immunity functions with correlation immunity. We also prove the existing problem of the above 2-order algebraic immunity functions and the optimal algebraic immunity functions. Meanwhile, we solve the compatibility of algebraic immunity and correlation immunity. What is more, the main theoretical results are verified through the examples and are revealed to be correct. Such researches are important in cryptographic primitive designs, and have significance and role in the theory and application range of cryptosystems.
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
Boolean Inner product Spaces and Boolean Matrices
Gudder, Stan; Latremoliere, Frederic
2009-01-01
This article discusses the concept of Boolean spaces endowed with a Boolean valued inner product and their matrices. A natural inner product structure for the space of Boolean n-tuples is introduced. Stochastic boolean vectors and stochastic and unitary Boolean matrices are studied. A dimension theorem for orthonormal bases of a Boolean space is proven. We characterize the invariant stochastic Boolean vectors for a Boolean stochastic matrix and show that they can be used to reduce a unitary m...
Difference equation for tracking perturbations in systems of Boolean nested canalyzing functions.
Dimitrova, Elena S; Yordanov, Oleg I; Matache, Mihaela T
2015-06-01
This paper studies the spread of perturbations through networks composed of Boolean functions with special canalyzing properties. Canalyzing functions have the property that at least for one value of one of the inputs the output is fixed, irrespective of the values of the other inputs. In this paper the focus is on partially nested canalyzing functions, in which multiple, but not all inputs have this property in a cascading fashion. They naturally describe many relationships in real networks. For example, in a gene regulatory network, the statement "if gene A is expressed, then gene B is not expressed regardless of the states of other genes" implies that A is canalyzing. On the other hand, the additional statement "if gene A is not expressed, and gene C is expressed, then gene B is automatically expressed; otherwise gene B's state is determined by some other type of rule" implies that gene B is expressed by a partially nested canalyzing function with more than two variables, but with two canalyzing variables. In this paper a difference equation model of the probability that a network node's value is affected by an initial perturbation over time is developed, analyzed, and validated numerically. It is shown that the effect of a perturbation decreases towards zero over time if the Boolean functions are canalyzing in sufficiently many variables. The maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network. Percolation limits are also explored; these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied, so that the initial perturbation does not scale up with the parameters once the percolation limits are reached.
Directory of Open Access Journals (Sweden)
Yih-Lon Lin
2013-01-01
Full Text Available If the given Boolean function is linearly separable, a robust uncoupled cellular neural network can be designed as a maximal margin classifier. On the other hand, if the given Boolean function is linearly separable but has a small geometric margin or it is not linearly separable, a popular approach is to find a sequence of robust uncoupled cellular neural networks implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are restricted to assume only a given finite set of integers, and this is certainly unnecessary for the template design. In this study, we try to remove this restriction. Minterm- and maxterm-based decomposition algorithms utilizing the soft margin and maximal margin support vector classifiers are proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.
A new class of hyper-bent Boolean functions in binomial forms
Wang, Baocheng; Qi, Yanfeng; Yang, Yixian; Xu, Maozhi
2011-01-01
Bent functions, which are maximally nonlinear Boolean functions with even numbers of variables and whose Hamming distance to the set of all affine functions equals $2^{n-1}\\pm 2^{\\frac{n}{2}-1}$, were introduced by Rothaus in 1976 when he considered problems in combinatorics. Bent functions have been extensively studied due to their applications in cryptography, such as S-box, block cipher and stream cipher. Further, they have been applied to coding theory, spread spectrum and combinatorial design. Hyper-bent functions, as a special class of bent functions, were introduced by Youssef and Gong in 2001, which have stronger properties and rarer elements. Many research focus on the construction of bent and hyper-bent functions. In this paper, we consider functions defined over $\\mathbb{F}_{2^n}$ by $f_{a,b}:=\\mathrm{Tr}_{1}^{n}(ax^{(2^m-1)})+\\mathrm{Tr}_{1}^{4}(bx^{\\frac{2^n-1}{5}})$, where $n=2m$, $m\\equiv 2\\pmod 4$, $a\\in \\mathbb{F}_{2^m}$ and $b\\in\\mathbb{F}_{16}$. When $a\\in \\mathbb{F}_{2^m}$ and $(b+1)(b^4+b...
From Boolean Network Model to Continuous Model Helps in Design of Functional Circuits
Zhang, Dongliang; Wu, Jiayi; Ouyang, Qi
2015-01-01
Computational circuit design with desired functions in a living cell is a challenging task in synthetic biology. To achieve this task, numerous methods that either focus on small scale networks or use evolutionary algorithms have been developed. Here, we propose a two-step approach to facilitate the design of functional circuits. In the first step, the search space of possible topologies for target functions is reduced by reverse engineering using a Boolean network model. In the second step, continuous simulation is applied to evaluate the performance of these topologies. We demonstrate the usefulness of this method by designing an example biological function: the SOS response of E. coli. Our numerical results show that the desired function can be faithfully reproduced by candidate networks with different parameters and initial conditions. Possible circuits are ranked according to their robustness against perturbations in parameter and gene expressions. The biological network is among the candidate networks, yet novel designs can be generated. Our method provides a scalable way to design robust circuits that can achieve complex functions, and makes it possible to uncover design principles of biological networks. PMID:26061094
Determining a singleton attractor of a boolean network with nested canalyzing functions.
Akutsu, Tatsuya; Melkman, Avraham A; Tamura, Takeyuki; Yamamoto, Masaki
2011-10-01
In this article, we study the problem of finding a singleton attractor for several biologically important subclasses of Boolean networks (BNs). The problem of finding a singleton attractor in a BN is known to be NP-hard in general. For BNs consisting of n nested canalyzing functions, we present an O(1.799(n)) time algorithm. The core part of this development is an O(min(2(k/2) · 2(m/2), 2(k)) · poly(k, m)) time algorithm for the satisfiability problem for m nested canalyzing functions over k variables. For BNs consisting of chain functions, a subclass of nested canalyzing functions, we present an O(1.619(n)) time algorithm and show that the problem remains NP-hard, even though the satisfiability problem for m chain functions over k variables is solvable in polynomial time. Finally, we present an o(2(n)) time algorithm for bounded degree BNs consisting of canalyzing functions.
Cardinal invariants on Boolean algebras
Monk, J Donald
2014-01-01
This book is concerned with cardinal number valued functions defined for any Boolean algebra. Examples of such functions are independence, which assigns to each Boolean algebra the supremum of the cardinalities of its free subalgebras, and cellularity, which gives the supremum of cardinalities of sets of pairwise disjoint elements. Twenty-one such functions are studied in detail, and many more in passing. The questions considered are the behaviour of these functions under algebraic operations such as products, free products, ultraproducts, and their relationships to one another. Assuming familiarity with only the basics of Boolean algebras and set theory, through simple infinite combinatorics and forcing, the book reviews current knowledge about these functions, giving complete proofs for most facts. A special feature of the book is the attention given to open problems, of which 185 are formulated. Based on Cardinal Functions on Boolean Algebras (1990) and Cardinal Invariants on Boolean Algebras (1996) by the...
Minimal Sign Representation of Boolean Functions: Algorithms and Exact Results for Low Dimensions.
Sezener, Can Eren; Oztop, Erhan
2015-08-01
Boolean functions (BFs) are central in many fields of engineering and mathematics, such as cryptography, circuit design, and combinatorics. Moreover, they provide a simple framework for studying neural computation mechanisms of the brain. Many representation schemes for BFs exist to satisfy the needs of the domain they are used in. In neural computation, it is of interest to know how many input lines a neuron would need to represent a given BF. A common BF representation to study this is the so-called polynomial sign representation where [Formula: see text] and 1 are associated with true and false, respectively. The polynomial is treated as a real-valued function and evaluated at its parameters, and the sign of the polynomial is then taken as the function value. The number of input lines for the modeled neuron is exactly the number of terms in the polynomial. This letter investigates the minimum number of terms, that is, the minimum threshold density, that is sufficient to represent a given BF and more generally aims to find the maximum over this quantity for all BFs in a given dimension. With this work, for the first time exact results for four- and five-variable BFs are obtained, and strong bounds for six-variable BFs are derived. In addition, some connections between the sign representation framework and bent functions are derived, which are generally studied for their desirable cryptographic properties.
Realisation of all 16 Boolean logic functions in a single magnetoresistance memory cell
Gao, Shuang; Yang, Guang; Cui, Bin; Wang, Shouguo; Zeng, Fei; Song, Cheng; Pan, Feng
2016-06-01
Stateful logic circuits based on next-generation nonvolatile memories, such as magnetoresistance random access memory (MRAM), promise to break the long-standing von Neumann bottleneck in state-of-the-art data processing devices. For the successful commercialisation of stateful logic circuits, a critical step is realizing the best use of a single memory cell to perform logic functions. In this work, we propose a method for implementing all 16 Boolean logic functions in a single MRAM cell, namely a magnetoresistance (MR) unit. Based on our experimental results, we conclude that this method is applicable to any MR unit with a double-hump-like hysteresis loop, especially pseudo-spin-valve magnetic tunnel junctions with a high MR ratio. Moreover, after simply reversing the correspondence between voltage signals and output logic values, this method could also be applicable to any MR unit with a double-pit-like hysteresis loop. These results may provide a helpful solution for the final commercialisation of MRAM-based stateful logic circuits in the near future.Stateful logic circuits based on next-generation nonvolatile memories, such as magnetoresistance random access memory (MRAM), promise to break the long-standing von Neumann bottleneck in state-of-the-art data processing devices. For the successful commercialisation of stateful logic circuits, a critical step is realizing the best use of a single memory cell to perform logic functions. In this work, we propose a method for implementing all 16 Boolean logic functions in a single MRAM cell, namely a magnetoresistance (MR) unit. Based on our experimental results, we conclude that this method is applicable to any MR unit with a double-hump-like hysteresis loop, especially pseudo-spin-valve magnetic tunnel junctions with a high MR ratio. Moreover, after simply reversing the correspondence between voltage signals and output logic values, this method could also be applicable to any MR unit with a double-pit-like hysteresis
Zhang, Rui; Cavalcante, Hugo L. D. de S.; Gao, Zheng; Gauthier, Daniel J.; Socolar, Joshua E. S.; Adams, Matthew M.; Lathrop, Daniel P.
2009-01-01
We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may fin...
Boolean-Lie algebras and the Leibniz rule
Energy Technology Data Exchange (ETDEWEB)
Bazso, Fueloep [KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, PO Box 49, H-1525 Budapest (Hungary); Labos, Elemer [Neurobiology Research Group, United Research Organization of the Hungarian Academy of Sciences and Semmelweis University, H-1450 Budapest, PO Box 95 (Hungary)
2006-06-02
Using internal negations acting on Boolean functions, the notion of Boolean-Lie algebra is introduced. The underlying Lie product is the Boolean analogue of the Poisson bracket. The structure of a Boolean-Lie algebra is determined; it turns out to be solvable, but not nilpotent. We prove that the adjoint representation of an element of the Boolean-Lie algebra acts as a derivative operator on the space of Boolean functions. The adjoint representation is related to the previously known concept of the sensitivity function. Using the notion of adjoint representation we give the definition of a temporal derivative applicable to iterative dynamics of Boolean mappings.
在仿射等价类中找具有好的密码学性质的布尔函数%Find Better Boolean Functions in the Affine Equivalence Class
Institute of Scientific and Technical Information of China (English)
陈卫红; 李娜
2005-01-01
The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.
Pawlak, Tomasz P; Krawiec, Krzysztof
2017-02-16
Program semantics is a promising recent research thread in Genetic Programming (GP). Over a dozen of semantic-aware search, selection, and initialization operators for GP have been proposed to date. Some of those operators are designed to exploit the geometric properties of semantic space, while some others focus on making offspring effective, i.e., semantically different from their parents. Only a small fraction of previous works aimed at addressing both these features simultaneously. In this paper, we propose a suite of competent operators that combine effectiveness with geometry for population initialization, mate selection, mutation and crossover. We present a theoretical rationale behind these operators and compare them experimentally to operators known from literature on symbolic regression and Boolean function synthesis benchmarks. We analyze each operator in isolation as well as verify how they fare together in an evolutionary run, concluding that the competent operators are superior on a wide range of performance indicators, including best-of-run fitness, test-set fitness, and program size.
The Boolean Isomorphism problem
Energy Technology Data Exchange (ETDEWEB)
Agrawal, M. [Indian Institute of Technology, Kanpur (India); Thierauf, T. [Universitaet Ulm (Germany)
1996-12-31
We investigate the computational complexity of the Boolean Isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be {sigma}{sup p}{sub 2} complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in [BRS95]. Further properties of BI are shown: BI has And- and Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.
Reichardt, Ben W.
2009-01-01
The general adversary bound is a semi-definite program (SDP) that lower-bounds the quantum query complexity of a function. We turn this lower bound into an upper bound, by giving a quantum walk algorithm based on the dual SDP that has query complexity at most the general adversary bound, up to a logarithmic factor. In more detail, the proof has two steps, each based on "span programs," a certain linear-algebraic model of computation. First, we give an SDP that outputs for any boolean function...
Energy Technology Data Exchange (ETDEWEB)
Gupta, P.P.; Sharma, R.K.
1986-01-01
The reliability behaviour of a non-repairable parallel redundant complex system which is nothing but a power plant is investigated. The object of the system is to supply power generated by three generators from a power house to a very critical consumer, connected by cables and switches etc. The reliability of the power supply to the critical consumer has been obtained by using the Boolean Function technique. Moreover, an important parameter of reliability, viz. M.T.T.F. (mean time to failure), has also been computed for exponential failure rates of components. A numerical example with graphs has also been appended in the end to highlight the important results.
Combinatorial optimization with Boolean constraints
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.; Worrell, R.B.
1983-02-01
This report shows how Boolean algebraic formula manipulation can be used to solve certain kinds of optimization problems. If the problem can be formulated in terms of 0 to 1 variables and if the feasible solutions can be described by a Boolean equation, then the method of this report can be used. The method generates feasible solutions algebraically as terms of a disjunctive normal form of a Boolean function. Many small sample problems are solved to illustrate the method and the practical situations in which these optimization problems arise.
Boolean universes above Boolean models
Wehrung, Friedrich
1993-01-01
We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory, and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are ``boundedly algebraically compact" in the language $( + , - , . , \\wedge , \\vee , \\leq )$, and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language $( + , \\v...
Boolean analysis of addition and multiplication
Energy Technology Data Exchange (ETDEWEB)
Faltin, F. (Cornell Univ., Ithaca, NY); Metropolis, N.; Ross, B.; Rota, G.-C.
1977-01-01
The notions of binary string and binary symmetric function are introduced, and basic results presented. Boolean algorithms are given for binary addition and multiplication. An analysis of the redundancies involved is straightforward. The examination of carry propagation which arises in the Boolean analysis of functions may lead to a new interpretation of the notion of computational complexity.
Boolean integral calculus for digital systems
Tucker, J. H.; Tapia, M. A.; Bennett, A. W.
1985-01-01
The concept of Boolean integration is introduced and developed. When the changes in a desired function are specified in terms of changes in its arguments, then ways of 'integrating' (i.e., realizing) the function, if it exists, are presented. Boolean integral calculus has applications in design of logic circuits.
DÍaz, R.; Rivas, M.
2010-01-01
In order to study Boolean algebras in the category of vector spaces we introduce a prop whose algebras in set are Boolean algebras. A probabilistic logical interpretation for linear Boolean algebras is provided. An advantage of defining Boolean algebras in the linear category is that we are able to study its symmetric powers. We give explicit formulae for products in symmetric and cyclic Boolean algebras of various dimensions and formulate symmetric forms of the inclusion-exclusion principle.
THE INVERSE PROBLEM FOR BOOLEAN EQUATIONS
Directory of Open Access Journals (Sweden)
Hussain Mobarak Albarakati
2012-01-01
Full Text Available The Forward Problem (FB of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X = 0 where f(X: Bn â B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB of Boolean equations aims to reconstruct the equation f (X = 0 given the set of solutions and hence to verify the correctness of this set. This study derives methods that handle this inverse problem for the main types of solutions of Boolean equations. These include: (a Subsumptive general solutions, in which each of the variables is expressed as an interval by deriving successive conjunctive or disjunctive eliminants of the original function, (b Parametric general solutions, in which each of the variables is expressed via arbitrary parameters which are freely chosen elements of the underlying Boolean algebra and (c Particular solutions, each of which is an assignment from the underlying Boolean algebra to every pertinent variable that makes the Boolean equation an identity. The reconstructed function f(X in every case is set in a canonical form, such as the complete-sum form, to facilitate proving its equivalence to the original function. The methods presented herein are demonstrated with carefully-chosen illustrative examples over big Boolean algebras of various sizes. Among the methods utilized in handling the inverse problem for Boolean equations, the ones utilizing the variable-entered Karnaugh map offered pictorial insight and exhibited an efficient divide-and-conquer strategy.
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.
Arizmendi, Octavio
2012-01-01
We determine which Boolean stable law is freely infinitely divisible and which is not. Some positive Boolean stable laws and a mixture of them have completely monotonic densities and they are both freely and classically infinitely divisible. Freely infinitely divisible Boolean stable laws and the corresponding free stable laws are non trivial examples whose free divisibility indicators are infinity.
Semenov, Alexander; Zaikin, Oleg
2016-01-01
In this paper we propose an approach for constructing partitionings of hard variants of the Boolean satisfiability problem (SAT). Such partitionings can be used for solving corresponding SAT instances in parallel. For the same SAT instance one can construct different partitionings, each of them is a set of simplified versions of the original SAT instance. The effectiveness of an arbitrary partitioning is determined by the total time of solving of all SAT instances from it. We suggest the approach, based on the Monte Carlo method, for estimating time of processing of an arbitrary partitioning. With each partitioning we associate a point in the special finite search space. The estimation of effectiveness of the particular partitioning is the value of predictive function in the corresponding point of this space. The problem of search for an effective partitioning can be formulated as a problem of optimization of the predictive function. We use metaheuristic algorithms (simulated annealing and tabu search) to move from point to point in the search space. In our computational experiments we found partitionings for SAT instances encoding problems of inversion of some cryptographic functions. Several of these SAT instances with realistic predicted solving time were successfully solved on a computing cluster and in the volunteer computing project SAT@home. The solving time agrees well with estimations obtained by the proposed method.
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.
Research on Algebraic Immunity of Vectorial Boolean Functions%向量布尔函数代数免疫性质研究
Institute of Scientific and Technical Information of China (English)
王永娟; 孙宇
2013-01-01
By discussing the algebraic degree of the annihilators of vectorial Boolean functions, it is found that the algebraic immunity of vectorial Boolean functions remains invariant after affine transformation of the input variables. And after permutation of the output variables, the algebraic immunity also remains invariant. The relations between the Hamming weight of Component functions, the algebraic immunity, Walsh spectrum and the nonlinearity of vectorial Boolean functions were also investigated.%通过讨论向量布尔函数零化子的代数次数,对向量布尔函数的代数免疫性质进行研究,得出其置换不变性,即在输入变量作仿射变换和输出变量作置换之后仍然保持不变,并得出向量布尔函数代数免疫与线性组合函数重量、Walsh谱以及非线性度之间的关系.
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
Effect of memory in non-Markovian Boolean networks
Ebadi, Haleh; Ausloos, Marcel; Jafari, GholamReza
2016-01-01
One successful model of interacting biological systems is the Boolean network. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function, - one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of a cell cycle network, we discover a power law memory with a more robust dynamics than the Markovian dynamics.
Boolean metric spaces and Boolean algebraic varieties
Avilés, Antonio
2009-01-01
The concepts of Boolean metric space and convex combination are used to characterize polynomial maps in a class of commutative Von Neumann regular rings including Boolean rings and p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e. sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces.
On Validating Boolean Optimizers
Morgado, Antonio
2011-01-01
Boolean optimization finds a wide range of application domains, that motivated a number of different organizations of Boolean optimizers since the mid 90s. Some of the most successful approaches are based on iterative calls to an NP oracle, using either linear search, binary search or the identification of unsatisfiable sub-formulas. The increasing use of Boolean optimizers in practical settings raises the question of confidence in computed results. For example, the issue of confidence is paramount in safety critical settings. One way of increasing the confidence of the results computed by Boolean optimizers is to develop techniques for validating the results. Recent work studied the validation of Boolean optimizers based on branch-and-bound search. This paper complements existing work, and develops methods for validating Boolean optimizers that are based on iterative calls to an NP oracle. This entails implementing solutions for validating both satisfiable and unsatisfiable answers from the NP oracle. The wo...
Boolean Differentiation Equations Applicable in Reconfigurable Computational Medium
Directory of Open Access Journals (Sweden)
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.
Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity
Institute of Scientific and Technical Information of China (English)
Sen-Shan Pan; Xiao-Tong Fu; Wei-Guo Zhangx
2011-01-01
This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler's upper bound of algebraic degree. Also a class of 1-resilient functions on any number n ＞ 2 of variables with at least sub-optimal algebraic immunity is provided.
Symmetry in critical random Boolean network dynamics
Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Symmetry in critical random Boolean network dynamics.
Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
On Boolean matrices with full factor rank
Energy Technology Data Exchange (ETDEWEB)
Shitov, Ya [National Research University " Higher School of Economics" , Moscow (Russian Federation)
2013-11-30
It is demonstrated that every (0,1)-matrix of size n×m having Boolean rank n contains a column with at least √n/2−1 zero entries. This bound is shown to be asymptotically optimal. As a corollary, it is established that the size of a full-rank Boolean matrix is bounded from above by a function of its tropical and determinantal ranks. Bibliography: 16 titles.
Testing Booleanity and the Uncertainty Principle
Gur, Tom
2012-01-01
Let f:{-1,1}^n -> R be a real function on the hypercube, given by its discrete Fourier expansion, or, equivalently, represented as a multilinear polynomial. We say that it is Boolean if its image is in {-1,1}. We show that every function on the hypercube with a sparse Fourier expansion must either be Boolean or far from Boolean. In particular, we show that a multilinear polynomial with at most k terms must either be Boolean, or output values different than -1 or 1 for a fraction of at least 2/(k+2)^2 of its domain. It follows that given black box access to f, together with the guarantee that its representation as a multilinear polynomial has at most k terms, one can test Booleanity using O(k^2) queries. We show an Omega(k) queries lower bound for this problem. We also consider the problem of deciding if a function is Boolean, given its explicit representation as a k term multilinear polynomial. The naive approach of evaluating it at every input has O(kn2^n) time complexity. For large k (i.e, exponential) we p...
Combinational Logic-Level Verification using Boolean Expression Diagrams
DEFF Research Database (Denmark)
Hulgaard, Henrik; Williams, Poul Frederick; Andersen, Henrik Reif
1997-01-01
Boolean Expression Diagrams (BEDs) is a new data structure for representing and manipulating Boolean functions. BEDs are a generalization of Binary Decision Diagrams (BDDs) that are capable of representing any Boolean circuit in linear space and still maintain many of the desirable properties...... of BDDs. This paper demonstrates that BEDs are well suited for solving the combinational logic-level verification problem which is, given two combinational circuits, to determine whether they implement the same Boolean functions. Based on all combinational circuits in the ISCAS 85 and LGSynth 91...
Institute of Scientific and Technical Information of China (English)
刘叙华; 邓安生
1994-01-01
A new approach of operator fuzzy logic, Boolean operator fuzzy logic (BOFL) based on Boolean algebra, is presented. The resolution principle is also introduced into BOFL. BOFL is a natural generalization of classical logic and can be applied to the qualitative description of fuzzy knowledge.
Tight omega(loglogn)-bound on the time for parallel RAMs to compute nondegenerated Boolean functions
Energy Technology Data Exchange (ETDEWEB)
Simon, H.U.
1982-10-01
A function f:(0,1)/sup n/=(0,1) is said to depend on dimension i iff there exists an input vector x such that f(x) differs from f(x/sup i/), where x/sup i/ agrees with x in every dimension except i. In this case x is said to be critical for f with respect to i. Function f is called nondegenerated iff it depends on all n dimensions. The main result of this paper is that for each nondegenerated function f:(0,1)/sup n/=(0,1) there exists an input vector x which is critical with respect to at least omega(log n) dimensions. A function achieving this bound is presented. Together with earlier results from Cook and Dwork (Proceedings, 14th ACM Symp. On Theory of Computing, 1982) and Reischuk (IBM Research Report, no.Rj 3431, 1982) it can be concluded that a parallel RAM requires at least omega(loglog n) steps to compute f. 3 references.
Ohta, Naoyuki; Waki, Kana; Mochizuki, Atsushi; Satou, Yutaka
2015-12-01
A complex system of multiple signaling molecules often produce differential gene expression patterns in animal embryos. In the ascidian embryo, four signaling ligands, Ephrin-A.d (Efna.d), Fgf9/16/20, Admp, and Gdf1/3-r, coordinately induce Otx expression in the neural lineage at the 32-cell stage. However, it has not been determined whether differential inputs of all of these signaling pathways are really necessary. It is possible that differential activation of one of these signaling pathways is sufficient and the remaining signaling pathways are activated in all cells at similar levels. To address this question, we developed a parameter-free method for determining a Boolean function for Otx expression in the present study. We treated activities of signaling pathways as Boolean values, and we also took all possible patterns of signaling gradients into consideration. We successfully determined a Boolean function that explains Otx expression in the animal hemisphere of wild-type and morphant embryos at the 32-cell stage. This Boolean function was not inconsistent with three sensing patterns, which represented whether or not individual cells received sufficient amounts of the signaling molecules. These sensing patterns all indicated that differential expression of Otx in the neural lineage is primarily determined by Efna.d, but not by differential inputs of Fgf9/16/20, Admp, and Gdf1/3-r signaling. To confirm this hypothesis experimentally, we simultaneously knocked-down Admp, Gdf1/3-r, and Fgf9/16/20, and treated this triple morphant with recombinant bFGF and BMP4 proteins, which mimic Fgf9/16/20 and Admp/Gdf1/3-r activity, respectively. Although no differential inputs of Admp, Gdf1/3-r and Fgf9/16/20 signaling were expected under this experimental condition, Otx was expressed specifically in the neural lineage. Thus, direct cell-cell interactions through Efna.d play a critical role in patterning the ectoderm of the early ascidian embryo.
广义Boolean-like环%Generalized Boolean-like Rings
Institute of Scientific and Technical Information of China (English)
秦蕊
2013-01-01
广义Boolean-like环是Boolean-like环的一个推广,文章主要介绍了广义Boolean-like环的构建,从而列举了若干广义Boolean-like环的相关例子及基本性质.并且,考虑了广义Boolean-like环的部分扩张,如上三角矩阵环.
Computing the Algebraic Immunity of Boolean Functions on the SRC-6 Reconfigurable Computer
2012-03-01
between the truth table form of the function and its algebraic normal form. The first known Verilog implementation of a reduced transeunt triangle was... Verilog , Algebraic Attack 15. NUMBER OF PAGES 172 16. PRICE CODE 17. SECURITY CLASSIFICATION OF REPORT Unclassified 18. SECURITY...The first known Verilog implementation of a reduced transeunt triangle was developed for this conversion. This reduced form requires many fewer
Reconstructing Boolean Models of Signaling
Karp, Richard M.
2013-01-01
Abstract Since the first emergence of protein–protein interaction networks more than a decade ago, they have been viewed as static scaffolds of the signaling–regulatory events taking place in cells, and their analysis has been mainly confined to topological aspects. Recently, functional models of these networks have been suggested, ranging from Boolean to constraint-based methods. However, learning such models from large-scale data remains a formidable task, and most modeling approaches rely on extensive human curation. Here we provide a generic approach to learning Boolean models automatically from data. We apply our approach to growth and inflammatory signaling systems in humans and show how the learning phase can improve the fit of the model to experimental data, remove spurious interactions, and lead to better understanding of the system at hand. PMID:23286509
Metzler, S; Miettinen, P
2015-01-01
Tensor factorizations are computationally hard problems, and in particular, are often significantly harder than their matrix counterparts. In case of Boolean tensor factorizations -- where the input tensor and all the factors are required to be binary and we use Boolean algebra -- much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences doe...
Symmetry in Critical Random Boolean Networks Dynamics
Bassler, Kevin E.; Hossein, Shabnam
2014-03-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used to both greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. Classes of functions occur at the same frequency. These classes are orbits of the controlling symmetry group. We find the nature of the symmetry that controls the dynamics of critical random Boolean networks by determining the frequency of output functions utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using symmetry to characterize complex network dynamics, and introduce a novel approach to the analysis of heterogeneous complex systems. This work was supported by the NSF through grants DMR-0908286 and DMR-1206839, and by the AFSOR and DARPA through grant FA9550-12-1-0405.
Boolean differentiation and integration using Karnaugh maps
Tucker, J. H.; Tapia, M. A.; Bennett, A. W.
1977-01-01
Algorithms are presented for differentiation and integration of Boolean functions by means of Karnaugh maps. The algorithms are considered simple when the number of variables is six or less; in this case Boolean differentiation and integration is said to be as easy as the Karnaugh map method of simplifying switching functions. It is suggested that the algorithms would be useful in the analysis of faults in combinational systems and in the synthesis of asynchronous sequential systems which utilize edge-sensitive flip-flops.
On diamond-free subposets of the Boolean lattice
Kramer, Lucas; Young, Michael
2012-01-01
The Boolean lattice of dimension two, also known as the diamond, consists of four distinct elements with the following property: $A\\subset B,C\\subset D$. A diamond-free family in the $n$-dimensional Boolean lattice is a subposet such that no four elements form a diamond. Note that elements $B$ and $C$ may or may not be related. There is a diamond-free family in the $n$-dimensional Boolean lattice of size $(2-o(1)){n\\choose\\lfloor n/2\\rfloor}$. In this paper, we prove that any diamond-free family in the $n$-dimensional Boolean lattice has size at most $(2.25+o(1)){n\\choose\\lfloor n/2\\rfloor}$. Furthermore, we show that the so-called Lubell function of a diamond-free family in the $n$-dimensional Boolean lattice is at most $2.25+o(1)$, which is asympotically best possible.
Inferring Boolean network states from partial information
2013-01-01
Networks of molecular interactions regulate key processes in living cells. Therefore, understanding their functionality is a high priority in advancing biological knowledge. Boolean networks are often used to describe cellular networks mathematically and are fitted to experimental datasets. The fitting often results in ambiguities since the interpretation of the measurements is not straightforward and since the data contain noise. In order to facilitate a more reliable mapping between datasets and Boolean networks, we develop an algorithm that infers network trajectories from a dataset distorted by noise. We analyze our algorithm theoretically and demonstrate its accuracy using simulation and microarray expression data. PMID:24006954
Nearly projective Boolean algebras
Heindorf, Lutz; Shapiro, Leonid B
1994-01-01
The book is a fairly complete and up-to-date survey of projectivity and its generalizations in the class of Boolean algebras. Although algebra adds its own methods and questions, many of the results presented were first proved by topologists in the more general setting of (not necessarily zero-dimensional) compact spaces. An appendix demonstrates the application of advanced set-theoretic methods to the field. The intended readers are Boolean and universal algebraists. The book will also be useful for general topologists wanting to learn about kappa-metrizable spaces and related classes. The text is practically self-contained but assumes experience with the basic concepts and techniques of Boolean algebras.
Berg, van den, Aad; Meester, R.; White, Damien
1997-01-01
Consider an ordinary Boolean model, that is, a homogeneous Poisson point process in Rd, where the points are all centres of random balls with i.i.d. radii. Now let these points move around according to i.i.d. stochastic processes. It is not hard to show that at each xed time t we again have a Boolean model with the original distribution. Hence if the original model is supercritical then, for any t, the probability of having an unbounded occupied component at time t equals 1. We show that unde...
Boolean networks with reliable dynamics
Peixoto, Tiago P
2009-01-01
We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks, and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occur, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen...
Quantum Boolean image denoising
Mastriani, Mario
2015-05-01
A quantum Boolean image processing methodology is presented in this work, with special emphasis in image denoising. A new approach for internal image representation is outlined together with two new interfaces: classical to quantum and quantum to classical. The new quantum Boolean image denoising called quantum Boolean mean filter works with computational basis states (CBS), exclusively. To achieve this, we first decompose the image into its three color components, i.e., red, green and blue. Then, we get the bitplanes for each color, e.g., 8 bits per pixel, i.e., 8 bitplanes per color. From now on, we will work with the bitplane corresponding to the most significant bit (MSB) of each color, exclusive manner. After a classical-to-quantum interface (which includes a classical inverter), we have a quantum Boolean version of the image within the quantum machine. This methodology allows us to avoid the problem of quantum measurement, which alters the results of the measured except in the case of CBS. Said so far is extended to quantum algorithms outside image processing too. After filtering of the inverted version of MSB (inside quantum machine), the result passes through a quantum-classical interface (which involves another classical inverter) and then proceeds to reassemble each color component and finally the ending filtered image. Finally, we discuss the more appropriate metrics for image denoising in a set of experimental results.
Formalization of Human Categorization Process Using Interpolative Boolean Algebra
Directory of Open Access Journals (Sweden)
Vladimir Dobrić
2015-01-01
Full Text Available Since the ancient times, it has been assumed that categorization has the basic form of classical sets. This implies that the categorization process rests on the Boolean laws. In the second half of the twentieth century, the classical theory has been challenged in cognitive science. According to the prototype theory, objects belong to categories with intensities, while humans categorize objects by comparing them to prototypes of relevant categories. Such categorization process is governed by the principles of perceived world structure and cognitive economy. Approaching the prototype theory by using truth-functional fuzzy logic has been harshly criticized due to not satisfying the complementation laws. In this paper, the prototype theory is approached by using structure-functional fuzzy logic, the interpolative Boolean algebra. The proposed formalism is within the Boolean frame. Categories are represented as fuzzy sets of objects, while comparisons between objects and prototypes are formalized by using Boolean consistent fuzzy relations. Such relations are directly constructed from a Boolean consistent fuzzy partial order relation, which is treated by Boolean implication. The introduced formalism secures the principles of categorization showing that Boolean laws are fundamental in the categorization process. For illustration purposes, the artificial cognitive system which mimics human categorization activity is proposed.
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}.
Boolean approach to zero-one linear programming
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.; Baca, L.S.
1984-07-01
Problems of minimizing or maximizing a linear objective function in zero-one variables subject to linear constraints can be solved by Boolean algebraic methods. This report gives both a general procedure for stating such problems in Boolean form and a solution procedure that has been implemented by a SETS user program. The program uses the Boolean algebraic formula manipulation techniques of the SETS language. Sample problems illustrate how to make optimum choices in the contexts of physical protection, packing knapsacks, designing manufacturing processes and making assignments.
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...
On Nega-Hadamard transform of Boolean functions%布尔函数的 Nega-Hada mard变换研究
Institute of Scientific and Technical Information of China (English)
卓泽朋; 崇金凤; 魏仕民; 余磊
2015-01-01
利用Nega-Hadamard变换的性质，研究了bent函数与其对偶函数Nega-Hadamard变换的关系，得出bent函数为negabent函数，其对偶函数也是negabent函数的结果；同时，得到了布尔函数在某个仿射子空间上Nega-Hadamard变换的性质；研究了布尔函数的导数与它的二进制移位关于Nega-Hadamard变换的关系。%By using the properties of Nega-Hadamard transform,this paper studied the relationship between bent function and its dual in the Nega-Hadamard transform.It showed that if bent function was a negabent,then its dual was again negabent. Also,it obtained the property of the Nega-Hadamard transform of Boolean function fin some affine subspace.At last,it pro-vided the relationship between the Nega-Hadamard transforms of the derivatives of fand the dyadic shifts.
Discrete interference modeling via boolean algebra.
Beckhoff, Gerhard
2011-01-01
Two types of boolean functions are considered, the locus function of n variables, and the interval function of ν = n - 1 variables. A 1-1 mapping is given that takes elements (cells) of the interval function to antidual pairs of elements in the locus function, and vice versa. A set of ν binary codewords representing the intervals are defined and used to generate the codewords of all genomic regions. Next a diallelic three-point system is reviewed in the light of boolean functions, which leads to redefining complete interference by a logic function. Together with the upper bound of noninterference already defined by a boolean function, it confines the region of interference. Extensions of these two functions to any finite number of ν are straightforward, but have been also made in terms of variables taken from the inclusion-exclusion principle (expressing "at least" and "exactly equal to" a decimal integer). Two coefficients of coincidence for systems with more than three loci are defined and discussed, one using the average of several individual coefficients and the other taking as coefficient a real number between zero and one. Finally, by way of a malfunction of the mod-2 addition, it is shown that a four-point system may produce two different functions, one of which exhibiting loss of a class of odd recombinants.
Institute of Scientific and Technical Information of China (English)
Antonio AIZPURU; Antonio GUTI(E)RREZ-D(A)VILA
2004-01-01
In this paper we will study some families and subalgebras ( ) of ( )(N) that let us characterize the unconditional convergence of series through the weak convergence of subseries ∑i∈A xi, A ∈ ( ).As a consequence, we obtain a new version of the Orlicz-Pettis theorem, for Banach spaces. We also study some relationships between algebraic properties of Boolean algebras and topological properties of the corresponding Stone spaces.
Fault Tolerant Boolean Satisfiability
Roy, A
2011-01-01
A delta-model is a satisfying assignment of a Boolean formula for which any small alteration, such as a single bit flip, can be repaired by flips to some small number of other bits, yielding a new satisfying assignment. These satisfying assignments represent robust solutions to optimization problems (e.g., scheduling) where it is possible to recover from unforeseen events (e.g., a resource becoming unavailable). The concept of delta-models was introduced by Ginsberg, Parkes and Roy (AAAI 1998), where it was proved that finding delta-models for general Boolean formulas is NP-complete. In this paper, we extend that result by studying the complexity of finding delta-models for classes of Boolean formulas which are known to have polynomial time satisfiability solvers. In particular, we examine 2-SAT, Horn-SAT, Affine-SAT, dual-Horn-SAT, 0-valid and 1-valid SAT. We see a wide variation in the complexity of finding delta-models, e.g., while 2-SAT and Affine-SAT have polynomial time tests for delta-models, testing w...
J-Boolean like环%J-Boolean Like Ring
Institute of Scientific and Technical Information of China (English)
秦蕊
2013-01-01
本文首先引进了Boolean-like环的一类新的扩张J-Boolean like环,即对任意环R中元素a,b都有(a-a2)(b-b2)∈J(R),这里J(R)为环R的Jacobson根,则环R称为J-Boolean like环.证明了两个定理分别为(1)设D是一个环,C是D的一个子环,R[D,C]是一个J-Boolean like环(=)(a)C,D是J-Boolean like环,(b)J2(C)(∈)J(D).(2)如果B/J(B)是Boolean环,并且B[i]={a+bi| i2=ui+η,a,b,u,η∈B},那么B[i]是J-Booleanlike环当且仅当uη∈J(B).
Adjunctions between Boolean spaces and skew Boolean algebras
Kudryavtseva, Ganna
2011-01-01
We apply the representation theory of left-handed skew Boolean algebras by sections of their dual \\'{e}tale spaces, given in \\cite{K}, to construct a series of dual adjunctions between the categories of locally compact Boolean spaces and left-handed skew Boolean algebras by means of extensions of certain enriched $\\Hom$-set functors induced by objects sitting in two categories. The constructed adjunctions are "deformations" of Stone duality obtained by the replacement in the latter of the category of Boolean algebras by the category of left-handed skew Boolean algebras. The constructions provide natural settings for the $\\omega$-functor constructed in \\cite{LS} and its left adjoint functor.
Classical Boolean logic gates with quantum systems
Energy Technology Data Exchange (ETDEWEB)
Renaud, N; Joachim, C, E-mail: n-renaud@northwestern.edu [Nanoscience Group and MANA Satellite CEMES/CNRS, 29 rue J Marvig, BP 94347, 31055 Toulouse Cedex (France)
2011-04-15
An analytical method is proposed to implement any classical Boolean function in a small quantum system by taking the advantage of its electronic transport properties. The logical input, {alpha} = {l_brace}{alpha}{sub 1}, ..., {alpha}{sub N}{r_brace}, is used to control well-identified parameters of the Hamiltonian of the system noted H{sub 0}({alpha}). The logical output is encoded in the tunneling current intensity passing through the quantum system when connected to conducting electrodes. It is demonstrated how to implement the six symmetric two-input/one-output Boolean functions in a quantum system. This system can be switched from one logic function to another by changing its structural parameters. The stability of the logic gates is discussed, perturbing the Hamiltonian with noise sources and studying the effect of decoherence.
Approximate Reasoning with Fuzzy Booleans
Broek, van den P.M.; Noppen, J.A.R.
2004-01-01
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 ante
Identifying a Probabilistic Boolean Threshold Network From Samples.
Melkman, Avraham A; Cheng, Xiaoqing; Ching, Wai-Ki; Akutsu, Tatsuya
2017-01-25
This paper studies the problem of exactly identifying the structure of a probabilistic Boolean network (PBN) from a given set of samples, where PBNs are probabilistic extensions of Boolean networks. Cheng et al. studied the problem while focusing on PBNs consisting of pairs of AND/OR functions. This paper considers PBNs consisting of Boolean threshold functions while focusing on those threshold functions that have unit coefficients. The treatment of Boolean threshold functions, and triplets and n-tuplets of such functions, necessitates a deepening of the theoretical analyses. It is shown that wide classes of PBNs with such threshold functions can be exactly identified from samples under reasonable constraints, which include: 1) PBNs in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2) PBNs consisting of pairs of threshold functions with different numbers of input variables. It is also shown that the problem of deciding the equivalence of two Boolean threshold functions is solvable in pseudopolynomial time but remains co-NP complete.
The Influence of Canalization on the Robustness of Boolean Networks
Kadelka, Claus; Laubenbacher, Reinhard
2016-01-01
Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by $k$-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to $c$-sensitivity and provides formulas for the activities and $c$-sensitivity of general $k$-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the $c$-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally eff...
optPBN: An Optimisation Toolbox for Probabilistic Boolean Networks
Trairatphisan, Panuwat; Mizera, Andrzej; Pang, Jun; Tantar, Alexandru Adrian; Sauter, Thomas
2014-01-01
Background There exist several computational tools which allow for the optimisation and inference of biological networks using a Boolean formalism. Nevertheless, the results from such tools yield only limited quantitative insights into the complexity of biological systems because of the inherited qualitative nature of Boolean networks. Results We introduce optPBN, a Matlab-based toolbox for the optimisation of probabilistic Boolean networks (PBN) which operates under the framework of the BN/PBN toolbox. optPBN offers an easy generation of probabilistic Boolean networks from rule-based Boolean model specification and it allows for flexible measurement data integration from multiple experiments. Subsequently, optPBN generates integrated optimisation problems which can be solved by various optimisers. In term of functionalities, optPBN allows for the construction of a probabilistic Boolean network from a given set of potential constitutive Boolean networks by optimising the selection probabilities for these networks so that the resulting PBN fits experimental data. Furthermore, the optPBN pipeline can also be operated on large-scale computational platforms to solve complex optimisation problems. Apart from exemplary case studies which we correctly inferred the original network, we also successfully applied optPBN to study a large-scale Boolean model of apoptosis where it allows identifying the inverse correlation between UVB irradiation, NFκB and Caspase 3 activations, and apoptosis in primary hepatocytes quantitatively. Also, the results from optPBN help elucidating the relevancy of crosstalk interactions in the apoptotic network. Summary The optPBN toolbox provides a simple yet comprehensive pipeline for integrated optimisation problem generation in the PBN formalism that can readily be solved by various optimisers on local or grid-based computational platforms. optPBN can be further applied to various biological studies such as the inference of gene regulatory
Uezu, Tatsuya; Kiyokawa, Shuji
2016-06-01
We investigate the supervised batch learning of Boolean functions expressed by a two-layer perceptron with a tree-like structure. We adopt continuous weights (spherical model) and the Gibbs algorithm. We study the Parity and And machines and two types of noise, input and output noise, together with the noiseless case. We assume that only the teacher suffers from noise. By using the replica method, we derive the saddle point equations for order parameters under the replica symmetric (RS) ansatz. We study the critical value αC of the loading rate α above which the learning phase exists for cases with and without noise. We find that αC is nonzero for the Parity machine, while it is zero for the And machine. We derive the exponents barβ of order parameters expressed as (α - α C)bar{β} when α is near to αC. Furthermore, in the Parity machine, when noise exists, we find a spin glass solution, in which the overlap between the teacher and student vectors is zero but that between student vectors is nonzero. We perform Markov chain Monte Carlo simulations by simulated annealing and also by exchange Monte Carlo simulations in both machines. In the Parity machine, we study the de Almeida-Thouless stability, and by comparing theoretical and numerical results, we find that there exist parameter regions where the RS solution is unstable, and that the spin glass solution is metastable or unstable. We also study asymptotic learning behavior for large α and derive the exponents hat{β } of order parameters expressed as α - hat{β } when α is large in both machines. By simulated annealing simulations, we confirm these results and conclude that learning takes place for the input noise case with any noise amplitude and for the output noise case when the probability that the teacher's output is reversed is less than one-half.
Energy and criticality in random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Andrecut, M. [Institute for Biocomplexity and Informatics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada)], E-mail: mandrecu@ucalgary.ca; Kauffman, S.A. [Institute for Biocomplexity and Informatics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, T2N 1N4 (Canada)
2008-06-30
The central issue of the research on the Random Boolean Networks (RBNs) model is the characterization of the critical transition between ordered and chaotic phases. Here, we discuss an approach based on the 'energy' associated with the unsatisfiability of the Boolean functions in the RBNs model, which provides an upper bound estimation for the energy used in computation. We show that in the ordered phase the RBNs are in a 'dissipative' regime, performing mostly 'downhill' moves on the 'energy' landscape. Also, we show that in the disordered phase the RBNs have to 'hillclimb' on the 'energy' landscape in order to perform computation. The analytical results, obtained using Derrida's approximation method, are in complete agreement with numerical simulations.
Ebadi, H.; Saeedian, M.; Ausloos, M.; Jafari, G. R.
2016-11-01
The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function —one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.
On the robustness of random Boolean formulae
Energy Technology Data Exchange (ETDEWEB)
Mozeika, Alexander; Saad, David [Non-linearity and Complexity Research Group, Aston University, Birmingham B4 7ET (United Kingdom); Raymond, Jack, E-mail: a.s.mozeika@aston.ac.u, E-mail: d.saad@aston.ac.u [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay (Hong Kong)
2010-06-01
Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models.
Improved Time Complexities for Learning Boolean Networks
Directory of Open Access Journals (Sweden)
Chee Keong Kwoh
2013-09-01
Full Text Available Existing algorithms for learning Boolean networks (BNs have time complexities of at least O(N · n0:7(k+1, where n is the number of variables, N is the number of samples and k is the number of inputs in Boolean functions. Some recent studies propose more efficient methods with O(N · n2 time complexities. However, these methods can only be used to learn monotonic BNs, and their performances are not satisfactory when the sample size is small. In this paper, we mathematically prove that OR/AND BNs, where the variables are related with logical OR/AND operations, can be found with the time complexity of O(k·(N+ logn·n2, if there are enough noiseless training samples randomly generated from a uniform distribution. We also demonstrate that our method can successfully learn most BNs, whose variables are not related with exclusive OR and Boolean equality operations, with the same order of time complexity for learning OR/AND BNs, indicating our method has good efficiency for learning general BNs other than monotonic BNs. When the datasets are noisy, our method can still successfully identify most BNs with the same efficiency. When compared with two existing methods with the same settings, our method achieves a better comprehensive performance than both of them, especially for small training sample sizes. More importantly, our method can be used to learn all BNs. However, of the two methods that are compared, one can only be used to learn monotonic BNs, and the other one has a much worse time complexity than our method. In conclusion, our results demonstrate that Boolean networks can be learned with improved time complexities.
Reaction-contingency based bipartite Boolean modelling
2013-01-01
Background Intracellular signalling systems are highly complex, rendering mathematical modelling of large signalling networks infeasible or impractical. Boolean modelling provides one feasible approach to whole-network modelling, but at the cost of dequantification and decontextualisation of activation. That is, these models cannot distinguish between different downstream roles played by the same component activated in different contexts. Results Here, we address this with a bipartite Boolean modelling approach. Briefly, we use a state oriented approach with separate update rules based on reactions and contingencies. This approach retains contextual activation information and distinguishes distinct signals passing through a single component. Furthermore, we integrate this approach in the rxncon framework to support automatic model generation and iterative model definition and validation. We benchmark this method with the previously mapped MAP kinase network in yeast, showing that minor adjustments suffice to produce a functional network description. Conclusions Taken together, we (i) present a bipartite Boolean modelling approach that retains contextual activation information, (ii) provide software support for automatic model generation, visualisation and simulation, and (iii) demonstrate its use for iterative model generation and validation. PMID:23835289
Computing preimages of Boolean networks
2013-01-01
In this paper we present an algorithm based on the sum-product algorithm that finds elements in the preimage of a feed-forward Boolean networks given an output of the network. Our probabilistic method runs in linear time with respect to the number of nodes in the network. We evaluate our algorithm for randomly constructed Boolean networks and a regulatory network of Escherichia coli and found that it gives a valid solution in most cases. PMID:24267277
A complexity theory based on Boolean algebra
DEFF Research Database (Denmark)
Skyum, Sven; Valiant, Leslie
1985-01-01
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.......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...
Boolean Searches--A Life Skill.
Ala, Judy; Cerabona, Kathy
1992-01-01
Discusses the importance of Boolean searching as a skill that students will need in the future. Methods for teaching Boolean searching are described, and the value of truncation as an online searching aid is considered. (MES)
Boolean networks with multiexpressions and parameters.
Zou, Yi Ming
2013-01-01
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic-based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.
Generalized periodic and generalized Boolean rings
Directory of Open Access Journals (Sweden)
Howard E. Bell
2001-01-01
Full Text Available We prove that a generalized periodic, as well as a generalized Boolean, ring is either commutative or periodic. We also prove that a generalized Boolean ring with central idempotents must be nil or commutative. We further consider conditions which imply the commutativity of a generalized periodic, or a generalized Boolean, ring.
Testing Properties of Boolean Functions
2012-01-01
01. (10.1) We will in fact prove a stronger statement. To understand it, let’s reconsider the com- plete random processes Pyes and Pno by which the...process Pno is very similar, differing only in the way it generates the argu- ment multiset from the query matrix. Recalling the definition of Fno, we...think of Pno as forming the argument multiset Sno by choosing ` = k − e random columns from Q 103 without replacement, and including an additional e
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 each player is the same as the work needed to compute the circuit in the clear, up to a constant factor. Our protocol is the first to obtain these properties for Boolean circuits. On the technical side, we develop new homomorphic authentication schemes based on asymptotically good codes...... 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....
Piecewise linear and Boolean models of chemical reaction networks.
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-12-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions ([Formula: see text]). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent [Formula: see text] is large. However, while the case of small constant [Formula: see text] appears in practice, it is not well understood. We provide a mathematical analysis of this limit and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed-form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator.
Constant-overhead secure computation of Boolean circuits using preprocessing
DEFF Research Database (Denmark)
Damgård, Ivan Bjerre; Zakarias, S.
2013-01-01
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 a preprocessing functionality that is not given the inputs. For a large number of players the work for each player is the same...... as computing the circuit in the clear, up to a constant factor. Our protocol is the first to obtain these properties for Boolean circuits. On the technical side, we develop new homomorphic authentication schemes based on asymptotically good codes 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 only achieved constant error....
Piecewise linear and Boolean models of chemical reaction networks
Veliz-Cuba, Alan; Kumar, Ajit; Josić, Krešimir
2014-01-01
Models of biochemical networks are frequently complex and high-dimensional. Reduction methods that preserve important dynamical properties are therefore essential for their study. Interactions in biochemical networks are frequently modeled using Hill functions (xn/(Jn + xn)). Reduced ODEs and Boolean approximations of such model networks have been studied extensively when the exponent n is large. However, while the case of small constant J appears in practice, it is not well understood. We provide a mathematical analysis of this limit, and show that a reduction to a set of piecewise linear ODEs and Boolean networks can be mathematically justified. The piecewise linear systems have closed form solutions that closely track those of the fully nonlinear model. The simpler, Boolean network can be used to study the qualitative behavior of the original system. We justify the reduction using geometric singular perturbation theory and compact convergence, and illustrate the results in network models of a toggle switch and an oscillator. PMID:25412739
Partial stability and stabilisation of Boolean networks
Chen, Hong-Wei; Sun, Liang-Jie; Liu, Yang
2016-07-01
In this paper, we investigate the stability of Boolean networks and the stabilisation of Boolean control networks with respect to part of the system's states. First, an algebraic expression of the Boolean (control) network is derived by the semi-tensor product of matrices. Then, some necessary and sufficient conditions for partial stability of Boolean networks are given. Finally, the stabilisation of Boolean control networks by a free control sequence and a state-feedback control is investigated and the respective necessary and sufficient conditions are obtained. Examples are provided to illustrate the efficiency of the obtained results.
Synchronization of Asynchronous Switched Boolean Network.
Zhang, Hao; Wang, Xingyuan; Lin, Xiaohui
2015-01-01
In this paper, the complete synchronizations for asynchronous switched Boolean network with free Boolean sequence controllers and close-loop controllers are studied. First, the basic asynchronous switched Boolean network model is provided. With the method of semi-tensor product, the Boolean dynamics is translated into linear representation. Second, necessary and sufficient conditions for ASBN synchronization with free Boolean sequence control and close-loop control are derived, respectively. Third, some illustrative examples are provided to show the efficiency of the proposed methods.
Boolean Operations on Conic Polygons
Institute of Scientific and Technical Information of China (English)
Yong-Xi Gong; Yu Liu; Lun Wu; Yu-Bo Xie
2009-01-01
An algorithm for Boolean operations on conic polygons is proposed. Conic polygons are polygons consisting of conic segments or bounded conics with directions. Preliminaries of Boolean operations on general polygons are presented. In our algorithm, the intersection points and the topological relationships between two conic polygons are computed. Boundaries are obtained by tracking path and selecting uncrossed boundaries following rule tables to build resulting conic polygons.We define a set of rules for the intersection, union, and subtraction operations on conic polygons. The algorithm considers degeneration cases such as homology, complement, interior, and exterior. The algorithm is also evaluated and implemented.
Sublogarithmic uniform Boolean proof nets
Aubert, Clément
2012-01-01
Using a proofs-as-programs correspondence, Terui was able to compare two models of parallel computation: Boolean circuits and proof nets for multiplicative linear logic. Mogbil et. al. gave a logspace translation allowing us to compare their computational power as uniform complexity classes. This paper presents a novel translation in AC0 and focuses on a simpler restricted notion of uniform Boolean proof nets. We can then encode constant-depth circuits and compare complexity classes below logspace, which were out of reach with the previous translations.
Unlimited multistability and Boolean logic in microbial signalling
DEFF Research Database (Denmark)
Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca;
2015-01-01
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...
Improving the User Query for the Boolean Model Using Genetic Algorithms
Nassar, Mohammad Othman; Mashagba, Eman Al
2011-01-01
The Use of genetic algorithms in the Information retrieval (IR) area, especially in optimizing a user query in Arabic data collections is presented in this paper. Very little research has been carried out on Arabic text collections. Boolean model have been used in this research. To optimize the query using GA we used different fitness functions, different mutation strategies to find which is the best strategy and fitness function that can be used with Boolean model when the data collection is the Arabic language. Our results show that the best GA strategy for the Boolean model is the GA (M2, Precision) method.
Mental Models of Boolean Concepts
Goodwin, Geoffrey P.; Johnson-Laird, P. N.
2011-01-01
Negation, conjunction, and disjunction are major building blocks in the formation of concepts. This article presents a new model-based theory of these Boolean components. It predicts that individuals simplify the models of instances of concepts. Evidence corroborates the theory and challenges alternative accounts, such as those based on minimal…
从布尔代数到布尔微积分%From Boolean algebra to Boolean calculus
Institute of Scientific and Technical Information of China (English)
程代展; 赵寅; 徐相如
2011-01-01
布尔函数作为最简单的有限值函数具有特殊的重要性．它在包括信息、控制等许多领域有着广泛的应用．本文综合介绍有关布尔函数的理论基础．包括从布尔代数到布尔微积分的主要理论结果，它们在信息与控制中的一些重要应用，以及其前沿动态与新进展．介绍的一个重点是矩阵半张量积在这些领域的应用．%Boolean functions are of special importance, though they are the simplest class of finite-valued functions. It is widely applied to many fields, including information, control and so on. The theoretical foundation of Boolean functions is introduced in this paper, involving some main results from Boolean algebra to Boolean Calculus, applications in information and control and some recent frontiers and developments. The semi-tensor product approach to these fields is introduced emohaticallv.
Profiling of genetic switches using boolean implications in expression data.
Çakır, Mehmet Volkan; Binder, Hans; Wirth, Henry
2014-01-01
Correlation analysis assuming coexpression of the genes is a widely used method for gene expression analysis in molecular biology. Yet growing extent, quality and dimensionality of the molecular biological data permits emerging, more sophisticated approaches like Boolean implications. We present an approach which is a combination of the SOM (self organizing maps) machine learning method and Boolean implication analysis to identify relations between genes, metagenes and similarly behaving metagene groups (spots). Our method provides a way to assign Boolean states to genes/metagenes/spots and offers a functional view over significantly variant elements of gene expression data on these three different levels. While being able to cover relations between weakly correlated entities Boolean implication method also decomposes these relations into six implication classes. Our method allows one to validate or identify potential relationships between genes and functional modules of interest and to assess their switching behaviour. Furthermore the output of the method renders it possible to construct and study the network of genes. By providing logical implications as updating rules for the network it can also serve to aid modelling approaches.
Boolean logic in artificial intelligence and Turing degrees of Boolean-valued sets
Energy Technology Data Exchange (ETDEWEB)
Cai, Maohua.
1989-01-01
Over the years a number of generalizations of recursion theory have been introduced and studied. In this dissertation the author presents yet another such generalization. Based on the concept of a weakly recursively presented Boolean algebra, he defines Boolean-valued sets, Boolean-valued recursive sets, and Boolean-valued recursively enumerable sets and discuss the basic relationships between a Boolean-valued set, its principal part, and its support. Then he generalizes many elementary concepts and results about recursive and recursively enumerable sets such as the s-m-n theorem, the recursion theorem, and the projection theorem, etc. to Boolean valued sets. By using finite and infinite injury arguments, he generalizes the Friedberg-Muchnik theorem, the theorem about nonrecursive low r.e. sets, the minimal pair theorem, and other results. Finally, he discusses the possible application of Boolean-valued logic in artificial intelligence, and gives an implementation of a parser for the four-valued Boolean logic.
Synchronization of Boolean Networks with Different Update Schemes.
Zhang, Hao; Wang, Xingyuan; Lin, Xiaohui
2014-01-01
In this paper, the synchronizations of Boolean networks with different update schemes (synchronized Boolean networks and asynchronous Boolean networks) are investigated. All nodes in Boolean network are represented in terms of semi-tensor product. First, we give the concept of inner synchronization and observe that all nodes in a Boolean network are synchronized with each other. Second, we investigate the outer synchronization between a driving Boolean network and a corresponding response Boolean network. We provide not only the concept of traditional complete synchronization, but also the anti-synchronization and get the anti-synchronization in simulation. Third, we extend the outer synchronization to asynchronous Boolean network and get the complete synchronization between an asynchronous Boolean network and a response Boolean network. Consequently, theorems for synchronization of Boolean networks and asynchronous Boolean networks are derived. Examples are provided to show the correctness of our theorems.
Design of Probabilistic Boolean Networks Based on Network Structure and Steady-State Probabilities.
Kobayashi, Koichi; Hiraishi, Kunihiko
2016-06-06
In this brief, we consider the problem of finding a probabilistic Boolean network (PBN) based on a network structure and desired steady-state properties. In systems biology and synthetic biology, such problems are important as an inverse problem. Using a matrix-based representation of PBNs, a solution method for this problem is proposed. The problem of finding a BN has been studied so far. In the problem of finding a PBN, we must calculate not only the Boolean functions, but also the probabilities of selecting a Boolean function and the number of candidates of the Boolean functions. Hence, the problem of finding a PBN is more difficult than that of finding a BN. The effectiveness of the proposed method is presented by numerical examples.
Properties of Boolean networks and methods for their tests
2013-01-01
Transcriptional regulation networks are often modeled as Boolean networks. We discuss certain properties of Boolean functions (BFs), which are considered as important in such networks, namely, membership to the classes of unate or canalizing functions. Of further interest is the average sensitivity (AS) of functions. In this article, we discuss several algorithms to test the properties of interest. To test canalizing properties of functions, we apply spectral techniques, which can also be used to characterize the AS of functions as well as the influences of variables in unate BFs. Further, we provide and review upper and lower bounds on the AS of unate BFs based on the spectral representation. Finally, we apply these methods to a transcriptional regulation network of Escherichia coli, which controls central parts of the E. coli metabolism. We find that all functions are unate. Also the analysis of the AS of the network reveals an exceptional robustness against transient fluctuations of the binary variables.a PMID:23311536
Rational Verification in Iterated Electric Boolean Games
Directory of Open Access Journals (Sweden)
Youssouf Oualhadj
2016-07-01
Full Text Available Electric boolean games are compact representations of games where the players have qualitative objectives described by LTL formulae and have limited resources. We study the complexity of several decision problems related to the analysis of rationality in electric boolean games with LTL objectives. In particular, we report that the problem of deciding whether a profile is a Nash equilibrium in an iterated electric boolean game is no harder than in iterated boolean games without resource bounds. We show that it is a PSPACE-complete problem. As a corollary, we obtain that both rational elimination and rational construction of Nash equilibria by a supervising authority are PSPACE-complete problems.
Boolean Factor Congruences and Property (*)
Terraf, Pedro Sánchez
2008-01-01
A variety V has Boolean factor congruences (BFC) if the set of factor congruences of every algebra in V is a distributive sublattice of its congruence lattice; this property holds in rings with unit and in every variety which has a semilattice operation. BFC has a prominent role in the study of uniqueness of direct product representations of algebras, since it is a strengthening of the refinement property. We provide an explicit Mal'cev condition for BFC. With the aid of this condition, it is shown that BFC is equivalent to a variant of the definability property (*), an open problem in R. Willard's work ("Varieties Having Boolean Factor Congruences," J. Algebra, 132 (1990)).
Generalizing Boolean Satisfiability III: Implementation
Dixon, H E; Hofer, D; Luks, E M; Parkes, A J; 10.1613/jair.1656
2011-01-01
This is the third of three papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high-performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal has been to define a representation in which this structure is apparent and can be exploited to improve computational performance. The first paper surveyed existing work that (knowingly or not) exploited problem structure to improve the performance of satisfiability engines, and the second paper showed that this structure could be understood in terms of groups of permutations acting on individual clauses in any particular Boolean theory. We conclude the series by discussing the techniques needed to implement our ideas, and by reporting on their performance on a variety of problem instances.
Constructive version of Boolean algebra
Ciraulo, Francesco; Toto, Paola
2012-01-01
The notion of overlap algebra introduced by G. Sambin provides a constructive version of complete Boolean algebra. Here we first show some properties concerning overlap algebras: we prove that the notion of overlap morphism corresponds classically to that of map preserving arbitrary joins; we provide a description of atomic set-based overlap algebras in the language of formal topology, thus giving a predicative characterization of discrete locales; we show that the power-collection of a set is the free overlap algebra join-generated from the set. Then, we generalize the concept of overlap algebra and overlap morphism in various ways to provide constructive versions of the category of Boolean algebras with maps preserving arbitrary existing joins.
Single axioms for Boolean algebra.
Energy Technology Data Exchange (ETDEWEB)
McCune, W.
2000-06-30
Explicit single axioms are presented for Boolean algebra in terms of (1) the Sheffer stroke; (2) disjunction and negation; (3) disjunction, conjunction, and negation; and (4) disjunction, conjunction, negation, 0, and 1. It was previously known that single axioms exist for these systems, but the procedures to generate them are exponential, producing huge equations. Automated deduction techniques were applied to find axioms of lengths 105, 131, 111, and 127, respectively, each with six variables.
Boolean networks with robust and reliable trajectories
Energy Technology Data Exchange (ETDEWEB)
Schmal, Christoph; Peixoto, Tiago P; Drossel, Barbara, E-mail: schmal@physik.uni-bielefeld.d, E-mail: tiago@fkp.tu-darmstadt.d, E-mail: drossel@fkp.tu-darmstadt.d [Institut fuer Festkoerperphysik, TU Darmstadt, Hochschulstrasse 6, 64289 Darmstadt (Germany)
2010-11-15
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.
Canalization and symmetry in Boolean models for genetic regulatory networks
Energy Technology Data Exchange (ETDEWEB)
Reichhardt, C J Olson [Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Bassler, Kevin E [Department of Physics, University of Houston, Houston, TX 77204-5005 (United States)
2007-04-20
Canalization of genetic regulatory networks has been argued to be favoured by evolutionary processes due to the stability that it can confer to phenotype expression. We explore whether a significant amount of canalization and partial canalization can arise in purely random networks in the absence of evolutionary pressures. We use a mapping of the Boolean functions in the Kauffman N-K model for genetic regulatory networks onto a k-dimensional Ising hypercube (where k = K) to show that the functions can be divided into different classes strictly due to geometrical constraints. The classes can be counted and their properties determined using results from group theory and isomer chemistry. We demonstrate that partially canalizing functions completely dominate all possible Boolean functions, particularly for higher k. This indicates that partial canalization is extremely common, even in randomly chosen networks, and has implications for how much information can be obtained in experiments on native state genetic regulatory networks.
A Note on Boolean Stochastic Processes
Fidaleo, Francesco
2015-03-01
For the quantum stochastic processes generated by the Boolean commutation relations, we prove the following version of De Finetti Theorem: each of such Boolean processes is exchangeable if and only if it is independent and identically distributed with respect to the tail algebra.
Boolean Search: Current State and Perspectives.
Frants, Valery I.; Shapiro, Jacob; Taksa, Isak; Voiskunskii, Vladimir G.
1999-01-01
Discusses the use of Boolean logic in information-retrieval systems and analyzes existing criticisms of operational systems. Considers users' ability to use and understand Boolean operators, ranking, the quality of query formulations, and negative effects of criticism; and concludes that criticism is directed at the methodology employed in…
Delay synchronization of temporal Boolean networks
Wei, Qiang; Xie, Cheng-jun; Liang, Yi; Niu, Yu-jun; Lin, Da
2016-01-01
This paper investigates the delay synchronization between two temporal Boolean networks base on semi-tensor product method, which improve complete synchronization. Necessary and sufficient conditions for delay synchronization are drawn base on algebraic expression of temporal Boolean networks. A example is presented to show the effectiveness of theoretical analysis.
Kazhdan-Lusztig polynomials of boolean elements
Mongelli, Pietro
2011-01-01
We give closed combinatorial product formulas for Kazhdan-Lusztig poynomials and their parabolic analogue of type q in the case of boolean elements, introduced in [M. Marietti, Boolean elements in Kazhdan-Lusztig theory, J. Algebra 295 (2006)], in Coxeter groups whose Coxeter graph is a tree.
Boolean networks as modelling framework
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Florian eGreil
2012-08-01
Full Text Available In a network, the components of a given system are represented as nodes, the interactions are abstracted as links between the nodes. Boolean networks refer to a class of dynamics on networks, in fact it is the simplest possible dynamics where each node has a value 0 or 1. This allows to investigate extensively the dynamics both analytically and by numerical experiments. The present article focuses on the theoretical concept of relevant components and the immediate application in plant biology, references for more in-depths treatment of the mathematical details are also given.
Problems in modeling a weighted Boolean retrieval system
Energy Technology Data Exchange (ETDEWEB)
Kraft, D.H.; Waller, W.G.
1979-01-01
The use of weights to denote a query representation and/or the indexing of a document is analyzed as a generalization of a Boolean retrieval system. Criteria are given for the functions used to evaluate the relevance of the records to a specific query. Various mechanisms for evaluating the relevance of records with regard to a given query are tested and found to be less than satisfactory. A new approach is suggested to avoid some of the perils.
CONSTRUCTION OF GENERAL SUBSUMPTIVE SOLUTIONS OF BOOLEAN EQUATIONS VIA COMPLETE-SUM DERIVATION
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Ali Muhammad Ali Rushdi
2014-01-01
Full Text Available Boolean-equation solving permeates many diverse areas of modern science. To solve a system of Boolean equations, one usually combines them into an equivalent single Boolean equation whose set of solutions is exactly the same as that of the original system of equations. One of the general classes of solutions for Boolean equations is the subsumptive general solution, in which each variable is expressed as an interval decided by a double inequality in terms of the succeeding variables. The solution validity depends on the satisfaction of a required consistency condition. In this study, we introduce a novel method (henceforth called the CS method for producing subsumptive Boolean-equation solutions based on deriving the complete sum of the pertinent Boolean function . The complete sum is a disjunction of all prime implicants of and nothing else. It explicitly shows all information about in the most compact form. We demonstrate the proposed CS solutions in terms of four examples, covering Boolean algebras of different sizes and using two prominent methods for deriving . Occasionally, the consistency condition results in a collapse of the underlying Boolean algebra into a smaller subalgebra. We also illustrate how an expansion tree (typically reduced to an acyclic graph can be used to deduce a complete list of all particular solutions from the subsumptive solution. The present CS method yields correct solutions, since it fits into the frame of the most general subsumptive solution. Among competing subsumptive methods, the CS method strikes a reasonable tradeoff between the conflicting requirements of less computational cost and more compact form for the solution obtained. In fact, it is the second best known method from both criteria of efficiency and compactness of solution.
Model Checking of Boolean Process Models
Schneider, Christoph
2011-01-01
In the field of Business Process Management formal models for the control flow of business processes have been designed since more than 15 years. Which methods are best suited to verify the bulk of these models? The first step is to select a formal language which fixes the semantics of the models. We adopt the language of Boolean systems as reference language for Boolean process models. Boolean systems form a simple subclass of coloured Petri nets. Their characteristics are low tokens to model explicitly states with a subsequent skipping of activations and arbitrary logical rules of type AND, XOR, OR etc. to model the split and join of the control flow. We apply model checking as a verification method for the safeness and liveness of Boolean systems. Model checking of Boolean systems uses the elementary theory of propositional logic, no modal operators are needed. Our verification builds on a finite complete prefix of a certain T-system attached to the Boolean system. It splits the processes of the Boolean sy...
Mining TCGA data using Boolean implications.
Sinha, Subarna; Tsang, Emily K; Zeng, Haoyang; Meister, Michela; Dill, David L
2014-01-01
Boolean implications (if-then rules) provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression) from the glioblastoma (GBM) and ovarian serous cystadenoma (OV) data sets from The Cancer Genome Atlas (TCGA). We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/.
Mining TCGA Data Using Boolean Implications
Sinha, Subarna; Tsang, Emily K.; Zeng, Haoyang; Meister, Michela; Dill, David L.
2014-01-01
Boolean implications (if-then rules) provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression) from the glioblastoma (GBM) and ovarian serous cystadenoma (OV) data sets from The Cancer Genome Atlas (TCGA). We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/. PMID:25054200
Mining TCGA data using Boolean implications.
Directory of Open Access Journals (Sweden)
Subarna Sinha
Full Text Available Boolean implications (if-then rules provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression from the glioblastoma (GBM and ovarian serous cystadenoma (OV data sets from The Cancer Genome Atlas (TCGA. We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/.
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.
Evolving sensitivity balances Boolean Networks.
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Jamie X Luo
Full Text Available We investigate the sensitivity of Boolean Networks (BNs to mutations. We are interested in Boolean Networks as a model of Gene Regulatory Networks (GRNs. We adopt Ribeiro and Kauffman's Ergodic Set and use it to study the long term dynamics of a BN. We define the sensitivity of a BN to be the mean change in its Ergodic Set structure under all possible loss of interaction mutations. In silico experiments were used to selectively evolve BNs for sensitivity to losing interactions. We find that maximum sensitivity was often achievable and resulted in the BNs becoming topologically balanced, i.e. they evolve towards network structures in which they have a similar number of inhibitory and excitatory interactions. In terms of the dynamics, the dominant sensitivity strategy that evolved was to build BNs with Ergodic Sets dominated by a single long limit cycle which is easily destabilised by mutations. We discuss the relevance of our findings in the context of Stem Cell Differentiation and propose a relationship between pluripotent stem cells and our evolved sensitive networks.
Directory of Open Access Journals (Sweden)
G.C. Rao
2012-11-01
Full Text Available A C- algebra is the algebraic form of the 3-valued conditional logic, which was introduced by F. Guzman and C. C. Squier in 1990. In this paper, some equivalent conditions for a C- algebra to become a boolean algebra in terms of congruences are given. It is proved that the set of all central elements B(A is isomorphic to the Boolean algebra of all C-algebras Sa, where a B(A. It is also proved that B(A is isomorphic to the Boolean algebra of all C-algebras Aa, where a B(A.
Robust Reachability of Boolean Control Networks.
Li, Fangfei; Tang, Yang
2016-04-20
Boolean networks serve a powerful tool in analysis of genetic regulatory networks since it emphasizes the fundamental principles and establishes a nature framework for capturing the dynamics of regulation of cellular states. In this paper, the robust reachability of Boolean control networks is investigated by means of semi-tensor product. Necessary and sufficient conditions for the robust reachability of Boolean control networks are provided, in which control inputs relying on disturbances or not are considered, respectively. Besides, the corresponding control algorithms are developed for these two cases. A reduced model of the lac operon in the Escherichia coli is presented to show the effectiveness of the presented results.
Flexible method for Boolean information retrieval
Energy Technology Data Exchange (ETDEWEB)
Salton, G.; Wu, H.
1983-01-01
A new flexible retrieval system is described which makes it possible to relax the strict conditions of Boolean query logic thereby retrieving useful items that are rejected in a conventional retrieval situation. The query structure inherent in the Boolean system is preserved, while at the same time weighted terms may be incorporated into both queries and stored documents; the retrieved output can also be ranked in strict similarity order with the user queries. A conventional retrieval system can be modified to make use of the flexible metric system. Laboratory tests indicate that the extended system produces better retrieval output than either the Boolean or the vector processing systems. 11 references.
Bahi, J M; Guyeux, C; Richard, A
2011-01-01
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a continuous function, whose discrete-time iterations are chaotic if and only if the iteration graph of the Boolean network is strongly connected. Then, sufficient conditions for this strong connectivity are expressed on the interaction graph of this network, leading to a constructive method of chaotic function computation. The whole approach is evaluated in the chaos-based pseudo-random number generation context.
Boolean Models of Biological Processes Explain Cascade-Like Behavior.
Chen, Hao; Wang, Guanyu; Simha, Rahul; Du, Chenghang; Zeng, Chen
2016-01-29
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.
Stability of Boolean Multiplex Networks
Cozzo, Emanuele; Moreno, Yamir
2012-01-01
We extend the formalism of Random Boolean Networks with canalizing rules to multilevel complex networks. The formalism allows to model genetic networks in which each gene might take part in more than one signaling pathway. We use a semi-annealed approach to study the stability of this class of models when coupled in a multiplex network and show that the analytical results are in good agreement with numerical simulations. Our main finding is that the multiplex structure provides a mechanism for the stabilization of the system and of chaotic regimes of individual layers. Our results help understanding why some genetic networks that are theoretically expected to operate in the chaotic regime can actually display dynamical stability.
Generalizing Boolean Satisfiability II: Theory
Dixon, H E; Luks, E M; Parkes, A J; 10.1613/jair.1555
2011-01-01
This is the second of three planned papers describing ZAP, a satisfiability engine that substantially generalizes existing tools while retaining the performance characteristics of modern high performance solvers. The fundamental idea underlying ZAP is that many problems passed to such engines contain rich internal structure that is obscured by the Boolean representation used; our goal is to define a representation in which this structure is apparent and can easily be exploited to improve computational performance. This paper presents the theoretical basis for the ideas underlying ZAP, arguing that existing ideas in this area exploit a single, recurring structure in that multiple database axioms can be obtained by operating on a single axiom using a subgroup of the group of permutations on the literals in the problem. We argue that the group structure precisely captures the general structure at which earlier approaches hinted, and give numerous examples of its use. We go on to extend the Davis-Putnam-Logemann-...
Boolean computation of optimum hitting sets
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.; Baca, L.S.; Shiver, A.W.; Worrell, R.B.
1984-04-01
This report presents the results of computational experience in solving weighted hitting set problems by Boolean algebraic methods. The feasible solutions are obtained by Boolean formula manipulations, and the optimum solutions are obtained by comparing the weight sums of the feasible solutions. Both the algebra and the optimization can be accomplished using the SETS language. One application is to physical protection problems. 8 references, 2 tables.
Non-Boolean probabilities and quantum measurement
Energy Technology Data Exchange (ETDEWEB)
Niestegge, Gerd
2001-08-03
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum mechanical Hilbert space formalism and exhibits a particular phenomenon (state-independent conditional probabilities) which may provide new opportunities for an understanding of the quantum measurement process. Examples of the proposed model are provided, using Jordan operator algebras. (author)
Stochastic coupling of two random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Ho, M.-C. [Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)]. E-mail: t1603@nknucc.nknu.edu.tw; Hung, Y.-C. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China)]. E-mail: d9123801@student.nsysu.edu.tw; Jiang, I-M. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China)
2005-08-29
We study the dynamics of two coupled random Boolean networks. Based on the Boolean model studied by Andrecut and Ali [Int. J. Mod. Phys. B 15 (2001) 17] and the stochastic coupling techniques, the density evolution of networks is precisely described by two deterministic coupled polynomial maps. The iteration results of the model match the real networks well. By using MSE and the maximal Lyapunov exponents, the synchronization phenomena of coupled networks is also under our discussion.
ILP/SMT-Based Method for Design of Boolean Networks Based on Singleton Attractors.
Kobayashi, Koichi; Hiraishi, Kunihiko
2014-01-01
Attractors in gene regulatory networks represent cell types or states of cells. In system biology and synthetic biology, it is important to generate gene regulatory networks with desired attractors. In this paper, we focus on a singleton attractor, which is also called a fixed point. Using a Boolean network (BN) model, we consider the problem of finding Boolean functions such that the system has desired singleton attractors and has no undesired singleton attractors. To solve this problem, we propose a matrix-based representation of BNs. Using this representation, the problem of finding Boolean functions can be rewritten as an Integer Linear Programming (ILP) problem and a Satisfiability Modulo Theories (SMT) problem. Furthermore, the effectiveness of the proposed method is shown by a numerical example on a WNT5A network, which is related to melanoma. The proposed method provides us a basic method for design of gene regulatory networks.
Acoustic logic gates and Boolean operation based on self-collimating acoustic beams
Zhang, Ting; Cheng, Ying; Guo, Jian-zhong; Xu, Jian-yi; Liu, Xiao-jun
2015-03-01
The reveal of self-collimation effect in two-dimensional (2D) photonic or acoustic crystals has opened up possibilities for signal manipulation. In this paper, we have proposed acoustic logic gates based on the linear interference of self-collimated beams in 2D sonic crystals (SCs) with line-defects. The line defects on the diagonal of the 2D square SCs are actually functioning as a 3 dB splitter. By adjusting the phase difference between two input signals, the basic Boolean logic functions such as XOR, OR, AND, and NOT are achieved both theoretically and experimentally. Due to the non-diffracting property of self-collimation beams, more complex Boolean logic and algorithms such as NAND, NOR, and XNOR can be realized by cascading the basic logic gates. The achievement of acoustic logic gates and Boolean operation provides a promising approach for acoustic signal computing and manipulations.
Acoustic logic gates and Boolean operation based on self-collimating acoustic beams
Energy Technology Data Exchange (ETDEWEB)
Zhang, Ting; Xu, Jian-yi [Key Laboratory of Modern Acoustics, Department of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China); Cheng, Ying, E-mail: chengying@nju.edu.cn; Liu, Xiao-jun, E-mail: liuxiaojun@nju.edu.cn [Key Laboratory of Modern Acoustics, Department of Physics and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China); State Key Laboratory of Acoustics, Chinese Academy of Sciences, Beijing 100190 (China); Guo, Jian-zhong [School of Physics and Information Technology, Shaanxi Normal University, Xian 710119 (China)
2015-03-16
The reveal of self-collimation effect in two-dimensional (2D) photonic or acoustic crystals has opened up possibilities for signal manipulation. In this paper, we have proposed acoustic logic gates based on the linear interference of self-collimated beams in 2D sonic crystals (SCs) with line-defects. The line defects on the diagonal of the 2D square SCs are actually functioning as a 3 dB splitter. By adjusting the phase difference between two input signals, the basic Boolean logic functions such as XOR, OR, AND, and NOT are achieved both theoretically and experimentally. Due to the non-diffracting property of self-collimation beams, more complex Boolean logic and algorithms such as NAND, NOR, and XNOR can be realized by cascading the basic logic gates. The achievement of acoustic logic gates and Boolean operation provides a promising approach for acoustic signal computing and manipulations.
Boolean Variables in Economic Models Solved by Linear Programming
Directory of Open Access Journals (Sweden)
Lixandroiu D.
2014-12-01
Full Text Available The article analyses the use of logical variables in economic models solved by linear programming. Focus is given to the presentation of the way logical constraints are obtained and of the definition rules based on predicate logic. Emphasis is also put on the possibility to use logical variables in constructing a linear objective function on intervals. Such functions are encountered when costs or unitary receipts are different on disjunct intervals of production volumes achieved or sold. Other uses of Boolean variables are connected to constraint systems with conditions and the case of a variable which takes values from a finite set of integers.
Boolean Networks with Multi-Expressions and Parameters.
Zou, Yi Ming
2013-07-01
To model biological systems using networks, it is desirable to allow more than two levels of expression for the nodes and to allow the introduction of parameters. Various modeling and simulation methods addressing these needs using Boolean models, both synchronous and asynchronous, have been proposed in the literature. However, analytical study of these more general Boolean networks models is lagging. This paper aims to develop a concise theory for these different Boolean logic based modeling methods. Boolean models for networks where each node can have more than two levels of expression and Boolean models with parameters are defined algebraically with examples provided. Certain classes of random asynchronous Boolean networks and deterministic moduli asynchronous Boolean networks are investigated in detail using the setting introduced in this paper. The derived theorems provide a clear picture for the attractor structures of these asynchronous Boolean networks.
Directory of Open Access Journals (Sweden)
Wensheng Guo
Full Text Available 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.
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.
Simulating Boolean circuits on a DNA computer
Energy Technology Data Exchange (ETDEWEB)
Ogihara, Mitsunori; Ray, A. [Univ. of Rochester, NY (United States)
1997-12-01
We demonstrate that DNA computers can simulate Boolean circuits with a small overhead. Boolean circuits embody the notion of massively parallel signal processing and are frequently encountered in many parallel algorithms. Many important problems such as sorting, integer arithmetic, and matrix multiplication are known to be computable by small size Boolean circuits much faster than by ordinary sequential digital computers. This paper shows that DNA chemistry allows one to simulate large semi-unbounded fan-in Boolean circuits with a logarithmic slowdown in computation time. Also, for the class NC{sup 1}, the slowdown can be reduced to a constant. In this algorithm we have encoded the inputs, the Boolean AND gates, and the OR gates to DNA oligonucleotide sequences. We operate on the gates and the inputs by standard molecular techniques of sequence-specific annealing, ligation, separation by size, amplification, sequence-specific cleavage, and detection by size. Additional steps of amplification are not necessary for NC{sup 1} circuits. Preliminary biochemical experiments on a small test circuit have produced encouraging results. Further confirmatory experiments are in progress. 19 refs., 3 figs., 1 tab.
A Simple Blueprint for Automatic Boolean Query Processing.
Salton, G.
1988-01-01
Describes a new Boolean retrieval environment in which an extended soft Boolean logic is used to automatically construct queries from original natural language formulations provided by users. Experimental results that compare the retrieval effectiveness of this method to conventional Boolean and vector processing are discussed. (27 references)…
Synchronization of coupled large-scale Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Li, Fangfei, E-mail: li-fangfei@163.com [Department of Mathematics, East China University of Science and Technology, No. 130, Meilong Road, Shanghai, Shanghai 200237 (China)
2014-03-15
This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.
Synchronization of coupled large-scale Boolean networks
Li, Fangfei
2014-03-01
This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.
Poret, Arnaud; Boissel, Jean-Pierre
2014-12-01
Target identification aims at identifying biomolecules whose function should be therapeutically altered to cure the considered pathology. An algorithm for in silico target identification using Boolean network attractors is proposed. It assumes that attractors correspond to phenotypes produced by the modeled biological network. It identifies target combinations which allow disturbed networks to avoid attractors associated with pathological phenotypes. The algorithm is tested on a Boolean model of the mammalian cell cycle and its applications are illustrated on a Boolean model of Fanconi anemia. Results show that the algorithm returns target combinations able to remove attractors associated with pathological phenotypes and then succeeds in performing the proposed in silico target identification. However, as with any in silico evidence, there is a bridge to cross between theory and practice. Nevertheless, it is expected that the algorithm is of interest for target identification.
Improving Quantum Query Complexity of Boolean Matrix Multiplication Using Graph Collision
Jeffery, Stacey
2011-01-01
The quantum query complexity of Boolean matrix multiplication is typically studied as a function of the matrix dimension, $n$, as well as the number of 1s in the output, $\\ell$. We show an improved quantum query complexity for Boolean matrix multiplication for all values of $\\ell$. To obtain this improvement, we build an algorithm directly upon a graph collision finding subroutine that is used in the best known quantum algorithm for triangle finding, bypassing the triangle finding subroutine used in previous quantum algorithms for Boolean matrix multiplication. We then obtain further improvements by applying the sparse/dense techniques of Lingas, and their quantum analogue by Le Gall, as well as some further improvements to these techniques.
Forced synchronization of autonomous dynamical Boolean networks.
Rivera-Durón, R R; Campos-Cantón, E; Campos-Cantón, I; Gauthier, Daniel J
2015-08-01
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.
Duality theories for Boolean algebras with operators
Givant, Steven
2014-01-01
In this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.
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.
Coherent spaces, Boolean rings and quantum gates
Vourdas, A.
2016-10-01
Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they transform into projectors of the same type, under displacement transformations, and also under time evolution. The set of these spaces, with the logical OR and AND operations is a distributive lattice, and with the logical XOR and AND operations is a Boolean ring (Stone's formalism). Applications of this Boolean ring into classical CNOT gates with n-ary variables, and also quantum CNOT gates with coherent states, are discussed.
EXACT SIMULATION OF A BOOLEAN MODEL
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Christian Lantuéjoul
2013-06-01
Full Text Available A Boolean model is a union of independent objects (compact random subsets located at Poisson points. Two algorithms are proposed for simulating a Boolean model in a bounded domain. The first one applies only to stationary models. It generates the objects prior to their Poisson locations. Two examples illustrate its applicability. The second algorithm applies to stationary and non-stationary models. It generates the Poisson points prior to the objects. Its practical difficulties of implementation are discussed. Both algorithms are based on importance sampling techniques, and the generated objects are weighted.
Azpeitia, Eugenio; Muñoz, Stalin; González-Tokman, Daniel; Martínez-Sánchez, Mariana Esther; Weinstein, Nathan; Naldi, Aurélien; Álvarez-Buylla, Elena R; Rosenblueth, David A; Mendoza, Luis
2017-02-10
Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures.
Azpeitia, Eugenio; Muñoz, Stalin; González-Tokman, Daniel; Martínez-Sánchez, Mariana Esther; Weinstein, Nathan; Naldi, Aurélien; Álvarez-Buylla, Elena R.; Rosenblueth, David A.; Mendoza, Luis
2017-01-01
Molecular regulation was initially assumed to follow both a unidirectional and a hierarchical organization forming pathways. Regulatory processes, however, form highly interlinked networks with non-hierarchical and non-unidirectional structures that contain statistically overrepresented circuits or motifs. Here, we analyze the behavior of pathways containing non-unidirectional (i.e. bidirectional) and non-hierarchical interactions that create motifs. In comparison with unidirectional and hierarchical pathways, our pathways have a high diversity of behaviors, characterized by the size and number of attractors. Motifs have been studied individually showing that feedback circuit motifs regulate the number and size of attractors. It is less clear what happens in molecular networks that usually contain multiple feedbacks. Here, we find that the way feedback circuits couple to each other (i.e., the combination of the functionalities of feedback circuits) regulate both the number and size of the attractors. We show that the different expected results of epistasis analysis (a method to infer regulatory interactions) are produced by many non-hierarchical and non-unidirectional structures. Thus, these structures cannot be correctly inferred by epistasis analysis. Finally, we show that the combinations of functionalities, combined with other network properties, allow for a better characterization of regulatory structures. PMID:28186191
Institute of Scientific and Technical Information of China (English)
刘卫锋
2013-01-01
将软集理论应用到布尔代数中，提出了软布尔代数、软布尔子代数、软布尔代数的软理想、软理想布尔代数等概念，研究了它们的相关性质，并初步讨论了软布尔代数与几类布尔代数的模糊子代数的关系。%The soft set theory is applied to the Boolean algebra.The concepts of soft Boolean algebra, soft Boolean sub-algebra, soft ideal of soft Boolean algebra and idealistic soft Boolean algebra are presented and some related algebraic properties are discussed.The relations between soft Boolean algebra and several kinds of fuzzy subalgebras of Boolean algebra are preliminarily investigated.
Periodic pattern detection in sparse boolean sequences
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Hérisson Joan
2010-09-01
Full Text Available Abstract Background The specific position of functionally related genes along the DNA has been shown to reflect the interplay between chromosome structure and genetic regulation. By investigating the statistical properties of the distances separating such genes, several studies have highlighted various periodic trends. In many cases, however, groups built up from co-functional or co-regulated genes are small and contain wrong information (data contamination so that the statistics is poorly exploitable. In addition, gene positions are not expected to satisfy a perfectly ordered pattern along the DNA. Within this scope, we present an algorithm that aims to highlight periodic patterns in sparse boolean sequences, i.e. sequences of the type 010011011010... where the ratio of the number of 1's (denoting here the transcription start of a gene to 0's is small. Results The algorithm is particularly robust with respect to strong signal distortions such as the addition of 1's at arbitrary positions (contaminated data, the deletion of existing 1's in the sequence (missing data and the presence of disorder in the position of the 1's (noise. This robustness property stems from an appropriate exploitation of the remarkable alignment properties of periodic points in solenoidal coordinates. Conclusions The efficiency of the algorithm is demonstrated in situations where standard Fourier-based spectral methods are poorly adapted. We also show how the proposed framework allows to identify the 1's that participate in the periodic trends, i.e. how the framework allows to allocate a positional score to genes, in the same spirit of the sequence score. The software is available for public use at http://www.issb.genopole.fr/MEGA/Softwares/iSSB_SolenoidalApplication.zip.
Inference of a Probabilistic Boolean Network from a Single Observed Temporal Sequence
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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
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
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.
Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations
Heckel, Reinhard; Bossert, Martin
2011-01-01
Consider a large Boolean network with a feed forward structure. Given a probability distribution for the inputs, can one find-possibly small-collections of input nodes that determine the states of most other nodes in the network? To identify these nodes, a notion that quantifies the determinative power of an input over states in the network is needed. We argue that the mutual information (MI) between a subset of the inputs X = {X_1, ..., X_n} of node i and the function f_i(X)$ associated with node i quantifies the determinative power of this subset of inputs over node i. To study the relation of determinative power to sensitivity to perturbations, we relate the MI to measures of perturbations, such as the influence of a variable, in terms of inequalities. The result shows that, maybe surprisingly, an input that has large influence does not necessarily have large determinative power. The main tool for the analysis is Fourier analysis of Boolean functions. Whether a function is sensitive to perturbations or not...
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.
Evolution and Controllability of Cancer Networks: A Boolean Perspective.
Srihari, Sriganesh; Raman, Venkatesh; Leong, Hon Wai; Ragan, Mark A
2014-01-01
Cancer forms a robust system capable of maintaining stable functioning (cell sustenance and proliferation) despite perturbations. Cancer progresses as stages over time typically with increasing aggressiveness and worsening prognosis. Characterizing these stages and identifying the genes driving transitions between them is critical to understand cancer progression and to develop effective anti-cancer therapies. In this work, we propose a novel model for the `cancer system' as a Boolean state space in which a Boolean network, built from protein-interaction and gene-expression data from different stages of cancer, transits between Boolean satisfiability states by "editing" interactions and "flipping" genes. Edits reflect rewiring of the PPI network while flipping of genes reflect activation or silencing of genes between stages. We formulate a minimization problem min flip to identify these genes driving the transitions. The application of our model (called BoolSpace) on three case studies-pancreatic and breast tumours in human and post spinal-cord injury (SCI) in rats-reveals valuable insights into the phenomenon of cancer progression: (i) interactions involved in core cell-cycle and DNA-damage repair pathways are significantly rewired in tumours, indicating significant impact to key genome-stabilizing mechanisms; (ii) several of the genes flipped are serine/threonine kinases which act as biological switches, reflecting cellular switching mechanisms between stages; and (iii) different sets of genes are flipped during the initial and final stages indicating a pattern to tumour progression. Based on these results, we hypothesize that robustness of cancer partly stems from "passing of the baton" between genes at different stages-genes from different biological processes and/or cellular components are involved in different stages of tumour progression thereby allowing tumour cells to evade targeted therapy, and therefore an effective therapy should target a "cover set" of
Stabilization of perturbed Boolean network attractors through compensatory interactions
2014-01-01
Background Understanding and ameliorating the effects of network damage are of significant interest, due in part to the variety of applications in which network damage is relevant. For example, the effects of genetic mutations can cascade through within-cell signaling and regulatory networks and alter the behavior of cells, possibly leading to a wide variety of diseases. The typical approach to mitigating network perturbations is to consider the compensatory activation or deactivation of system components. Here, we propose a complementary approach wherein interactions are instead modified to alter key regulatory functions and prevent the network damage from triggering a deregulatory cascade. Results We implement this approach in a Boolean dynamic framework, which has been shown to effectively model the behavior of biological regulatory and signaling networks. We show that the method can stabilize any single state (e.g., fixed point attractors or time-averaged representations of multi-state attractors) to be an attractor of the repaired network. We show that the approach is minimalistic in that few modifications are required to provide stability to a chosen attractor and specific in that interventions do not have undesired effects on the attractor. We apply the approach to random Boolean networks, and further show that the method can in some cases successfully repair synchronous limit cycles. We also apply the methodology to case studies from drought-induced signaling in plants and T-LGL leukemia and find that it is successful in both stabilizing desired behavior and in eliminating undesired outcomes. Code is made freely available through the software package BooleanNet. Conclusions The methodology introduced in this report offers a complementary way to manipulating node expression levels. A comprehensive approach to evaluating network manipulation should take an "all of the above" perspective; we anticipate that theoretical studies of interaction modification
Demonstrating Boolean Logic Using Simple Electrical Circuits
McElhaney, Kevin W.
2004-01-01
While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.
A Boolean Map Theory of Visual Attention
Huang, Liqiang; Pashler, Harold
2007-01-01
A theory is presented that attempts to answer two questions. What visual contents can an observer consciously access at one moment? Answer: only one feature value (e.g., green) per dimension, but those feature values can be associated (as a group) with multiple spatially precise locations (comprising a single labeled Boolean map). How can an…
Short single axioms for boolean algebra.
Energy Technology Data Exchange (ETDEWEB)
McCune, W.; Veroff, R.; Fitelson, B.; Harris, K.; Feist, A.; Wos, L.; Mathematics and Computer Science; Univ. of New Mexico; Univ. of Wisconsin at Madison; Duke Univ.
2002-01-01
We present short single equational axioms for Boolean algebra in terms of disjunction and negation and in terms of the Sheffer stroke. Previously known single axioms for these theories are much longer than the ones we present. We show that there is no shorter axiom in terms of the Sheffer stroke. Automated deduction techniques were used in several parts of the work.
A Short Sheffer axiom for Boolean algebra.
Energy Technology Data Exchange (ETDEWEB)
Veroff, R.; McCune, W.
2000-06-30
A short Sheffer stroke identity is shown to be a single axiom for Boolean algebra. The axiom has length 15 and 3 variables. The proof shows that it is equivalent to Sheffer's original 3-basis for the theory. Automated deduction techniques were used to find the proof. The shortest single axiom previously known to us has length 105 and 6 variables.
Bent and Generalized Bent Boolean Functions
2012-01-01
from Zn2 to Z2. Then the crosscorrelation between f and g at u ∈ Zn2 is C f,g(u) = 1 2 ( Cb1 ,b2(u)+ Ca1+b1,a2+b2(u) )+ ı 2 ( Cb1 ,a2+b2(u)− Ca1+b1,b2(u...x⊕u) = 1 2 ( Cb1 ,b2(u)+ Ca1+b1,a2+b2(u) )+ ı 2 ( Cb1 ,a2+b2(u)− Ca1+b1,b2(u) ) . (20) which follows directly from the formula ıa−b = 1+(−1)a+b2 + (−1
Finite size effects and symmetry breaking in the evolution of networks of competing Boolean nodes
Energy Technology Data Exchange (ETDEWEB)
Liu, M; Bassler, K E, E-mail: bassler@uh.edu [Department of Physics, University of Houston, 617 Science and Research 1, Houston, TX 77204-5005 (United States)
2011-01-28
Finite size effects on the evolutionary dynamics of Boolean networks are analyzed. In the model considered, Boolean networks evolve via a competition between nodes that punishes those in the majority. Previous studies have found that large networks evolve to a statistical steady state that is both critical and highly canalized, and that the evolution of canalization, which is a form of robustness found in genetic regulatory networks, is associated with a particular symmetry of the evolutionary dynamics. Here, it is found that finite size networks evolve in a fundamentally different way than infinitely large networks do. The symmetry of the evolutionary dynamics of infinitely large networks that selects for canalizing Boolean functions is broken in the evolutionary dynamics of finite size networks. In finite size networks, there is an additional selection for input-inverting Boolean functions that output a value opposite to the majority of input values. The reason for the symmetry breaking in the evolutionary dynamics is found to be due to the need for nodes in finite size networks to behave differently in order to cooperate so that the system collectively performs as efficiently as possible. The results suggest that both finite size effects and symmetry are fundamental for understanding the evolution of real-world complex networks, including genetic regulatory networks.
Chaos Control in Random Boolean Networks by Reducing Mean Damage Percolation Rate
Institute of Scientific and Technical Information of China (English)
JIANG Nan; CHEN Shi-Jian
2011-01-01
Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase. However, controlled nodes are only viewed as passive blocks to prevent perturbation spread. We propose a new control method in which controlled nodes can exert an active impact on the network.Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions. Simulation results showy that the number of nodes needed to achieve control is largely reduced compared to the previous method. Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control.%Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase.However, controlled nodes are only viewed as passive blocks to prevent perturbation spread.We propose a new control method in which controlled nodes can exert an active impact on the network.Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions.Simulation results show that the number of nodes needed to achieve control is largely reduced compared to the previous method.Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control
Synchronization Analysis of Master-Slave Probabilistic Boolean Networks
Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W. C.; Cao, Jinde
2015-01-01
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. PMID:26315380
Synchronization Analysis of Master-Slave Probabilistic Boolean Networks.
Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W C; Cao, Jinde
2015-01-01
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.
Direct relations between morphology and transport in Boolean models.
Scholz, Christian; Wirner, Frank; Klatt, Michael A; Hirneise, Daniel; Schröder-Turk, Gerd E; Mecke, Klaus; Bechinger, Clemens
2015-10-01
We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.
Quantum half-adder Boolean logic gate with a nano-graphene molecule and graphene nano-electrodes
Srivastava, Saurabh; Kino, Hiori; Joachim, Christian
2017-01-01
A molecule Boolean 1 / 2 -adder is designed and the XOR and AND truth table calculated at +0.1 V using 4 graphene electrodes. It functions with level repulsion and destructive interferences effects using 4 molecule electronic states in a quantum Hamiltonian computing approach (QHC) with the abrupt change of the molecular orbital weight of those 4 calculating states as a function of the logical input configuration. The logical inputs enter rotating the two nitro groups of the central board. With QHC, a complex Boolean digital function can be implemented employing the same graphene material for interconnects and the molecule calculating parts.
Exact and heuristic methods for solving Boolean games
DE CLERCQ, Sofie; Bauters, Kim; Schockaert, Steven; Mihaylov, Mihail; Nowé, Ann; De Cock, Martine
2015-01-01
Boolean games are a framework for reasoning about the rational behavior of agents whose goals are formalized using propositional formulas. Compared to normal form games, a well-studied and related game framework, Boolean games allow for an intuitive and more compact representation of the agents’ goals. So far, Boolean games have been mainly studied in the literature from the Knowledge Representation perspective, and less attention has been paid on the algorithmic issues underlying the computa...
An efficient algorithm for computing attractors of synchronous and asynchronous Boolean networks.
Directory of Open Access Journals (Sweden)
Desheng Zheng
Full Text Available 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 [Formula: see text] faster in computing attractors for empirical experimental systems.The software package is available at https://sites.google.com/site/desheng619/download.
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
A Generalization of J-Boolean Like Rings%J-Boolean like 环的扩张
Institute of Scientific and Technical Information of China (English)
秦蕊
2014-01-01
对 J-Boolean like环进行了扩张，并且将 J-Boolean like环与广义矩阵环和Morita Context环联系起来，进而探索了部分环为 J-Boolean like环时应具备的条件，且给出若干相关例子。%The paper mainly explored the generalization of J-Boolean like rings ,and connected J-Boolean like rings with generalized matrix rings and Morita Context rings ,then studied the conditions when a part of other rings became J-Boolean like rings ,and listed some examples .
Random Boolean network models and the yeast transcriptional network
Kauffman, Stuart; Peterson, Carsten; Samuelsson, Björn; Troein, Carl
2003-12-01
The recently measured yeast transcriptional network is analyzed in terms of simplified Boolean network models, with the aim of determining feasible rule structures, given the requirement of stable solutions of the generated Boolean networks. We find that for ensembles of generated models, those with canalyzing Boolean rules are remarkably stable, whereas those with random Boolean rules are only marginally stable. Furthermore, substantial parts of the generated networks are frozen, in the sense that they reach the same state regardless of initial state. Thus, our ensemble approach suggests that the yeast network shows highly ordered dynamics.
Boolean network robotics: a proof of concept
Roli, Andrea; Pinciroli, Carlo; Birattari, Mauro
2011-01-01
Dynamical systems theory and complexity science provide powerful tools for analysing artificial agents and robots. Furthermore, they have been recently proposed also as a source of design principles and guidelines. Boolean networks are a prominent example of complex dynamical systems and they have been shown to effectively capture important phenomena in gene regulation. From an engineering perspective, these models are very compelling, because they can exhibit rich and complex behaviours, in spite of the compactness of their description. In this paper, we propose the use of Boolean networks for controlling robots' behaviour. The network is designed by means of an automatic procedure based on stochastic local search techniques. We show that this approach makes it possible to design a network which enables the robot to accomplish a task that requires the capability of navigating the space using a light stimulus, as well as the formation and use of an internal memory.
Fast Vertical Mining Using Boolean Algebra
Directory of Open Access Journals (Sweden)
Hosny M. Ibrahim
2015-01-01
Full Text Available The vertical association rules mining algorithm is an efficient mining method, which makes use of support sets of frequent itemsets to calculate the support of candidate itemsets. It overcomes the disadvantage of scanning database many times like Apriori algorithm. In vertical mining, frequent itemsets can be represented as a set of bit vectors in memory, which enables for fast computation. The sizes of bit vectors for itemsets are the main space expense of the algorithm that restricts its expansibility. Therefore, in this paper, a proposed algorithm that compresses the bit vectors of frequent itemsets will be presented. The new bit vector schema presented here depends on Boolean algebra rules to compute the intersection of two compressed bit vectors without making any costly decompression operation. The experimental results show that the proposed algorithm, Vertical Boolean Mining (VBM algorithm is better than both Apriori algorithm and the classical vertical association rule mining algorithm in the mining time and the memory usage.
Non-monotony and Boolean automata networks
Noual, Mathilde; Sené, Sylvain
2011-01-01
This paper aims at setting the keystone of a prospective theoretical study on the role of non-monotone interactions in biological regulation networks. Focusing on discrete models of these networks, namely, Boolean automata networks, we propose to analyse the contribution of non-monotony to the diversity and complexity in their dynamical behaviours. More precisely, in this paper, we start by detailing some motivations, both mathematical and biological, for our interest in non-monotony, and we discuss how it may account for phenomena that cannot be produced by monotony only. Then, to build some understanding in this direction, we propose some preliminary results on the dynamical behaviour of some specific non-monotone Boolean automata networks called XOR circulant networks.
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...
Estimation for the simple linear Boolean model
2006-01-01
We consider the simple linear Boolean model, a fundamental coverage process also known as the Markov/General/infinity queue. In the model, line segments of independent and identically distributed length are located at the points of a Poisson process. The segments may overlap, resulting in a pattern of "clumps"-regions of the line that are covered by one or more segments-alternating with uncovered regions or "spacings". Study and application of the model have been impeded by the difficult...
Boolean methods of optimization over independence systems
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.
1983-01-01
This paper presents both a direct and an iterative method of solving the combinatorial optimization problem associated with any independence system. The methods use Boolean algebraic computations to produce solutions. In addition, the iterative method employs a version of the greedy algorithm both to compute upper bounds on the optimum value and to produce the additional circuits needed at every stage. The methods are extensions of those used to solve a problem of fire protection at nuclear reactor power plants.
Boolean approach to common event analysis
Energy Technology Data Exchange (ETDEWEB)
Worrell, R.B.; Stack, D.W.
1980-01-01
Although different phenomena may be involved, the problem that must be solved for each kind of common event analysis is essentially the same: to determine the effect of common events on the behavior of a system. A Boolean approach to the problem is set forth. Because of the large equations that arise, processing must be done by computers. Vital location analysis is a particular kind of common event analysis that is used to study ways to prevent the sabotage of nuclear reactors. (RWR)
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
Spectra of Tukey types of ultrafilters on Boolean algebras
Brown, Jennifer A.; Dobrinen, Natasha
2014-01-01
Extending recent investigations on the structure of Tukey types of ultrafilters on $\\mathcal{P}(\\omega)$ to Boolean algebras in general, we classify the spectra of Tukey types of ultrafilters for several classes of Boolean algebras, including interval algebras, tree algebras, and pseudo-tree algebras.
Boolean Queries and Term Dependencies in Probabilistic Retrieval Models.
Croft, W. Bruce
1986-01-01
Proposes approach to integrating Boolean and statistical systems where Boolean queries are interpreted as a means of specifying term dependencies in relevant set of documents. Highlights include series of retrieval experiments designed to test retrieval strategy based on term dependence model and relation of results to other work. (18 references)…
Noise as a Boolean algebra of sigma-fields
Tsirelson, Boris
2011-01-01
The black noise of two-dimensional percolation, disclosed recently by O. Schramm, S. Smirnov and C. Garban, exceeds the limits of the existing framework based on one-dimensional intervals. A remake of the theory of noises, provided here, treats them as Boolean algebras of sigma-fields. Completeness of the Boolean algebra implies classicality, which answers an old question of J. Feldman.
Graphical interpretation of Boolean operators for protein NMR assignments
Energy Technology Data Exchange (ETDEWEB)
Verdegem, Dries [Universite des Sciences et Technologies de Lille, Unite de Glycobiologie Structurale et Fonctionelle, UMR 8576 CNRS, IFR 147 (France); Dijkstra, Klaas [University of Groningen, Department of Biophysical Chemistry (Netherlands); Hanoulle, Xavier; Lippens, Guy [Universite des Sciences et Technologies de Lille, Unite de Glycobiologie Structurale et Fonctionelle, UMR 8576 CNRS, IFR 147 (France)], E-mail: guy.lippens@univ-lille1.fr
2008-09-15
We have developed a graphics based algorithm for semi-automated protein NMR assignments. Using the basic sequential triple resonance assignment strategy, the method is inspired by the Boolean operators as it applies 'AND'-, 'OR'- and 'NOT'-like operations on planes pulled out of the classical three-dimensional spectra to obtain its functionality. The method's strength lies in the continuous graphical presentation of the spectra, allowing both a semi-automatic peaklist construction and sequential assignment. We demonstrate here its general use for the case of a folded protein with a well-dispersed spectrum, but equally for a natively unfolded protein where spectral resolution is minimal.
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
Boolean Algebra. Geometry Module for Use in a Mathematics Laboratory Setting.
Brotherton, Sheila; And Others
This module is recommended as an honors unit to follow a unit on logic. There are four basic parts: (1) What is a Boolean Algebra; (2) Using Boolean Algebra to Prove Theorems; (3) Using Boolean Algebra to Simplify Logical Statements; and (4) Circuit Problems with Logic and Boolean Algebra. Of these, sections 1, 2, and 3 are primarily written…
Reasoning formalism in Boolean operator fuzzy logic
Institute of Scientific and Technical Information of China (English)
邓安生; 刘叙华
1995-01-01
Based on the newly introduced concepts of true-level and false-level, the formal structure of reasoning in Boolean operator fuzzy logic is presented. As a generalization of the theory of epistemic process in open logic, a formalism is also proposed to describe human reasoning with uncertain, inconsistent and insufficient knowledge, which can characterize the knowledge increment and revision, as well as the epistemic evolution. The formalism provides an explanation to the dynamic properties of human reasoning, i. e. continuous revision and combination of beliefs.
Towards boolean operations with thermal photons
Ben-Abdallah, Philippe
2016-01-01
The Boolean algebra is the natural theoretical framework for a classical information treatment. The basic logical operations are usually performed using logic gates. In this Letter we demonstrate that NOT, OR and AND gates can be realized exploiting the near-field radiative interaction in N-body systems with phase change materials. With the recent development of a photon thermal transistor and thermal memory, this result paves the way for a full information treatment and smart solutions for active thermal management at nanoscale with photons.
Boolean algebraic analysis of fire protection
Energy Technology Data Exchange (ETDEWEB)
Hulme, B.L.; Shiver, A.W.; Slater, P.J.
1982-01-01
This paper describes a computational procedure which can be used to find minimum cost ways to protect the critical combinations of equipment from a single-source fire by protecting certain areas and strengthening certain barriers against fire. The procedure yields a complete set of optimum solutions by iteratively computing upper and lower bounds on the minimum cost. The fire protection sets evolve from Boolean algebraic computations which obtain minimum cost blocking sets associated with the lower bounds while the upper bounds are producd by maxflow-mincut calculations in a network.
Towards Boolean operations with thermal photons
Ben-Abdallah, Philippe; Biehs, Svend-Age
2016-12-01
The Boolean algebra is the natural theoretical framework for a classical information treatment. The basic logical operations are usually performed using logic gates. In this Rapid Communication we demonstrate that not, or, and and gates can be realized exploiting the near-field radiative interaction in N -body systems with phase change materials. With the recent development of a photon thermal transistor and thermal memory, this result paves the way for a full information treatment and smart solutions for active thermal management at nanoscale with photons.
The Boolean algebra and central Galois algebras
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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.
Partial Synchronization of Interconnected Boolean Networks.
Chen, Hongwei; Liang, Jinling; Lu, Jianquan
2017-01-01
This paper addresses the partial synchronization problem for the interconnected Boolean networks (BNs) via the semi-tensor product (STP) of matrices. First, based on an algebraic state space representation of BNs, a necessary and sufficient criterion is presented to ensure the partial synchronization of the interconnected BNs. Second, by defining an induced digraph of the partial synchronized states set, an equivalent graphical description for the partial synchronization of the interconnected BNs is established. Consequently, the second partial synchronization criterion is derived in terms of adjacency matrix of the induced digraph. Finally, two examples (including an epigenetic model) are provided to illustrate the efficiency of the obtained results.
Relative stability of network states in Boolean network models of gene regulation in development.
Zhou, Joseph Xu; Samal, Areejit; d'Hérouël, Aymeric Fouquier; Price, Nathan D; Huang, Sui
2016-01-01
Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.
Stochastic Pseudo-Boolean Optimization
2011-07-31
explicit storage of value functions in computer memory . This is why our computations are based on instances that have large number of columns and...quadratic problems. European Journal of Operational Research, 137(2):272–287, 2002. [66] F. Glover, G.A. Kochenberger, and B. Alidaee. Adaptive memory tabu...Letters, 33:312–318, 2005. [127] O.A. Prokopyev, C. Meneses , C.A.S. Oliveira, and P.M. Pardalos. On multiple-ratio hyperbolic 0–1 programming problems
Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited
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Babak Faryabi
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.
Controllability of asynchronous Boolean multiplex control networks
Luo, Chao; Wang, Xingyuan; Liu, Hong
2014-09-01
In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) is studied. First, the model of Boolean multiplex control networks under Harvey' asynchronous update is presented. By means of semi-tensor product approach, the logical dynamics is converted into linear representation, and a generalized formula of control-depending network transition matrices is achieved. Second, a necessary and sufficient condition is proposed to verify that only control-depending fixed points of ABMCNs can be controlled with probability one. Third, using two types of controls, the controllability of system is studied and formulae are given to show: (a) when an initial state is given, the reachable set at time s under a group of specified controls; (b) the reachable set at time s under arbitrary controls; (c) the specific probability values from a given initial state to destination states. Based on the above formulae, an algorithm to calculate overall reachable states from a specified initial state is presented. Moreover, we also discuss an approach to find the particular control sequence which steers the system between two states with maximum probability. Examples are shown to illustrate the feasibility of the proposed scheme.
Controllability of asynchronous Boolean multiplex control networks.
Luo, Chao; Wang, Xingyuan; Liu, Hong
2014-09-01
In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) is studied. First, the model of Boolean multiplex control networks under Harvey' asynchronous update is presented. By means of semi-tensor product approach, the logical dynamics is converted into linear representation, and a generalized formula of control-depending network transition matrices is achieved. Second, a necessary and sufficient condition is proposed to verify that only control-depending fixed points of ABMCNs can be controlled with probability one. Third, using two types of controls, the controllability of system is studied and formulae are given to show: (a) when an initial state is given, the reachable set at time s under a group of specified controls; (b) the reachable set at time s under arbitrary controls; (c) the specific probability values from a given initial state to destination states. Based on the above formulae, an algorithm to calculate overall reachable states from a specified initial state is presented. Moreover, we also discuss an approach to find the particular control sequence which steers the system between two states with maximum probability. Examples are shown to illustrate the feasibility of the proposed scheme.
Synchronization of coupled Boolean phase oscillators
Rosin, David P.; Rontani, Damien; Gauthier, Daniel J.
2014-04-01
We design, characterize, and couple Boolean phase oscillators that include state-dependent feedback delay. The state-dependent delay allows us to realize an adjustable coupling strength, even though only Boolean signals are exchanged. Specifically, increasing the coupling strength via the range of state-dependent delay leads to larger locking ranges in uni- and bidirectional coupling of oscillators in both experiment and numerical simulation with a piecewise switching model. In the unidirectional coupling scheme, we unveil asymmetric triangular-shaped locking regions (Arnold tongues) that appear at multiples of the natural frequency of the oscillators. This extends observations of a single locking region reported in previous studies. In the bidirectional coupling scheme, we map out a symmetric locking region in the parameter space of frequency detuning and coupling strength. Because of the large scalability of our setup, our observations constitute a first step towards realizing large-scale networks of coupled oscillators to address fundamental questions on the dynamical properties of networks in a new experimental setting.
nLukac, Maarti; Kameyama, Michitaka
2011-01-01
It has been experimentally proven that realizing universal quantum gates using higher-radices logic is practically and technologically possible. We developed a Parallel Genetic Algorithm that synthesizes Boolean reversible circuits realized with a variety of quantum gates on qudits with various radices. In order to allow synthesizing circuits of medium sizes in the higher radix quantum space we performed the experiments using a GPU accelerated Genetic Algorithm. Using the accelerated GA we compare heuristic improvements to the mutation process based on cost minimization, on the adaptive cost of the primitives and improvements due to Baldwinian vs. Lamarckian GA. We also describe various fitness function formulations that allowed for various realizations of well known universal Boolean reversible or quantum-probabilistic circuits.
Directory of Open Access Journals (Sweden)
Yanguang Zhu
2011-06-01
Full Text Available A military decision maker is typically confronted by the task of determining optimal course of action under some constraints in complex uncertain situation. Thus, a new class of Combinational Constraint Optimization Problem (CCOP is formalized, that is utilized to solve this complex Operation Optimization Problem. The object function of CCOP is modeled by Influence net, and the constraints of CCOP relate to resource and collaboration. These constraints are expressed by Pseudo-Boolean and Boolean constraints. Thus CCOP holds a complex mathematical configuration, which is expressed as a 0 1 integer optimization problem with compositional constraints and unobvious optimal object function. A novel method of Genetic Algorithm (GA combination of Boolean Constraint Programming (BCP is proposed to solve CCOP. The constraints of CCOP can be easily reduced and transformed into Disjunctive Normal Form (DNF by BCP. The DNF representation then can be used to drive GA so as to solve CCOP. Finally, a numerical experiment is given to demonstrate the effectiveness of above method.
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.
Directory of Open Access Journals (Sweden)
Claudia Stötzel
Full Text Available 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.
布尔代数的软商布尔代数%Soft quotient Boolean algebra of Boolean algebra
Institute of Scientific and Technical Information of China (English)
刘卫锋
2015-01-01
The concepts of soft congruence relation,soft quotient algebra and soft quotient Boolean algebra of Boolean algebra are defined,and it is proved that soft congruence relation and soft ideal of Boolean algebra can be determined by each other.Then soft quotient Boolean algebra of Boolean algebra is obtained from soft proper ideal of Boolean algebra. Finally,the nature of preserving soft congruence relation of soft homomorphism of Boolean algebras is proved.%定义了布尔代数的软合同关系、软商代数和软商布尔代数等概念，证明了布尔代数的软合同关系与软理想相互确定，进而由布尔代数的软真理想得到布尔代数的软商布尔代数。最后，证明了布尔代数的软同态具有保软合同性。
Robbins algebra : conditions that make a near-Boolean algebra Boolean.
Energy Technology Data Exchange (ETDEWEB)
Winker, S.; Mathematics and Computer Science
1990-01-01
Some problems posed years ago remain challenging today. In particular, the Robbins problem, which is still open and which is the focus of attention in this paper, offers interesting challenges for attack with the assistance of an automated reasoning program; for the study presented here, we used the program OTTER. For example, when one submits this problem, which asks for a proof that every Robbins algebra is a Boolean algebra, a large number of deduced clauses results. One must, therefore, consider the possibility that there exists a Robbins algebra that is not Boolean; such an algebra would have to be infinite. One can instead search for properties that, if adjoined to those of a Robbins algebra, guarantee that the algebra is Boolean. Here we present a number of such properties, and we show how an automated reasoning program was used to obtain the corresponding proofs. Additional properties have been identified, and we include here examples of using such a program to check that the corresponding hand-proofs are correct. We present the appropriate input for many of the examples and also include the resulting proofs in clause notation.
Boolean Burritos: How the Faculty Ate Up Keyword Searching.
York, Sherry
1999-01-01
Describes an activity that librarians can use to acquaint teachers with keyword searching and Boolean operators to more successfully use the library's online catalog. Uses food ingredients to represent various possible combinations. (LRW)
A Full Bayesian Approach for Boolean Genetic Network Inference
Han, Shengtong; Wong, Raymond K. W.; Lee, Thomas C. M.; Shen, Linghao; Li, Shuo-Yen R.; Fan, Xiaodan
2014-01-01
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. PMID:25551820
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.
Phase transition in NK-Kauffman networks and its correction for Boolean irreducibility
Zertuche, Federico
2014-05-01
In a series of articles published in 1986, Derrida and his colleagues studied two mean field treatments (the quenched and the annealed) for NK-Kauffman networks. Their main results lead to a phase transition curve Kc 2 pc(1-pc)=1 (0
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.
PATHLOGIC-S: a scalable Boolean framework for modelling cellular signalling.
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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.
Multipath Detection Using Boolean Satisfiability Techniques
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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.
Message passing for quantified Boolean formulas
Zhang, Pan; Zdeborová, Lenka; Zecchina, Riccardo
2012-01-01
We introduce two types of message passing algorithms for quantified Boolean formulas (QBF). The first type is a message passing based heuristics that can prove unsatisfiability of the QBF by assigning the universal variables in such a way that the remaining formula is unsatisfiable. In the second type, we use message passing to guide branching heuristics of a Davis-Putnam Logemann-Loveland (DPLL) complete solver. Numerical experiments show that on random QBFs our branching heuristics gives robust exponential efficiency gain with respect to the state-of-art solvers. We also manage to solve some previously unsolved benchmarks from the QBFLIB library. Apart from this our study sheds light on using message passing in small systems and as subroutines in complete solvers.
Reduction Mappings between Probabilistic Boolean Networks
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Ivan Ivanov
2004-01-01
Full Text Available Probabilistic Boolean networks (PBNs comprise a model describing a directed graph with rule-based dependences between its nodes. The rules are selected, based on a given probability distribution which provides a flexibility when dealing with the uncertainty which is typical for genetic regulatory networks. Given the computational complexity of the model, the characterization of mappings reducing the size of a given PBN becomes a critical issue. Mappings between PBNs are important also from a theoretical point of view. They provide means for developing a better understanding about the dynamics of PBNs. This paper considers two kinds of mappings reduction and projection and their effect on the original probability structure of a given PBN.
Robust Boolean Operation for Sculptured Models
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
To enhance the ability of current modeling system, an uniformed representation is designed to represent wire-frame, solid, surface models. We present an algorithm for Boolean operation between the models under this representation. Accuracy, efficiency and robustness are the main consideration. The geometric information is represented with trimmed parametric patches and trimmed parametric splines. The topological information is represented with an extended half-edge data structure. In the process of intersection calculation, hierarchy intersection method is applied for unified classification. Tracing the intersection curve to overcome degenerate cases that occur frequently in practice. The algorithm has been implemented as the modeling kernel of a feature based modeling system named GS-CAD98, which was developed on Windows/NT platform.
Synchronization of Arbitrarily Switched Boolean Networks.
Chen, Hongwei; Liang, Jinling; Huang, Tingwen; Cao, Jinde
2017-03-01
This paper investigates the complete synchronization problem for the drive-response switched Boolean networks (SBNs) under arbitrary switching signals, where the switching signals of the response SBN follow those generated by the drive SBN at each time instant. First, the definition of complete synchronization is introduced for the drive-response SBNs under arbitrary switching signals. Second, the concept of switching reachable set starting from a given initial state set is put forward. Based on it, a necessary and sufficient condition is derived for the complete synchronization of the drive-response SBNs. Last, we give a simple algebraic expression for the switching reachable set in a given number of time steps, and two computable algebraic criteria are obtained for the complete synchronization of the SBNs. A biological example is given to demonstrate the effectiveness of the obtained main results.
A Boolean Approach to Airline Business Model Innovation
DEFF Research Database (Denmark)
Hvass, Kristian Anders
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....
Boolean network model predicts knockout mutant phenotypes of fission yeast.
Directory of Open Access Journals (Sweden)
Maria I Davidich
Full Text Available BOOLEAN NETWORKS (OR: networks of switches are extremely simple mathematical models of biochemical signaling networks. Under certain circumstances, Boolean networks, despite their simplicity, are capable of predicting dynamical activation patterns of gene regulatory networks in living cells. For example, the temporal sequence of cell cycle activation patterns in yeasts S. pombe and S. cerevisiae are faithfully reproduced by Boolean network models. An interesting question is whether this simple model class could also predict a more complex cellular phenomenology as, for example, the cell cycle dynamics under various knockout mutants instead of the wild type dynamics, only. Here we show that a Boolean network model for the cell cycle control network of yeast S. pombe correctly predicts viability of a large number of known mutants. So far this had been left to the more detailed differential equation models of the biochemical kinetics of the yeast cell cycle network and was commonly thought to be out of reach for models as simplistic as Boolean networks. The new results support our vision that Boolean networks may complement other mathematical models in systems biology to a larger extent than expected so far, and may fill a gap where simplicity of the model and a preference for an overall dynamical blueprint of cellular regulation, instead of biochemical details, are in the focus.
Boolean Network Model Predicts Knockout Mutant Phenotypes of Fission Yeast
Davidich, Maria I.; Bornholdt, Stefan
2013-01-01
Boolean networks (or: networks of switches) are extremely simple mathematical models of biochemical signaling networks. Under certain circumstances, Boolean networks, despite their simplicity, are capable of predicting dynamical activation patterns of gene regulatory networks in living cells. For example, the temporal sequence of cell cycle activation patterns in yeasts S. pombe and S. cerevisiae are faithfully reproduced by Boolean network models. An interesting question is whether this simple model class could also predict a more complex cellular phenomenology as, for example, the cell cycle dynamics under various knockout mutants instead of the wild type dynamics, only. Here we show that a Boolean network model for the cell cycle control network of yeast S. pombe correctly predicts viability of a large number of known mutants. So far this had been left to the more detailed differential equation models of the biochemical kinetics of the yeast cell cycle network and was commonly thought to be out of reach for models as simplistic as Boolean networks. The new results support our vision that Boolean networks may complement other mathematical models in systems biology to a larger extent than expected so far, and may fill a gap where simplicity of the model and a preference for an overall dynamical blueprint of cellular regulation, instead of biochemical details, are in the focus. PMID:24069138
Synchronization in an array of coupled Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Li, Rui, E-mail: rui.li@pku.edu.cn [State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871 (China); Chu, Tianguang, E-mail: chutg@pku.edu.cn [State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871 (China)
2012-10-01
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.
N-learners problem: Learning Boolean combinations of halfspaces
Energy Technology Data Exchange (ETDEWEB)
Rao, N.S.V. (Old Dominion Univ., Norfolk, VA (United States). Dept. of Computer Science); Oblow, E.M.; Glover, C.W. (Oak Ridge National Lab., TN (United States))
1992-03-01
Given two subsets S{sub 1} and S{sub 2} (not necessarily finite) of {Re}{sup d} separable by a Boolean combination of N halfspaces, we consider the problem of learning the separation function from a finite set of examples, i.e. we produce with high probability a function close to the actual separating function. Our solution consists of a system of N perceptrons and a single consolidator which combines the outputs of the individual perceptrons. We show that an off-line version of this problem, where the examples are given in a batch, can be solved in time polynomial in the number of examples. We also provide an on-line learning algorithm that incrementally solves the problem by suitably training a system of N perceptrons much in the spirit of the classical perceptron learning algorithm. This solution constitutes an example of a composite system of N learners capable of accomplishing a task that is not achievable by a single learner, for a single perceptron is incapable of separating sets that are not linearly separable.
Tabus, I; Petrescu, D; Gabbouj, M
1996-01-01
A training framework is developed in this paper to design optimal nonlinear filters for various signal and image processing tasks. The targeted families of nonlinear filters are the Boolean filters and stack filters. The main merit of this framework at the implementation level is perhaps the absence of constraining models, making it nearly universal in terms of application areas. We develop fast procedures to design optimal or close to optimal filters, based on some representative training set. Furthermore, the training framework shows explicitly the essential part of the initial specification and how it affects the resulting optimal solution. Symmetry constraints are imposed on the data and, consequently, on the resulting optimal solutions for improved performance and ease of implementation. The case study is dedicated to natural images. The properties of optimal Boolean and stack filters, when the desired signal in the training set is the image of a natural scene, are analyzed. Specifically, the effect of changing the desired signal (using various natural images) and the characteristics of the noise (the probability distribution function, the mean, and the variance) is analyzed. Elaborate experimental conditions were selected to investigate the robustness of the optimal solutions using a sensitivity measure computed on data sets. A remarkably low sensitivity and, consequently, a good generalization power of Boolean and stack filters are revealed. Boolean-based filters are thus shown to be not only suitable for image restoration but also robust, making it possible to build libraries of "optimal" filters, which are suitable for a set of applications.
Harmonic analysis of Boolean networks: determinative power and perturbations
2013-01-01
Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X={X1,...,Xn} of some node i and its associated function fi(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs. PMID:23642003
Boolean Logic: An Aid for Searching Computer Databases in Special Education and Rehabilitation.
Summers, Edward G.
1989-01-01
The article discusses using Boolean logic as a tool for searching computerized information retrieval systems in special education and rehabilitation technology. It includes discussion of the Boolean search operators AND, OR, and NOT; Venn diagrams; and disambiguating parentheses. Six suggestions are offered for development of good Boolean logic…
Noise as a Boolean algebra of sigma-fields. II. Classicality, blackness, spectrum
Tsirelson, Boris
2011-01-01
Similarly to noises, Boolean algebras of sigma-fields can be black. A noise may be treated as a homomorphism from a Boolean algebra of regular open sets to a Boolean algebra of sigma-fields. Spectral sets are useful also in this framework.
Efficient Analog Circuits for Boolean Satisfiability
Yin, Xunzhao; Varga, Melinda; Ercsey-Ravasz, Maria; Toroczkai, Zoltan; Hu, Xiaobo Sharon
2016-01-01
Efficient solutions to NP-complete problems would significantly benefit both science and industry. However, such problems are intractable on digital computers based on the von Neumann architecture, thus creating the need for alternative solutions to tackle such problems. Recently, a deterministic, continuous-time dynamical system (CTDS) was proposed (Nature Physics, 7(12), 966 (2011)) to solve a representative NP-complete problem, Boolean Satisfiability (SAT). This solver shows polynomial analog time-complexity on even the hardest benchmark $k$-SAT ($k \\geq 3$) formulas, but at an energy cost through exponentially driven auxiliary variables. With some modifications to the CTDS equations, here we present a novel analog hardware SAT solver, AC-SAT, implementing the CTDS. AC-SAT is intended to be used as a co-processor, and with its modular design can be readily extended to different problem sizes. The circuit is designed and simulated based on a 32nm CMOS technology. SPICE simulation results show speedup factor...
Boolean Satisfiability using Noise Based Logic
Lin, Pey-Chang Kent; Khatri, Sunil P
2011-01-01
In this paper, we present a novel algorithm to solve the Boolean Satisfiability (SAT) problem, using noise-based logic (NBL). Contrary to what the name may suggest, NBL is not a random/fuzzy logic system. In fact, it is a completely deterministic logic system. A key property of NBL is that it allows us to apply a superposition of many input vectors to a SAT instance at the same time, circumventing a key restriction and assumption in the traditional approach to solving SAT. By exploiting the superposition property of NBL, our NBL-based SAT algorithm can determine whether an instance is SAT or not in a single operation. A satisfying solution can be found by iteratively performing SAT check operations up to n times, where n is the number of variables in the SAT instance. Although this paper does not focus on the realization of an NBL-based SAT engine, such an engine can be conceived using analog circuits (wide-band amplifiers, adders and multipliers), FPGAs or ASICs. Additionally, we also discus scalability of o...
A more robust Boolean model describing inhibitor binding
Institute of Scientific and Technical Information of China (English)
Zhaoqian Steven XIE; Chao TANG
2008-01-01
From the first application of the Boolean model to the cell cycle regulation network of budding yeast, new regulative pathways have been discovered, par-ticularly in the G1/S transition circuit. This discovery called for finer modeling to study the essential biology, and the resulting outcomes are first introduced in the ar-ticle. A traditional Boolean network model set up for the new G1/S transition circuit shows that it cannot correctly simulate real biology unless the model parameters are fine tuned. The deficiency is caused by an overly coarse-grained description of the inhibitor binding process, which shall be overcome by a two-vector model proposed whose robustness is surveyed using random perturba-tions. Simulations show that the proposed two-vector model is much more robust in describing inhibitor binding processes within the Boolean framework.
Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach.
Zhang, Jianming; Sclaroff, Stan
2016-05-01
We demonstrate the usefulness of surroundedness for eye fixation prediction by proposing a Boolean Map based Saliency model (BMS). In our formulation, an image is characterized by a set of binary images, which are generated by randomly thresholding the image's feature maps in a whitened feature space. Based on a Gestalt principle of figure-ground segregation, BMS computes a saliency map by discovering surrounded regions via topological analysis of Boolean maps. Furthermore, we draw a connection between BMS and the Minimum Barrier Distance to provide insight into why and how BMS can properly captures the surroundedness cue via Boolean maps. The strength of BMS is verified by its simplicity, efficiency and superior performance compared with 10 state-of-the-art methods on seven eye tracking benchmark datasets.
Control of Large-Scale Boolean Networks via Network Aggregation.
Zhao, Yin; Ghosh, Bijoy K; Cheng, Daizhan
2016-07-01
A major challenge to solve problems in control of Boolean networks is that the computational cost increases exponentially when the number of nodes in the network increases. We consider the problem of controllability and stabilizability of Boolean control networks, address the increasing cost problem by partitioning the network graph into several subnetworks, and analyze the subnetworks separately. Easily verifiable necessary conditions for controllability and stabilizability are proposed for a general aggregation structure. For acyclic aggregation, we develop a sufficient condition for stabilizability. It dramatically reduces the computational complexity if the number of nodes in each block of the acyclic aggregation is small enough compared with the number of nodes in the entire Boolean network.
Synchronization in output-coupled temporal Boolean networks
Lu, Jianquan; Zhong, Jie; Tang, Yang; Huang, Tingwen; Cao, Jinde; Kurths, Jürgen
2014-09-01
This paper presents an analytical study of synchronization in an array of output-coupled temporal Boolean networks. A temporal Boolean network (TBN) is a logical dynamic system developed to model Boolean networks with regulatory delays. Both state delay and output delay are considered, and these two delays are assumed to be different. By referring to the algebraic representations of logical dynamics and using the semi-tensor product of matrices, the output-coupled TBNs are firstly converted into a discrete-time algebraic evolution system, and then the relationship between the states of coupled TBNs and the initial state sequence is obtained. Then, some necessary and sufficient conditions are derived for the synchronization of an array of TBNs with an arbitrary given initial state sequence. Two numerical examples including one epigenetic model are finally given to illustrate the obtained results.
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.
A Boolean action of C(M,U(1)) without a spatial model
Moore, Justin Tatch
2012-01-01
We will demonstrate that if M is an uncountable compact metric space, then there is an action of the Polish group of all continuous functions from M to U(1) on a separable probability algebra which preserves the measure and yet does not admit a point realization (in a standard probability space) in the sense of Mackey. This contrasts Mackey's point realization theorem for locally compact, second countable groups which asserts that any measure preserving Boolean action of a locally compact, second countable group on a separable probability algebra can be realized as an action on the points of a standard probability space.
Security analysis of boolean algebra based on Zhang-Wang digital signature scheme
Zheng, Jinbin
2014-10-01
In 2005, Zhang and Wang proposed an improvement signature scheme without using one-way hash function and message redundancy. In this paper, we show that this scheme exits potential safety concerns through the analysis of boolean algebra, such as bitwise exclusive-or, and point out that mapping is not one to one between assembly instructions and machine code actually by means of the analysis of the result of the assembly program segment, and which possibly causes safety problems unknown to the software.
Coevolution of Information Processing and Topology in Hierarchical Adaptive Random Boolean Networks
Gorski, Piotr J; Holyst, Janusz A
2015-01-01
Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of distinct adaptive RBNs - subnetworks - connected by a set of permanent interlinks. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. We investigate mean node information, mean edge information as well as a mean node degree as functions of model parameters and demonstrate HARBN's ability to describe complex hierarchical systems.
Security analysis of boolean algebra based on Zhang-Wang digital signature scheme
Energy Technology Data Exchange (ETDEWEB)
Zheng, Jinbin, E-mail: jbzheng518@163.com [School of Mathematics and Computer Science, Long Yan University, Longyan 364012 (China)
2014-10-06
In 2005, Zhang and Wang proposed an improvement signature scheme without using one-way hash function and message redundancy. In this paper, we show that this scheme exits potential safety concerns through the analysis of boolean algebra, such as bitwise exclusive-or, and point out that mapping is not one to one between assembly instructions and machine code actually by means of the analysis of the result of the assembly program segment, and which possibly causes safety problems unknown to the software.
Structured scale dependence in the Lyapunov exponent of a Boolean chaotic map.
Cohen, Seth D
2015-04-01
We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network, which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we show that the structured scale-dependence in the system's Lyapunov exponent is the result of the discrete logic elements in the map operator's stretching function.
Boolean versus ranked querying for biomedical systematic reviews
Directory of Open Access Journals (Sweden)
Cavedon Lawrence
2010-10-01
Full Text Available Abstract Background The process of constructing a systematic review, a document that compiles the published evidence pertaining to a specified medical topic, is intensely time-consuming, often taking a team of researchers over a year, with the identification of relevant published research comprising a substantial portion of the effort. The standard paradigm for this information-seeking task is to use Boolean search; however, this leaves the user(s the requirement of examining every returned result. Further, our experience is that effective Boolean queries for this specific task are extremely difficult to formulate and typically require multiple iterations of refinement before being finalized. Methods We explore the effectiveness of using ranked retrieval as compared to Boolean querying for the purpose of constructing a systematic review. We conduct a series of experiments involving ranked retrieval, using queries defined methodologically, in an effort to understand the practicalities of incorporating ranked retrieval into the systematic search task. Results Our results show that ranked retrieval by itself is not viable for this search task requiring high recall. However, we describe a refinement of the standard Boolean search process and show that ranking within a Boolean result set can improve the overall search performance by providing early indication of the quality of the results, thereby speeding up the iterative query-refinement process. Conclusions Outcomes of experiments suggest that an interactive query-development process using a hybrid ranked and Boolean retrieval system has the potential for significant time-savings over the current search process in the systematic reviewing.
Analysis of Boolean Equation Systems through Structure Graphs
Reniers, Michel A; 10.4204/EPTCS.18.7
2010-01-01
We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems with bisimilar structure graphs have the same solution. We show that our work conservatively extends earlier work, conducted by Keiren and Willemse, in which dependency graphs were used to analyse a subclass of Boolean equation systems, viz., equation systems in standard recursive form. We illustrate our approach by a small example, demonstrating the effect of simplifying an equation system through minimisation of its structure graph.
Perturbation propagation in random and evolved Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Fretter, Christoph [Instistut fuer Informatik, Martin-Luther-Universitaet Halle-Wittenberg, Von-Seckendorffplatz 1, 06120 Halle (Germany); Szejka, Agnes; Drossel, Barbara [Institut fuer Festkoerperphysik, Technische Universitaet Darmstadt, Hochschulstrasse 6, 64289 Darmstadt (Germany)], E-mail: Christoph.Fretter@informatik.uni-halle.de
2009-03-15
In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.
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.
Unlimited multistability and Boolean logic in microbial signalling.
Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S
2015-07-01
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.
Unlimited multistability and Boolean logic in microbial signalling
Kothamachu, Varun B.; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S.
2015-01-01
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. PMID:26040599
2013-01-01
Background Cancer is a complex disease where molecular mechanism remains elusive. A systems approach is needed to integrate diverse biological information for the prognosis and therapy risk assessment using mechanistic approach to understand gene interactions in pathways and networks and functional attributes to unravel the biological behaviour of tumors. Results We weighted the functional attributes based on various functional properties observed between cancerous and non-cancerous genes reported from literature. This weighing schema was then encoded in a Boolean logic framework to rank differentially expressed genes. We have identified 17 genes to be differentially expressed from a total of 11,173 genes, where ten genes are reported to be down-regulated via epigenetic inactivation and seven genes are up-regulated. Here, we report that the overexpressed genes IRAK1, CHEK1 and BUB1 may play an important role in ovarian cancer. We also show that these 17 genes can be used to form an ovarian cancer signature, to distinguish normal from ovarian cancer subjects and that the set of three genes, CHEK1, AR, and LYN, can be used to classify good and poor prognostic tumors. Conclusion We provided a workflow using a Boolean logic schema for the identification of differentially expressed genes by integrating diverse biological information. This integrated approach resulted in the identification of genes as potential biomarkers in ovarian cancer. PMID:23383610
FPGA implementation of a stochastic neural network for monotonic pseudo-Boolean optimization.
Grossi, Giuliano; Pedersini, Federico
2008-08-01
In this paper a FPGA implementation of a novel neural stochastic model for solving constrained NP-hard problems is proposed and developed. The model exploits pseudo-Boolean functions both to express the constraints and to define the cost function, interpreted as energy of a neural network. A wide variety of NP-hard problems falls in the class of problems that can be solved by this model, particularly those having a quadratic pseudo-Boolean penalty function. The proposed hardware implementation provides high computation speed by exploiting parallelism, as the neuron update and the constraint violation check can be performed in parallel over the whole network. The neural system has been tested on random and benchmark graphs, showing good performance with respect to the same heuristic for the same problems. Furthermore, the computational speed of the FPGA implementation has been measured and compared to software implementation. The developed architecture featured dramatically faster computation, with respect to the software implementation, even adopting a low-cost FPGA chip.
Mean-Field and Non-Mean-Field Behaviors in Scale-free Networks with Random Boolean Dynamics
Silva, A Castro e
2009-01-01
We study two types of simplified Boolean dynamics over scale-free networks, both with synchronous update. Assigning only Boolean functions AND and XOR to the nodes with probability $1-p$ and $p$, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamic as its own input (self-regulation) or not. The same conclusion holds for the Kauffman KN model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation, and (ii) disagree for small $p$ when self-regulation is present in the model.
Mean-field and non-mean-field behaviors in scale-free networks with random Boolean dynamics
Energy Technology Data Exchange (ETDEWEB)
Castro e Silva, A [Departamento de Fisica, Universidade Federal de Ouro Preto, Campus Universitario, 35.400-000 Ouro Preto, Minas Gerais (Brazil); Kamphorst Leal da Silva, J, E-mail: alcidescs@gmail.co, E-mail: jaff@fisica.ufmg.b [Departamento de Fisica, Universidade Federal de Minas Gerais, Caixa Postal 702, 30.161-970, Belo Horizonte, Minas Gerais (Brazil)
2010-06-04
We study two types of simplified Boolean dynamics in scale-free networks, both with a synchronous update. Assigning only the Boolean functions AND and XOR to the nodes with probabilities 1 - p and p, respectively, we are able to analyze the density of 1's and the Hamming distance on the network by numerical simulations and by a mean-field approximation (annealed approximation). We show that the behavior is quite different if the node always enters in the dynamics as its own input (self-regulation) or not. The same conclusion holds for the Kauffman NK model. Moreover, the simulation results and the mean-field ones (i) agree well when there is no self-regulation and (ii) disagree for small p when self-regulation is present in the model.
Boolean approaches to graph embeddings related to VLSI
Institute of Scientific and Technical Information of China (English)
刘彦佩
2001-01-01
This paper discusses the development of Boolean methods in some topics on graph em-beddings which are related to VLSI. They are mainly the general theory of graph embeddability, the orientabilities of a graph and the rectilinear layout of an electronic circuit.
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.
Linear Strategy for Boolean Ring Based Theorem Proving
Institute of Scientific and Technical Information of China (English)
WU Jinzhao; LIU Zhuojun
2000-01-01
Two inference rules are discussed in boolean ring based theorem proving, and linear strategy is developed. It is shown that both of them are complete for linear strategy. Moreover, by introducing a partial ordering on atoms, pseudo O-linear and O-linear strategies are presented. The former is complete, the latter, however, is complete for clausal theorem proving.
Feedback Controller Design for the Synchronization of Boolean Control Networks.
Liu, Yang; Sun, Liangjie; Lu, Jianquan; Liang, Jinling
2016-09-01
This brief investigates the partial and complete synchronization of two Boolean control networks (BCNs). Necessary and sufficient conditions for partial and complete synchronization are established by the algebraic representations of logical dynamics. An algorithm is obtained to construct the feedback controller that guarantees the synchronization of master and slave BCNs. Two biological examples are provided to illustrate the effectiveness of the obtained results.
Boolean linear differential operators on elementary cellular automata
Martín Del Rey, Ángel
2014-12-01
In this paper, the notion of boolean linear differential operator (BLDO) on elementary cellular automata (ECA) is introduced and some of their more important properties are studied. Special attention is paid to those differential operators whose coefficients are the ECA with rule numbers 90 and 150.
Pointwise Approximation for the Iterated Boolean Sums of Bernstein Operators
Institute of Scientific and Technical Information of China (English)
HUO Xiao-yan; LI Cui-xiang; YAO Qiu-mei
2013-01-01
In this paper,with the help of modulus of smoothness ω2r(4)(f,t),we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator Bnn and obtain direct and inverse theorems when 1-1/r ≤ λ ≤ 1,r ∈ N.
Learning restricted Boolean network model by time-series data
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 μhame, the normalized Hamming distance of state transition μhamst, and the steady-state distribution distance μssd. Results show that the proposed algorithm outperforms the others according to both μhame and μhamst, whereas its performance according to μssd 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. PMID:25093019
Stochastic Boolean networks: An efficient approach to modeling gene regulatory networks
Directory of Open Access Journals (Sweden)
Liang Jinghang
2012-08-01
network inferred from a T cell immune response dataset. An SBN can also implement the function of an asynchronous PBN and is potentially useful in a hybrid approach in combination with a continuous or single-molecule level stochastic model. Conclusions Stochastic Boolean networks (SBNs are proposed as an efficient approach to modelling gene regulatory networks (GRNs. The SBN approach is able to recover biologically-proven regulatory behaviours, such as the oscillatory dynamics of the p53-Mdm2 network and the dynamic attractors in a T cell immune response network. The proposed approach can further predict the network dynamics when the genes are under perturbation, thus providing biologically meaningful insights for a better understanding of the dynamics of GRNs. The algorithms and methods described in this paper have been implemented in Matlab packages, which are attached as Additional files.
Modeling Integrated Cellular Machinery Using Hybrid Petri-Boolean Networks
Berestovsky, Natalie; Zhou, Wanding; Nagrath, Deepak; Nakhleh, Luay
2013-01-01
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 using such more
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
Gene perturbation and intervention in context-sensitive stochastic Boolean networks
2014-01-01
Background In a gene regulatory network (GRN), gene expressions are affected by noise, and stochastic fluctuations exist in the interactions among genes. These stochastic interactions are context dependent, thus it becomes important to consider noise in a context-sensitive manner in a network model. As a logical model, context-sensitive probabilistic Boolean networks (CSPBNs) account for molecular and genetic noise in the temporal context of gene functions. In a CSPBN with n genes and k contexts, however, a computational complexity of O(nk222n ) (or O(nk2 n )) is required for an accurate (or approximate) computation of the state transition matrix (STM) of the size (2 n ∙ k) × (2 n ∙ k) (or 2 n × 2 n ). The evaluation of a steady state distribution (SSD) is more challenging. Recently, stochastic Boolean networks (SBNs) have been proposed as an efficient implementation of an instantaneous PBN. Results The notion of stochastic Boolean networks (SBNs) is extended for the general model of PBNs, i.e., CSPBNs. This yields a novel structure of context-sensitive SBNs (CSSBNs) for modeling the stochasticity in a GRN. A CSSBN enables an efficient simulation of a CSPBN with a complexity of O(nLk2 n ) for computing the state transition matrix, where L is a factor related to the required sequence length in CSSBN for achieving a desired accuracy. A time-frame expanded CSSBN can further efficiently simulate the stationary behavior of a CSPBN and allow for a tunable tradeoff between accuracy and efficiency. The CSSBN approach is more efficient than an analytical method and more accurate than an approximate analysis. Conclusions Context-sensitive stochastic Boolean networks (CSSBNs) are proposed as an efficient approach to modeling the effects of gene perturbation and intervention in gene regulatory networks. A CSSBN analysis provides biologically meaningful insights into the oscillatory dynamics of the p53-Mdm2 network in a context-switching environment. It is shown that
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
Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks
Villegas, Pablo; Ruiz-Franco, José; Hidalgo, Jorge; Muñoz, Miguel A.
2016-01-01
Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent tradeoff between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way –even for asynchronous updating rules– and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity. PMID:27713479
Boolean network-based model of the Bcl-2 family mediated MOMP regulation
2013-01-01
Background Mitochondrial outer membrane permeabilization (MOMP) is one of the most important points in the majority of apoptotic signaling cascades and it is controlled by a network of interactions between the members of the Bcl-2 family. Methods To understand the role of individual members of this family within the MOMP regulation, we have constructed a Boolean network-based model of interactions between the Bcl-2 proteins. Results Computational simulations have revealed the existence of trapping states which, independently from the incoming stimuli, block the occurrence of MOMP. Our results emphasize the role of the antiapoptotic protein Mcl-1 in the majority of these configurations. We demonstrate here the importance of the Bid and Bim for activation of effectors Bax and Bak, and the irreversibility of this activation. The model further points to the antiapoptotic protein Bcl-w as a key factor preventing Bax activation. Conclusions In spite of relative simplicity, the Boolean network-based model provides useful insight into main functioning logic of the Bcl-2 switch, consistent with experimental findings. PMID:23767791
Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks
Villegas, Pablo; Ruiz-Franco, José; Hidalgo, Jorge; Muñoz, Miguel A.
2016-10-01
Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent tradeoff between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way –even for asynchronous updating rules– and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity.
Appearance of implicative regularities in Boolean criterion space and pattern recognition
Energy Technology Data Exchange (ETDEWEB)
Zakrevskii, A.D.
1982-01-01
A new approach to the solution of problems in recognition theory is noted within the framework of the more general problem of the appearance of regularities in the data flow, and of the problem of converting the latter into knowledge, is some adequate model of the class of objects under investigation that operationally permit finding the solution of diverse problems of pattern recognition, classification, empirical prediction, filling in the blanks in experimental tables, etc. This approach is developed in application to the case of binary criteria, which permits efficient utilization of the apparatus of Boolean function theory, but allows extension also of the case of multi-valued criteria. A method is proposed for the determination, by a training sample, of the general properties of a single class of real objects representable by appropriate points of the Boolean space m of all criteria. The method relies on a unique a priori hypothesis about the preference of regularities connecting minimal groups of criteria. The expediency of the appearance of sufficiently strong regularities of the type elementary exclusions that yield implicative relations between criteria and the construction of differentiated prediction procedures on their basis, which permit extrapolation of partially assigned properties of objects not in the training sample with a foundation will follow logically from this hypothesis. 12 references.
Boolean Ring and Its Spectrum%布尔环及其素谱
Institute of Scientific and Technical Information of China (English)
曲伟
2012-01-01
利用交换代数、拓扑等相关知识，讨论了布尔代数、布尔格、布尔环三者之间的对应关系，给出了布尔环及其素谱的一些性质并证明了由布尔环诱导出的布尔格与布尔环上素谱的既开又闲的子集构成的格同构．%In this paper,we show that Boolean rings,Boolean lattices and Boolean algebra are essentially the same. Moreover, every Boolean lattice induced by Boolean ring is isomorphic to the lattice of open and closed subsets of the Boolean ring's spectrum.
Interval soft Boolean algebras%区间软布尔代数
Institute of Scientific and Technical Information of China (English)
刘卫锋; 杜迎雪; 许宏伟
2014-01-01
将区间软集应用于布尔代数之中，定义了区间软布尔代数、区间软布尔子代数、区间理想软布尔代数和区间软布尔代数的区间软同态等概念，并研究了它们的相关性质。推广了软布尔代数及其相关结论。%The interval soft set is applied to the Boolean algebras.The concepts of interval soft Boolean algebras, inter-val soft Boolean subalgebras, interval idealistic soft Boolean algebras and interval soft homomorphism between interval soft Boolean algebras are defined and some related properties are discussed.Soft Boolean algebras and related results are generalized.
An efficient approach of attractor calculation for large-scale Boolean gene regulatory networks.
He, Qinbin; Xia, Zhile; Lin, Bin
2016-11-07
Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which improved the predecessor-based approach. Furthermore, the proposed approach combined with the identification of constant nodes and simplified Boolean networks to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks. If the average degree of the network is not too large, the algorithm can get all attractors of a Boolean network with dozens or even hundreds of nodes.
2014-01-01
A negating functionality is fundamental to information processing of logic circuits within cells and computers. Aiming to adapt unutilized electronic concepts to the interrogation of signaling circuits in cells, we first took a bottom-up strategy whereby we created protein-based devices that perform negating Boolean logic operations such as NOT, NOR, NAND, and N-IMPLY. These devices function in living cells within a minute by precisely commanding the localization of an activator molecule among three subcellular spaces. We networked these synthetic gates to an endogenous signaling circuit and devised a physiological output. In search of logic functions in signal transduction, we next took a top–down approach and computationally screened 108 signaling pathways to identify commonalities and differences between these biological pathways and electronic circuits. This combination of synthetic and systems approaches will guide us in developing foundations for deconstruction of intricate cell signaling, as well as construction of biomolecular computers. PMID:25000210
An Evaluation of Methods for Inferring Boolean Networks from Time-Series Data.
Berestovsky, Natalie; Nakhleh, Luay
2013-01-01
Regulatory networks play a central role in cellular behavior and decision making. Learning these regulatory networks is a major task in biology, and devising computational methods and mathematical models for this task is a major endeavor in bioinformatics. Boolean networks have been used extensively for modeling regulatory networks. In this model, the state of each gene can be either 'on' or 'off' and that next-state of a gene is updated, synchronously or asynchronously, according to a Boolean rule that is applied to the current-state of the entire system. Inferring a Boolean network from a set of experimental data entails two main steps: first, the experimental time-series data are discretized into Boolean trajectories, and then, a Boolean network is learned from these Boolean trajectories. In this paper, we consider three methods for data discretization, including a new one we propose, and three methods for learning Boolean networks, and study the performance of all possible nine combinations on four regulatory systems of varying dynamics complexities. We find that employing the right combination of methods for data discretization and network learning results in Boolean networks that capture the dynamics well and provide predictive power. Our findings are in contrast to a recent survey that placed Boolean networks on the low end of the "faithfulness to biological reality" and "ability to model dynamics" spectra. Further, contrary to the common argument in favor of Boolean networks, we find that a relatively large number of time points in the time-series data is required to learn good Boolean networks for certain data sets. Last but not least, while methods have been proposed for inferring Boolean networks, as discussed above, missing still are publicly available implementations thereof. Here, we make our implementation of the methods available publicly in open source at http://bioinfo.cs.rice.edu/.
Local digital estimators of intrinsic volumes for Boolean models and in the design based setting
DEFF Research Database (Denmark)
Svane, Anne Marie
In order to estimate the specific intrinsic volumes of a planar Boolean model from a binary image, we consider local digital algorithms based on weigted sums of 2×2 configuration counts. For Boolean models with balls as grains, explicit formulas for the bias of such algorithms are derived...... for the bias obtained for Boolean models are applied to existing algorithms in order to compare their accuracy....
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.
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.
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...
Inference of asynchronous Boolean network from biological pathways.
Das, Haimabati; Layek, Ritwik Kumar
2015-01-01
Gene regulation is a complex process with multiple levels of interactions. In order to describe this complex dynamical system with tractable parameterization, the choice of the dynamical system model is of paramount importance. The right abstraction of the modeling scheme can reduce the complexity in the inference and intervention design, both computationally and experimentally. This article proposes an asynchronous Boolean network framework to capture the transcriptional regulation as well as the protein-protein interactions in a genetic regulatory system. The inference of asynchronous Boolean network from biological pathways information and experimental evidence are explained using an algorithm. The suitability of this paradigm for the variability of several reaction rates is also discussed. This methodology and model selection open up new research challenges in understanding gene-protein interactive system in a coherent way and can be beneficial for designing effective therapeutic intervention strategy.
Boolean network representation of contagion dynamics during a financial crisis
Caetano, Marco Antonio Leonel; Yoneyama, Takashi
2015-01-01
This work presents a network model for representation of the evolution of certain patterns of economic behavior. More specifically, after representing the agents as points in a space in which each dimension associated to a relevant economic variable, their relative "motions" that can be either stationary or discordant, are coded into a boolean network. Patterns with stationary averages indicate the maintenance of status quo, whereas discordant patterns represent aggregation of new agent into the cluster or departure from the former policies. The changing patterns can be embedded into a network representation, particularly using the concept of autocatalytic boolean networks. As a case study, the economic tendencies of the BRIC countries + Argentina were studied. Although Argentina is not included in the cluster formed by BRIC countries, it tends to follow the BRIC members because of strong commercial ties.
Algorithms for Finding Small Attractors in Boolean Networks
Directory of Open Access Journals (Sweden)
Hayashida Morihiro
2007-01-01
Full Text Available A Boolean network is a model used to study the interactions between different genes in genetic regulatory networks. In this paper, we present several algorithms using gene ordering and feedback vertex sets to identify singleton attractors and small attractors in Boolean networks. We analyze the average case time complexities of some of the proposed algorithms. For instance, it is shown that the outdegree-based ordering algorithm for finding singleton attractors works in time for , which is much faster than the naive time algorithm, where is the number of genes and is the maximum indegree. We performed extensive computational experiments on these algorithms, which resulted in good agreement with theoretical results. In contrast, we give a simple and complete proof for showing that finding an attractor with the shortest period is NP-hard.
Kramers-Wannier duality applied to the boolean satifiability problem
Mitchell, Joe; Hsu, Benjamin; Galitski, Victor
2014-03-01
Kramers-Wannier duality, first considered in 1941, is an exact technique used in statistical mechanics to relate two models together through an order-disorder transformation, and thereby study their structure and critical phenomena. The boolean satisfiability problem is one of the most important problems in computer science, specifically complexity theory; it is the first proven NP-complete problem. Using a mapping to a multi-spin Ising model in the limit of zero temperature, we present an application of Kramers-Wannier duality to this problem. This results in a novel relationship between solving the boolean satisfiability counting problem and a different computational problem: listing the non-negative solutions to a particular system of linear integer equations. This mapping relates the complexity of the two problems. We discuss the generality of Kramers-Wannier duality and its possible application to other computational problems. This research was supported by NSF-CAREER award No. DMR-0847224 and Simons Foundation.
Stability of biological networks as represented in Random Boolean Nets.
Energy Technology Data Exchange (ETDEWEB)
Slepoy, Alexander; Thompson, Marshall
2004-09-01
We explore stability of Random Boolean Networks as a model of biological interaction networks. We introduce surface-to-volume ratio as a measure of stability of the network. Surface is defined as the set of states within a basin of attraction that maps outside the basin by a bit-flip operation. Volume is defined as the total number of states in the basin. We report development of an object-oriented Boolean network analysis code (Attract) to investigate the structure of stable vs. unstable networks. We find two distinct types of stable networks. The first type is the nearly trivial stable network with a few basins of attraction. The second type contains many basins. We conclude that second type stable networks are extremely rare.
Effects of a silenced gene in Boolean network models
Directory of Open Access Journals (Sweden)
Emir Haliki
2017-03-01
Full Text Available Gene regulation and their regulatory networks are one of the most challenging research problems of computational biology and complexity sciences. Gene regulation is formed by indirect interaction between DNA segments which are protein coding genes to configure the expression level of one another. Prevention of expression of any genes in gene regulation at the levels of transcription or translation indicates the gene silencing event. The present study examined what types of results in gene silencing would bring about in the dynamics of Boolean genetic regulatory mechanisms. The analytical study was performed in gene expression variations of Boolean dynamics first, then the related numerical analysis was simulated in real networks in the literature.
Fault Based Techniques for Testing Boolean Expressions: A Survey
Badhera, Usha; Taruna, S
2012-01-01
Boolean expressions are major focus of specifications and they are very much prone to introduction of faults, this survey presents various fault based testing techniques. It identifies that the techniques differ in their fault detection capabilities and generation of test suite. The various techniques like Cause effect graph, meaningful impact strategy, Branch Operator Strategy (BOR), BOR+MI, MUMCUT, Modified Condition/ Decision Coverage (MCDC) has been considered. This survey describes the basic algorithms and fault categories used by these strategies for evaluating their performance. Finally, it contains short summaries of the papers that use Boolean expressions used to specify the requirements for detecting faults. These techniques have been empirically evaluated by various researchers on a simplified safety related real time control system.
Estimation of delays in generalized asynchronous Boolean networks.
Das, Haimabati; Layek, Ritwik Kumar
2016-10-20
A new generalized asynchronous Boolean network (GABN) model has been proposed in this paper. This continuous-time discrete-state model captures the biological reality of cellular dynamics without compromising the computational efficiency of the Boolean framework. The GABN synthesis procedure is based on the prior knowledge of the logical structure of the regulatory network, and the experimental transcriptional parameters. The novelty of the proposed methodology lies in considering different delays associated with the activation and deactivation of a particular protein (especially the transcription factors). A few illustrative examples of some well-studied network motifs have been provided to explore the scope of using the GABN model for larger networks. The GABN model of the p53-signaling pathway in response to γ-irradiation has also been simulated in the current paper to provide an indirect validation of the proposed schema.
Autonomous Boolean modelling of developmental gene regulatory networks
Cheng, Xianrui; Sun, Mengyang; Socolar, Joshua E. S.
2013-01-01
During early embryonic development, a network of regulatory interactions among genes dynamically determines a pattern of differentiated tissues. We show that important timing information associated with the interactions can be faithfully represented in autonomous Boolean models in which binary variables representing expression levels are updated in continuous time, and that such models can provide a direct insight into features that are difficult to extract from ordinary differential equation (ODE) models. As an application, we model the experimentally well-studied network controlling fly body segmentation. The Boolean model successfully generates the patterns formed in normal and genetically perturbed fly embryos, permits the derivation of constraints on the time delay parameters, clarifies the logic associated with different ODE parameter sets and provides a platform for studying connectivity and robustness in parameter space. By elucidating the role of regulatory time delays in pattern formation, the results suggest new types of experimental measurements in early embryonic development. PMID:23034351
borealis - A generalized global update algorithm for Boolean optimization problems
Zhu, Zheng; Katzgraber, Helmut G
2016-01-01
Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficie...
J-rings of characteristic two that are boolean
Directory of Open Access Journals (Sweden)
D. J. Hansen
1994-01-01
Full Text Available This paper is concerned with determining all integers n, with n≥2, such that if R is a ring having the property that xn=x and 2x=0 for each x∈R, then R is boolean. The solution to the above problem extends previous results obtained by Shiue and Chao in [5] and that of MacHale in [4].
Selection of probability based weighting models for Boolean retrieval system
Energy Technology Data Exchange (ETDEWEB)
Ebinuma, Y. (Japan Atomic Energy Research Inst., Tokai, Ibaraki. Tokai Research Establishment)
1981-09-01
Automatic weighting models based on probability theory were studied if they can be applied to boolean search logics including logical sum. The INIS detabase was used for searching of one particular search formula. Among sixteen models three with good ranking performance were selected. These three models were further applied to searching of nine search formulas in the same database. It was found that two models among them show slightly better average ranking performance while the other model, the simplest one, seems also practical.
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.
MILES FORMULAE FOR BOOLEAN MODELS OBSERVED ON LATTICES
Directory of Open Access Journals (Sweden)
Joachim Ohser
2011-05-01
Full Text Available The densities of the intrinsic volumes – in 3D the volume density, surface density, the density of the integral of the mean curvature and the density of the Euler number – are a very useful collection of geometric characteristics of random sets. Combining integral and digital geometry we develop a method for efficient and simultaneous calculation of the intrinsic volumes of random sets observed in binary images in arbitrary dimensions. We consider isotropic and reflection invariant Boolean models sampled on homogeneous lattices and compute the expectations of the estimators of the intrinsic volumes. It turns out that the estimator for the surface density is proved to be asymptotically unbiased and thusmultigrid convergent for Boolean models with convex grains. The asymptotic bias of the estimators for the densities of the integral of the mean curvature and of the Euler number is assessed for Boolean models of balls of random diameters. Miles formulae with corresponding correction terms are derived for the 3D case.
Experimental design schemes for learning Boolean network models
Atias, Nir; Gershenzon, Michal; Labazin, Katia; Sharan, Roded
2014-01-01
Motivation: A holy grail of biological research is a working model of the cell. Current modeling frameworks, especially in the protein–protein interaction domain, are mostly topological in nature, calling for stronger and more expressive network models. One promising alternative is logic-based or Boolean network modeling, which was successfully applied to model signaling regulatory circuits in human. Learning such models requires observing the system under a sufficient number of different conditions. To date, the amount of measured data is the main bottleneck in learning informative Boolean models, underscoring the need for efficient experimental design strategies. Results: We developed novel design approaches that greedily select an experiment to be performed so as to maximize the difference or the entropy in the results it induces with respect to current best-fit models. Unique to our maximum difference approach is the ability to account for all (possibly exponential number of) Boolean models displaying high fit to the available data. We applied both approaches to simulated and real data from the EFGR and IL1 signaling systems in human. We demonstrate the utility of the developed strategies in substantially improving on a random selection approach. Our design schemes highlight the redundancy in these datasets, leading up to 11-fold savings in the number of experiments to be performed. Availability and implementation: Source code will be made available upon acceptance of the manuscript. Contact: roded@post.tau.ac.il PMID:25161232
Detecting Emergent Behaviors with Semi-Boolean Algebra
Energy Technology Data Exchange (ETDEWEB)
Haglich, Peter [Lockheed Martin Corporation; Rouff, Christopher [Lockheed Martin Corporation; Pullum, Laura L [ORNL
2010-01-01
As systems continue to be interconnected, their collective behavior becomes increasingly difficult to predict. The emergent properties of systems of systems make them powerful, but at the same time make them more difficult to design, assure proper behaviors emerge, operate correctly, and have no new security holes. Learning and adaptation cause additional concerns because emergent behavior patterns simply cannot be fully predicted through the use of traditional system development methods, such as testing and model checking. In addition, self-organization can occur as the individual systems optimize to address inefficiencies in the larger system. Designing for and detecting emergent behavior is something that has not been addressed in current systems development methodologies. This paper gives background on approaches for modeling and verifying emergent behavior and then discusses the use of semi-Boolean algebra as a means for detecting emergence in combined behaviors. Semi-Boolean algebra is a generalization of the Boolean algebra concept obtained by weakening the requirement that any two elements have a common upper bound. An example is given and several ways are described that allow emergent behavior to be detected with this technique.
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.
Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms
Khardon, R; Servedio, R A; 10.1613/jair.1655
2011-01-01
The paper studies machine learning problems where each example is described using a set of Boolean features and where hypotheses are represented by linear threshold elements. One method of increasing the expressiveness of learned hypotheses in this context is to expand the feature set to include conjunctions of basic features. This can be done explicitly or where possible by using a kernel function. Focusing on the well known Perceptron and Winnow algorithms, the paper demonstrates a tradeoff between the computational efficiency with which the algorithm can be run over the expanded feature space and the generalization ability of the corresponding learning algorithm. We first describe several kernel functions which capture either limited forms of conjunctions or all conjunctions. We show that these kernels can be used to efficiently run the Perceptron algorithm over a feature space of exponentially many conjunctions; however we also show that using such kernels, the Perceptron algorithm can provably make an ex...
Tran, Van; McCall, Matthew N.; McMurray, Helene R.; Almudevar, Anthony
2013-01-01
Boolean networks (BoN) are relatively simple and interpretable models of gene regulatory networks. Specifying these models with fewer parameters while retaining their ability to describe complex regulatory relationships is an ongoing methodological challenge. Additionally, extending these models to incorporate variable gene decay rates, asynchronous gene response, and synergistic regulation while maintaining their Markovian nature increases the applicability of these models to genetic regulatory networks (GRN). We explore a previously-proposed class of BoNs characterized by linear threshold functions, which we refer to as threshold Boolean networks (TBN). Compared to traditional BoNs with unconstrained transition functions, these models require far fewer parameters and offer a more direct interpretation. However, the functional form of a TBN does result in a reduction in the regulatory relationships which can be modeled. We show that TBNs can be readily extended to permit self-degradation, with explicitly modeled degradation rates. We note that the introduction of variable degradation compromises the Markovian property fundamental to BoN models but show that a simple state augmentation procedure restores their Markovian nature. Next, we study the effect of assumptions regarding self-degradation on the set of possible steady states. Our findings are captured in two theorems relating self-degradation and regulatory feedback to the steady state behavior of a TBN. Finally, we explore assumptions of synchronous gene response and asynergistic regulation and show that TBNs can be easily extended to relax these assumptions. Applying our methods to the budding yeast cell-cycle network revealed that although the network is complex, its steady state is simplified by the presence of self-degradation and lack of purely positive regulatory cycles. PMID:24376454
Directory of Open Access Journals (Sweden)
Van eTran
2013-12-01
Full Text Available Boolean networks (BoN are relatively simple and interpretable models of gene regulatorynetworks. Specifying these models with fewer parameters while retaining their ability to describe complex regulatory relationships is an ongoing methodological challenge. Additionally, extending these models to incorporate variable gene decay rates, asynchronous gene response, and synergistic regulation while maintaining their Markovian nature increases the applicability of these models to genetic regulatory networks.We explore a previously-proposed class of BoNs characterized by linear threshold functions, which we refer to as threshold Boolean networks (TBN. Compared to traditional BoNs with unconstrained transition functions, these models require far fewer parameters and offer a more direct interpretation. However, the functional form of a TBN does result in a reduction in the regulatory relationships which can be modeled.We show that TBNs can be readily extended to permit self-degradation, with explicitly modeled degradation rates. We note that the introduction of variable degradation compromises the Markovian property fundamental to BoN models but show that a simple state augmentation procedure restores their Markovian nature. Next, we study the effect of assumptions regarding self-degradation on the set of possible steady states. Our findings are captured in two theorems relating self-degradation and regulatory feedback to the steady state behavior of a TBN. Finally, we explore assumptions of synchronous gene response and asynergistic regulation and show that TBNs can be easily extended to relax these assumptions.Applying our methods to the budding yeast cell-cycle network revealed that although the network is complex, its steady state is simplified by the presence of self-degradation and lack of purely positive regulatory cycles.
Bent functions results and applications to cryptography
Tokareva, Natalia
2015-01-01
Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions. The text is appropriate for novices and advanced
BEAT: A Web-Based Boolean Expression Fault-Based Test Case Generation Tool
Chen, T. Y.; Grant, D. D.; Lau, M. F.; Ng, S. P.; Vasa, V. R.
2006-01-01
BEAT is a Web-based system that generates fault-based test cases from Boolean expressions. It is based on the integration of our several fault-based test case selection strategies. The generated test cases are considered to be fault-based, because they are aiming at the detection of particular faults. For example, when the Boolean expression is in…
Comparing Boolean and Probabilistic Information Retrieval Systems Across Queries and Disciplines.
Losee, Robert M.
1997-01-01
Suggests a method that allows searchers to analytically compare the Boolean and probabilistic information retrieval approaches. Sample performance figures are provided for queries using the Boolean strategy, and for probabilistic systems. The variation of performance across sublanguages and queries is examined, as well as the performance of models…
Boolean Operators and the Naive End-User: Moving to AND.
Proctor, Edward
2002-01-01
Discusses the confusion among end users in using Boolean operators when searching electronic resources. Highlights include search engines; site-specific search engines; the counterintuitive nature of Boolean logic; hidden defaults; the problem of conceptualization; reprogramming defaults; and a lack of user education. (LRW)
Freestyle Vs. Boolean: A Comparison of Partial and Exact Match Retrieval Systems.
Paris, Lee Anne H.; Tibbo, Helen R.
1998-01-01
Compares results of traditional Boolean searching with those of Freestyle, LEXIS/NEXIS's natural language application. Study found that though the Boolean searches had better results more often, neither method demonstrated superior performance for every query, suggesting that different queries demand different techniques. Concludes that further…
Boolean Classes and Qualitative Inquiry. WCER Working Paper No. 2006-3
Nathan, Mitchell J.; Jackson, Kristi
2006-01-01
The prominent role of Boolean classes in qualitative data analysis software is viewed by some as an encroachment of logical positivism on qualitative research methodology. The authors articulate an embodiment perspective, in which Boolean classes are viewed as conceptual metaphors for apprehending and manipulating data, concepts, and categories in…
On Boolean algebras which have the Vitali-Hahn-Saks property
Directory of Open Access Journals (Sweden)
Dimitru Popa
1997-05-01
Full Text Available Given a boolean algebra A, we say when A verifies the Drewnowski condition. In thepaper we prove that if a boolean algebra verifies the Drewnowski condition then A has the Vitali-Hahn-Saks property. Also other related questions are investigated.
Affine Equivalence and Constructions of Cryptographically Strong Boolean Functions
2013-09-01
3 (mod n) aiaj, . . . , n⊕ i, j=1 i+j≡n (mod n) aiaj, n⊕ i=1 i+j≡1 (mod n) aiaj = C(a1, adn /2e+1, a2, adn /2e+2, . . . , adn /2e) if...a3, . . . , ak, a2k+1, ak+1) = C(a1, adn /2e+1, a2, adn /2e+2, . . . , adn /2e). 46 If n = 2k for k = 0, 1, 2, ..., n⊕ i=1 i+j≡2 (mod n) aiaj = a1a1...3.4.5, C(a1, . . . , an) 2 = C(a1, adn /2e+1, a2, adn /2e+2, . . . , adn /2e) = C((a1, . . . , an)Pτ ) = C(aτ(1), . . . , aτ(n)). 64 Therefore, (a1
On bent and semi-bent quadratic Boolean functions
DEFF Research Database (Denmark)
Charpin, P.; Pasalic, Enes; Tavernier, C.
2005-01-01
The maximum-length sequences, also called m-sequences, have received a lot of attention since the late 1960s. In terms of linear-feedback shift register (LFSR) synthesis they are usually generated by certain power polynomials over a finite field and in addition are characterized by a low cross co...
On a Conjecture for Balanced Symmetric Boolean Functions
2009-01-01
Characteristics, Ph.D. thesis, State Uni- versity of New York at Buffalo, 1998. [2] J.O. Brüer, On pseudorandom sequences as crypto generators, pp. 157–161...Alexanderson, Sums of partition sets in generalized Pascal triangles I, Fibonacci Quarterly 14 (1976), pp. 117–125. [8] T. Lengyel, On the order of lacunary
16 Boolean logics in three steps with two anti-serially connected memristors
Zhou, Yaxiong; Li, Yi; Xu, Lei; Zhong, Shujing; Sun, Huajun; Miao, Xiangshui
2015-06-01
Memristor based logic gates that can execute memory and logic operations are regarded as building blocks for non Von Neumann computation architecture. In this letter, Ta/GeTe/Ag memristors were fabricated and showed reproducible binary switches between high-resistance and low-resistance states. Utilizing a structure with two anti-serially connected memristors, we propose a logic operation methodology, based on which arbitrary Boolean logic can be realized in three steps, and the logic result can be nonvolatilely stored. A functionally complete logic operation: NAND is further verified by HSPICE simulation and experiments. The implementation of logic-in-memory unit may stimulate the development of future massive parallel computing.
On Natural Genetic Engineering: Structural Dynamism in Random Boolean Networks
Bull, Larry
2012-01-01
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include changes in node connectivity based upon the current cell state, e.g., via transposable elements. The underlying behaviour of the resulting dynamical networks is investigated before their evolvability is explored using a version of the NK model of fitness landscapes. Structural dynamism is found to be selected for in non-stationary environments and subsequently shown capable of providing a mechanism for evolutionary innovation when such reorganizations are inherited.
Boolean approaches to graph embeddings related to VLSI
Institute of Scientific and Technical Information of China (English)
LIU; Yanpei(
2001-01-01
［1］Hu, T. C., Kuh, S. E., Theory and concepts of circuit layout, in VLSI Circuit Layout: Theory and Design, New York:IEEE Press, 1985, 3-18.［2］Liu Yanpei, Embeddability in Graphs, Boston-Beijing: Kluwer Science, 1995.［3］Liu Yanpei, Some combinatorial optimization problems arising from VLSI circuit design, Applied Math. -JCU, 1993, 38:218-235.［4］Liu Yanpei, Marchioro, P. , Petreschi, R., At most single bend embeddings of cubic graphs, Applied Math. -CJU, 1994,39: 127-142.［5］Liu Yanpei, Marchioro, P. , Petreschi, R. et al. , Theoretical results on at most 1-bend embeddability of graphs, Acta Math.Appl. Sinica, 1992, 8: 188-192.［6］Liu Yanpei, Morgana, A., Simeone, B., General theoretical results on rectilinear embeddability of graphs, Acta Math. Ap- pl. Simca, 1991, 7: 187-192.［7］Calamoneri, T., Petreschi, R., Liu Yanpei, Optimally Extending Bistandard Graphs on the Orthogonal Grid, ASCM2000 Symposium, Tailand, Dec.17-21, 2000.［8］Liu Yanpei, Morgana, A., Simeone, B., A graph partition problem, Acta Math. Appl. Sinica, 1996, 12: 393-400.［9］Liu Yanpei, Morgana, A. , Simeone, B. , A linear algorithm for 2-bend embeddings of planar graphs in the two dimensional grid, Discrete Appl. Math., 1998, 81: 69-91.［10］Liu Yanpei, Boolean approach to planar embeddings of a graph, Acta Math. Sinica, New Series, 1989, 5: 64-79.［11］Hammer, P. L., Liu Yanpei, Simeone, B., Boolean approaches to combinatorial optimization, J. Math. Res. Expos.,1990, 10: 300-312, 455-468, 619-628.［12］Liu Yanpei, Boolean planarity characterization of graphs, Acta Math. Sinica, New Series, 1988, 4: 316-329.［13］Liu Yanpei, Boolean characterizations of planarity and planar embeddings of graphs, Ann. O. R., 1990, 24: 165-174.
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
On orders of two transformation semigroups of the boolean
Directory of Open Access Journals (Sweden)
I. V. Livinsky
2014-12-01
Full Text Available We consider the semigroup $\\mathcal{O}(\\mathcal{B}_n$ of all order--preserving transformations $\\varphi : \\mathcal{B}_n \\rightarrow \\mathcal{B}_n$ of ordered by inclusion boolean $\\mathcal{B}_n$ of $n$-element set (i.e. such transformations that$A \\subseteq B$ implies $\\varphi(A \\subseteq \\varphi(B$ and its subsemigroup $\\mathcal{C}(\\mathcal{B}_n$ of those transformations for which $\\varphi(A \\subseteq A$ for all $A \\in \\mathcal{B}_n$. Orders of these semigroups are calculated.
Seismic imaging and evaluation of channels modeled by boolean approach
Energy Technology Data Exchange (ETDEWEB)
Spinola, M.; Aggio, A. [PETROBRAS, Rio de Janeiro, RJ (Brazil). Centro de Pesquisas
1999-07-01
The seismic method attempt to image the subsurface architecture and has been able to significantly contribute to detect areal and vertical changes in rock properties. This work presents a seismic imaging study of channel objects generated using the boolean technique. Three channels having different thicknesses were simulated, using the same width, sinuosity and direction. A velocity model was constructed in order to allow seismic contrasts between the interior of channels and the embedding rock. To examine the seismic response for different channel thicknesses, a 3D ray tracing with a normal incident point survey was performed. The three channels were resolved and the way the seismic could image them was studied. (author)
Boolean difference equations. I - Formulation and dynamic behavior
Dee, D.; Ghil, M.
1984-01-01
In many biological and physical systems, feedback mechanisms depend on a set of thresholds associated with the state variables. Each feedback has a characteristic time scale. It is suggested that delay-difference equations for Boolean-valued variables are an appropriate mathematical framework for such situations: the feedback thresholds result in the discrete, on-off character of the variables, and the interaction time scales of the feedbacks are expressed as delays. The initial-value problem for Boolean delay equations (B-Delta-Es) is formulated, and shown to have unique solutions for all times. Examples of periodic and aperiodic solutions are given. Aperiodic solutions have increasing complexity which depends on time t roughly as t to the l-1 power, l being the number of delays. Stability of solutions is defined, and some examples of stability analysis are given; additional stability questions are raised. The present formulation of (B-Delta-Es) is compared with related work and generalizations are suggested.
Adaptive Local Information Transfer in Random Boolean Networks.
Haruna, Taichi
2017-01-01
Living systems such as gene regulatory networks and neuronal networks have been supposed to work close to dynamical criticality, where their information-processing ability is optimal at the whole-system level. We investigate how this global information-processing optimality is related to the local information transfer at each individual-unit level. In particular, we introduce an internal adjustment process of the local information transfer and examine whether the former can emerge from the latter. We propose an adaptive random Boolean network model in which each unit rewires its incoming arcs from other units to balance stability of its information processing based on the measurement of the local information transfer pattern. First, we show numerically that random Boolean networks can self-organize toward near dynamical criticality in our model. Second, the proposed model is analyzed by a mean-field theory. We recognize that the rewiring rule has a bootstrapping feature. The stationary indegree distribution is calculated semi-analytically and is shown to be close to dynamical criticality in a broad range of model parameter values.
Complex network analysis of state spaces for random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Shreim, Amer [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Berdahl, Andrew [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Sood, Vishal [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Grassberger, Peter [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada); Paczuski, Maya [Complexity Science Group, Department of Physics and Astronomy, University of Calgary, Calgary, AB, T2N 1N4 (Canada)
2008-01-15
We apply complex network analysis to the state spaces of random Boolean networks (RBNs). An RBN contains N Boolean elements each with K inputs. A directed state space network (SSN) is constructed by linking each dynamical state, represented as a node, to its temporal successor. We study the heterogeneity of these SSNs at both local and global scales, as well as sample to-sample fluctuations within an ensemble of SSNs. We use in-degrees of nodes as a local topological measure, and the path diversity (Shreim A et al 2007 Phys. Rev. Lett. 98 198701) of an SSN as a global topological measure. RBNs with 2 {<=} K {<=} 5 exhibit non-trivial fluctuations at both local and global scales, while K = 2 exhibits the largest sample-to-sample (possibly non-self-averaging) fluctuations. We interpret the observed 'multi scale' fluctuations in the SSNs as indicative of the criticality and complexity of K = 2 RBNs. 'Garden of Eden' (GoE) states are nodes on an SSN that have in-degree zero. While in-degrees of non-GoE nodes for K > 1 SSNs can assume any integer value between 0 and 2{sup N}, for K = 1 all the non-GoE nodes in a given SSN have the same in-degree which is always a power of two.
Boolean network models of cellular regulation: prospects and limitations.
Bornholdt, Stefan
2008-08-06
Computer models are valuable tools towards an understanding of the cell's biochemical regulatory machinery. Possible levels of description of such models range from modelling the underlying biochemical details to top-down approaches, using tools from the theory of complex networks. The latter, coarse-grained approach is taken where regulatory circuits are classified in graph-theoretical terms, with the elements of the regulatory networks being reduced to simply nodes and links, in order to obtain architectural information about the network. Further, considering dynamics on networks at such an abstract level seems rather unlikely to match dynamical regulatory activity of biological cells. Therefore, it came as a surprise when recently examples of discrete dynamical network models based on very simplistic dynamical elements emerged which in fact do match sequences of regulatory patterns of their biological counterparts. Here I will review such discrete dynamical network models, or Boolean networks, of biological regulatory networks. Further, we will take a look at such models extended with stochastic noise, which allow studying the role of network topology in providing robustness against noise. In the end, we will discuss the interesting question of why at all such simple models can describe aspects of biology despite their simplicity. Finally, prospects of Boolean models in exploratory dynamical models for biological circuits and their mutants will be discussed.
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.
Directory of Open Access Journals (Sweden)
Helmy Thendean
2007-01-01
Full Text Available Artificial neural networks (ANN implementation in image classification problem requires a lot of training time which caused by enormous data size. This kind of data is known as raw data. An image data is extracted directly without any preprocessing. Many feature extraction techniques are offered to reduce the time consumed in training image data. Boolean function algorithm (BFA in ANN (first and second approach produces identical output values that can be used as feature of an image data. This feature can then be used as input in Back Propagation ANN that is known as the best ANN method in problems classification. The experiment shows that BFA can be used well as one of feature extraction methods. The second approach BFA in Back Propagation ANN shows better performance in recognition and is lesser time consuming in training than the first approach. Abstract in Bahasa Indonesia : Penerapan Jaringan Syaraf Tiruan (JST pada masalah klasifikasi citra sering membutuhkan waktu proses pembelajaran yang cukup lama yang disebabkan oleh besarnya jumlah data input. Penggunaan data seperti ini dikenal sebagai penggunaan data yang bersifat mentah. Data input sebuah citra diambil secara langsung untuk diberikan sebagai data pembelajaran dalam algoritma JST. Permasalahan ini menimbulkan berbagai metode ekstrasi ciri (feature extraction yang diterapkan pada sebuah citra sebelum dijadikan sebagai data pembelajaran dalam sebuah algoritma JST. Algoritma Fungsi Boolean (AFB menunjukkan bahwa JST dengan penerapan AFB memiliki nilai output yang bersifat identik. Sifat identik pada hasil pemrosesan sebuah data citra inilah yang kemudian diterapkan pada algoritma JST Propagasi Balik (JST PB sebagai algoritma JST yang terbaik untuk permasalahan klasifikasi. Hasil percobaan menunjukkan bahwa JST AFB dapat diterapkan sebagai salah satu metode feature extraction pada citra. Kinerja JST AFB dengan pendekatan kedua memberikan hasil yang lebih baik dari tingkat pengenalan
Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach
Lin, Guo-Qiang; Ao, Bin; Chen, Jia-Wei; Wang, Wen-Xu; Di, Zeng-Ru
2014-12-01
Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.
Feedback control design for the complete synchronisation of two coupled Boolean networks
Li, Fangfei
2016-09-01
In the literatures, to design state feedback controllers to make the response Boolean network synchronise with the drive Boolean network is rarely considered. Motivated by this, feedback control design for the complete synchronisation of two coupled Boolean networks is investigated in this paper. A necessary condition for the existence of a state feedback controller achieving the complete synchronisation is established first. Then, based on the necessary condition, the feedback control law is proposed. Finally, an example is worked out to illustrate the proposed design procedure.
Minimum energy control and optimal-satisfactory control of Boolean control network
Energy Technology Data Exchange (ETDEWEB)
Li, Fangfei, E-mail: li_fangfei@163.com; Lu, Xiwen
2013-12-09
In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floyd's algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.
Kaplan, J C; Junien, C
2000-12-01
The major impact of the completion of the human genome sequence will be the understanding of diseases, with deduced therapy. In the field of genetic disorders, we will complete the catalogue of monogenic diseases, also called Mendelian diseases because they obey the Boolean logic of Mendel's laws. The major challenge now is to decipher the polygenic and multifactorial etiology of common diseases, such as cancer, cardio-vascular, nutritional, allergic, auto-immune and degenerative diseases. In fact, every gene, when mutated, is a potential disease gene, and we end up with the new concept of 'reverse medicine'; i.e., deriving new diseases or pathogenic pathways from the knowledge of the structure and function of every gene. By going from sequence to function (functional genomics and proteomics) we will gain insight into basic mechanisms of major functions such as cell proliferation, differentiation and development, which are perturbed in many pathological processes. By learning the meaning of some non-coding and of regulatory sequences our understanding will gain in complexity, generating a molecular and supramolecular integrated physiology, helping to build a molecular patho-physiology of the different syndromes. Besides those cognitive advances, there are also other issues at stake, such as: progress in diagnostic and prediction (predictive medicine); progress in therapy (pharmacogenomics and gene-based therapy); ethical issues; impact on business.
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.
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.
Coletti, Cristian F.; Miranda, Daniel; Mussini, Filipe
2016-02-01
In this work we study the Poisson Boolean model of percolation in locally compact Polish metric spaces and we prove the invariance of subcritical and supercritical phases under mm-quasi-isometries. More precisely, we prove that if a metric space M is mm-quasi-isometric to another metric space N and the Poisson Boolean model in M exhibits any of the following: (a) a subcritical phase; (b) a supercritical phase; or (c) a phase transition, then respectively so does the Poisson Boolean model of percolation in N. Then we use these results in order to understand the phase transition phenomenon in a large family of metric spaces. Indeed, we study the Poisson Boolean model of percolation in the context of Riemannian manifolds, in a large family of nilpotent Lie groups and in Cayley graphs. Also, we prove the existence of a subcritical phase in Gromov spaces with bounded growth at some scale.
A new approach for global controllability of higher order Boolean control network.
Chen, Hao; Sun, Jitao
2013-03-01
Using the semi-tensor product, the global control problem of the higher order Boolean control network with avoiding set is considered. First, the number of different control sequences that drive the higher order Boolean control network from the initial state to the destination state while avoiding undesirable set is provided. Then, the definition of global controllability of higher order Boolean control network is given. Third, by using the classical theory of nonnegative matrices, the necessary and sufficient condition for the global controllability of higher order Boolean control network with avoiding set is presented. Furthermore, a sufficient condition for k fixed-time global controllability of the system is also obtained. At last, an example is given to illustrate the main results.
Institute of Scientific and Technical Information of China (English)
Fengjuan CHAI; Xiao-Shan GAO; Chunming YUAN
2008-01-01
This paper presents a characteristic set method for solving Boolean equations, which is more efficient and has better properties than the general characteristic set method. In particular, the authors give a disjoint and monic zero decomposition algorithm for the zero set of a Boolean equation system and an explicit formula for the number of solutions of a Boolean equation system. The authors also prove that a characteristic set can be computed with a polynomial number of multiplications of Boolean polynomials in terms of the number of variables. As experiments, the proposed method is used to solve equations from cryptanalysis of a class of stream ciphers based on nonlinear filter generators. Extensive experiments show that the method is quite effective.
Automatic test pattern generation for logic circuits using the Boolean tree
Energy Technology Data Exchange (ETDEWEB)
Jeong Taegwon.
1991-01-01
The goal of this study was to develop an algorithm that can generate test patterns for combinational circuits and sequential logic circuits automatically. The new proposed algorithm generates a test pattern by using a special tree called a modified Boolean tree. In this algorithm, the construction of a modified Boolean tree is the most time-consuming step. Following the construction of a modified Boolean tree, a test pattern can be found by simply assigning a logic value 1 for even primary inputs and a logic value 0 for odd primary inputs of the constructed modified Boolean tree. The algorithm is applied to several benchmark circuits. The results showed the following: (1) for combinational circuits, the algorithm can generate test patterns 10-15% faster than the FAN algorithm, which is known as one of the most efficient algorithms to-date; (2) for sequential circuits, the algorithm shows more fault coverage than the nine valued algorithm.
Model construction from orthographic views as Pseudo Boolean constraint satisfaction problem
Energy Technology Data Exchange (ETDEWEB)
Itoh, Kiyoshi; Suzuki, Shigemich [Sophia Univ., Tokyo (Japan)
1996-12-31
A surface model representation of a solid can be constructed in straightforward fashion from a set of three orthographic views. The surface model may include ghost vertexes, ghost edges and ghost faces. The authors` project, called Sophia-Alsovig, treats the problem for obtaining valid combination of surfaces and edges as Pseudo Boolean constraint satisfaction problem (CSP). It can remove such ghosts. As CSP, Sophia-Alsovig adopts a set of units consisting of edges and surfaces, a set of Boolean labels, and a set of constraints with the formulation of a collection of topological/geometrical rules for edges and surfaces by Pseudo Boolean equations. Sophia-Alsovig obtains solutions by Pseudo Boolean Nonlinear Programming.
Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem
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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.
Complete Boolean Satisfiability Solving Algorithms Based on Local Search
Institute of Scientific and Technical Information of China (English)
Wen-Sheng Guo; Guo-Wu Yang; William N.N.Hung; Xiaoyu Song
2013-01-01
Boolean satisfiability (SAT) is a well-known problem in computer science,artificial intelligence,and operations research.This paper focuses on the satisfiability problem of Model RB structure that is similar to graph coloring problems and others.We propose a translation method and three effective complete SAT solving algorithms based on the characterization of Model RB structure.We translate clauses into a graph with exclusive sets and relative sets.In order to reduce search depth,we determine search order using vertex weights and clique in the graph.The results show that our algorithms are much more effective than the best SAT solvers in numerous Model RB benchmarks,especially in those large benchmark instances.
An optimal control approach to probabilistic Boolean networks
Liu, Qiuli
2012-12-01
External control of some genes in a genetic regulatory network is useful for avoiding undesirable states associated with some diseases. For this purpose, a number of stochastic optimal control approaches have been proposed. Probabilistic Boolean networks (PBNs) as powerful tools for modeling gene regulatory systems have attracted considerable attention in systems biology. In this paper, we deal with a problem of optimal intervention in a PBN with the help of the theory of discrete time Markov decision process. Specifically, we first formulate a control model for a PBN as a first passage model for discrete time Markov decision processes and then find, using a value iteration algorithm, optimal effective treatments with the minimal expected first passage time over the space of all possible treatments. In order to demonstrate the feasibility of our approach, an example is also displayed.
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.
Sampled-Data State Feedback Stabilization of Boolean Control Networks.
Liu, Yang; Cao, Jinde; Sun, Liangjie; Lu, Jianquan
2016-04-01
In this letter, we investigate the sampled-data state feedback control (SDSFC) problem of Boolean control networks (BCNs). Some necessary and sufficient conditions are obtained for the global stabilization of BCNs by SDSFC. Different from conventional state feedback controls, new phenomena observed the study of SDSFC. Based on the controllability matrix, we derive some necessary and sufficient conditions under which the trajectories of BCNs can be stabilized to a fixed point by piecewise constant control (PCC). It is proved that the global stabilization of BCNs under SDSFC is equivalent to that by PCC. Moreover, algorithms are given to construct the sampled-data state feedback controllers. Numerical examples are given to illustrate the efficiency of the obtained results.
Synchronization for the Realization-Dependent Probabilistic Boolean Networks.
Chen, Hongwei; Liang, Jinling; Lu, Jianquan; Qiu, Jianlong
2017-01-24
This paper investigates the synchronization problem for the realization-dependent probabilistic Boolean networks (PBNs) coupled unidirectionally in the drive-response configuration. The realization of the response PBN is assumed to be uniquely determined by the realization signal generated by the drive PBN at each discrete time instant. First, the drive-response PBNs are expressed in their algebraic forms based on the semitensor product method, and then, a necessary and sufficient condition is presented for the synchronization of the PBNs. Second, by resorting to a newly defined matrix operator, the reachable set from any initial state is expressed by a column vector. Consequently, an easily computable algebraic criterion is derived assuring the synchronization of the drive-response PBNs. Finally, three illustrative examples are employed to demonstrate the applicability and usefulness of the developed theoretical results.
Broad edge of chaos in strongly heterogeneous Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Lee, Deok-Sun [Center for Complex Network Research and Department of Physics, Northeastern University, Boston, MA 02115 (United States); Rieger, Heiko [Theoretische Physik, Universitaet des Saarlandes, 66041 Saarbruecken (Germany)
2008-10-17
The dynamic stability of the Boolean networks representing a model for the gene transcriptional regulation (Kauffman model) is studied by calculating analytically and numerically the Hamming distance between two evolving configurations. This turns out to behave in a universal way close to the phase boundary only for in-degree distributions with a finite second moment. In-degree distributions of the form P{sub d}(k) {approx} k{sup -{gamma}} with 2 < {gamma} < 3, thus having a diverging second moment, lead to a slower increase of the Hamming distance when moving towards the unstable phase and to a broadening of the phase boundary for finite N with decreasing {gamma}. We conclude that the heterogeneous regulatory network connectivity facilitates the balancing between robustness and evolvability in living organisms.
Chaos synchronization of two stochastically coupled random Boolean networks
Energy Technology Data Exchange (ETDEWEB)
Hung, Y.-C. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China) and Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)]. E-mail: d9123801@student.nsysu.edu.tw; Ho, M.-C. [Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)]. E-mail: t1603@nknucc.nknu.edu.tw; Lih, J.-S. [Department of Physics and Geoscience, National Pingtung University of Education, Pingtung, Taiwan (China); Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China); Jiang, I-M. [Department of Physics, National Sun Yat-sen University, Kaohsiung, Taiwan (China); Nonlinear Science Group, Department of Physics, National Kaohsiung Normal University, Kaohsiung, Taiwan (China)
2006-07-24
In this Letter, we study the chaos synchronization of two stochastically coupled random Boolean networks (RBNs). Instead of using the 'site-by-site and all-to-all' coupling, the coupling mechanism we consider here is that: the nth cell in a network is linked by an arbitrarily chosen cell in the other network with probability {rho}, and it possesses no links with probability 1-{rho}. The mechanism is useful to investigate the coevolution of biological species via horizontal genetic exchange. We show that the density evolution of networks can be described by two deterministic coupled polynomial maps. The complete synchronization occurs when the coupling parameter exceeds a critical value. Moreover, the reverse bifurcations in inhomogeneous condition are observed and under our discussion.
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.
Optimization, Randomized Approximability, and Boolean Constraint Satisfaction Problems
Yamakami, Tomoyuki
2011-01-01
We give a unified treatment to optimization problems that can be expressed in the form of nonnegative-real-weighted Boolean constraint satisfaction problems. Creignou, Khanna, Sudan, Trevisan, and Williamson studied the complexity of approximating their optimal solutions whose optimality is measured by the sums of outcomes of constraints. To explore a wider range of optimization constraint satisfaction problems, following an early work of Marchetti-Spaccamela and Romano, we study the case where the optimality is measured by products of constraints' outcomes. We completely classify those problems into three categories: PO problems, NPO-hard problems, and intermediate problems that lie between the former two categories. To prove this trichotomy theorem, we analyze characteristics of nonnegative-real-weighted constraints using a variant of the notion of T-constructibility developed earlier for complex-weighted counting constraint satisfaction problems.
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.
Embedding meshes in Boolean cubes by graph decomposition
Energy Technology Data Exchange (ETDEWEB)
Ho, C.T. (IBM Almaden Research Center, San Jose, CA (US)); Johnsson, S.L. (Dept. of Computer Science and Electrical Engineering, Yale Univ., New Haven, CT (US))
1990-04-01
This paper explores the embeddings of multidimensional meshes into minimal Boolean cubes by graph decomposition. The graph decomposition technique can be used to improve the average dilation and average congestion. The graph decomposition technique combined with some particular two-dimensional embeddings allows for minimal-expansion, dilation-two, congestion-two embeddings of about 87% of all two-dimensional meshes, with a significantly lower average dilation and congestion than by modified line compression. For three-dimensional meshes the authors show that the graph decomposition technique, together with two three-dimensional mesh embeddings presented in this paper and modified line compression, yields dilation-two embeddings of more than 96% of all three dimensional meshes contained in a 512 {times} 512 {times} 512 mesh.
Degree two approximate Boolean #CSPs with variable weights
McQuillan, Colin
2012-01-01
A counting constraint satisfaction problem (#CSP) asks for the number of ways to satisfy a given list of constraints, drawn from a fixed constraint language \\Gamma. We study how hard it is to evaluate this number approximately. There is an interesting partial classification, due to Dyer, Goldberg, Jalsenius and Richerby, of Boolean constraint languages when the degree of instances is bounded by d>=3 - every variable appears in at most d constraints - under the assumption that "pinning" is allowed as part of the instance. We study the d=2 case under the stronger assumption that "variable weights" are allowed as part of the instance. We give a dichotomy: in each case, either the #CSP is tractable, or one of two important open problems, #BIS or #PM, reduces to the #CSP.
Feedback control and output feedback control for the stabilisation of switched Boolean networks
Li, Fangfei; Yu, Zhaoxu
2016-02-01
This paper presents the feedback control and output feedback control for the stabilisation of switched Boolean network. A necessary condition for the existence of a state feedback controller for the stabilisation of switched Boolean networks under arbitrary switching signal is derived first, and constructive procedures for feedback control and output feedback control design are provided. An example is introduced to show the effectiveness of this paper.
Multiple fault analysis in synchronous sequential circuits by means of vector Boolean difference
Energy Technology Data Exchange (ETDEWEB)
Goldstein, L.H.
1977-01-01
The Boolean difference is an elegant mathematical concept which has found significant application in the study of single faults of a stuck-at nature in combinational logic circuits. Recently, several authors have extended this technique to the analysis of multiple faults in combinational circuits. The concept of vector Boolean difference is further extended to the analysis of multiple stuck-at faults in synchronous sequential circuits.
An attractor-based complexity measurement for Boolean recurrent neural networks.
Directory of Open Access Journals (Sweden)
Jérémie Cabessa
Full Text Available 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 ω-automata, and then translating the most refined classification of ω-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.
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 ω-automata, and then translating the most refined classification of ω-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.
In silico design and in vivo implementation of yeast gene Boolean gates.
Marchisio, Mario A
2014-01-01
In our previous computational work, we showed that gene digital circuits can be automatically designed in an electronic fashion. This demands, first, a conversion of the truth table into Boolean formulas with the Karnaugh map method and, then, the translation of the Boolean formulas into circuit schemes organized into layers of Boolean gates and Pools of signal carriers. In our framework, gene digital circuits that take up to three different input signals (chemicals) arise from the composition of three kinds of basic Boolean gates, namely YES, NOT, and AND. Here we present a library of YES, NOT, and AND gates realized via plasmidic DNA integration into the yeast genome. Boolean behavior is reproduced via the transcriptional control of a synthetic bipartite promoter that contains sequences of the yeast VPH1 and minimal CYC1 promoters together with operator binding sites for bacterial (i.e. orthogonal) repressor proteins. Moreover, model-driven considerations permitted us to pinpoint a strategy for re-designing gates when a better digital performance is required. Our library of well-characterized Boolean gates is the basis for the assembly of more complex gene digital circuits. As a proof of concepts, we engineered two 2-input OR gates, designed by our software, by combining YES and NOT gates present in our library.
In silico design and in vivo implementation of yeast gene Boolean gates
2014-01-01
In our previous computational work, we showed that gene digital circuits can be automatically designed in an electronic fashion. This demands, first, a conversion of the truth table into Boolean formulas with the Karnaugh map method and, then, the translation of the Boolean formulas into circuit schemes organized into layers of Boolean gates and Pools of signal carriers. In our framework, gene digital circuits that take up to three different input signals (chemicals) arise from the composition of three kinds of basic Boolean gates, namely YES, NOT, and AND. Here we present a library of YES, NOT, and AND gates realized via plasmidic DNA integration into the yeast genome. Boolean behavior is reproduced via the transcriptional control of a synthetic bipartite promoter that contains sequences of the yeast VPH1 and minimal CYC1 promoters together with operator binding sites for bacterial (i.e. orthogonal) repressor proteins. Moreover, model-driven considerations permitted us to pinpoint a strategy for re-designing gates when a better digital performance is required. Our library of well-characterized Boolean gates is the basis for the assembly of more complex gene digital circuits. As a proof of concepts, we engineered two 2-input OR gates, designed by our software, by combining YES and NOT gates present in our library. PMID:24485181
Efficient Boolean and multi-input flow techniques for advanced mask data processing
Salazar, Daniel; Moore, Bill; Valadez, John
2012-11-01
Mask data preparation (MDP) typically involves multiple flows, sometimes consisting of many steps to ensure that the data is properly written on the mask. This may include multiple inputs, transformations (scaling, orientation, etc.), and processing (layer extraction, sizing, Boolean operations, data filtering). Many MDP techniques currently in practice require multiple passes through the input data and/or multiple file I/O steps to achieve these goals. This paper details an approach which efficiently process the data, resulting in minimal I/O and greatly improved turnaround times (TAT). This approach takes advanced processing algorithms and adapts them to produce efficient and reliable data flow. In tandem with this processing flow, an internal jobdeck mapping approach, transparent to the user, allows an essentially unlimited number of pattern inputs to be handled in a single pass, resulting in increased flexibility and ease of use. Transformations and processing operations are critical to MDP. Transformations such as scaling, reverse tone and orientation, along with processing including sizing, Boolean operations and data filtering are key parts of this. These techniques are often employed in sequence and/or in parallel in a complex functional chain. While transformations typically are done "up front" when the data is input, processing is less straightforward, involving multiple reads and writes to handle the more intricate functionality and also the collection of input patterns which may be required to produce the data that comprises a single mask. The approach detailed in this paper consists of two complementary techniques: efficient MDP flow and jobdeck mapping. Efficient MDP flow is achieved by pipelining the output of each step to the input of the subsequent step. Rather than writing the output of a particular processing step to file and then reading it in to the following step, the pipelining or chaining of the steps results in an efficient flow with
Directory of Open Access Journals (Sweden)
Mikko Niilo-Rämä
2014-06-01
Full Text Available A novel estimator for estimating the mean length of fibres is proposed for censored data observed in square shaped windows. Instead of observing the fibre lengths, we observe the ratio between the intensity estimates of minus-sampling and plus-sampling. It is well-known that both intensity estimators are biased. In the current work, we derive the ratio of these biases as a function of the mean length assuming a Boolean line segment model with exponentially distributed lengths and uniformly distributed directions. Having the observed ratio of the intensity estimators, the inverse of the derived function is suggested as a new estimator for the mean length. For this estimator, an approximation of its variance is derived. The accuracies of the approximations are evaluated by means of simulation experiments. The novel method is compared to other methods and applied to real-world industrial data from nanocellulose crystalline.
Boolean and brain-inspired computing using spin-transfer torque devices
Fan, Deliang
Several completely new approaches (such as spintronic, carbon nanotube, graphene, TFETs, etc.) to information processing and data storage technologies are emerging to address the time frame beyond current Complementary Metal-Oxide-Semiconductor (CMOS) roadmap. The high speed magnetization switching of a nano-magnet due to current induced spin-transfer torque (STT) have been demonstrated in recent experiments. Such STT devices can be explored in compact, low power memory and logic design. In order to truly leverage STT devices based computing, researchers require a re-think of circuit, architecture, and computing model, since the STT devices are unlikely to be drop-in replacements for CMOS. The potential of STT devices based computing will be best realized by considering new computing models that are inherently suited to the characteristics of STT devices, and new applications that are enabled by their unique capabilities, thereby attaining performance that CMOS cannot achieve. The goal of this research is to conduct synergistic exploration in architecture, circuit and device levels for Boolean and brain-inspired computing using nanoscale STT devices. Specifically, we first show that the non-volatile STT devices can be used in designing configurable Boolean logic blocks. We propose a spin-memristor threshold logic (SMTL) gate design, where memristive cross-bar array is used to perform current mode summation of binary inputs and the low power current mode spintronic threshold device carries out the energy efficient threshold operation. Next, for brain-inspired computing, we have exploited different spin-transfer torque device structures that can implement the hard-limiting and soft-limiting artificial neuron transfer functions respectively. We apply such STT based neuron (or 'spin-neuron') in various neural network architectures, such as hierarchical temporal memory and feed-forward neural network, for performing "human-like" cognitive computing, which show more than
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.
Majority Rules with Random Tie-Breaking in Boolean Gene Regulatory Networks
Chaouiya, Claudine; Ourrad, Ouerdia; Lima, Ricardo
2013-01-01
We consider threshold Boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively) and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out), it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing. PMID:23922761
A new class of codes for Boolean masking of cryptographic computations
Carlet, Claude; Kim, Jon-Lark; Solé, Patrick
2011-01-01
We introduce a new class of rate one half binary codes: complementary information set codes. A binary linear code of length 2n and dimension n is called a complementary information set code (CIS code for short) if it has two disjoint information sets. This class of codes contains self-dual codes as a subclass. It is connected to graph correlation immune Boolean functions of use in the security of hardware implementations of cryptographic primitives. Such codes permit to improve the cost of masking cryptographic algorithms against side channel attacks. In this paper we investigate this new class of codes: we give optimal or best known CIS codes of length < 132. We derive general constructions based on cyclic codes and on double circulant codes. We derive a Varshamov-Gilbert bound for long CIS codes, and show that they can all be classified in small lengths \\leq 12 by the building up construction. Some nonlinear S-boxes are constructed by using Z4-codes, based on the notion of dual distance of an unrestricte...
Majority rules with random tie-breaking in Boolean gene regulatory networks.
Directory of Open Access Journals (Sweden)
Claudine Chaouiya
Full Text Available We consider threshold boolean gene regulatory networks, where the update function of each gene is described as a majority rule evaluated among the regulators of that gene: it is turned ON when the sum of its regulator contributions is positive (activators contribute positively whereas repressors contribute negatively and turned OFF when this sum is negative. In case of a tie (when contributions cancel each other out, it is often assumed that the gene keeps it current state. This framework has been successfully used to model cell cycle control in yeast. Moreover, several studies consider stochastic extensions to assess the robustness of such a model. Here, we introduce a novel, natural stochastic extension of the majority rule. It consists in randomly choosing the next value of a gene only in case of a tie. Hence, the resulting model includes deterministic and probabilistic updates. We present variants of the majority rule, including alternate treatments of the tie situation. Impact of these variants on the corresponding dynamical behaviours is discussed. After a thorough study of a class of two-node networks, we illustrate the interest of our stochastic extension using a published cell cycle model. In particular, we demonstrate that steady state analysis can be rigorously performed and can lead to effective predictions; these relate for example to the identification of interactions whose addition would ensure that a specific state is absorbing.
Robust method for infrared small-target detection based on Boolean map visual theory.
Qi, Shengxiang; Ming, Delie; Ma, Jie; Sun, Xiao; Tian, Jinwen
2014-06-20
In this paper, we present an infrared small target detection method based on Boolean map visual theory. The scheme is inspired by the phenomenon that small targets can often attract human attention due to two characteristics: brightness and Gaussian-like shape in the local context area. Motivated by this observation, we perform the task under a visual attention framework with Boolean map theory, which reveals that an observer's visual awareness corresponds to one Boolean map via a selected feature at any given instant. Formally, the infrared image is separated into two feature channels, including a color channel with the original gray intensity map and an orientation channel with the orientation texture maps produced by a designed second order directional derivative filter. For each feature map, Boolean maps delineating targets are computed from hierarchical segmentations. Small targets are then extracted from the target enhanced map, which is obtained by fusing the weighted Boolean maps of the two channels. In experiments, a set of real infrared images covering typical backgrounds with sky, sea, and ground clutters are tested to verify the effectiveness of our method. The results demonstrate that it outperforms the state-of-the-art methods with good performance.
Grieb, Melanie; Burkovski, Andre; Sträng, J Eric; Kraus, Johann M; Groß, Alexander; Palm, Günther; Kühl, Michael; Kestler, Hans A
2015-01-01
Gene interactions in cells can be represented by gene regulatory networks. A Boolean network models gene interactions according to rules where gene expression is represented by binary values (on / off or {1, 0}). In reality, however, the gene's state can have multiple values due to biological properties. Furthermore, the noisy nature of the experimental design results in uncertainty about a state of the gene. Here we present a new Boolean network paradigm to allow intermediate values on the interval [0, 1]. As in the Boolean network, fixed points or attractors of such a model correspond to biological phenotypes or states. We use our new extension of the Boolean network paradigm to model gene expression in first and second heart field lineages which are cardiac progenitor cell populations involved in early vertebrate heart development. By this we are able to predict additional biological phenotypes that the Boolean model alone is not able to identify without utilizing additional biological knowledge. The additional phenotypes predicted by the model were confirmed by published biological experiments. Furthermore, the new method predicts gene expression propensities for modelled but yet to be analyzed genes.
Maximum-Likelihood Adaptive Filter for Partially Observed Boolean Dynamical Systems
Imani, Mahdi; Braga-Neto, Ulisses M.
2017-01-01
Partially-observed Boolean dynamical systems (POBDS) are a general class of nonlinear models with application in estimation and control of Boolean processes based on noisy and incomplete measurements. The optimal minimum mean square error (MMSE) algorithms for POBDS state estimation, namely, the Boolean Kalman filter (BKF) and Boolean Kalman smoother (BKS), are intractable in the case of large systems, due to computational and memory requirements. To address this, we propose approximate MMSE filtering and smoothing algorithms based on the auxiliary particle filter (APF) method from sequential Monte-Carlo theory. These algorithms are used jointly with maximum-likelihood (ML) methods for simultaneous state and parameter estimation in POBDS models. In the presence of continuous parameters, ML estimation is performed using the expectation-maximization (EM) algorithm; we develop for this purpose a special smoother which reduces the computational complexity of the EM algorithm. The resulting particle-based adaptive filter is applied to a POBDS model of Boolean gene regulatory networks observed through noisy RNA-Seq time series data, and performance is assessed through a series of numerical experiments using the well-known cell cycle gene regulatory model.
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.
Stability depends on positive autoregulation in Boolean gene regulatory networks.
Directory of Open Access Journals (Sweden)
Ricardo Pinho
2014-11-01
Full Text Available Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs. The most basic motif, autoregulation, has been associated with bistability (when positive and with homeostasis and robustness to noise (when negative, but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals.
Stability Depends on Positive Autoregulation in Boolean Gene Regulatory Networks
Pinho, Ricardo; Garcia, Victor; Irimia, Manuel; Feldman, Marcus W.
2014-01-01
Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals. PMID:25375153
Refinements to the Boolean approach to automatic data editing
Energy Technology Data Exchange (ETDEWEB)
Liepins, G.E.
1980-09-01
Automatic data editing consists of three components: identification of erroneous records, identification of most likely erroneous fields within an erroneous record (fields to impute), and assignment of acceptable values to failing records. Moreover the types of data considered naturally fall into three categories: coded (categorical) data, continuous data, and mixed data (both coded and continuous). For the case of coded data, a natural way to approach automatic data is commonly referred to as the Boolean approach, first developed by Fellegi and Holt. For the fields to impute problem, central to the operation of the Fellegi-Holt approach is the explicit recognition of certain implied edits; Fellegi and Holt orginally required a complete set of edits, and their algorithm to generate this complete set has occasionally had the distinct disadvantage of failing to converge within reasonable time. The primary results of this paper is an algorithm that significantly prunes the Fellegi-Holt edit generation process, yet, nonetheless, generates a sufficient collection of implied edits adequate for the solution of the fields to impute problem. 3 figures.
Recent development and biomedical applications of probabilistic Boolean networks
2013-01-01
Probabilistic Boolean network (PBN) modelling is a semi-quantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rule-based representation and probability makes PBN appealing for large-scale modelling of biological networks where degrees of uncertainty need to be considered. A considerable expansion of our knowledge in the field of theoretical research on PBN can be observed over the past few years, with a focus on network inference, network intervention and control. With respect to areas of applications, PBN is mainly used for the study of gene regulatory networks though with an increasing emergence in signal transduction, metabolic, and also physiological networks. At the same time, a number of computational tools, facilitating the modelling and analysis of PBNs, are continuously developed. A concise yet comprehensive review of the state-of-the-art on PBN modelling is offered in this article, including a comparative discussion on PBN versus similar models with respect to concepts and biomedical applications. Due to their many advantages, we consider PBN to stand as a suitable modelling framework for the description and analysis of complex biological systems, ranging from molecular to physiological levels. PMID:23815817
Formal Verification Techniques Based on Boolean Satisfiability Problem
Institute of Scientific and Technical Information of China (English)
Xiao-Wei Li; Guang-Hui Li; Ming Shao
2005-01-01
This paper exploits Boolean satisfiability problem in equivalence checking and model checking respectively. A combinational equivalence checking method based on incremental satisfiability is presented. This method chooses the can didate equivalent pairs with some new techniques, and uses incremental satisfiability algorithm to improve its performance. By substituting the internal equivalent pairs and converting the equivalence relations into conjunctive normal form (CNF) formulas, this approach can avoid the false negatives, and reduce the search space of SAT procedure. Experimental results on ISCAS'85 benchmark circuits show that, the presented approach is faster and more robust than those existed in literature.This paper also presents an algorithm for extracting of unsatisfiable core, which has an important application in abstraction and refinement for model checking to alleviate the state space explosion bottleneck. The error of approximate extraction is analyzed by means of simulation. An analysis reveals that an interesting phenomenon occurs, with the increasing density of the formula, the average error of the extraction is decreasing. An exact extraction approach for MU subformula, referred to as pre-assignment algorithm, is proposed. Both theoretical analysis and experimental results show that it is more efficient.
Boolean network model predicts cell cycle sequence of fission yeast.
Directory of Open Access Journals (Sweden)
Maria I Davidich
Full Text Available A Boolean network model of the cell-cycle regulatory network of fission yeast (Schizosaccharomyces Pombe is constructed solely on the basis of the known biochemical interaction topology. Simulating the model in the computer faithfully reproduces the known activity sequence of regulatory proteins along the cell cycle of the living cell. Contrary to existing differential equation models, no parameters enter the model except the structure of the regulatory circuitry. The dynamical properties of the model indicate that the biological dynamical sequence is robustly implemented in the regulatory network, with the biological stationary state G1 corresponding to the dominant attractor in state space, and with the biological regulatory sequence being a strongly attractive trajectory. Comparing the fission yeast cell-cycle model to a similar model of the corresponding network in S. cerevisiae, a remarkable difference in circuitry, as well as dynamics is observed. While the latter operates in a strongly damped mode, driven by external excitation, the S. pombe network represents an auto-excited system with external damping.
Learning Techniques for Automatic Test Pattern Generation using Boolean Satisfiability
Directory of Open Access Journals (Sweden)
Liu Xin
2013-07-01
Full Text Available Automatic Test Pattern Generation (ATPG is one of the core problems in testing of digital circuits. ATPG algorithms based on Boolean Satisfiability (SAT turned out to be very powerful, due to great advances in the performance of satisfiability solvers for propositional logic in the last two decades. SAT-based ATPG clearly outperforms classical approaches especially for hard-to-detect faults. But its inaccessibility of structural information and don’t care, there exists the over-specification problem of input patterns. In this paper we present techniques to delve into an additional layer to make use of structural properties of the circuit and value justification relations to a generic SAT algorithm. It joins binary decision graphs (BDD and SAT techniques to improve the efficiency of ATPG. It makes a study of inexpensive reconvergent fanout analysis of circuit to gather information on the local signal correlation by using BDD learning, then uses the above learned information to restrict and focus the overall search space of SAT-based ATPG. The learning technique is effective and lightweight. Experimental results show the effectiveness of the approach.
Wolfram, Dietmar; Dimitroff, Alexandra
1998-01-01
Describes a study that compared a hypertext-based bibliographic retrieval system with a traditional Boolean-based system. Results, conducted with novice and experienced searchers, revealed that the Boolean system performed better for tasks with a large number of relevant items, and that searcher experience level did not play a significant role.…
Controllability of Boolean networks via input controls under Harvey's update scheme
Luo, Chao; Zhang, Xiaolin; Shao, Rui; Zheng, YuanJie
2016-02-01
In this article, the controllability of Boolean networks via input controls under Harvey's update scheme is investigated. First, the model of Boolean control networks under Harvey's stochastic update is proposed, by means of semi-tensor product approach, which is converted into discrete-time linear representation. And, a general formula of control-depending network transition matrix is provided. Second, based on discrete-time dynamics, controllability of the proposed model is analytically discussed by revealing the necessary and sufficient conditions of the reachable sets, respectively, for three kinds of controls, i.e., free Boolean control sequence, input control networks, and close-loop control. Examples are showed to demonstrate the effectiveness and feasibility of the proposed scheme.
Pulse-transmission Oscillators: Autonomous Boolean Models and the Yeast Cell Cycle
Sevim, Volkan; Gong, Xinwei; Socolar, Joshua
2010-03-01
Models of oscillatory gene expression typically involve a constitutively expressed or positively autoregulated gene which is repressed by a negative feedback loop. In Boolean representations of such systems, which include the repressilator and relaxation oscillators, dynamical stability stems from the impossibility of satisfying all of the Boolean rules at once. We consider a different class of networks, in which oscillations are due to the transmission of a pulse of gene activation around a ring. Using autonomous Boolean modeling methods, we show how the circulating pulse can be stabilized by decoration of the ring with certain feedback and feed-forward motifs. We then discuss the relation of these models to ODE models of transcriptional networks, emphasizing the role of explicit time delays. Finally, we show that a network recently proposed as a generator of cell cycle oscillations in yeast contains the motifs required to support stable transmission oscillations.
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.
Controllability of Boolean networks via input controls under Harvey's update scheme.
Luo, Chao; Zhang, Xiaolin; Shao, Rui; Zheng, YuanJie
2016-02-01
In this article, the controllability of Boolean networks via input controls under Harvey's update scheme is investigated. First, the model of Boolean control networks under Harvey's stochastic update is proposed, by means of semi-tensor product approach, which is converted into discrete-time linear representation. And, a general formula of control-depending network transition matrix is provided. Second, based on discrete-time dynamics, controllability of the proposed model is analytically discussed by revealing the necessary and sufficient conditions of the reachable sets, respectively, for three kinds of controls, i.e., free Boolean control sequence, input control networks, and close-loop control. Examples are showed to demonstrate the effectiveness and feasibility of the proposed scheme.
Structure-Based Local Search Heuristics for Circuit-Level Boolean Satisfiability
Belov, Anton
2011-01-01
This work focuses on improving state-of-the-art in stochastic local search (SLS) for solving Boolean satisfiability (SAT) instances arising from real-world industrial SAT application domains. The recently introduced SLS method CRSat has been shown to noticeably improve on previously suggested SLS techniques in solving such real-world instances by combining justification-based local search with limited Boolean constraint propagation on the non-clausal formula representation form of Boolean circuits. In this work, we study possibilities of further improving the performance of CRSat by exploiting circuit-level structural knowledge for developing new search heuristics for CRSat. To this end, we introduce and experimentally evaluate a variety of search heuristics, many of which are motivated by circuit-level heuristics originally developed in completely different contexts, e.g., for electronic design automation applications. To the best of our knowledge, most of the heuristics are novel in the context of SLS for S...
Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks
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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.
Nested Canalizing Functions and Their Networks
Kadelka, Claus; Adeyeye, John O; Laubenbacher, Reinhard
2014-01-01
The concept of a nested canalizing Boolean function has been studied over the last decade in the context of understanding the regulatory logic of molecular interaction networks, such as gene regulatory networks. Such networks are predominantly governed by nested canalizing functions. Derrida values are frequently used to analyze the robustness of a Boolean network to perturbations. This paper introduces closed formulas for the calculation of Derrida values of networks governed by Boolean nested canalizing functions, which previously required extensive simulations. Recently, the concept of nested canalizing functions has been generalized to include multistate functions, and a recursive formula has been derived for their number, as a function of the number of variables. This paper contains a detailed analysis of the class of nested canalizing functions over an arbitrary finite field. In addition, the concept of nested canalization is further generalized and closed formulas for the number of such generalized fun...
Nonvolatile “AND,” “OR,” and “NOT” Boolean logic gates based on phase-change memory
Energy Technology Data Exchange (ETDEWEB)
Li, Y.; Zhong, Y. P.; Deng, Y. F.; Zhou, Y. X.; Xu, L.; Miao, X. S., E-mail: miaoxs@mail.hust.edu.cn [Wuhan National Laboratory for Optoelectronics (WNLO), Huazhong University of Science and Technology (HUST), Wuhan 430074 (China); School of Optical and Electronic Information, Huazhong University of Science and Technology, Wuhan 430074 (China)
2013-12-21
Electronic devices or circuits that can implement both logic and memory functions are regarded as the building blocks for future massive parallel computing beyond von Neumann architecture. Here we proposed phase-change memory (PCM)-based nonvolatile logic gates capable of AND, OR, and NOT Boolean logic operations verified in SPICE simulations and circuit experiments. The logic operations are parallel computing and results can be stored directly in the states of the logic gates, facilitating the combination of computing and memory in the same circuit. These results are encouraging for ultralow-power and high-speed nonvolatile logic circuit design based on novel memory devices.
Fuzzy Boolean Algebras Based on Implication Operator%基于蕴涵算子上的模糊布尔代数
Institute of Scientific and Technical Information of China (English)
陈华新
2011-01-01
文中给出R-模糊布尔代数的定义,讨论了其与模糊布尔代数的关系,证明在一定的条件下,有限个R-模糊布尔代数的交(并)还是R-模糊布尔代数,R-模糊布尔代数的同态像(原像)仍是R-模糊布尔代数.%In this paper ,we introduce the definition of fuzzy Boolean algebra. Based on that, the differences and connection between R-fuzzy Boolean algebra and fuzzy Boolean algebra are discussed. Furhtermore, it is proved that the finite intersection (union) of R-fuzzy Boolean algebra is still R-fuzzy Boolean algebra , and the homomorphic image (preimage) of R-fuzzy Boolean algebra is still R-fuzzy Boolean algebra.
Weights of Exact Threshold Functions
DEFF Research Database (Denmark)
Babai, László; Hansen, Kristoffer Arnsfelt; Podolskii, Vladimir V.;
2010-01-01
We consider Boolean exact threshold functions defined by linear equations, and in general degree d polynomials. We give upper and lower bounds on the maximum magnitude (absolute value) of the coefficients required to represent such functions. These bounds are very close and in the linear case...
On a Boolean-valued Model of the Strict Implication System(Continuous)
Institute of Scientific and Technical Information of China (English)
LI Na; LIU Hua-ke
2004-01-01
The reference [4] proved the consistency of S 1 and S 2 among Lewis'five strict implicationsystems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S 3 , S 4 and S 5 in Lewis'five strictimplication systems is not decided. This paper makes use of the properties : (1) the equivalence of the modal systems S 3 andP 3 , S 4 and P 4 ; (2) the modal systems P 3 and P 4 all contained the modal axiom T(□p) ; (3) the modal axiom T is correspondence to the reflexiveproperty in VB . Hence, the paper proves: (a) |A S 31|=1 ; (b) |A S 41|=1 ;(c) |A S 51|=1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB ). Therefore, the paper finallyproves that the Boolean-valued model VB of the ZFC axiomsystem in set theory is also a Boolean-valued model of Lewis'the strict implication system S 3 , S 4 and S 5 .
Application of fuzzy logic to Boolean models for digital soil assessment
Gruijter, de J.J.; Walvoort, D.J.J.; Bragato, G.
2011-01-01
Boolean models based on expert knowledge are often used to classify soils into a limited number of classes of a difficult-to-measure soil attribute. Although the primary data used for these classifications contain information on whether the soil is a typical class member or a boundary case between t
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.
Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem
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Vladimir A. Emelichev
2002-07-01
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. MSC: 90C29, 90C31
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…
Karakonstantis, J.; Patronis, T.
2010-01-01
In this article we study a specific lattice classification of converse quadrilaterals, based on the relations between diagonals. This lattice contains 16 = 2[superscript 4] elements, which form a hypercube, and therefore it is a Boolean lattice. "Complementary" species of quadrilaterals thus appear and may be related in the lattice diagram. We…
Dragović, Ivana; Turajlić, Nina; Pilčević, Dejan; Petrović, Bratislav; Radojević, Dragan
2015-01-01
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.
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.
A new separation algorithm for the Boolean quadric and cut polytopes
DEFF Research Database (Denmark)
Sørensen, Michael Malmros; Letchford, Adam N.
2014-01-01
A separation algorithm is a procedure for generating cutting planes. Up to now, only a few polynomial-time separation algorithms were known for the Boolean quadric and cut polytopes. These polytopes arise in connection with zero–one quadratic programming and the max-cut problem, respectively. We...
Analysis of multiple faults in synchronous sequential circuits by Boolean difference techniques
Energy Technology Data Exchange (ETDEWEB)
Goldstein, L.H.
1978-04-01
The Boolean difference is a mathematical concept which has found significant application in the study of single and multiple ''stuck at'' faults in combinational logic circuits. The concept of vector Boolean difference is extended to the analysis of multiple stuck-at faults in synchronous sequential circuits. A vector Boolean difference technique is utilized to determine the set of input/state pairs that will produce a difference in either output or next-state between the fault-free and faulty circuits. Assuming that the fault-free and faulty circuits start in the same initial state, they must be driven by applying a sequence of input vectors to a state in which either a difference in output or next-state is evidenced. If a difference in output cannot be achieved immediately, a second sequence of input vectors must be applied in order to propagate the state difference to the output. Methods for combining the Boolean difference analysis with techniques for deriving the required input vector sequence are discussed.
Energy Technology Data Exchange (ETDEWEB)
Smorodinskiy, B.I.
1984-01-01
A theoretical justification is given for a method for solving one of the common problems in whole number linear programming with Boolean variables. It is shown that a number of optimization problems in the oil industry can be reduced to this model.
A Special Role of Boolean Quadratic Polytopes among Other Combinatorial Polytopes
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A. N. Maksimenko
2016-01-01
Full Text Available We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set, 3-assignment. For comparing two families of polytopes we use the following method. We say that a family
Dragović, Ivana; Turajlić, Nina; Pilčević, Dejan; Petrović, Bratislav; Radojević, Dragan
2015-01-01
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. PMID:27069500
Describing the What and Why of Students' Difficulties in Boolean Logic
Herman, Geoffrey L.; Loui, Michael C.; Kaczmarczyk, Lisa; Zilles, Craig
2012-01-01
The ability to reason with formal logic is a foundational skill for computer scientists and computer engineers that scaffolds the abilities to design, debug, and optimize. By interviewing students about their understanding of propositional logic and their ability to translate from English specifications to Boolean expressions, we characterized…
Ostrowski, M; Paulevé, L; Schaub, T; Siegel, A; Guziolowski, C
2016-11-01
Boolean networks (and more general logic models) are useful frameworks to study signal transduction across multiple pathways. Logic models can be learned from a prior knowledge network structure and multiplex phosphoproteomics data. However, most efficient and scalable training methods focus on the comparison of two time-points and assume that the system has reached an early steady state. In this paper, we generalize such a learning procedure to take into account the time series traces of phosphoproteomics data in order to discriminate Boolean networks according to their transient dynamics. To that end, we identify a necessary condition that must be satisfied by the dynamics of a Boolean network to be consistent with a discretized time series trace. Based on this condition, we use Answer Set Programming to compute an over-approximation of the set of Boolean networks which fit best with experimental data and provide the corresponding encodings. Combined with model-checking approaches, we end up with a global learning algorithm. Our approach is able to learn logic models with a true positive rate higher than 78% in two case studies of mammalian signaling networks; for a larger case study, our method provides optimal answers after 7min of computation. We quantified the gain in our method predictions precision compared to learning approaches based on static data. Finally, as an application, our method proposes erroneous time-points in the time series data with respect to the optimal learned logic models.
Decision Points: Boolean Logic for Computer Users and Beginning Online Searchers.
Houghton, Janaye M.; Houghton, Robert S.
This guide and activity book helps educators build information literacy and teach students the information retrieval skills they need to excel in school and beyond. Using the techniques of Boolean logic (using simple terms such as AND, OR, and NOT to aid in decision-making), the book clarifies search concepts, terms and strategies. After…
Influence of a Structure on System's Dynamics on Example of Boolean Networks
Kirillova, O.
1999-01-01
In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation. The regular structures do not give a critical regime in the investigated cases. Hierarchy together with the irregular structure reveals characteristic features of criticality.
Hersh, William; Turpin, Andrew; Price, Susan; Kraemer, Dale; Olson, Daniel; Chan, Benjamin; Sacherek, Lynetta
2001-01-01
Describes research conducted at the TREC (Text Retrieval Conference) interactive track that compared Boolean and natural language searching, showing they achieved comparable results; and assessed the validity of batch-oriented retrieval evaluations, showing that the results from batch evaluations were not comparable to those obtained in…
"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis
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Arellano Gustavo
2011-12-01
Full Text Available Abstract Background In Thomas' formalism for modeling gene regulatory networks (GRNs, branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a asynchrony, (b incompletely specified behavior, and (c interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths. Results We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/, a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche. There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs. Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary
An autonomous in vivo dual selection protocol for boolean genetic circuits.
Beneš, David; Sosík, Petr; Rodríguez-Patón, Alfonso
2015-01-01
Success in synthetic biology depends on the efficient construction of robust genetic circuitry. However, even the direct engineering of the simplest genetic elements (switches, logic gates) is a challenge and involves intense lab work. As the complexity of biological circuits grows, it becomes more complicated and less fruitful to rely on the rational design paradigm, because it demands many time-consuming trial-and-error cycles. One of the reasons is the context-dependent behavior of small assembly parts (like BioBricks), which in a complex environment often interact in an unpredictable way. Therefore, the idea of evolutionary engineering (artificial directed in vivo evolution) based on screening and selection of randomized combinatorial genetic circuit libraries became popular. In this article we build on the so-called dual selection technique. We propose a plasmid-based framework using toxin-antitoxin pairs together with the relaxase conjugative protein, enabling an efficient autonomous in vivo evolutionary selection of simple Boolean circuits in bacteria (E. coli was chosen for demonstration). Unlike previously reported protocols, both on and off selection steps can run simultaneously in various cells in the same environment without human intervention; and good circuits not only survive the selection process but are also horizontally transferred by conjugation to the neighbor cells to accelerate the convergence rate of the selection process. Our directed evolution strategy combines a new dual selection method with fluorescence-based screening to increase the robustness of the technique against mutations. As there are more orthogonal toxin-antitoxin pairs in E. coli, the approach is likely to be scalable to more complex functions. In silico experiments based on empirical data confirm the high search and selection capability of the protocol.
2014-01-01
Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate
2015-12-24
reliable components”. In James Glimm, John Impagliazzo, and Isadore Singer, editors, Proc. Symp. Pure Mathematics , Vol. 50: The Legacy of John Von Neu- mann...DEMONSTRATION OF INEXACT COMPUTING IMPLEMENTED IN THE JPEG COMPRESSION ALGORITHM USING PROBABILISTIC BOOLEAN LOGIC APPLIED TO CMOS COMPONENTS...DS-15-D-001 DEMONSTRATION OF INEXACT COMPUTING IMPLEMENTED IN THE JPEG COMPRESSION ALGORITHM USING PROBABILISTIC BOOLEAN LOGIC APPLIED TO CMOS
Szallasi, Zoltan; Liang, Shoudan
2000-01-01
In this paper we show how Boolean genetic networks could be used to address complex problems in cancer biology. First, we describe a general strategy to generate Boolean genetic networks that incorporate all relevant biochemical and physiological parameters and cover all of their regulatory interactions in a deterministic manner. Second, we introduce 'realistic Boolean genetic networks' that produce time series measurements very similar to those detected in actual biological systems. Third, we outline a series of essential questions related to cancer biology and cancer therapy that could be addressed by the use of 'realistic Boolean genetic network' modeling.
Control of Boolean networks: hardness results and algorithms for tree structured networks.
Akutsu, Tatsuya; Hayashida, Morihiro; Ching, Wai-Ki; Ng, Michael K
2007-02-21
Finding control strategies of cells is a challenging and important problem in the post-genomic era. This paper considers theoretical aspects of the control problem using the Boolean network (BN), which is a simplified model of genetic networks. It is shown that finding a control strategy leading to the desired global state is computationally intractable (NP-hard) in general. Furthermore, this hardness result is extended for BNs with considerably restricted network structures. These results justify existing exponential time algorithms for finding control strategies for probabilistic Boolean networks (PBNs). On the other hand, this paper shows that the control problem can be solved in polynomial time if the network has a tree structure. Then, this algorithm is extended for the case where the network has a few loops and the number of time steps is small. Though this paper focuses on theoretical aspects, biological implications of the theoretical results are also discussed.