WorldWideScience

Sample records for boolean algebra

  1. Boolean algebra

    CERN Document Server

    Goodstein, R L

    2007-01-01

    This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.

  2. Algebraic partial Boolean algebras

    CERN Document Server

    Smith, D

    2003-01-01

    Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial...

  3. Algebraic partial Boolean algebras

    Science.gov (United States)

    Smith, Derek

    2003-04-01

    Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space Script H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E8.

  4. 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}.

  5. Boolean algebra essentials

    CERN Document Server

    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

  6. The Boolean algebra and central Galois algebras

    Directory of Open Access Journals (Sweden)

    George Szeto

    2001-01-01

    Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb   for all   x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.

  7. The Boolean algebra of Galois algebras

    Directory of Open Access Journals (Sweden)

    Lianyong Xue

    2003-02-01

    Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B|bx=g(xb for all x∈B} for each g∈G, and BJg=Beg for a central idempotent eg, Ba the Boolean algebra generated by {0,eg|g∈G}, e a nonzero element in Ba, and He={g∈G|eeg=e}. Then, a monomial e is characterized, and the Galois extension Be, generated by e with Galois group He, is investigated.

  8. Quotients of Boolean algebras and regular subalgebras

    Czech Academy of Sciences Publication Activity Database

    Balcar, Bohuslav; Pazák, Tomáš

    2010-01-01

    Roč. 49, č. 3 (2010), s. 329-342 ISSN 1432-0665 R&D Projects: GA AV ČR IAA100190509; GA MŠk MEB060909 Institutional research plan: CEZ:AV0Z10190503; CEZ:AV0Z10750506 Keywords : Boolean algebra * sequential topology * ZFC extension * ideal Subject RIV: BA - General Mathematics Impact factor: 0.414, year: 2010 http://link.springer.com/article/10.1007%2Fs00153-010-0174-y

  9. Free Boolean algebras over unions of two well orderings

    Czech Academy of Sciences Publication Activity Database

    Bonnet, R.; Faouzi, L.; Kubiś, Wieslaw

    2009-01-01

    Roč. 156, č. 7 (2009), s. 1177-1185 ISSN 0166-8641 Institutional research plan: CEZ:AV0Z10190503 Keywords : Well quasi orderings * Poset algebras * Superatomic Boolean algebras * Compact distributive lattices Subject RIV: BA - General Mathematics Impact factor: 0.441, year: 2009

  10. A complexity theory based on Boolean algebra

    DEFF Research Database (Denmark)

    Skyum, Sven; Valiant, Leslie

    1985-01-01

    A projection of a Boolean function is a function obtained by substituting for each of its variables a variable, the negation of a variable, or a constant. Reducibilities among computational problems under this relation of projection are considered. It is shown that much of what is of everyday rel...... relevance in Turing-machine-based complexity theory can be replicated easily and naturally in this elementary framework. Finer distinctions about the computational relationships among natural problems can be made than in previous formulations and some negative results are proved....

  11. Algebraic characteristics and satisfiability threshold of random Boolean equations

    Science.gov (United States)

    Guo, Binghui; Wei, Wei; Sun, Yifan; Zheng, Zhiming

    2010-03-01

    The satisfiability of a class of random Boolean equations named massive algebraic system septated to linear and nonlinear subproblems is studied in this paper. On one hand, the correlation between the magnetization of generators and the clustering of solutions of the linear subproblem is investigated by analyzing the Gaussian elimination process. On the other hand, the characteristics of maximal elements of solutions of the nonlinear subproblem are studied by introducing the partial order among solutions. Based on the algebraic characteristics of these two subproblems, the upper and lower bounds of satisfiability threshold of massive algebraic system are obtained by unit-clause propagation and leaf-removal process, and coincide as the ratio of nonlinear equations q>0.739 in which analytical values of the satisfiability threshold can be derived. Furthermore, a complete algorithm with heuristic decimation is proposed to observe the approximation of the satisfiability threshold, which performs more efficiently than the classical ones.

  12. 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.

  13. Constructivizability of the Boolean algebra B(ω) with a distinguished automorphism

    Czech Academy of Sciences Publication Activity Database

    Bazhenov, N. A.; Tukhbatullina, Regina

    2012-01-01

    Roč. 51, č. 5 (2012), s. 384-403 ISSN 0002-5232 Institutional support: PRVOUK-P23 Keywords : Boolean algebra * constructivizability * degree spectra of structures Subject RIV: AH - Economics Impact factor: 0.493, year: 2012

  14. Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann

    Czech Academy of Sciences Publication Activity Database

    Balcar, Bohuslav; Jech, Thomas; Pazák, Tomáš

    2005-01-01

    Roč. 37, č. 6 (2005), s. 885-898 ISSN 0024-6093 Institutional research plan: CEZ:AV0Z10750506; CEZ:AV0Z10190503 Keywords : Boolean algebras * Maharam submeasure * weak distributivity * independent reals Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2005

  15. Computable categoricity of the Boolean algebra B(omega) with a distinguished automorphism

    Czech Academy of Sciences Publication Activity Database

    Bazhenov, N. A.; Tukhbatullina, Regina

    2013-01-01

    Roč. 52, č. 2 (2013), s. 89-97 ISSN 0002-5232 Institutional support: PRVOUK-P23 Keywords : Boolean algebra with distinguished automorphism * computable categoricity * categoricity spectrum Subject RIV: BA - General Mathematics Impact factor: 0.488, year: 2013

  16. Complete CCC Boolean Algebras, the order Sequential Topology, and a Problem of von Neumann

    Czech Academy of Sciences Publication Activity Database

    Balcar, Bohuslav; Jech, Thomas; Pazák, Tomáš

    2005-01-01

    Roč. 37, č. 6 (2005), s. 885-898 ISSN 0024-6093 R&D Projects: GA ČR(CZ) GA201/02/0857; GA ČR(CZ) GA201/03/0933 Institutional research plan: CEZ:AV0Z10190503 Keywords : Boolean algebra * Maharam submeasure * weak distributivity Subject RIV: BA - General Mathematics Impact factor: 0.477, year: 2005

  17. Completely positive matrices over Boolean algebras and their CP-rank

    Directory of Open Access Journals (Sweden)

    Mohindru Preeti

    2015-04-01

    Full Text Available Drew, Johnson and Loewy conjectured that for n ≥ 4, the CP-rank of every n × n completely positive real matrix is at most [n2/4]. In this paper, we prove this conjecture for n × n completely positive matrices over Boolean algebras (finite or infinite. In addition,we formulate various CP-rank inequalities of completely positive matrices over special semirings using semiring homomorphisms.

  18. Ones and zeros understanding Boolean algebra digital circuits and the logic of sets

    CERN Document Server

    Gregg, John

    1998-01-01

    "Ones and Zeros explains, in lay terms, Boolean algebra, the suprisingly simple system of mathematical logic used in digital computer circuitry. Ones and Zeros follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. Readers will learn about the interesting history of the development of symbolic logic in particular, and the often misunderstood process of mathematical invention and scientific discovery, in general. Ones and Zeros also features practical exercises with answers, real-world examples of digital circuit design, and a reading list." "Ones and Zeros will be of particular interest to software engineers who want to gain a comprehensive understanding of computer hardware." "Outstanding features include: a history of mathematical logic, an explanation of the logic of digital circuits, and hands-on exercises and examples."--Jacket.

  19. The boolean algebra with restricted variables as a tool for fault tree modularization

    International Nuclear Information System (INIS)

    Caldarola, L.; Wickenhaeuser, A.

    1981-08-01

    The number of minimal cut sets (m.c.s.) of very complex and highly interconnected fault trees can become extremely large (e.g. more than 10 7 ). In this case the usual analytical approach of dissecting the fault tree TOP variable into m.c.s. is not only computationally prohibitively expensive, but also meaningless because it does not offer any synthetic overview of system behavior. The method proposed in this paper overcomes the deficiencies of the analytical method. It is shown that, by applying boolean algebra with restricted variables (b.a.w.r.v.), the concept of fault tree modularization can be straightforwardly extended from a single gate to a set of gates. Thus, large fault trees are divided into smaller fault trees (modules), which are connected to each other according to a simple scheme. This scheme is represented by a block diagram in which each block is a module. The modules are analyzed separately by the m.c.s. method, and the results are combined according of the TOP event. The method allows the calculation of very large fault trees in a short time and offers a synthetic overview of systems behavior through the block diagram. Numerical examples are also included. Calculations have been carried out by using the computer code MUSTAMO, which is based on the theory developed in this paper. (orig.) [de

  20. Characterization of Boolean Algebras in Terms of Certain States of Jauch-Piron Type

    Science.gov (United States)

    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.

  1. Boolean reasoning the logic of boolean equations

    CERN Document Server

    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.

  2. Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras

    OpenAIRE

    Andrade, Jefferson O.; Kameyama, Yukiyoshi

    2012-01-01

    Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In thi...

  3. Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras

    Science.gov (United States)

    Andrade, Jefferson O.; Kameyama, Yukiyoshi

    Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In this paper, we propose a novel, efficient algorithm for multi-valued bounded model checking. A notable feature of our algorithm is that it is not based on reduction of multi-values into two-values; instead, it generates a single formula which represents multi-valuedness by a suitable encoding, and asks a standard SAT solver to check its satisfiability. Our experimental results show a significant improvement in the number of variables and clauses and also in execution time compared with the reduction-based one.

  4. Properties of Boolean orthoposets

    Science.gov (United States)

    Tkadlec, Josef

    1993-10-01

    A Boolean orthoposet is the orthoposet P fulfilling the following condition: If a, b ∈ P and a ∧ b = 0, then a ⊥ b. This condition seems to be a sound generalization of distributivity in orthoposets. Also, the class of (orthomodular) Boolean orthoposets may play an interesting role in quantum logic theory. This class is wide enough and, on the other hand, enjoys some properties of Boolean algebras. In this paper we summarize results on Boolean orthoposets involving distributivity, set representation, properties of the state space, existence of Jauch-Piron states, and results concerning orthocompleteness and completion.

  5. The Boolean Algebra of Cubical Areas as a Tensor Product in the Category of Semilattices with Zero

    Directory of Open Access Journals (Sweden)

    Nicolas Ninin

    2014-10-01

    Full Text Available In this paper we describe a model of concurrency together with an algebraic structure reflecting the parallel composition. For the sake of simplicity we restrict to linear concurrent programs i.e. the ones with no loops nor branching. Such programs are given a semantics using cubical areas. Such a semantics is said to be geometric. The collection of all these cubical areas enjoys a structure of tensor product in the category of semi-lattice with zero. These results naturally extend to fully fledged concurrent programs up to some technical tricks.

  6. Boolean-Valued Belief Functions

    Czech Academy of Sciences Publication Activity Database

    Kramosil, Ivan

    2002-01-01

    Roč. 31, č. 2 (2002), s. 153-181 ISSN 0308-1079 R&D Projects: GA AV ČR IAA1030803 Institutional research plan: AV0Z1030915 Keywords : Dempster-Schafer theory * Boolean algebra Subject RIV: BA - General Mathematics Impact factor: 0.241, year: 2002

  7. Algebra

    CERN Document Server

    Tabak, John

    2004-01-01

    Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.

  8. Algebra

    CERN Document Server

    Flanders, Harley

    1975-01-01

    Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a

  9. Algebra

    CERN Document Server

    Sepanski, Mark R

    2010-01-01

    Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems

  10. Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

    NARCIS (Netherlands)

    Kant, Gijs; van de Pol, Jan Cornelis; Wijs, A.J.; Bošnački, D.; Edelkamp, S.

    Parameterised Boolean Equation Systems (PBESs) are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal μ-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then

  11. Algebraic characterizations of measure algebras

    Czech Academy of Sciences Publication Activity Database

    Jech, Thomas

    2008-01-01

    Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008

  12. Coreflections in Algebraic Quantum Logic

    Science.gov (United States)

    Jacobs, Bart; Mandemaker, Jorik

    2012-07-01

    Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.

  13. 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.

  14. Boolean integral calculus

    Science.gov (United States)

    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.

  15. Boolean orthoposets and two-valued states on them

    Science.gov (United States)

    Tkadlec, Josef

    1992-06-01

    A Boolean orthoposet (see e.g. [2]) is the orthoposet P fulfilling the following condition: If a, b ∈ P and a ∧ b = 0 then a⊥ b. This condition seems to be a sound generalization of distributivity in orthoposets (see e.g. [8]). Also, the class of (orthomodular) Boolean orthoposets may play an interesting role in quantum logic theory. This class is wide enough (see [4,3]) and on the other hand, enjoys some properties of Boolean algebras [4,8,5]. In quantum logic theory an important role is played by so-called Jauch-Piron states [1,6,7]. In this paper we clarify the connection between Boolean orthoposets and orthoposets with "enough" two-valued Jauch-Piron states. Further, we obtain a characterization of Boolean orthoposets in terms of two-valued states.

  16. Boolean representations of simplicial complexes and matroids

    CERN Document Server

    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...

  17. Synchronization in an array of coupled Boolean networks

    International Nuclear Information System (INIS)

    Li, Rui; Chu, Tianguang

    2012-01-01

    This Letter presents an analytical study of synchronization in an array of coupled deterministic Boolean networks. A necessary and sufficient criterion for synchronization is established based on algebraic representations of logical dynamics in terms of the semi-tensor product of matrices. Some basic properties of a synchronized array of Boolean networks are then derived for the existence of transient states and the upper bound of the number of fixed points. Particularly, an interesting consequence indicates that a “large” mismatch between two coupled Boolean networks in the array may result in loss of synchrony in the entire system. Examples, including the Boolean model of coupled oscillations in the cell cycle, are given to illustrate the present results. -- Highlights: ► We analytically study synchronization in an array of coupled Boolean networks. ► The study is based on the algebraic representations of logical dynamics. ► A necessary and sufficient algebraic criterion for synchronization is established. ► It reveals some basic properties of a synchronized array of Boolean networks. ► A large mismatch between two coupled networks may result in the loss of synchrony.

  18. Introduction to relation algebras relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...

  19. Refinement monoids, equidecomposability types, and boolean inverse semigroups

    CERN Document Server

    Wehrung, Friedrich

    2017-01-01

    Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.

  20. Algebraic and stochastic coding theory

    CERN Document Server

    Kythe, Dave K

    2012-01-01

    Using a simple yet rigorous approach, Algebraic and Stochastic Coding Theory makes the subject of coding theory easy to understand for readers with a thorough knowledge of digital arithmetic, Boolean and modern algebra, and probability theory. It explains the underlying principles of coding theory and offers a clear, detailed description of each code. More advanced readers will appreciate its coverage of recent developments in coding theory and stochastic processes. After a brief review of coding history and Boolean algebra, the book introduces linear codes, including Hamming and Golay codes.

  1. Proposed method to construct Boolean functions with maximum possible annihilator immunity

    Science.gov (United States)

    Goyal, Rajni; Panigrahi, Anupama; Bansal, Rohit

    2017-07-01

    Nonlinearity and Algebraic(annihilator) immunity are two core properties of a Boolean function because optimum values of Annihilator Immunity and nonlinearity are required to resist fast algebraic attack and differential cryptanalysis respectively. For a secure cypher system, Boolean function(S-Boxes) should resist maximum number of attacks. It is possible if a Boolean function has optimal trade-off among its properties. Before constructing Boolean functions, we fixed the criteria of our constructions based on its properties. In present work, our construction is based on annihilator immunity and nonlinearity. While keeping above facts in mind,, we have developed a multi-objective evolutionary approach based on NSGA-II and got the optimum value of annihilator immunity with good bound of nonlinearity. We have constructed balanced Boolean functions having the best trade-off among balancedness, Annihilator immunity and nonlinearity for 5, 6 and 7 variables by the proposed method.

  2. On the Computation of Comprehensive Boolean Gröbner Bases

    Science.gov (United States)

    Inoue, Shutaro

    We show that a comprehensive Boolean Gröbner basis of an ideal I in a Boolean polynomial ring B (bar A,bar X) with main variables bar X and parameters bar A can be obtained by simply computing a usual Boolean Gröbner basis of I regarding both bar X and bar A as variables with a certain block term order such that bar X ≫ bar A. The result together with a fact that a finite Boolean ring is isomorphic to a direct product of the Galois field mathbb{GF}_2 enables us to compute a comprehensive Boolean Gröbner basis by only computing corresponding Gröbner bases in a polynomial ring over mathbb{GF}_2. Our implementation in a computer algebra system Risa/Asir shows that our method is extremely efficient comparing with existing computation algorithms of comprehensive Boolean Gröbner bases.

  3. Cylindric-like algebras and algebraic logic

    CERN Document Server

    Ferenczi, Miklós; Németi, István

    2013-01-01

    Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways:  as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.

  4. Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras

    Science.gov (United States)

    Paseka, Jan; Riečanová, Zdenka

    2010-12-01

    We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.

  5. Atomic effect algebras with compression bases

    International Nuclear Information System (INIS)

    Caragheorgheopol, Dan; Tkadlec, Josef

    2011-01-01

    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean.

  6. Modeling digital switching circuits with linear algebra

    CERN Document Server

    Thornton, Mitchell A

    2014-01-01

    Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transf

  7. Elements of Boolean-Valued Dempster-Shafer Theory

    Czech Academy of Sciences Publication Activity Database

    Kramosil, Ivan

    2000-01-01

    Roč. 10, č. 5 (2000), s. 825-835 ISSN 1210-0552. [SOFSEM 2000 Workshop on Soft Computing. Milovy, 27.11.2000-28.11.2000] R&D Projects: GA ČR GA201/00/1489 Institutional research plan: AV0Z1030915 Keywords : Boolean algebra * belief function * Dempster-Shafer theory * Dempster combination rule * nonspecifity degree Subject RIV: BA - General Mathematics

  8. Approximate Reasoning with Fuzzy Booleans

    NARCIS (Netherlands)

    van den Broek, P.M.; Noppen, J.A.R.

    This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp

  9. Geometric Operators on Boolean Functions

    DEFF Research Database (Denmark)

    Frisvad, Jeppe Revall; Falster, Peter

    In truth-functional propositional logic, any propositional formula represents a Boolean function (according to some valuation of the formula). We describe operators based on Decartes' concept of constructing coordinate systems, for translation of a propositional formula to the image of a Boolean...... function. With this image of a Boolean function corresponding to a propositional formula, we prove that the orthogonal projection operator leads to a theorem describing all rules of inference in propositional reasoning. In other words, we can capture all kinds of inference in propositional logic by means...... of a few geometric operators working on the images of Boolean functions. The operators we describe, arise from the niche area of array-based logic and have previously been tightly bound to an array-based representation of Boolean functions. We redefine the operators in an abstract form to make them...

  10. Cryptographic Boolean functions and applications

    CERN Document Server

    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...

  11. Top Element Problem and Macneille Completions of Generalized Effect Algebras

    Science.gov (United States)

    RieČanová, Z.; Kalina, M.

    2014-10-01

    Effect algebras (EAs), introduced by D. J. Foulis and M. K. Bennett, as common generalizations of Boolean algebras, orthomodular lattices and MV-algebras, are nondistributive algebraic structures including unsharp elements. Their unbounded versions, called generalized effect algebras, are posets which may have or may have not an EA-MacNeille completion, or cannot be embedded into any complete effect algebra. We give a necessary and sufficient condition for a generalized effect algebra to have an EA-MacNeille completion. Some examples are provided.

  12. Lie n-derivations on 7 -subspace lattice algebras

    Indian Academy of Sciences (India)

    tice algebra, or briefly, JSL algebra. Note that a JSL algebra may not be prime. It also should be mentioned that both atomic Boolean subspace lattices and pentagon subspace lattices are 7 .... there exists some P ∈ JL(K) such that A = P AP and B = PBP. So JL(K) is a local matrix algebra. Note that K ∧ K− = {0} and K ∨ K.

  13. Strengthening Effect Algebras in a Logical Perspective: Heyting-Wajsberg Algebras

    Science.gov (United States)

    Konig, Martinvaldo

    2014-10-01

    Heyting effect algebras are lattice-ordered pseudoboolean effect algebras endowed with a pseudocomplementation that maps on the center (i.e. Boolean elements). They are the algebraic counterpart of an extension of both Łukasiewicz many-valued logic and intuitionistic logic. We show that Heyting effect algebras are termwise equivalent to Heyting-Wajsberg algebras where the two different logical implications are defined as primitive operators. We prove this logic to be decidable, to be strongly complete and to have the deduction-detachment theorem.

  14. Type-Decomposition of an Effect Algebra

    Science.gov (United States)

    Foulis, David J.; Pulmannová, Sylvia

    2010-10-01

    Effect algebras (EAs), play a significant role in quantum logic, are featured in the theory of partially ordered Abelian groups, and generalize orthoalgebras, MV-algebras, orthomodular posets, orthomodular lattices, modular ortholattices, and boolean algebras. We study centrally orthocomplete effect algebras (COEAs), i.e., EAs satisfying the condition that every family of elements that is dominated by an orthogonal family of central elements has a supremum. For COEAs, we introduce a general notion of decomposition into types; prove that a COEA factors uniquely as a direct sum of types I, II, and III; and obtain a generalization for COEAs of Ramsay’s fourfold decomposition of a complete orthomodular lattice.

  15. Synchronization Analysis of Master-Slave Probabilistic Boolean Networks.

    Science.gov (United States)

    Lu, Jianquan; Zhong, Jie; Li, Lulu; Ho, Daniel W C; Cao, Jinde

    2015-08-28

    In this paper, we analyze the synchronization problem of master-slave probabilistic Boolean networks (PBNs). The master Boolean network (BN) is a deterministic BN, while the slave BN is determined by a series of possible logical functions with certain probability at each discrete time point. In this paper, we firstly define the synchronization of master-slave PBNs with probability one, and then we investigate synchronization with probability one. By resorting to new approach called semi-tensor product (STP), the master-slave PBNs are expressed in equivalent algebraic forms. Based on the algebraic form, some necessary and sufficient criteria are derived to guarantee synchronization with probability one. Further, we study the synchronization of master-slave PBNs in probability. Synchronization in probability implies that for any initial states, the master BN can be synchronized by the slave BN with certain probability, while synchronization with probability one implies that master BN can be synchronized by the slave BN with probability one. Based on the equivalent algebraic form, some efficient conditions are derived to guarantee synchronization in probability. Finally, several numerical examples are presented to show the effectiveness of the main results.

  16. Development of Boolean calculus and its application

    Science.gov (United States)

    Tapia, M. A.

    1979-01-01

    Formal procedures for synthesis of asynchronous sequential system using commercially available edge-sensitive flip-flops are developed. Boolean differential is defined. The exact number of compatible integrals of a Boolean differential were calculated.

  17. Modular Decomposition of Boolean Functions

    NARCIS (Netherlands)

    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

  18. Binary higher order neural networks for realizing Boolean functions.

    Science.gov (United States)

    Zhang, Chao; Yang, Jie; Wu, Wei

    2011-05-01

    In order to more efficiently realize Boolean functions by using neural networks, we propose a binary product-unit neural network (BPUNN) and a binary π-ς neural network (BPSNN). The network weights can be determined by one-step training. It is shown that the addition " σ," the multiplication " π," and two kinds of special weighting operations in BPUNN and BPSNN can implement the logical operators " ∨," " ∧," and " ¬" on Boolean algebra 〈Z(2),∨,∧,¬,0,1〉 (Z(2)={0,1}), respectively. The proposed two neural networks enjoy the following advantages over the existing networks: 1) for a complete truth table of N variables with both truth and false assignments, the corresponding Boolean function can be realized by accordingly choosing a BPUNN or a BPSNN such that at most 2(N-1) hidden nodes are needed, while O(2(N)), precisely 2(N) or at most 2(N), hidden nodes are needed by existing networks; 2) a new network BPUPS based on a collaboration of BPUNN and BPSNN can be defined to deal with incomplete truth tables, while the existing networks can only deal with complete truth tables; and 3) the values of the weights are all simply -1 or 1, while the weights of all the existing networks are real numbers. Supporting numerical experiments are provided as well. Finally, we present the risk bounds of BPUNN, BPSNN, and BPUPS, and then analyze their probably approximately correct learnability.

  19. Boolean gates on actin filaments

    Energy Technology Data Exchange (ETDEWEB)

    Siccardi, Stefano, E-mail: ssiccardi@2ssas.it [The Unconventional Computing Centre, University of the West of England, Bristol (United Kingdom); Tuszynski, Jack A., E-mail: jackt@ualberta.ca [Department of Oncology, University of Alberta, Edmonton, Alberta (Canada); Adamatzky, Andrew, E-mail: andrew.adamatzky@uwe.ac.uk [The Unconventional Computing Centre, University of the West of England, Bristol (United Kingdom)

    2016-01-08

    Actin is a globular protein which forms long polar filaments in the eukaryotic cytoskeleton. Actin networks play a key role in cell mechanics and cell motility. They have also been implicated in information transmission and processing, memory and learning in neuronal cells. The actin filaments have been shown to support propagation of voltage pulses. Here we apply a coupled nonlinear transmission line model of actin filaments to study interactions between voltage pulses. To represent digital information we assign a logical TRUTH value to the presence of a voltage pulse in a given location of the actin filament, and FALSE to the pulse's absence, so that information flows along the filament with pulse transmission. When two pulses, representing Boolean values of input variables, interact, then they can facilitate or inhibit further propagation of each other. We explore this phenomenon to construct Boolean logical gates and a one-bit half-adder with interacting voltage pulses. We discuss implications of these findings on cellular process and technological applications. - Highlights: • We simulate interaction between voltage pulses using on actin filaments. • We use a coupled nonlinear transmission line model. • We design Boolean logical gates via interactions between the voltage pulses. • We construct one-bit half-adder with interacting voltage pulses.

  20. (Modular Effect Algebras are Equivalent to (Frobenius Antispecial Algebras

    Directory of Open Access Journals (Sweden)

    Dusko Pavlovic

    2017-01-01

    Full Text Available Effect algebras are one of the generalizations of Boolean algebras proposed in the quest for a quantum logic. Frobenius algebras are a tool of categorical quantum mechanics, used to present various families of observables in abstract, often nonstandard frameworks. Both effect algebras and Frobenius algebras capture their respective fragments of quantum mechanics by elegant and succinct axioms; and both come with their conceptual mysteries. A particularly elegant and mysterious constraint, imposed on Frobenius algebras to characterize a class of tripartite entangled states, is the antispecial law. A particularly contentious issue on the quantum logic side is the modularity law, proposed by von Neumann to mitigate the failure of distributivity of quantum logical connectives. We show that, if quantum logic and categorical quantum mechanics are formalized in the same framework, then the antispecial law of categorical quantum mechanics corresponds to the natural requirement of effect algebras that the units are each other's unique complements; and that the modularity law corresponds to the Frobenius condition. These correspondences lead to the equivalence announced in the title. Aligning the two formalisms, at the very least, sheds new light on the concepts that are more clearly displayed on one side than on the other (such as e.g. the orthogonality. Beyond that, it may also open up new approaches to deep and important problems of quantum mechanics (such as the classification of complementary observables.

  1. Reliable dynamics in Boolean and continuous networks

    International Nuclear Information System (INIS)

    Ackermann, Eva; Drossel, Barbara; Peixoto, Tiago P

    2012-01-01

    We investigate the dynamical behavior of a model of robust gene regulatory networks which possess ‘entirely reliable’ trajectories. In a Boolean representation, these trajectories are characterized by being insensitive to the order in which the nodes are updated, i.e. they always go through the same sequence of states. The Boolean model for gene activity is compared with a continuous description in terms of differential equations for the concentrations of mRNA and proteins. We found that entirely reliable Boolean trajectories can be reproduced perfectly in the continuous model when realistic Hill coefficients are used. We investigate to what extent this high correspondence between Boolean and continuous trajectories depends on the extent of reliability of the Boolean trajectories, and we identify simple criteria that enable the faithful reproduction of the Boolean dynamics in the continuous description. (paper)

  2. 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.

  3. Maiorana-McFarland class: Degree optimization and algebraic properties

    DEFF Research Database (Denmark)

    Pasalic, Enes

    2006-01-01

    degree of functions in the extended Maiorana-McFarland (MM) class (nonlinear resilient functions F : GF (2)(n) -> GF (2)(m) derived from linear codes). We also show that in the Boolean case, the same subclass seems not to have an optimized algebraic immunity, hence not providing a maximum resistance......In this paper, we consider a subclass of the Maiorana-McFarland class used in the design of resilient nonlinear Boolean functions. We show that these functions allow a simple modification so that resilient Boolean functions of maximum algebraic degree may be generated instead of suboptimized degree...... in the original class. Preserving a high-nonlinearity value immanent to the original construction method, together with the degree optimization gives in many cases functions with cryptographic properties superior to all previously known construction methods. This approach is then used to increase the algebraic...

  4. Grassmann algebras

    International Nuclear Information System (INIS)

    Garcia, R.L.

    1983-11-01

    The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt

  5. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  6. Chiral algebras

    CERN Document Server

    Beilinson, Alexander

    2004-01-01

    Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras. The exposition of this book covers the following topics: the "classical" counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries; the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the ch

  7. Testing Properties of Boolean Functions

    Science.gov (United States)

    2012-01-01

    The JUNTATEST algorithm is based on two simple but powerful ideas. The first idea, initially presented by Fischer et al. [52], is that there is a very...Computer and System Sciences, 61(3):428 – 456, 2000. 12 [75] Subhash Khot. On the power of unique 2-prover 1-round games. In Proc. 34th ACM Symposium on...Sharpness of KKL on Schreier graphs, 2009. Manuscript. 6.4 [84] Michal Parnas, Dana Ron, and Alex Samorodnitsky. Testing basic boolean formu- lae . SIAM J

  8. Version Spaces and Generalized Monotone Boolean Functions

    NARCIS (Netherlands)

    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

  9. Boolean gates on actin filaments

    Science.gov (United States)

    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.

  10. Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games

    Directory of Open Access Journals (Sweden)

    Gijs Kant

    2012-10-01

    Full Text Available Parameterised Boolean Equation Systems (PBESs are sequences of Boolean fixed point equations with data variables, used for, e.g., verification of modal mu-calculus formulae for process algebraic specifications with data. Solving a PBES is usually done by instantiation to a Parity Game and then solving the game. Practical game solvers exist, but the instantiation step is the bottleneck. We enhance the instantiation in two steps. First, we transform the PBES to a Parameterised Parity Game (PPG, a PBES with each equation either conjunctive or disjunctive. Then we use LTSmin, that offers transition caching, efficient storage of states and both distributed and symbolic state space generation, for generating the game graph. To that end we define a language module for LTSmin, consisting of an encoding of variables with parameters into state vectors, a grouped transition relation and a dependency matrix to indicate the dependencies between parts of the state vector and transition groups. Benchmarks on some large case studies, show that the method speeds up the instantiation significantly and decreases memory usage drastically.

  11. Algebra for cryptologists

    CERN Document Server

    Meijer, Alko R

    2016-01-01

    This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his o...

  12. Boolean Dependence Logic and Partially-Ordered Connectives

    OpenAIRE

    Ebbing, Johannes; Hella, Lauri; Lohmann, Peter; Virtema, Jonni

    2014-01-01

    We introduce a new variant of dependence logic called Boolean dependence logic. In Boolean dependence logic dependence atoms are of the type =(x_1,...,x_n,\\alpha), where \\alpha is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions. We compare the expressive power of Boolean dependence logic to dependence logic and first-order logic enriched by partially-ordered connec...

  13. Modern algebra

    CERN Document Server

    Warner, Seth

    1990-01-01

    Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.

  14. Random networks of Boolean cellular automata

    International Nuclear Information System (INIS)

    Miranda, Enrique

    1990-01-01

    Some recent results about random networks of Boolean automata -the Kauffman model- are reviewed. The structure of configuration space is explored. Ultrametricity between cycles is analyzed and the effects of noise in the dynamics are studied. (Author)

  15. Leibniz Algebras and Lie Algebras

    Directory of Open Access Journals (Sweden)

    Geoffrey Mason

    2013-10-01

    Full Text Available This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.

  16. Boolean Networks in Inference and Dynamic Modeling of Biological Systems at the Molecular and Physiological Level

    Science.gov (United States)

    Thakar, Juilee; Albert, Réka

    The following sections are included: * Introduction * Boolean Network Concepts and History * Extensions of the Classical Boolean Framework * Boolean Inference Methods and Examples in Biology * Dynamic Boolean Models: Examples in Plant Biology, Developmental Biology and Immunology * Conclusions * References

  17. Separable algebras

    CERN Document Server

    Ford, Timothy J

    2017-01-01

    This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.

  18. Elliptic algebras

    International Nuclear Information System (INIS)

    Odesskii, A V

    2002-01-01

    This survey is devoted to associative Z ≥0 -graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations

  19. Algebraic geometry

    National Research Council Canada - National Science Library

    Hartshorne, Robin

    1977-01-01

    .... 141 BECKERIWEISPFENNINGIKREDEL. Grabner Bases. A Computational Approach to Commutative Algebra. 142 LANG. Real and Functional Analysis. 3rd ed. 143 DOOB. Measure Theory. 144 DENNIS/FARB. Noncommutat...

  20. Forced synchronization of autonomous dynamical Boolean networks

    International Nuclear Information System (INIS)

    Rivera-Durón, R. R.; Campos-Cantón, E.; Campos-Cantón, I.; Gauthier, Daniel J.

    2015-01-01

    We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics

  1. 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.

  2. A New Calculation for Boolean Derivative Using Cheng Product

    Directory of Open Access Journals (Sweden)

    Hao Chen

    2012-01-01

    Full Text Available The matrix expression and relationships among several definitions of Boolean derivatives are given by using the Cheng product. We introduce several definitions of Boolean derivatives. By using the Cheng product, the matrix expressions of Boolean derivative are given, respectively. Furthermore, the relationships among different definitions are presented. The logical calculation is converted into matrix product. This helps to extend the application of Boolean derivative. At last, an example is given to illustrate the main results.

  3. The Permeability of Boolean Sets of Cylinders

    Directory of Open Access Journals (Sweden)

    Willot F.

    2016-07-01

    Full Text Available Numerical and analytical results on the permeability of Boolean models of randomly-oriented cylinders with circular cross-section are reported. The present work investigates cylinders of prolate (highly-elongated and oblate (nearly flat types. The fluid flows either inside or outside of the cylinders. The Stokes flow is solved using full-fields Fourier-based computations on 3D binarized microstructures. The permeability is given for varying volume fractions of pores. A new upper-bound is derived for the permeability of the Boolean model of oblate cylinders. The behavior of the permeability in the dilute limit is discussed.

  4. Implicative Algebras

    African Journals Online (AJOL)

    Tadesse

    Department of Mathematics, Faculty of Computer and Mathematical Sciences, Addis Ababa. University, Addis Ababa, Ethiopia(*drkvenkateswarlu@gmail.com, **berhanufk@yahoo.co.uk). ABSTRACT. In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra ...

  5. Implicative Algebras

    African Journals Online (AJOL)

    Tadesse

    metric space. Also we prove that every implicative algebra can be made into a regular. Autometrized Algebra of Swamy (1964) (see theorem 2.9). We recall the definition of Xu (1993). Defintion [2]: Let (L,∨,∧,0,1) be a bounded lattice with order reversing involution. “ ' ”and a binary operation → satisfying the following ...

  6. Linear Algebra and Smarandache Linear Algebra

    OpenAIRE

    Vasantha, Kandasamy

    2003-01-01

    The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...

  7. Evolutionary Algorithms for Boolean Queries Optimization

    Czech Academy of Sciences Publication Activity Database

    Húsek, Dušan; Snášel, Václav; Neruda, Roman; Owais, S.S.J.; Krömer, P.

    2006-01-01

    Roč. 3, č. 1 (2006), s. 15-20 ISSN 1790-0832 R&D Projects: GA AV ČR 1ET100300414 Institutional research plan: CEZ:AV0Z10300504 Keywords : evolutionary algorithms * genetic algorithms * information retrieval * Boolean query Subject RIV: BA - General Mathematics

  8. Boolean Queries Optimization by Genetic Algorithms

    Czech Academy of Sciences Publication Activity Database

    Húsek, Dušan; Owais, S.S.J.; Krömer, P.; Snášel, Václav

    2005-01-01

    Roč. 15, - (2005), s. 395-409 ISSN 1210-0552 R&D Projects: GA AV ČR 1ET100300414 Institutional research plan: CEZ:AV0Z10300504 Keywords : evolutionary algorithms * genetic algorithms * genetic programming * information retrieval * Boolean query Subject RIV: BB - Applied Statistics, Operational Research

  9. College algebra

    CERN Document Server

    Fine, Henry Burchard

    2005-01-01

    At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten. In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discus

  10. Abstract algebra

    CERN Document Server

    Garrett, Paul B

    2007-01-01

    Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal

  11. College algebra

    CERN Document Server

    Kolman, Bernard

    1985-01-01

    College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c

  12. Dynamics of random Boolean networks under fully asynchronous stochastic update based on linear representation.

    Directory of Open Access Journals (Sweden)

    Chao Luo

    Full Text Available A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs. In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length[Formula: see text] in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.

  13. Algebraic Geometry

    CERN Document Server

    Holme, Audun

    1988-01-01

    This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.

  14. Elementary algebra

    CERN Document Server

    McKeague, Charles P

    1986-01-01

    Elementary Algebra, Third Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first ponders on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the elimination method, solving linear systems by graphing, word problems, addition property of equality, solving linear equations, linear inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then takes a look at exponents and polynomials, factoring, and rational expressions. Topics include reducing ra

  15. Elementary algebra

    CERN Document Server

    McKeague, Charles P

    1981-01-01

    Elementary Algebra 2e, Second Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first tackles the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the substitution method, solving linear systems by graphing, solutions to linear equations in two variables, multiplication property of equality, word problems, addition property of equality, and subtraction, addition, multiplication, and division of real numbers. The manuscript then examines exponents and polynomials, factoring, and rational e

  16. Totally optimal decision trees for Boolean functions

    KAUST Repository

    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.

  17. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  18. Linear algebra

    CERN Document Server

    Edwards, Harold M

    1995-01-01

    In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

  19. Optimal stabilization of Boolean networks through collective influence

    Science.gov (United States)

    Wang, Jiannan; Pei, Sen; Wei, Wei; Feng, Xiangnan; Zheng, Zhiming

    2018-03-01

    Boolean networks have attracted much attention due to their wide applications in describing dynamics of biological systems. During past decades, much effort has been invested in unveiling how network structure and update rules affect the stability of Boolean networks. In this paper, we aim to identify and control a minimal set of influential nodes that is capable of stabilizing an unstable Boolean network. For locally treelike Boolean networks with biased truth tables, we propose a greedy algorithm to identify influential nodes in Boolean networks by minimizing the largest eigenvalue of a modified nonbacktracking matrix. We test the performance of the proposed collective influence algorithm on four different networks. Results show that the collective influence algorithm can stabilize each network with a smaller set of nodes compared with other heuristic algorithms. Our work provides a new insight into the mechanism that determines the stability of Boolean networks, which may find applications in identifying virulence genes that lead to serious diseases.

  20. Algebraic arithmetic

    CERN Document Server

    Bell, Eric T

    1927-01-01

    The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the Bôcher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, ellipti

  1. Lie algebras

    CERN Document Server

    Jacobson, Nathan

    1979-01-01

    Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its

  2. Linear algebra

    CERN Document Server

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  3. Basic algebra

    CERN Document Server

    Jacobson, Nathan

    2009-01-01

    A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L

  4. Linear algebra and probability for computer science applications

    CERN Document Server

    Davis, Ernest

    2012-01-01

    MATLABDesk calculator operations Booleans Nonstandard numbers Loops and conditionals Script file Functions Variable scope and parameter passingI: Linear Algebra Vectors Definition of vectors Applications of vectorsBasic operations on vectorsDot productVectors in MATLAB: Basic operationsPlotting vectors in MATLABVectors in other programming languagesMatrices Definition of matrices Applications of matrices Simple operations on matrices Multiplying a matrix times a vector Linear transformation Systems of linear equations Matrix multiplication Vectors as matrices Algebraic properties of matrix mul

  5. 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.

  6. 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.

  7. Algebraic Topology

    CERN Document Server

    Oliver, Bob; Pawałowski, Krzystof

    1991-01-01

    As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.

  8. ALGEBRAIC TOPOLOGY

    Indian Academy of Sciences (India)

    tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).

  9. Large Sets in Boolean and Non-Boolean Groups and Topology

    Directory of Open Access Journals (Sweden)

    Ol’ga V. Sipacheva

    2017-10-01

    Full Text Available Various notions of large sets in groups, including the classical notions of thick, syndetic, and piecewise syndetic sets and the new notion of vast sets in groups, are studied with emphasis on the interplay between such sets in Boolean groups. Natural topologies closely related to vast sets are considered; as a byproduct, interesting relations between vast sets and ultrafilters are revealed.

  10. Boolean Factor Analysis by Attractor Neural Network

    Czech Academy of Sciences Publication Activity Database

    Frolov, A. A.; Húsek, Dušan; Muraviev, I. P.; Polyakov, P.Y.

    2007-01-01

    Roč. 18, č. 3 (2007), s. 698-707 ISSN 1045-9227 R&D Projects: GA AV ČR 1ET100300419; GA ČR GA201/05/0079 Institutional research plan: CEZ:AV0Z10300504 Keywords : recurrent neural network * Hopfield-like neural network * associative memory * unsupervised learning * neural network architecture * neural network application * statistics * Boolean factor analysis * dimensionality reduction * features clustering * concepts search * information retrieval Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.769, year: 2007

  11. On 2-Banach algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Siddiqui, A.H.

    1987-11-01

    The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

  12. Color Algebras

    Science.gov (United States)

    Mulligan, Jeffrey B.

    2017-01-01

    A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.

  13. An adaptable Boolean net trainable to control a computing robot

    International Nuclear Information System (INIS)

    Lauria, F. E.; Prevete, R.; Milo, M.; Visco, S.

    1999-01-01

    We discuss a method to implement in a Boolean neural network a Hebbian rule so to obtain an adaptable universal control system. We start by presenting both the Boolean neural net and the Hebbian rule we have considered. Then we discuss, first, the problems arising when the latter is naively implemented in a Boolean neural net, second, the method consenting us to overcome them and the ensuing adaptable Boolean neural net paradigm. Next, we present the adaptable Boolean neural net as an intelligent control system, actually controlling a writing robot, and discuss how to train it in the execution of the elementary arithmetic operations on operands represented by numerals with an arbitrary number of digits

  14. Dually quasi-De Morgan Stone semi-Heyting algebras II. Regularity

    Directory of Open Access Journals (Sweden)

    Hanamantagouda P. Sankappanavar

    2014-07-01

    Full Text Available This paper is the second of a two part series. In this Part, we prove, using the description of simples obtained in Part I, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--the latter is known to be generated by the expansions of the three 4-element Boolean semi-Heyting algebras. As consequences of our main theorem, we present (equational axiomatizations for several subvarieties of $mathbf{RDQDStSH_1}$. The paper concludes with some open problems for further investigation.

  15. Algebraic theory of molecules

    CERN Document Server

    Iachello, F

    1995-01-01

    1. The Wave Mechanics of Diatomic Molecules. 2. Summary of Elements of Algebraic Theory. 3. Mechanics of Molecules. 4. Three-Body Algebraic Theory. 5. Four-Body Algebraic Theory. 6. Classical Limit and Coordinate Representation. 8. Prologue to the Future. Appendices. Properties of Lie Algebras; Coupling of Algebras; Hamiltonian Parameters

  16. On Fuzzy Ideals of BL-Algebras

    Science.gov (United States)

    Xin, Xiao Long

    2014-01-01

    In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω(0) = 1 and |Im⁡(ω)| = 2. We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true. PMID:24892085

  17. Bistability and Asynchrony in a Boolean Model of the L-arabinose Operon in Escherichia coli.

    Science.gov (United States)

    Jenkins, Andy; Macauley, Matthew

    2017-08-01

    The lactose operon in Escherichia coli was the first known gene regulatory network, and it is frequently used as a prototype for new modeling paradigms. Historically, many of these modeling frameworks use differential equations. More recently, Stigler and Veliz-Cuba proposed a Boolean model that captures the bistability of the system and all of the biological steady states. In this paper, we model the well-known arabinose operon in E. coli with a Boolean network. This has several complex features not found in the lac operon, such as a protein that is both an activator and repressor, a DNA looping mechanism for gene repression, and the lack of inducer exclusion by glucose. For 11 out of 12 choices of initial conditions, we use computational algebra and Sage to verify that the state space contains a single fixed point that correctly matches the biology. The final initial condition, medium levels of arabinose and no glucose, successfully predicts the system's bistability. Finally, we compare the state space under synchronous and asynchronous update and see that the former has several artificial cycles that go away under a general asynchronous update.

  18. Real Algebraic Geometry

    CERN Document Server

    Mahé, Louis; Roy, Marie-Françoise

    1992-01-01

    Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...

  19. Hom-Novikov algebras

    International Nuclear Information System (INIS)

    Yau, Donald

    2011-01-01

    We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.

  20. Algebraic functions

    CERN Document Server

    Bliss, Gilbert Ames

    1933-01-01

    This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t

  1. Dually quasi-De Morgan Stone semi-Heyting algebras I. Regularity

    Directory of Open Access Journals (Sweden)

    Hanamantagouda P. Sankappanavar

    2014-07-01

    Full Text Available This paper is the first of a two part series. In this paper, we first prove that the variety of dually quasi-De Morgan Stone semi-Heyting algebras of level 1 satisfies the strongly blended $lor$-De Morgan law introduced in cite{Sa12}. Then, using this result and the results of cite{Sa12}, we prove our main result which gives an explicit description of simple algebras(=subdirectly irreducibles in the variety of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1. It is shown that there are 25 nontrivial simple algebras in this variety. In Part II, we prove, using the description of simples obtained in this Part, that the variety $mathbf{RDQDStSH_1}$ of regular dually quasi-De Morgan Stone semi-Heyting algebras of level 1 is the join of the variety generated by the twenty 3-element $mathbf{RDQDStSH_1}$-chains and the variety of dually quasi-De Morgan Boolean semi-Heyting algebras--the latter is known to be generated by the expansions of the three 4-element Boolean semi-Heyting algebras. As consequences of this theorem, we present (equational axiomatizations for several subvarieties of $mathbf{RDQDStSH_1}$. The Part II concludes with some open problems for further investigation.

  2. Evolutionary Algorithms for Boolean Functions in Diverse Domains of Cryptography.

    Science.gov (United States)

    Picek, Stjepan; Carlet, Claude; Guilley, Sylvain; Miller, Julian F; Jakobovic, Domagoj

    2016-01-01

    The role of Boolean functions is prominent in several areas including cryptography, sequences, and coding theory. Therefore, various methods for the construction of Boolean functions with desired properties are of direct interest. New motivations on the role of Boolean functions in cryptography with attendant new properties have emerged over the years. There are still many combinations of design criteria left unexplored and in this matter evolutionary computation can play a distinct role. This article concentrates on two scenarios for the use of Boolean functions in cryptography. The first uses Boolean functions as the source of the nonlinearity in filter and combiner generators. Although relatively well explored using evolutionary algorithms, it still presents an interesting goal in terms of the practical sizes of Boolean functions. The second scenario appeared rather recently where the objective is to find Boolean functions that have various orders of the correlation immunity and minimal Hamming weight. In both these scenarios we see that evolutionary algorithms are able to find high-quality solutions where genetic programming performs the best.

  3. Intervention in Context-Sensitive Probabilistic Boolean Networks Revisited

    Directory of Open Access Journals (Sweden)

    Faryabi Babak

    2009-01-01

    Full Text Available An approximate representation for the state space of a context-sensitive probabilistic Boolean network has previously been proposed and utilized to devise therapeutic intervention strategies. Whereas the full state of a context-sensitive probabilistic Boolean network is specified by an ordered pair composed of a network context and a gene-activity profile, this approximate representation collapses the state space onto the gene-activity profiles alone. This reduction yields an approximate transition probability matrix, absent of context, for the Markov chain associated with the context-sensitive probabilistic Boolean network. As with many approximation methods, a price must be paid for using a reduced model representation, namely, some loss of optimality relative to using the full state space. This paper examines the effects on intervention performance caused by the reduction with respect to various values of the model parameters. This task is performed using a new derivation for the transition probability matrix of the context-sensitive probabilistic Boolean network. This expression of transition probability distributions is in concert with the original definition of context-sensitive probabilistic Boolean network. The performance of optimal and approximate therapeutic strategies is compared for both synthetic networks and a real case study. It is observed that the approximate representation describes the dynamics of the context-sensitive probabilistic Boolean network through the instantaneously random probabilistic Boolean network with similar parameters.

  4. Boolean networks with robust and reliable trajectories

    International Nuclear Information System (INIS)

    Schmal, Christoph; Peixoto, Tiago P; Drossel, Barbara

    2010-01-01

    We construct and investigate Boolean networks that follow a given reliable trajectory in state space, which is insensitive to fluctuations in the updating schedule and which is also robust against noise. Robustness is quantified as the probability that the dynamics return to the reliable trajectory after a perturbation of the state of a single node. In order to achieve high robustness, we navigate through the space of possible update functions by using an evolutionary algorithm. We constrain the networks to those having the minimum number of connections required to obtain the reliable trajectory. Surprisingly, we find that robustness always reaches values close to 100% during the evolutionary optimization process. The set of update functions can be evolved such that it differs only slightly from that of networks that were not optimized with respect to robustness. The state space of the optimized networks is dominated by the basin of attraction of the reliable trajectory.

  5. Theory reduction and non-Boolean theories.

    Science.gov (United States)

    Primas, H

    1977-07-19

    It is suggested that biological theories should be embedded into the family of non-Boolean theories based on an orthomodular propositional calculus. The structure of universal theories that include quantal phenomena is investigated and it is shown that their subtheories form a directed set which cannot be totally orders. A precise definition of theory reduction is given; it turns out that hierarchically different descriptive levels are not related by a homomorphic map. A subtheory that is reducible to a more general theory can be associated with the emergence of novel concepts and is in general subject to a wider empirical clissification scheme than the reducing theory. The implications of these results for reductionism, holism, emergence, and their conceptual unification are discussed.

  6. Multipath Detection Using Boolean Satisfiability Techniques

    Directory of Open Access Journals (Sweden)

    Fadi A. Aloul

    2011-01-01

    Full Text Available A new technique for multipath detection in wideband mobile radio systems is presented. The proposed scheme is based on an intelligent search algorithm using Boolean Satisfiability (SAT techniques to search through the uncertainty region of the multipath delays. The SAT-based scheme utilizes the known structure of the transmitted wideband signal, for example, pseudo-random (PN code, to effectively search through the entire space by eliminating subspaces that do not contain a possible solution. The paper presents a framework for modeling the multipath detection problem as a SAT application. It also provides simulation results that demonstrate the effectiveness of the proposed scheme in detecting the multipath components in frequency-selective Rayleigh fading channels.

  7. Representing Boolean Functions by Decision Trees

    KAUST Repository

    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.

  8. Universal algebra

    CERN Document Server

    Grätzer, George

    1979-01-01

    Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...

  9. 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...

  10. Yoneda algebras of almost Koszul algebras

    Indian Academy of Sciences (India)

    Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...

  11. Open algebraic surfaces

    CERN Document Server

    Miyanishi, Masayoshi

    2000-01-01

    Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...

  12. Generalized Hermitian Algebras

    Science.gov (United States)

    Foulis, David J.; Pulmannová, Sylvia

    2009-05-01

    We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. In this paper we define and launch a study of a class of generalized Hermitian (GH) algebras. Among the examples of GH-algebras are ordered special Jordan algebras, JW-algebras, and AJW-algebras, but unlike these more restricted cases, a GH-algebra is not necessarily a Banach space and its lattice of projections is not necessarily complete. In this paper we develop the basic theory of GH-algebras, identify their unit intervals as effect algebras, and observe that their projection lattices are sigma-complete orthomodular lattices. We show that GH-algebras are spectral order-unit spaces and that they admit a substantial spectral theory.

  13. Universal enveloping algebras for Malcev color algebras

    OpenAIRE

    de-la-Concepción, Daniel

    2015-01-01

    In this paper we give a construction of the universal enveloping algebra of a Malcev algebra in categories of group algebra comodules with a symmetry given by a bicharacter of the group. A particular example of such categories is the category of super vector spaces.

  14. Linear algebra

    CERN Document Server

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

  15. 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.

  16. Attractor Transformation by Impulsive Control in Boolean Control Network

    Directory of Open Access Journals (Sweden)

    Bo Gao

    2013-01-01

    Full Text Available Boolean control networks have recently been attracting considerable interests as computational models for genetic regulatory networks. In this paper, we present an approach of impulsive control for attractor transitions in Boolean control networks based on the recent developed matrix semitensor product theory. The reachability of attractors is estimated, and the controller is also obtained. The general derivation proposed here is exemplified with a kind of gene model, which is the protein-nucleic acid interactions network, on numerical simulations.

  17. Split Malcev algebras

    Indian Academy of Sciences (India)

    Introduction and preliminaries. The class of Malcev algebras contains one of the Lie algebras and so a question arises whether some known results on Lie algebras can be extended to the framework of Malcev algebras (see [4, 7, 9, 10]). In the present paper, we are interested in studying the structure of arbitrary Malcev ...

  18. Embeddings of Heyting Algebras

    NARCIS (Netherlands)

    Jongh, D.H.J. de; Visser, A.

    In this paper we study embeddings of Heyting Algebras. It is pointed out that such embeddings are naturally connected with Derived Rules. We compare the Heyting Algebras embeddable in the Heyting Algebra of the Intuitionistic Propositional Calculus (IPC), i.e. the free Heyting Algebra on countably

  19. Novikov-Jordan algebras

    OpenAIRE

    Dzhumadil'daev, A. S.

    2002-01-01

    Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.

  20. Wavelets and quantum algebras

    International Nuclear Information System (INIS)

    Ludu, A.; Greiner, M.

    1995-09-01

    A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs

  1. Algebraic Side-Channel Attack on Twofish

    Directory of Open Access Journals (Sweden)

    Chujiao Ma

    2017-05-01

    Full Text Available While algebraic side-channel attack (ASCA has been successful in breaking simple cryptographic algorithms, it has never been done on larger or more complex algorithms such as Twofish. Compared to other algorithms that ASCA has been used on, Twofish is more difficult to attack due to the key-dependent S-boxes as well as the complex key scheduling. In this paper, we propose the first algebraic side-channel attack on Twofish, and examine the importance of side-channel information in getting past the key-dependent S-boxes and the complex key scheduling. The cryptographic algorithm and side-channel information are both expressed as boolean equations and a SAT solver is used to recover the key. While algebraic attack by itself is not sufficient to break the algorithm, with the help of side-channel information such as Hamming weights, we are able to correctly solve for 96 bits of the 128 bits key in under 2 hours with known plaintext/ciphertext.

  2. Uniform Frechet algebras

    CERN Document Server

    Goldmann, H

    1990-01-01

    The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorphic functions on Stein spaces) within the class of Fréchet algebras.

  3. Leavitt path algebras

    CERN Document Server

    Abrams, Gene; Siles Molina, Mercedes

    2017-01-01

    This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...

  4. Operator algebras generated by commuting projections a vector measure approach

    CERN Document Server

    Ricker, Werner

    1999-01-01

    This book presents a systematic investigation of the theory of those commutative, unital subalgebras (of bounded linear operators acting in a Banach space) which are closed for some given topology and are generated by a uniformly bounded Boolean algebra of projections. One of the main aims is to employ the methods of vector measures and integration as a unifying theme throughout. This yields proofs of several classical results which are quite different to the classical ones. This book is directed to both those wishing to learn this topic for the first time and to current experts in the field.

  5. Algebraic theory of numbers

    CERN Document Server

    Samuel, Pierre

    2008-01-01

    Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

  6. Workshop on Lie Algebras

    CERN Document Server

    Osborn, J

    1989-01-01

    During the academic year 1987-1988 the University of Wisconsin in Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the workshop was the long-standing problem of classifying the simple finite-dimensional Lie algebras over algebraically closed field of prime characteristic. However, other lectures at the workshop dealt with the related areas of algebraic groups, representation theory, and Kac-Moody Lie algebras. Fourteen papers were presented and nine of these (eight research articles and one expository article) make up this volume.

  7. Relation between dual S-algebras and BE-algebras

    Directory of Open Access Journals (Sweden)

    Arsham Borumand Saeid

    2015-05-01

    Full Text Available In this paper, we investigate the relationship between dual (Weak Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.  

  8. Distributivity of the algebra of regular open subsets of .beta. R / R

    Czech Academy of Sciences Publication Activity Database

    Balcar, Bohuslav; Hrušák, M.

    2005-01-01

    Roč. 149, č. 1 (2005), s. 1-7 ISSN 0166-8641 R&D Projects: GA ČR(CZ) GA201/03/0933; GA ČR(CZ) GA201/02/0857 Institutional research plan: CEZ:AV0Z10190503 Keywords : distributivity of Boolean algebras * cardinal invariants of the continuum * Čech-Stone compactification Subject RIV: BA - General Mathematics Impact factor: 0.297, year: 2005

  9. Algebraic isotopy in genetics.

    Science.gov (United States)

    Campos, T M; Holgate, P

    1987-01-01

    It is shown that many of the algebras arising in nonselective genetics are isotopes of the algebras for particularly simple systems of inheritance. Moreover, interesting aspects of the structure are preserved under the relevant isotopies.

  10. Rudiments of algebraic geometry

    CERN Document Server

    Jenner, WE

    2017-01-01

    Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.

  11. Order-to-chaos transition in the hardness of random Boolean satisfiability problems

    Science.gov (United States)

    Varga, Melinda; Sumi, Róbert; Toroczkai, Zoltán; Ercsey-Ravasz, Mária

    2016-05-01

    Transient chaos is a ubiquitous phenomenon characterizing the dynamics of phase-space trajectories evolving towards a steady-state attractor in physical systems as diverse as fluids, chemical reactions, and condensed matter systems. Here we show that transient chaos also appears in the dynamics of certain efficient algorithms searching for solutions of constraint satisfaction problems that include scheduling, circuit design, routing, database problems, and even Sudoku. In particular, we present a study of the emergence of hardness in Boolean satisfiability (k -SAT), a canonical class of constraint satisfaction problems, by using an analog deterministic algorithm based on a system of ordinary differential equations. Problem hardness is defined through the escape rate κ , an invariant measure of transient chaos of the dynamical system corresponding to the analog algorithm, and it expresses the rate at which the trajectory approaches a solution. We show that for a given density of constraints and fixed number of Boolean variables N , the hardness of formulas in random k -SAT ensembles has a wide variation, approximable by a lognormal distribution. We also show that when increasing the density of constraints α , hardness appears through a second-order phase transition at αχ in the random 3-SAT ensemble where dynamical trajectories become transiently chaotic. A similar behavior is found in 4-SAT as well, however, such a transition does not occur for 2-SAT. This behavior also implies a novel type of transient chaos in which the escape rate has an exponential-algebraic dependence on the critical parameter κ ˜NB |α - αχ|1-γ with 0 <γ <1 . We demonstrate that the transition is generated by the appearance of metastable basins in the solution space as the density of constraints α is increased.

  12. The stability of Boolean network with transmission sensitivity

    Science.gov (United States)

    Wang, Jiannan; Guo, Binghui; Wei, Wei; Mi, Zhilong; Yin, Ziqiao; Zheng, Zhiming

    2017-09-01

    Boolean network has been widely used in modeling biological systems and one of the key problems is its stability in response to small perturbations. Based on the hypothesis that the states of all nodes are homogenously updated, great progress has been made in previous works. In real biological networks, however, the updates of genes typically show much heterogeneity. To address such conditions, we introduce transmission sensitivity into Boolean network model. By the method of semi-annealed approximation, we illustrate that in a homogenous network, the critical condition of stability has no connection with its transmission sensitivity. As for heterogeneous networks, it reveals that correlations between network topology and transmission sensitivity can have profound effects on the its stability. This result shows a new mechanism that affects the stability of Boolean network, which could be used to control the dynamics in real biological systems.

  13. A comparison of hypertext and Boolean access to biomedical information.

    Science.gov (United States)

    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.

  14. New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology

    OpenAIRE

    Pinczon, Georges; Ushirobira, Rosane

    2005-01-01

    We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.

  15. Algebraic statistics computational commutative algebra in statistics

    CERN Document Server

    Pistone, Giovanni; Wynn, Henry P

    2000-01-01

    Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.

  16. Dynamic Network-Based Epistasis Analysis: Boolean Examples

    Science.gov (United States)

    Azpeitia, Eugenio; Benítez, Mariana; Padilla-Longoria, Pablo; Espinosa-Soto, Carlos; Alvarez-Buylla, Elena R.

    2011-01-01

    In this article we focus on how the hierarchical and single-path assumptions of epistasis analysis can bias the inference of gene regulatory networks. Here we emphasize the critical importance of dynamic analyses, and specifically illustrate the use of Boolean network models. Epistasis in a broad sense refers to gene interactions, however, as originally proposed by Bateson, epistasis is defined as the blocking of a particular allelic effect due to the effect of another allele at a different locus (herein, classical epistasis). Classical epistasis analysis has proven powerful and useful, allowing researchers to infer and assign directionality to gene interactions. As larger data sets are becoming available, the analysis of classical epistasis is being complemented with computer science tools and system biology approaches. We show that when the hierarchical and single-path assumptions are not met in classical epistasis analysis, the access to relevant information and the correct inference of gene interaction topologies is hindered, and it becomes necessary to consider the temporal dynamics of gene interactions. The use of dynamical networks can overcome these limitations. We particularly focus on the use of Boolean networks that, like classical epistasis analysis, relies on logical formalisms, and hence can complement classical epistasis analysis and relax its assumptions. We develop a couple of theoretical examples and analyze them from a dynamic Boolean network model perspective. Boolean networks could help to guide additional experiments and discern among alternative regulatory schemes that would be impossible or difficult to infer without the elimination of these assumption from the classical epistasis analysis. We also use examples from the literature to show how a Boolean network-based approach has resolved ambiguities and guided epistasis analysis. Our article complements previous accounts, not only by focusing on the implications of the hierarchical and

  17. Split Malcev algebras

    Indian Academy of Sciences (India)

    We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras is of the form M = U + ∑ j I j with U a subspace of the abelian Malcev subalgebra and any I j a well described ideal of satisfying [ I j , I k ] = 0 if ≠ .

  18. Foundations of algebraic geometry

    CERN Document Server

    Weil, A

    1946-01-01

    This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.

  19. Equivalence Checking of Combinational Circuits using Boolean Expression Diagrams

    DEFF Research Database (Denmark)

    Hulgaard, Henrik; Williams, Poul Frederick; Andersen, Henrik Reif

    1999-01-01

    or by a design automation tool).This paper introduces a data structure called Boolean Expression Diagrams (BEDs) and two algorithms for transforming a BED into a Reduced Ordered Binary Decision Diagram (OBDD). BEDs are capable of representing any Boolean circuit in linear space and can exploit structural...... similarities between the two circuits that are compared. These properties make BEDs suitable for verifying the equivalence of combinational circuits. BEDs can be seen as an intermediate representation between circuits (which are compact) and OBDDs (which are canonical).Based on a large number of combinational...

  20. A Boolean Approach to Airline Business Model Innovation

    DEFF Research Database (Denmark)

    Hvass, Kristian Anders

    Research in business model innovation has identified its significance in creating a sustainable competitive advantage for a firm, yet there are few empirical studies identifying which combination of business model activities lead to success and therefore deserve innovative attention. This study...... analyzes the business models of North America low-cost carriers from 2001 to 2010 using a Boolean minimization algorithm to identify which combinations of business model activities lead to operational profitability. The research aim is threefold: complement airline literature in the realm of business model...... innovation, introduce Boolean minimization methods to the field, and propose alternative business model activities to North American carriers striving for positive operating results....

  1. 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.

  2. 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.

  3. Constant-Overhead Secure Computation of Boolean Circuits using Preprocessing

    DEFF Research Database (Denmark)

    Damgård, Ivan Bjerre; Zakarias, Sarah Nouhad Haddad

    We present a protocol for securely computing a Boolean circuit $C$ in presence of a dishonest and malicious majority. The protocol is unconditionally secure, assuming access to a preprocessing functionality that is not given the inputs to compute on. For a large number of players the work done by...... with an additional multiplication property. We also show a new algorithm for verifying the product of Boolean matrices in quadratic time with exponentially small error probability, where previous methods would only give a constant error....

  4. Linearizing W-algebras

    International Nuclear Information System (INIS)

    Krivonos, S.O.; Sorin, A.S.

    1994-06-01

    We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs

  5. Algorithms in Algebraic Geometry

    CERN Document Server

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  6. Computing the Algebraic Immunity of Boolean Functions on the SRC-6 Reconfigurable Computer

    Science.gov (United States)

    2012-03-01

    INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE...BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR...believing in me. I thank my mother-in- law , Denise, and her husband, Rodney, for their support during some critical times. Without the tireless efforts of

  7. Wn(2) algebras

    International Nuclear Information System (INIS)

    Feigin, B.L.; Semikhatov, A.M.

    2004-01-01

    We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W n (2) generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W 3 (2) algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W n (2) algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras

  8. Algebraic conformal field theory

    International Nuclear Information System (INIS)

    Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica

    1991-11-01

    Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs

  9. Discrete Minimal Surface Algebras

    Directory of Open Access Journals (Sweden)

    Joakim Arnlind

    2010-05-01

    Full Text Available We consider discrete minimal surface algebras (DMSA as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself. A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  10. Bicovariant quantum algebras and quantum Lie algebras

    International Nuclear Information System (INIS)

    Schupp, P.; Watts, P.; Zumino, B.

    1993-01-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

  11. Document Ranking in E-Extended Boolean Logic

    Czech Academy of Sciences Publication Activity Database

    Holub, M.; Húsek, Dušan; Pokorný, J.

    1996-01-01

    Roč. 4, č. 7 (1996), s. 3-17 ISSN 1310-0513. [Annual Colloquium on IR Research /19./. Aberdeen, 08.04.1997-09.04.1997] R&D Projects: GA ČR GA102/94/0728 Keywords : information retrieval * document ranking * extended Boolean logic

  12. On the Road to Genetic Boolean Matrix Factorization

    Czech Academy of Sciences Publication Activity Database

    Snášel, V.; Platoš, J.; Krömer, P.; Húsek, Dušan; Frolov, A.

    2007-01-01

    Roč. 17, č. 6 (2007), s. 675-688 ISSN 1210-0552 Institutional research plan: CEZ:AV0Z10300504 Keywords : data mining * genetic algorithms * Boolean factorization * binary data * machine learning * feature extraction Subject RIV: IN - Informatics, Computer Science Impact factor: 0.280, year: 2007

  13. Complexity of Identification and Dualization of Positive Boolean Functions

    NARCIS (Netherlands)

    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

  14. Development of Boolean calculus and its applications. [digital systems design

    Science.gov (United States)

    Tapia, M. A.

    1980-01-01

    The development of Boolean calculus for its application to developing digital system design methodologies that would reduce system complexity, size, cost, speed, power requirements, etc., is discussed. Synthesis procedures for logic circuits are examined particularly asynchronous circuits using clock triggered flip flops.

  15. Learning restricted Boolean network model by time-series data.

    Science.gov (United States)

    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.

  16. Hurwitz Algebras and the Octonion Algebra

    Science.gov (United States)

    Burdik, Čestmir; Catto, Sultan

    2018-02-01

    We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.

  17. Linear algebra meets Lie algebra: the Kostant-Wallach theory

    OpenAIRE

    Shomron, Noam; Parlett, Beresford N.

    2008-01-01

    In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.

  18. AT -algebras and extensions of AT-algebras

    Indian Academy of Sciences (India)

    algebra by an AT-algebra and E has real rank zero, then E is an AT-algebra if and only if the index maps are both zero. Accordingly, in this paper, we attempt to describe a characterization of an extension E of an AT-algebra by an AF-algebra if E ...

  19. 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

  20. Yoneda algebras of almost Koszul algebras

    Indian Academy of Sciences (India)

    a left (2, hQ − 2)-Koszul algebra (see Definition 2.1 below), and the Yoneda algebra of. A is isomorphic to a twisted ... is quadratic if R is a subspace of V ⊗ V . The quadratic dual A! of A is defined to be. T (V ∗)/(R⊥) .... (Q, ρ) is a stable bound quiver of Loewy length p + 1, and the Nakayama translation on. Q0 is induced by a ...

  1. Evolution algebras and their applications

    CERN Document Server

    Tian, Jianjun Paul

    2008-01-01

    Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics.

  2. On hyper BCC-algebras

    OpenAIRE

    Borzooei, R. A.; Dudek, W. A.; Koohestani, N.

    2006-01-01

    We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

  3. On hyper BCC-algebras

    Directory of Open Access Journals (Sweden)

    R. A. Borzooei

    2006-01-01

    Full Text Available We study hyper BCC-algebras which are a common generalization of BCC-algebras and hyper BCK-algebras. In particular, we investigate different types of hyper BCC-ideals and describe the relationship among them. Next, we calculate all nonisomorphic 22 hyper BCC-algebras of order 3 of which only three are not hyper BCK-algebras.

  4. Simple relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatme...

  5. Twisted classical Poincare algebras

    International Nuclear Information System (INIS)

    Lukierski, J.; Ruegg, H.; Tolstoy, V.N.; Nowicki, A.

    1993-11-01

    We consider the twisting of Hopf structure for classical enveloping algebra U(g), where g is the inhomogeneous rotations algebra, with explicite formulae given for D=4 Poincare algebra (g=P 4 ). The comultiplications of twisted U F (P 4 ) are obtained by conjugating primitive classical coproducts by F element of U(c)xU(c), where c denotes any Abelian subalgebra of P 4 , and the universal R-matrices for U F (P 4 ) are triangular. As an example we show that the quantum deformation of Poincare algebra recently proposed by Chaichian and Demiczev is a twisted classical Poincare algebra. The interpretation of twisted Poincare algebra as describing relativistic symmetries with clustered 2-particle states is proposed. (orig.)

  6. Lie algebras and applications

    CERN Document Server

    Iachello, Francesco

    2015-01-01

    This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...

  7. Introduction to abstract algebra

    CERN Document Server

    Smith, Jonathan D H

    2008-01-01

    Taking a slightly different approach from similar texts, Introduction to Abstract Algebra presents abstract algebra as the main tool underlying discrete mathematics and the digital world. It helps students fully understand groups, rings, semigroups, and monoids by rigorously building concepts from first principles. A Quick Introduction to Algebra The first three chapters of the book show how functional composition, cycle notation for permutations, and matrix notation for linear functions provide techniques for practical computation. The author also uses equivalence relations to introduc

  8. Lectures in general algebra

    CERN Document Server

    Kurosh, A G; Stark, M; Ulam, S

    1965-01-01

    Lectures in General Algebra is a translation from the Russian and is based on lectures on specialized courses in general algebra at Moscow University. The book starts with the basics of algebra. The text briefly describes the theory of sets, binary relations, equivalence relations, partial ordering, minimum condition, and theorems equivalent to the axiom of choice. The text gives the definition of binary algebraic operation and the concepts of groups, groupoids, and semigroups. The book examines the parallelism between the theory of groups and the theory of rings; such examinations show the

  9. Cohomology of Effect Algebras

    Directory of Open Access Journals (Sweden)

    Frank Roumen

    2017-01-01

    Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

  10. Structure of algebras

    CERN Document Server

    Albert, A A

    1939-01-01

    The first three chapters of this work contain an exposition of the Wedderburn structure theorems. Chapter IV contains the theory of the commutator subalgebra of a simple subalgebra of a normal simple algebra, the study of automorphisms of a simple algebra, splitting fields, and the index reduction factor theory. The fifth chapter contains the foundation of the theory of crossed products and of their special case, cyclic algebras. The theory of exponents is derived there as well as the consequent factorization of normal division algebras into direct factors of prime-power degree. Chapter VI con

  11. From Rota-Baxter algebras to pre-Lie algebras

    International Nuclear Information System (INIS)

    An Huihui; Ba, Chengming

    2008-01-01

    Rota-Baxter algebras were introduced to solve some analytic and combinatorial problems and have appeared in many fields in mathematics and mathematical physics. Rota-Baxter algebras provide a construction of pre-Lie algebras from associative algebras. In this paper, we give all Rota-Baxter operators of weight 1 on complex associative algebras in dimension ≤3 and their corresponding pre-Lie algebras

  12. Algebraic monoids, group embeddings, and algebraic combinatorics

    CERN Document Server

    Li, Zhenheng; Steinberg, Benjamin; Wang, Qiang

    2014-01-01

    This book contains a collection of fifteen articles and is dedicated to the sixtieth birthdays of Lex Renner and Mohan Putcha, the pioneers of the field of algebraic monoids.   Topics presented include:   v  structure and representation theory of reductive algebraic monoids v  monoid schemes and applications of monoids v  monoids related to Lie theory v  equivariant embeddings of algebraic groups v  constructions and properties of monoids from algebraic combinatorics v  endomorphism monoids induced from vector bundles v  Hodge–Newton decompositions of reductive monoids   A portion of these articles are designed to serve as a self-contained introduction to these topics, while the remaining contributions are research articles containing previously unpublished results, which are sure to become very influential for future work. Among these, for example, the important recent work of Michel Brion and Lex Renner showing that the algebraic semigroups are strongly π-regular.   Graduate students as well a...

  13. Noisy random Boolean formulae: a statistical physics perspective.

    Science.gov (United States)

    Mozeika, Alexander; Saad, David; Raymond, Jack

    2010-10-01

    Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

  14. High Quality Test Pattern Generation and Boolean Satisfiability

    CERN Document Server

    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...

  15. Mapping knowledge to boolean dynamic systems in Bateson's epistemology.

    Science.gov (United States)

    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.

  16. C*-algebras

    Science.gov (United States)

    Bär, Christian; Becker, Christian

    In this chapter we will collect those basic concepts and facts related to C*-algebras that will be needed later on. We give complete proofs. In Sects. 1, 2, 3, and 6 we follow closely the presentation in [1]. For more information on C*-algebras, see, e.g. [2-6].

  17. Linear-Algebra Programs

    Science.gov (United States)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  18. Analytic real algebras.

    Science.gov (United States)

    Seo, Young Joo; Kim, Young Hee

    2016-01-01

    In this paper we construct some real algebras by using elementary functions, and discuss some relations between several axioms and its related conditions for such functions. We obtain some conditions for real-valued functions to be a (edge) d -algebra.

  19. Pre-Algebra Lexicon.

    Science.gov (United States)

    Hayden, Dunstan; Cuevas, Gilberto

    The pre-algebra lexicon is a set of classroom exercises designed to teach the technical words and phrases of pre-algebra mathematics, and includes the terms most commonly found in related mathematics courses. The lexicon has three parts, each with its own introduction. The first introduces vocabulary items in three groups forming a learning…

  20. Computer algebra applications

    International Nuclear Information System (INIS)

    Calmet, J.

    1982-01-01

    A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)

  1. Discourses on Algebra

    Indian Academy of Sciences (India)

    Discourses on Algebra. Rajaram Nityananda. Discourses on Algebra. Igor R Shafarevich. Narosa Publishing. Pages: 273, Price in India: | 1750. To the Indian reader, the word discourse, evokes a respected figure interpreting divine wisdom to common folk in an accessible fash- ion. I dug a bit deeper with Google trans-.

  2. Algebraic Description of Motion

    Science.gov (United States)

    Davidon, William C.

    1974-01-01

    An algebraic definition of time differentiation is presented and used to relate independent measurements of position and velocity. With this, students can grasp certain essential physical, geometric, and algebraic properties of motion and differentiation before undertaking the study of limits. (Author)

  3. Algebra of anomalies

    International Nuclear Information System (INIS)

    Talon, M.

    1987-01-01

    The algebraic set up for anomalies, a la Stora, is reviewed. Then a brief account is provided of the work of M. Dubois Violette, M. Talon, C. Viallet, in which the general algebraic solution to the consistency conditions is described. 34 references

  4. Boolean Functions with a Simple Certificate for CNF Complexity

    Czech Academy of Sciences Publication Activity Database

    Čepek, O.; Kučera, P.; Savický, Petr

    2012-01-01

    Roč. 160, 4-5 (2012), s. 365-382 ISSN 0166-218X R&D Projects: GA MŠk(CZ) 1M0545 Grant - others:GA ČR(CZ) GP201/07/P168; GA ČR(CZ) GAP202/10/1188 Institutional research plan: CEZ:AV0Z10300504 Keywords : Boolean functions * CNF representations Subject RIV: BA - General Mathematics Impact factor: 0.718, year: 2012

  5. Elements of mathematics algebra

    CERN Document Server

    Bourbaki, Nicolas

    2003-01-01

    This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algèbre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and...

  6. SETS, Boolean Manipulation for Network Analysis and Fault Tree Analysis

    International Nuclear Information System (INIS)

    Worrell, R.B.

    1985-01-01

    Description of problem or function - SETS is used for symbolic manipulation of set (or Boolean) equations, particularly the reduction of set equations by the application of set identities. It is a flexible and efficient tool for performing probabilistic risk analysis (PRA), vital area analysis, and common cause analysis. The equation manipulation capabilities of SETS can also be used to analyze non-coherent fault trees and determine prime implicants of Boolean functions, to verify circuit design implementation, to determine minimum cost fire protection requirements for nuclear reactor plants, to obtain solutions to combinatorial optimization problems with Boolean constraints, and to determine the susceptibility of a facility to unauthorized access through nullification of sensors in its protection system. 4. Method of solution - The SETS program is used to read, interpret, and execute the statements of a SETS user program which is an algorithm that specifies the particular manipulations to be performed and the order in which they are to occur. 5. Restrictions on the complexity of the problem - Any properly formed set equation involving the set operations of union, intersection, and complement is acceptable for processing by the SETS program. Restrictions on the size of a set equation that can be processed are not absolute but rather are related to the number of terms in the disjunctive normal form of the equation, the number of literals in the equation, etc. Nevertheless, set equations involving thousands and even hundreds of thousands of terms can be processed successfully

  7. Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.

    Science.gov (United States)

    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.

  8. Boolean models can explain bistability in the lac operon.

    Science.gov (United States)

    Veliz-Cuba, Alan; Stigler, Brandilyn

    2011-06-01

    The lac operon in Escherichia coli has been studied extensively and is one of the earliest gene systems found to undergo both positive and negative control. The lac operon is known to exhibit bistability, in the sense that the operon is either induced or uninduced. Many dynamical models have been proposed to capture this phenomenon. While most are based on complex mathematical formulations, it has been suggested that for other gene systems network topology is sufficient to produce the desired dynamical behavior. We present a Boolean network as a discrete model for the lac operon. Our model includes the two main glucose control mechanisms of catabolite repression and inducer exclusion. We show that this Boolean model is capable of predicting the ON and OFF steady states and bistability. Further, we present a reduced model which shows that lac mRNA and lactose form the core of the lac operon, and that this reduced model exhibits the same dynamics. This work suggests that the key to model qualitative dynamics of gene systems is the topology of the network and Boolean models are well suited for this purpose.

  9. Controllability and observability of Boolean networks arising from biology

    Science.gov (United States)

    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.

  10. Approximating attractors of Boolean networks by iterative CTL model checking

    Directory of Open Access Journals (Sweden)

    Hannes eKlarner

    2015-09-01

    Full Text Available This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: faithfulness which requires that the oscillating variables of all attractors in a trapspace correspond to their dimensions, univocality which requires that there is a unique attractor in each trap space and completeness which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal and complete which suggests that they are in general good approximations for the asymptotics of Boolean networks.

  11. Boolean Models of Biological Processes Explain Cascade-Like Behavior

    Science.gov (United States)

    Chen, Hao; Wang, Guanyu; Simha, Rahul; Du, Chenghang; Zeng, Chen

    2016-01-01

    Biological networks play a key role in determining biological function and therefore, an understanding of their structure and dynamics is of central interest in systems biology. In Boolean models of such networks, the status of each molecule is either “on” or “off” and along with the molecules interact with each other, their individual status changes from “on” to “off” or vice-versa and the system of molecules in the network collectively go through a sequence of changes in state. This sequence of changes is termed a biological process. In this paper, we examine the common perception that events in biomolecular networks occur sequentially, in a cascade-like manner, and ask whether this is likely to be an inherent property. In further investigations of the budding and fission yeast cell-cycle, we identify two generic dynamical rules. A Boolean system that complies with these rules will automatically have a certain robustness. By considering the biological requirements in robustness and designability, we show that those Boolean dynamical systems, compared to an arbitrary dynamical system, statistically present the characteristics of cascadeness and sequentiality, as observed in the budding and fission yeast cell- cycle. These results suggest that cascade-like behavior might be an intrinsic property of biological processes. PMID:26821940

  12. Cluster algebras bases on vertex operator algebras

    Czech Academy of Sciences Publication Activity Database

    Zuevsky, Alexander

    2016-01-01

    Roč. 30, 28-29 (2016), č. článku 1640030. ISSN 0217-9792 Institutional support: RVO:67985840 Keywords : cluster alegbras * vertex operator algebras * Riemann surfaces Subject RIV: BA - General Mathematics Impact factor: 0.736, year: 2016 http://www.worldscientific.com/doi/abs/10.1142/S0217979216400300

  13. The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.

    Science.gov (United States)

    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.

  14. Endomorphisms of graph algebras

    DEFF Research Database (Denmark)

    Conti, Roberto; Hong, Jeong Hee; Szymanski, Wojciech

    2012-01-01

    We initiate a systematic investigation of endomorphisms of graph C*-algebras C*(E), extending several known results on endomorphisms of the Cuntz algebras O_n. Most but not all of this study is focused on endomorphisms which permute the vertex projections and globally preserve the diagonal MASA D......_E of C*(E). Our results pertain both automorphisms and proper endomorphisms. Firstly, the Weyl group and the restricted Weyl group of a graph C*-algebra are introduced and investigated. In particular, criteria of outerness for automorphisms in the restricted Weyl group are found. We also show...

  15. Matrices and linear algebra

    CERN Document Server

    Schneider, Hans

    1989-01-01

    Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

  16. Topology general & algebraic

    CERN Document Server

    Chatterjee, D

    2007-01-01

    About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the

  17. Orthogonal symmetries and Clifford algebras

    Indian Academy of Sciences (India)

    algebra over a field K, can be regarded as the Clifford algebra of a suitable nondegenerate quadratic form q over the base field K. In [13], such a form q is also explicitly constructed. The Grassmann algebra (or the exterior algebra) may also be regarded as the Clifford alge- bra of the null (totally isotropic) quadratic form.

  18. Linear algebra done right

    CERN Document Server

    Axler, Sheldon

    2015-01-01

    This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have been added since the previous edition. Many new examples have been added to illustrate the key ideas of linear algebra. New topics covered in the book include product spaces, quotient spaces, and dual spaces. Beautiful new formatting creates pages with an unusually pleasant appearance in both print and electronic versions. No prerequisites are assumed other than the ...

  19. Elliptic biquaternion algebra

    Science.gov (United States)

    Özen, Kahraman Esen; Tosun, Murat

    2018-01-01

    In this study, we define the elliptic biquaternions and construct the algebra of elliptic biquaternions over the elliptic number field. Also we give basic properties of elliptic biquaternions. An elliptic biquaternion is in the form A0 + A1i + A2j + A3k which is a linear combination of {1, i, j, k} where the four components A0, A1, A2 and A3 are elliptic numbers. Here, 1, i, j, k are the quaternion basis of the elliptic biquaternion algebra and satisfy the same multiplication rules which are satisfied in both real quaternion algebra and complex quaternion algebra. In addition, we discuss the terms; conjugate, inner product, semi-norm, modulus and inverse for elliptic biquaternions.

  20. Algebraic Semantics for Narrative

    Science.gov (United States)

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  1. Deficiently extremal Gorenstein algebras

    Indian Academy of Sciences (India)

    Thus, R/I is a Cohen–. Macaulay algebra of Type 1, and hence R/I is Gorenstein. In view of Theorem 2.1, R/I is a nearly (or 1-deficient) extremal Gorenstein algebra. We now shall describe a result of Bruns and Hibi [1] which characterizes the Stanley–. Reisner rings having 2-pure but not 2-linear resolutions. Theorem 2.3.

  2. Intermediate algebra a textworkbook

    CERN Document Server

    McKeague, Charles P

    1985-01-01

    Intermediate Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in intermediate algebra. The publication first takes a look at basic properties and definitions, first-degree equations and inequalities, and exponents and polynomials. Discussions focus on properties of exponents, polynomials, sums, and differences, multiplication of polynomials, inequalities involving absolute value, word problems, first-degree inequalities, real numbers, opposites, reciprocals, and absolute value, and addition and subtraction of real numbers. The text then ex

  3. Beginning algebra a textworkbook

    CERN Document Server

    McKeague, Charles P

    1985-01-01

    Beginning Algebra: A Text/Workbook, Second Edition focuses on the principles, operations, and approaches involved in algebra. The publication first elaborates on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on solving linear systems by graphing, elimination method, graphing ordered pairs and straight lines, linear and compound inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then examines exponents and polynomials, factoring, and rational expressions. Topics include multiplication and division

  4. Gauging the octonion algebra

    International Nuclear Information System (INIS)

    Waldron, A.K.; Joshi, G.C.

    1992-01-01

    By considering representation theory for non-associative algebras the fundamental adjoint representations of the octonion algebra is constructed. It is then shown how these representations by associative matrices allow a consistent octonionic gauge theory to be realized. It was found that non-associativity implies the existence of new terms in the transformation laws of fields and the kinetic term of an octonionic Lagrangian. 13 refs

  5. Currents on Grassmann algebras

    International Nuclear Information System (INIS)

    Coquereaux, R.; Ragoucy, E.

    1993-09-01

    Currents are defined on a Grassmann algebra Gr(N) with N generators as distributions on its exterior algebra (using the symmetric wedge product). The currents are interpreted in terms of Z 2 -graded Hochschild cohomology and closed currents in terms of cyclic cocycles (they are particular multilinear forms on Gr(N)). An explicit construction of the vector space of closed currents of degree p on Gr(N) is given by using Berezin integration. (authors). 10 refs

  6. Intermediate algebra & analytic geometry

    CERN Document Server

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

  7. The 'golden' algebraic equations

    International Nuclear Information System (INIS)

    Stakhov, A.; Rozin, B.

    2006-01-01

    The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman

  8. Real division algebras and other algebras motivated by physics

    Energy Technology Data Exchange (ETDEWEB)

    Benkart, G.; Osborn, J.M.

    1981-02-01

    In this survey we discuss several general techniques which have been productive in the study of real division algebras, flexible Lie-admissible algebras, and other nonassociative algebras, and we summarize results obtained using these methods. The principal method involved in this work is to view an algebra A as a module for a semisimple Lie algebra of derivations of A and to use representation theory to study products in A. In the case of real division algebras, we also discuss the use of isotopy and the use of a generalized Peirce decomposition. Most of the work summarized here has appeared in more detail in various other papers. The exceptions are results on a class of algebras of dimension 15, motivated by physics, which admit the Lie algebra sl(3) as an algebra of derivations.

  9. Digital clocks: simple Boolean models can quantitatively describe circadian systems.

    Science.gov (United States)

    Akman, Ozgur E; Watterson, Steven; Parton, Andrew; Binns, Nigel; Millar, Andrew J; Ghazal, Peter

    2012-09-07

    The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day-night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we anticipate

  10. Digital clocks: simple Boolean models can quantitatively describe circadian systems

    Science.gov (United States)

    Akman, Ozgur E.; Watterson, Steven; Parton, Andrew; Binns, Nigel; Millar, Andrew J.; Ghazal, Peter

    2012-01-01

    The gene networks that comprise the circadian clock modulate biological function across a range of scales, from gene expression to performance and adaptive behaviour. The clock functions by generating endogenous rhythms that can be entrained to the external 24-h day–night cycle, enabling organisms to optimally time biochemical processes relative to dawn and dusk. In recent years, computational models based on differential equations have become useful tools for dissecting and quantifying the complex regulatory relationships underlying the clock's oscillatory dynamics. However, optimizing the large parameter sets characteristic of these models places intense demands on both computational and experimental resources, limiting the scope of in silico studies. Here, we develop an approach based on Boolean logic that dramatically reduces the parametrization, making the state and parameter spaces finite and tractable. We introduce efficient methods for fitting Boolean models to molecular data, successfully demonstrating their application to synthetic time courses generated by a number of established clock models, as well as experimental expression levels measured using luciferase imaging. Our results indicate that despite their relative simplicity, logic models can (i) simulate circadian oscillations with the correct, experimentally observed phase relationships among genes and (ii) flexibly entrain to light stimuli, reproducing the complex responses to variations in daylength generated by more detailed differential equation formulations. Our work also demonstrates that logic models have sufficient predictive power to identify optimal regulatory structures from experimental data. By presenting the first Boolean models of circadian circuits together with general techniques for their optimization, we hope to establish a new framework for the systematic modelling of more complex clocks, as well as other circuits with different qualitative dynamics. In particular, we

  11. An Association Rule Mining Algorithm Based on a Boolean Matrix

    Directory of Open Access Journals (Sweden)

    Hanbing Liu

    2007-09-01

    Full Text Available Association rule mining is a very important research topic in the field of data mining. Discovering frequent itemsets is the key process in association rule mining. Traditional association rule algorithms adopt an iterative method to discovery, which requires very large calculations and a complicated transaction process. Because of this, a new association rule algorithm called ABBM is proposed in this paper. This new algorithm adopts a Boolean vector "relational calculus" method to discovering frequent itemsets. Experimental results show that this algorithm can quickly discover frequent itemsets and effectively mine potential association rules.

  12. A Construction of Boolean Functions with Good Cryptographic Properties

    Science.gov (United States)

    2014-01-01

    over Fn2 defined by Wf (u) = ∑ x∈Fn2 (−1)f(x)+u·x, where u ∈ Fn2 and u · x is an inner product , for instance, u · x = u1x1 + u2x3 + · · · + unxn, where u...later on for all these classes. We mention also the paper of Pasalic [27], which introduces the notion of high degree product (HDP) to mea- sure the...2008, LNCS 5350, Springer–Verlag, 2008, pp. 425–440. [10] C. Carlet and K. Feng, “An Infinite Class of Balanced Vectorial Boolean Functions with Optimum

  13. A Boolean Approach to Airline Business Model Innovation

    DEFF Research Database (Denmark)

    Hvass, Kristian Anders

    Research in business model innovation has identified its significance in creating a sustainable competitive advantage for a firm, yet there are few empirical studies identifying which combination of business model activities lead to success and therefore deserve innovative attention. This study...... analyzes the business models of North America low-cost carriers from 2001 to 2010 using a Boolean minimization algorithm to identify which combinations of business model activities lead to operational profitability. The research aim is threefold: complement airline literature in the realm of business model...

  14. Bebop to the Boolean boogie an unconventional guide to electronics

    CERN Document Server

    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

  15. Two Expectation-Maximization Algorithms for Boolean Factor Analysis

    Czech Academy of Sciences Publication Activity Database

    Frolov, A. A.; Húsek, Dušan; Polyakov, P.Y.

    2014-01-01

    Roč. 130, 23 April (2014), s. 83-97 ISSN 0925-2312 R&D Projects: GA ČR GAP202/10/0262 Grant - others:GA MŠk(CZ) ED1.1.00/02.0070; GA MŠk(CZ) EE.2.3.20.0073 Program:ED Institutional research plan: CEZ:AV0Z10300504 Keywords : Boolean Factor analysis * Binary Matrix factorization * Neural networks * Binary data model * Dimension reduction * Bars problem Subject RIV: IN - Informatics, Computer Science Impact factor: 2.083, year: 2014

  16. Hecke algebras with unequal parameters

    CERN Document Server

    Lusztig, G

    2003-01-01

    Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over p-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives rese...

  17. Complexity classifications for different equivalence and audit problems for Boolean circuits

    OpenAIRE

    Böhler, Elmar; Creignou, Nadia; Galota, Matthias; Reith, Steffen; Schnoor, Henning; Vollmer, Heribert

    2010-01-01

    We study Boolean circuits as a representation of Boolean functions and conskier different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all other gate types we show these problems are at least NP-hard.

  18. Chemical Visualization of Boolean Functions: A Simple Chemical Computer

    Science.gov (United States)

    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.

  19. 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.

  20. Evolution of a designless nanoparticle network into reconfigurable Boolean logic.

    Science.gov (United States)

    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.

  1. Algebra II workbook for dummies

    CERN Document Server

    Sterling, Mary Jane

    2014-01-01

    To succeed in Algebra II, start practicing now Algebra II builds on your Algebra I skills to prepare you for trigonometry, calculus, and a of myriad STEM topics. Working through practice problems helps students better ingest and retain lesson content, creating a solid foundation to build on for future success. Algebra II Workbook For Dummies, 2nd Edition helps you learn Algebra II by doing Algebra II. Author and math professor Mary Jane Sterling walks you through the entire course, showing you how to approach and solve the problems you encounter in class. You'll begin by refreshing your Algebr

  2. C*-algebras by example

    CERN Document Server

    Davidson, Kenneth R

    1996-01-01

    The subject of C*-algebras received a dramatic revitalization in the 1970s by the introduction of topological methods through the work of Brown, Douglas, and Fillmore on extensions of C*-algebras and Elliott's use of K-theory to provide a useful classification of AF algebras. These results were the beginning of a marvelous new set of tools for analyzing concrete C*-algebras. This book is an introductory graduate level text which presents the basics of the subject through a detailed analysis of several important classes of C*-algebras. The development of operator algebras in the last twenty yea

  3. Interactions Between Representation Ttheory, Algebraic Topology and Commutative Algebra

    CERN Document Server

    Pitsch, Wolfgang; Zarzuela, Santiago

    2016-01-01

    This book includes 33 expanded abstracts of selected talks given at the two workshops "Homological Bonds Between Commutative Algebra and Representation Theory" and "Brave New Algebra: Opening Perspectives," and the conference "Opening Perspectives in Algebra, Representations, and Topology," held at the Centre de Recerca Matemàtica (CRM) in Barcelona between January and June 2015. These activities were part of the one-semester intensive research program "Interactions Between Representation Theory, Algebraic Topology and Commutative Algebra (IRTATCA)." Most of the abstracts present preliminary versions of not-yet published results and cover a large number of topics (including commutative and non commutative algebra, algebraic topology, singularity theory, triangulated categories, representation theory) overlapping with homological methods. This comprehensive book is a valuable resource for the community of researchers interested in homological algebra in a broad sense, and those curious to learn the latest dev...

  4. Quantum cluster algebra structures on quantum nilpotent algebras

    CERN Document Server

    Goodearl, K R

    2017-01-01

    All algebras in a very large, axiomatically defined class of quantum nilpotent algebras are proved to possess quantum cluster algebra structures under mild conditions. Furthermore, it is shown that these quantum cluster algebras always equal the corresponding upper quantum cluster algebras. Previous approaches to these problems for the construction of (quantum) cluster algebra structures on (quantized) coordinate rings arising in Lie theory were done on a case by case basis relying on the combinatorics of each concrete family. The results of the paper have a broad range of applications to these problems, including the construction of quantum cluster algebra structures on quantum unipotent groups and quantum double Bruhat cells (the Berenstein-Zelevinsky conjecture), and treat these problems from a unified perspective. All such applications also establish equality between the constructed quantum cluster algebras and their upper counterparts.

  5. Identities and derivations for Jacobian algebras

    International Nuclear Information System (INIS)

    Dzhumadil'daev, A.S.

    2001-09-01

    Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-Jacobian algebra are found. (author)

  6. Algebraic topology a primer

    CERN Document Server

    Deo, Satya

    2018-01-01

    This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...

  7. Algebraic quantum field theory

    International Nuclear Information System (INIS)

    Foroutan, A.

    1996-12-01

    The basic assumption that the complete information relevant for a relativistic, local quantum theory is contained in the net structure of the local observables of this theory results first of all in a concise formulation of the algebraic structure of the superselection theory and an intrinsic formulation of charge composition, charge conjugation and the statistics of an algebraic quantum field theory. In a next step, the locality of massive particles together with their spectral properties are wed for the formulation of a selection criterion which opens the access to the massive, non-abelian quantum gauge theories. The role of the electric charge as a superselection rule results in the introduction of charge classes which in term lead to a set of quantum states with optimum localization properties. Finally, the asymptotic observables of quantum electrodynamics are investigated within the framework of algebraic quantum field theory. (author)

  8. Algebraic number theory

    CERN Document Server

    Jarvis, Frazer

    2014-01-01

    The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...

  9. Complex algebraic geometry

    CERN Document Server

    Kollár, János

    1997-01-01

    This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

  10. Basic linear algebra

    CERN Document Server

    Blyth, T S

    2002-01-01

    Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...

  11. Higher regulators, algebraic

    CERN Document Server

    Bloch, Spencer J

    2000-01-01

    This book is the long-awaited publication of the famous Irvine lectures. Delivered in 1978 at the University of California at Irvine, these lectures turned out to be an entry point to several intimately-connected new branches of arithmetic algebraic geometry, such as regulators and special values of L-functions of algebraic varieties, explicit formulas for them in terms of polylogarithms, the theory of algebraic cycles, and eventually the general theory of mixed motives which unifies and underlies all of the above (and much more). In the 20 years since, the importance of Bloch's lectures has not diminished. A lucky group of people working in the above areas had the good fortune to possess a copy of old typewritten notes of these lectures. Now everyone can have their own copy of this classic work.

  12. Problems in abstract algebra

    CERN Document Server

    Wadsworth, A R

    2017-01-01

    This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.

  13. Complex Algebraic Varieties

    CERN Document Server

    Peternell, Thomas; Schneider, Michael; Schreyer, Frank-Olaf

    1992-01-01

    The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibra...

  14. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    Science.gov (United States)

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  15. On Associative Conformal Algebras of Linear Growth

    OpenAIRE

    Retakh, Alexander

    2000-01-01

    Lie conformal algebras appear in the theory of vertex algebras. Their relation is similar to that of Lie algebras and their universal enveloping algebras. Associative conformal algebras play a role in conformal representation theory. We introduce the notions of conformal identity and unital associative conformal algebras and classify finitely generated simple unital associative conformal algebras of linear growth. These are precisely the complete algebras of conformal endomorphisms of finite ...

  16. Computer Program For Linear Algebra

    Science.gov (United States)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  17. Atomistic and orthoatomistic effect algebras

    Science.gov (United States)

    Tkadlec, Josef

    2008-05-01

    We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.

  18. Algebra for Gifted Third Graders.

    Science.gov (United States)

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  19. Contractions of quantum algebraic structures

    International Nuclear Information System (INIS)

    Doikou, A.; Sfetsos, K.

    2010-01-01

    A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)

  20. Elementary matrix algebra

    CERN Document Server

    Hohn, Franz E

    2012-01-01

    This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur

  1. Algebra & trigonometry super review

    CERN Document Server

    2012-01-01

    Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Algebra and Trigonometry Super Review includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much y

  2. Principles of algebraic geometry

    CERN Document Server

    Griffiths, Phillip A

    1994-01-01

    A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top

  3. Algebra with Galois theory

    CERN Document Server

    Artin, Emil

    2007-01-01

    The present text was first published in 1947 by the Courant Institute of Mathematical Sciences of New York University. Published under the title Modern Higher Algebra. Galois Theory, it was based on lectures by Emil Artin and written by Albert A. Blank. This volume became one of the most popular in the series of lecture notes published by Courant. Many instructors used the book as a textbook, and it was popular among students as a supplementary text as well as a primary textbook. Because of its popularity, Courant has republished the volume under the new title Algebra with Galois Theory.

  4. Helmholtz algebraic solitons

    International Nuclear Information System (INIS)

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2010-01-01

    We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

  5. Pseudo Algebraically Closed Extensions

    Science.gov (United States)

    Bary-Soroker, Lior

    2009-07-01

    This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.

  6. Handbook of linear algebra

    CERN Document Server

    Hogben, Leslie

    2013-01-01

    With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

  7. Algebraic curves and cryptography

    CERN Document Server

    Murty, V Kumar

    2010-01-01

    It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \\ell-adic point counting algorithm, the p-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on

  8. Partially ordered algebraic systems

    CERN Document Server

    Fuchs, Laszlo

    2011-01-01

    Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i

  9. Elementary algebraic geometry

    CERN Document Server

    Kendig, Keith

    2015-01-01

    Designed to make learning introductory algebraic geometry as easy as possible, this text is intended for advanced undergraduates and graduate students who have taken a one-year course in algebra and are familiar with complex analysis. This newly updated second edition enhances the original treatment's extensive use of concrete examples and exercises with numerous figures that have been specially redrawn in Adobe Illustrator. An introductory chapter that focuses on examples of curves is followed by a more rigorous and careful look at plane curves. Subsequent chapters explore commutative ring th

  10. Algebraic number theory

    CERN Document Server

    Weiss, Edwin

    1998-01-01

    Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

  11. Algebra & trigonometry I essentials

    CERN Document Server

    REA, Editors of

    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. Algebra & Trigonometry I includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, eq

  12. Linear Algebra Thoroughly Explained

    CERN Document Server

    Vujičić, Milan

    2008-01-01

    Linear Algebra Thoroughly Explained provides a comprehensive introduction to the subject suitable for adoption as a self-contained text for courses at undergraduate and postgraduate level. The clear and comprehensive presentation of the basic theory is illustrated throughout with an abundance of worked examples. The book is written for teachers and students of linear algebra at all levels and across mathematics and the applied sciences, particularly physics and engineering. It will also be an invaluable addition to research libraries as a comprehensive resource book for the subject.

  13. Adapted Boolean network models for extracellular matrix formation

    Directory of Open Access Journals (Sweden)

    Wollbold Johannes

    2009-07-01

    Full Text Available Abstract Background Due to the rapid data accumulation on pathogenesis and progression of chronic inflammation, there is an increasing demand for approaches to analyse the underlying regulatory networks. For example, rheumatoid arthritis (RA is a chronic inflammatory disease, characterised by joint destruction and perpetuated by activated synovial fibroblasts (SFB. These abnormally express and/or secrete pro-inflammatory cytokines, collagens causing joint fibrosis, or tissue-degrading enzymes resulting in destruction of the extra-cellular matrix (ECM. We applied three methods to analyse ECM regulation: data discretisation to filter out noise and to reduce complexity, Boolean network construction to implement logic relationships, and formal concept analysis (FCA for the formation of minimal, but complete rule sets from the data. Results First, we extracted literature information to develop an interaction network containing 18 genes representing ECM formation and destruction. Subsequently, we constructed an asynchronous Boolean network with biologically plausible time intervals for mRNA and protein production, secretion, and inactivation. Experimental gene expression data was obtained from SFB stimulated by TGFβ1 or by TNFα and discretised thereafter. The Boolean functions of the initial network were improved iteratively by the comparison of the simulation runs to the experimental data and by exploitation of expert knowledge. This resulted in adapted networks for both cytokine stimulation conditions. The simulations were further analysed by the attribute exploration algorithm of FCA, integrating the observed time series in a fine-tuned and automated manner. The resulting temporal rules yielded new contributions to controversially discussed aspects of fibroblast biology (e.g., considerable expression of TNF and MMP9 by fibroblasts stimulation and corroborated previously known facts (e.g., co-expression of collagens and MMPs after TNF

  14. 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

  15. Homomorphisms between C∗ -algebra extensions

    Indian Academy of Sciences (India)

    C∗. -algebra extensions, Ext groups do not classify extension algebras. So one has to study the isomorphism equivalence of extensions. In fact, a homomorphism between two extension algebras may not map the essential ideal into the other in general, so we have to consider properties of extension homomorphisms.

  16. An algebra of reversible computation.

    Science.gov (United States)

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

  17. Process Algebra and Markov Chains

    NARCIS (Netherlands)

    Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.

    This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study

  18. Ternary Virasoro-Witt algebra

    International Nuclear Information System (INIS)

    Curtright, Thomas L.; Fairlie, David B.; Zachos, Cosmas K.

    2008-01-01

    A 3-bracket variant of the Virasoro-Witt algebra is constructed through the use of su(1,1) enveloping algebra techniques. The Leibniz rules for 3-brackets acting on other 3-brackets in the algebra are discussed and verified in various situations

  19. Assessing Elementary Algebra with STACK

    Science.gov (United States)

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  20. Griffin: A Tool for Symbolic Inference of Synchronous Boolean Molecular Networks

    Science.gov (United States)

    Muñoz, Stalin; Carrillo, Miguel; Azpeitia, Eugenio; Rosenblueth, David A.

    2018-01-01

    Boolean networks are important models of biochemical systems, located at the high end of the abstraction spectrum. A number of Boolean gene networks have been inferred following essentially the same method. Such a method first considers experimental data for a typically underdetermined “regulation” graph. Next, Boolean networks are inferred by using biological constraints to narrow the search space, such as a desired set of (fixed-point or cyclic) attractors. We describe Griffin, a computer tool enhancing this method. Griffin incorporates a number of well-established algorithms, such as Dubrova and Teslenko's algorithm for finding attractors in synchronous Boolean networks. In addition, a formal definition of regulation allows Griffin to employ “symbolic” techniques, able to represent both large sets of network states and Boolean constraints. We observe that when the set of attractors is required to be an exact set, prohibiting additional attractors, a naive Boolean coding of this constraint may be unfeasible. Such cases may be intractable even with symbolic methods, as the number of Boolean constraints may be astronomically large. To overcome this problem, we employ an Artificial Intelligence technique known as “clause learning” considerably increasing Griffin's scalability. Without clause learning only toy examples prohibiting additional attractors are solvable: only one out of seven queries reported here is answered. With clause learning, by contrast, all seven queries are answered. We illustrate Griffin with three case studies drawn from the Arabidopsis thaliana literature. Griffin is available at: http://turing.iimas.unam.mx/griffin. PMID:29559993

  1. Boolean modeling in systems biology: an overview of methodology and applications

    International Nuclear Information System (INIS)

    Wang, Rui-Sheng; Albert, Réka; Saadatpour, Assieh

    2012-01-01

    Mathematical modeling of biological processes provides deep insights into complex cellular systems. While quantitative and continuous models such as differential equations have been widely used, their use is obstructed in systems wherein the knowledge of mechanistic details and kinetic parameters is scarce. On the other hand, a wealth of molecular level qualitative data on individual components and interactions can be obtained from the experimental literature and high-throughput technologies, making qualitative approaches such as Boolean network modeling extremely useful. In this paper, we build on our research to provide a methodology overview of Boolean modeling in systems biology, including Boolean dynamic modeling of cellular networks, attractor analysis of Boolean dynamic models, as well as inferring biological regulatory mechanisms from high-throughput data using Boolean models. We finally demonstrate how Boolean models can be applied to perform the structural analysis of cellular networks. This overview aims to acquaint life science researchers with the basic steps of Boolean modeling and its applications in several areas of systems biology. (paper)

  2. Reconfigurable Boolean logic using magnetic single-electron transistors.

    Directory of Open Access Journals (Sweden)

    M Fernando Gonzalez-Zalba

    Full Text Available We propose a novel hybrid single-electron device for reprogrammable low-power logic operations, the magnetic single-electron transistor (MSET. The device consists of an aluminium single-electron transistor with a GaMnAs magnetic back-gate. Changing between different logic gate functions is realized by reorienting the magnetic moments of the magnetic layer, which induces a voltage shift on the Coulomb blockade oscillations of the MSET. We show that we can arbitrarily reprogram the function of the device from an n-type SET for in-plane magnetization of the GaMnAs layer to p-type SET for out-of-plane magnetization orientation. Moreover, we demonstrate a set of reprogrammable Boolean gates and its logical complement at the single device level. Finally, we propose two sets of reconfigurable binary gates using combinations of two MSETs in a pull-down network.

  3. Reconfigurable Boolean Logic Using Magnetic Single-Electron Transistors

    Science.gov (United States)

    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

  4. Identification of Boolean Networks Using Premined Network Topology Information.

    Science.gov (United States)

    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.

  5. ZKBoo: Faster Zero-Knowledge for Boolean Circuits

    DEFF Research Database (Denmark)

    Giacomelli, Irene; Madsen, Jesper; Orlandi, Claudio

    2016-01-01

    variants of IKOS, which highlights their pros and cons for practically rele- vant soundness parameters; ◦ A generalization and simplification of their approach, which leads to faster Σ-protocols (that can be made non-interactive using the Fiat-Shamir heuristic) for state- ments of the form “I know x...... such that y = φ (x)” (where φ is a circuit and y a public value); ◦ A case study, where we provide explicit protocols, implementations and benchmarking of zero-knowledge protocols for the SHA-1 and SHA-256 circuits.......In this paper we describe ZKBoo, a proposal for practically efficient zero-knowledge arguments especially tailored for Boolean circuits and report on a proof-of- concept implementation. As an highlight, we can generate (resp. verify) a non-interactive proof for the SHA-1 circuit in approximately 13...

  6. Unlimited multistability and Boolean logic in microbial signalling

    DEFF Research Database (Denmark)

    Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca

    2015-01-01

    reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We...... further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two......-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger...

  7. Logical Attractors: a Boolean Approach to the Dynamics of Psychosis

    Science.gov (United States)

    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.

  8. Commutative algebra with a view toward algebraic geometry

    CERN Document Server

    Eisenbud, David

    1995-01-01

    Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...

  9. Quantitative Algebraic Reasoning

    DEFF Research Database (Denmark)

    Mardare, Radu Iulian; Panangaden, Prakash; Plotkin, Gordon

    2016-01-01

    We develop a quantitative analogue of equational reasoning which we call quantitative algebra. We define an equality relation indexed by rationals: a =ε b which we think of as saying that “a is approximately equal to b up to an error of ε”. We have 4 interesting examples where we have a quantitative...

  10. A course in algebra

    CERN Document Server

    Fan, Yun; Zheng, Y L

    2000-01-01

    This volume is based on the lectures given by the authors at Wuhan University and Hubei University in courses on abstract algebra. It presents the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them and other mathematical branches and applied aspects.

  11. Algebraic geometry in India

    Indian Academy of Sciences (India)

    from India, I will describe mainly some work in four topics with which I am familiar: Moduli problem of vector bundles (and the related geometric invariant theory), the work of. CPRamanujam, Frobenius split varieties and algebraic .... One important series of works, by Seshadri in collaboration with V Lakshmibai, C Musili, and.

  12. Discourses on Algebra

    Indian Academy of Sciences (India)

    To the Indian reader, the word discourse, evokes a respected figure interpreting divine wisdom to common folk in an accessible fash- ion. I dug a bit deeper with Google trans- late, and found that the original Russian ti- tle of Shafarevich's book was more like Se- lected Chapters of Algebra and that it was first published in a ...

  13. Probabilistic thread algebra

    NARCIS (Netherlands)

    Bergstra, J.A.; Middelburg, C.A.

    2015-01-01

    We add probabilistic features to basic thread algebra and its extensions with thread-service interaction and strategic interleaving. Here, threads represent the behaviours produced by instruction sequences under execution and services represent the behaviours exhibited by the components of execution

  14. Compressible effect algebras

    Science.gov (United States)

    Gudder, Stan

    2004-08-01

    We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J( a) ≤ a for all a ɛ E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.

  15. Thinking Visually about Algebra

    Science.gov (United States)

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  16. Algebraic Thinking through Origami.

    Science.gov (United States)

    Higginson, William; Colgan, Lynda

    2001-01-01

    Describes the use of paper folding to create a rich environment for discussing algebraic concepts. Explores the effect that changing the dimensions of two-dimensional objects has on the volume of related three-dimensional objects. (Contains 13 references.) (YDS)

  17. Operator algebras and topology

    International Nuclear Information System (INIS)

    Schick, T.

    2002-01-01

    These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)

  18. Advanced modern algebra part 2

    CERN Document Server

    Rotman, Joseph J

    2017-01-01

    This book is the second part of the new edition of Advanced Modern Algebra (the first part published as Graduate Studies in Mathematics, Volume 165). Compared to the previous edition, the material has been significantly reorganized and many sections have been rewritten. The book presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.

  19. On Dunkl angular momenta algebra

    Energy Technology Data Exchange (ETDEWEB)

    Feigin, Misha [School of Mathematics and Statistics, University of Glasgow,15 University Gardens, Glasgow G12 8QW (United Kingdom); Hakobyan, Tigran [Yerevan State University,1 Alex Manoogian, 0025 Yerevan (Armenia); Tomsk Polytechnic University,Lenin Ave. 30, 634050 Tomsk (Russian Federation)

    2015-11-17

    We consider the quantum angular momentum generators, deformed by means of the Dunkl operators. Together with the reflection operators they generate a subalgebra in the rational Cherednik algebra associated with a finite real reflection group. We find all the defining relations of the algebra, which appear to be quadratic, and we show that the algebra is of Poincaré-Birkhoff-Witt (PBW) type. We show that this algebra contains the angular part of the Calogero-Moser Hamiltonian and that together with constants it generates the centre of the algebra. We also consider the gl(N) version of the subalgebra of the rational Cherednik algebra and show that it is a non-homogeneous quadratic algebra of PBW type as well. In this case the central generator can be identified with the usual Calogero-Moser Hamiltonian associated with the Coxeter group in the harmonic confinement.

  20. Continuum analogues of contragredient Lie algebras

    International Nuclear Information System (INIS)

    Saveliev, M.V.; Vershik, A.M.

    1989-03-01

    We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs

  1. Free Malcev algebra of rank three

    OpenAIRE

    Kornev, Alexandr

    2011-01-01

    We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated by a simple seven-dimensional Malcev algebra.

  2. Boolean and advanced searching for EDGAR data on www.sec.gov

    Data.gov (United States)

    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.

  3. Sensitivity analysis of efficient solution in vector MINMAX boolean programming problem

    Directory of Open Access Journals (Sweden)

    Vladimir A. Emelichev

    2002-11-01

    Full Text Available We consider a multiple criterion Boolean programming problem with MINMAX partial criteria. The extreme level of independent perturbations of partial criteria parameters such that efficient (Pareto optimal solution preserves optimality was obtained.

  4. A SAT-based algorithm for finding attractors in synchronous Boolean networks.

    Science.gov (United States)

    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.

  5. A novel generalized design methodology and realization of Boolean operations using DNA.

    Science.gov (United States)

    Zoraida, B S E; Arock, Michael; Ronald, B S M; Ponalagusamy, R

    2009-09-01

    The biological deoxyribonucleic acid (DNA) strand has been increasingly seen as a promising computing unit. A new algorithm is formulated in this paper to design any DNA Boolean operator with molecular beacons (MBs) as its input. Boolean operators realized using the proposed design methodology is presented. The developed operators adopt a uniform representation for logical 0 and 1 for any Boolean operator. The Boolean operators designed in this work employ only a hybridization operation at each stage. Further, this paper for the first time brings out the realization of a binary adder and subtractor using molecular beacons. Simulation results of the DNA-based binary adder and subtractor are given to validate the design.

  6. Real algebraic geometry

    CERN Document Server

    Bochnak, Jacek; Roy, Marie-Françoise

    1998-01-01

    This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.

  7. Totally Optimal Decision Trees for Monotone Boolean Functions with at Most Five Variables

    KAUST Repository

    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.

  8. 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....

  9. Correlation Immunity, Avalanche Features, and Other Cryptographic Properties of Generalized Boolean Functions

    Science.gov (United States)

    2017-09-01

    duties due to Sailors, across the globe, who stand the watch. As Winston Churchill once said, “we sleep safely at night because rough men stand ready...Chapter 2 contains definitions and preliminary generalized Boolean function material. This is followed by Chapters 3–5, which contain the bulk of the...Generalized Boolean Functions Sic Parvis Magna Sir Francis DrakeA In this chapter we begin by covering some basic definitions and properties which we will make

  10. Jacobson-Witt algebras and Lie-admissible algebras

    International Nuclear Information System (INIS)

    Tomber, M.L.

    1981-01-01

    For any field PHI of characteristics p > 0 and integer m greater than or equal to 1, there is a Jacobson-Witt algebra which is a Lie algebra. In this paper, all flexible Lie-admissible algebras U, such that U - is a Jacobson-Witt algebra W/sub m/(p), are determined. For any W/sub m/(p), p > 2 there is exactly one such U and it is isomorphic to W/sub m/(p). There are two non-isomorphic algebras U such that U - is isomorphic to W 1 (2), and there are no algebras U with U - isomorphic to W/sub m/(2), m > 1

  11. Algebras of Information States

    Czech Academy of Sciences Publication Activity Database

    Punčochář, Vít

    2017-01-01

    Roč. 27, č. 5 (2017), s. 1643-1675 ISSN 0955-792X R&D Projects: GA ČR(CZ) GC16-07954J Institutional support: RVO:67985955 Keywords : information states * relational semantics * algebraic semantics * intuitionistic logic * inquisitive disjunction Subject RIV: AA - Philosophy ; Religion OBOR OECD: Philosophy, History and Philosophy of science and technology Impact factor: 0.909, year: 2016

  12. Algebra, Arithmetic, and Geometry

    CERN Document Server

    Tschinkel, Yuri

    2009-01-01

    The two volumes of "Algebra, Arithmetic, and Geometry: In Honor of Y.I. Manin" are composed of invited expository articles and extensions detailing Manin's contributions to the subjects, and are in celebration of his 70th birthday. The well-respected and distinguished contributors include: Behrend, Berkovich, Bost, Bressler, Calaque, Carlson, Chambert-Loir, Colombo, Connes, Consani, Dabrowski, Deninger, Dolgachev, Donaldson, Ekedahl, Elsenhans, Enriques, Etingof, Fock, Friedlander, Geemen, Getzler, Goncharov, Harris, Iskovskikh, Jahnel, Kaledin, Kapranov, Katz, Kaufmann, Kollar, Kont

  13. Split Malcev algebras

    Indian Academy of Sciences (India)

    project of the Spanish Ministerio de Educación y Ciencia MTM2007-60333. References. [1] Calderón A J, On split Lie algebras with symmetric root systems, Proc. Indian. Acad. Sci (Math. Sci.) 118(2008) 351–356. [2] Calderón A J, On split Lie triple systems, Proc. Indian. Acad. Sci (Math. Sci.) 119(2009). 165–177.

  14. Fundamentals of linear algebra

    CERN Document Server

    Dash, Rajani Ballav

    2008-01-01

    FUNDAMENTALS OF LINEAR ALGEBRA is a comprehensive Text Book, which can be used by students and teachers of All Indian Universities. The Text has easy, understandable form and covers all topics of UGC Curriculum. There are lots of worked out examples which helps the students in solving the problems without anybody's help. The Problem sets have been designed keeping in view of the questions asked in different examinations.

  15. Clifford Algebras and Spinors

    International Nuclear Information System (INIS)

    Todorov, Ivan

    2010-12-01

    Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on neutrino masses. It has a more mathematical flavour than the over twenty-six-year-old Introduction to Majorana masses [M84] and includes historical notes and biographical data on past participants in the story. (author)

  16. Modern algebra essentials

    CERN Document Server

    Lutfiyya, Lutfi A

    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. Modern Algebra includes set theory, operations, relations, basic properties of the integers, group theory, and ring theory.

  17. Algebra & trigonometry II essentials

    CERN Document Server

    REA, Editors of

    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. Algebra & Trigonometry II includes logarithms, sequences and series, permutations, combinations and probability, vectors, matrices, determinants and systems of equations, mathematica

  18. Further linear algebra

    CERN Document Server

    Blyth, T S

    2002-01-01

    Most of the introductory courses on linear algebra develop the basic theory of finite­ dimensional vector spaces, and in so doing relate the notion of a linear mapping to that of a matrix. Generally speaking, such courses culminate in the diagonalisation of certain matrices and the application of this process to various situations. Such is the case, for example, in our previous SUMS volume Basic Linear Algebra. The present text is a continuation of that volume, and has the objective of introducing the reader to more advanced properties of vector spaces and linear mappings, and consequently of matrices. For readers who are not familiar with the contents of Basic Linear Algebra we provide an introductory chapter that consists of a compact summary of the prerequisites for the present volume. In order to consolidate the student's understanding we have included a large num­ ber of illustrative and worked examples, as well as many exercises that are strategi­ cally placed throughout the text. Solutions to the ex...

  19. An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks

    Science.gov (United States)

    Cabessa, Jérémie; Villa, Alessandro E. P.

    2014-01-01

    We provide a novel refined attractor-based complexity measurement for Boolean recurrent neural networks that represents an assessment of their computational power in terms of the significance of their attractor dynamics. This complexity measurement is achieved by first proving a computational equivalence between Boolean recurrent neural networks and some specific class of -automata, and then translating the most refined classification of -automata to the Boolean neural network context. As a result, a hierarchical classification of Boolean neural networks based on their attractive dynamics is obtained, thus providing a novel refined attractor-based complexity measurement for Boolean recurrent neural networks. These results provide new theoretical insights to the computational and dynamical capabilities of neural networks according to their attractive potentialities. An application of our findings is illustrated by the analysis of the dynamics of a simplified model of the basal ganglia-thalamocortical network simulated by a Boolean recurrent neural network. This example shows the significance of measuring network complexity, and how our results bear new founding elements for the understanding of the complexity of real brain circuits. PMID:24727866

  20. Pre-ideals of Basic Algebras

    Science.gov (United States)

    Krňávek, Jan; Kühr, Jan

    2011-12-01

    Basic algebras are a generalization of MV-algebras, also including orthomodular lattices and lattice effect algebras. A pre-ideal of a basic algebra is a non-empty subset that is closed under the addition ⊕ and downwards closed with respect to the underlying order. In this paper, we study the pre-ideal lattices of algebras in a particular subclass of basic algebras which are closer to MV-algebras than basic algebras in general. We also prove that finite members of this subclass are exactly finite MV-algebras.

  1. Assessing Algebraic Solving Ability: A Theoretical Framework

    Science.gov (United States)

    Lian, Lim Hooi; Yew, Wun Thiam

    2012-01-01

    Algebraic solving ability had been discussed by many educators and researchers. There exists no definite definition for algebraic solving ability as it can be viewed from different perspectives. In this paper, the nature of algebraic solving ability in terms of algebraic processes that demonstrate the ability in solving algebraic problem is…

  2. Associative and Lie deformations of Poisson algebras

    OpenAIRE

    Remm, Elisabeth

    2011-01-01

    Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.

  3. Einstein algebras and general relativity

    International Nuclear Information System (INIS)

    Heller, M.

    1992-01-01

    A purely algebraic structure called an Einstein algebra is defined in such a way that every spacetime satisfying Einstein's equations is an Einstein algebra but not vice versa. The Gelfand representation of Einstein algebras is defined, and two of its subrepresentations are discussed. One of them is equivalent to the global formulation of the standard theory of general relativity; the other one leads to a more general theory of gravitation which, in particular, includes so-called regular singularities. In order to include other types of singularities one must change to sheaves of Einstein algebras. They are defined and briefly discussed. As a test of the proposed method, the sheaf of Einstein algebras corresponding to the space-time of a straight cosmic string with quasiregular singularity is constructed. 22 refs

  4. Fusion rules of chiral algebras

    International Nuclear Information System (INIS)

    Gaberdiel, M.

    1994-01-01

    Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)

  5. Categorical Algebra and its Applications

    CERN Document Server

    1988-01-01

    Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.

  6. Graphene-based non-Boolean logic circuits

    Science.gov (United States)

    Liu, Guanxiong; Ahsan, Sonia; Khitun, Alexander G.; Lake, Roger K.; Balandin, Alexander A.

    2013-10-01

    Graphene revealed a number of unique properties beneficial for electronics. However, graphene does not have an energy band-gap, which presents a serious hurdle for its applications in digital logic gates. The efforts to induce a band-gap in graphene via quantum confinement or surface functionalization have not resulted in a breakthrough. Here we show that the negative differential resistance experimentally observed in graphene field-effect transistors of "conventional" design allows for construction of viable non-Boolean computational architectures with the gapless graphene. The negative differential resistance—observed under certain biasing schemes—is an intrinsic property of graphene, resulting from its symmetric band structure. Our atomistic modeling shows that the negative differential resistance appears not only in the drift-diffusion regime but also in the ballistic regime at the nanometer-scale—although the physics changes. The obtained results present a conceptual change in graphene research and indicate an alternative route for graphene's applications in information processing.

  7. Boolean network model of the Pseudomonas aeruginosa quorum sensing circuits.

    Science.gov (United States)

    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.

  8. "Lost chains" in algebraic models

    Science.gov (United States)

    Fortunato, L.; de Graaf, W. A.

    2011-03-01

    The algebraic structure of some of the simplest algebraic models u(2), u(3) and u(4), widely used in several branches of physics either as toy models or as working instruments, are reanalyzed under a new perspective that releases the requirement that chains should terminate or pass through the angular momentum algebra. Unitary algebras are non-semisimple, therefore we first apply the Levi-Malcev decomposition. Then we use the theory of weighted Dynkin diagrams to identify conjugacy classes of A1 ~ su(2) ~ so(3) subalgebras: a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries follows that we substantiate with examples.

  9. Applications of Computer Algebra Conference

    CERN Document Server

    Martínez-Moro, Edgar

    2017-01-01

    The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

  10. Introduction to algebraic independence theory

    CERN Document Server

    Philippon, Patrice

    2001-01-01

    In the last five years there has been very significant progress in the development of transcendence theory. A new approach to the arithmetic properties of values of modular forms and theta-functions was found. The solution of the Mahler-Manin problem on values of modular function j(tau) and algebraic independence of numbers pi and e^(pi) are most impressive results of this breakthrough. The book presents these and other results on algebraic independence of numbers and further, a detailed exposition of methods created in last the 25 years, during which commutative algebra and algebraic geometry exerted strong catalytic influence on the development of the subject.

  11. Chiral algebras for trinion theories

    International Nuclear Information System (INIS)

    Lemos, Madalena; Peelaers, Wolfger

    2015-01-01

    It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T n theories. We also explicitly construct the chiral algebra arising from the T 4 theory. Its null relations give rise to new T 4 Higgs branch chiral ring relations.

  12. Computational aspects of algebraic curves

    CERN Document Server

    Shaska, Tanush

    2005-01-01

    The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book cove

  13. The planar algebra of a semisimple and cosemisimple Hopf algebra

    Indian Academy of Sciences (India)

    M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22

    [TngGlk] Etingof Pavel and Gelaki Shlomo, On finite-dimensional semisimple and cosemisimple Hopf algebras in positive characteristic. Int. Math. Res. Notices,. 16 (1998) 851–864. [DasKdy] Das Paramita and Vijay Kodiyalam, Planar algebras and the Ocneanu–. Szymanski theorem, Proc. AMS, 133 (2005) 2751–2759.

  14. Galois Theory of Differential Equations, Algebraic Groups and Lie Algebras

    NARCIS (Netherlands)

    Put, Marius van der

    1999-01-01

    The Galois theory of linear differential equations is presented, including full proofs. The connection with algebraic groups and their Lie algebras is given. As an application the inverse problem of differential Galois theory is discussed. There are many exercises in the text.

  15. Dynamical entropy of C* algebras and Von Neumann algebras

    International Nuclear Information System (INIS)

    Connes, A.; Narnhofer, H.; Thirring, W.

    1986-01-01

    The definition of the dynamical entropy is extended for automorphism groups of C * algebras. As example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density. (Author)

  16. Algebraic K-theory of generalized schemes

    DEFF Research Database (Denmark)

    Anevski, Stella Victoria Desiree

    Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry and ge...

  17. Quantum deformation of the affine transformation algebra

    International Nuclear Information System (INIS)

    Aizawa, N.; Sato, Haru-Tada

    1994-01-01

    We discuss a quantum deformation of the affine transformation algebra in one-dimensional space. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators. (orig.)

  18. Algebraic K-theory of generalized schemes

    DEFF Research Database (Denmark)

    Anevski, Stella Victoria Desiree

    Nikolai Durov has developed a generalization of conventional scheme theory in which commutative algebraic monads replace commutative unital rings as the basic algebraic objects. The resulting geometry is expressive enough to encompass conventional scheme theory, tropical algebraic geometry...

  19. Matlab linear algebra

    CERN Document Server

    Lopez, Cesar

    2014-01-01

    MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to

  20. Geometric Algebra Computing

    CERN Document Server

    Corrochano, Eduardo Bayro

    2010-01-01

    This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int

  1. Algebraic topology and concurrency

    DEFF Research Database (Denmark)

    Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric

    2006-01-01

    We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...

  2. Handbook of algebra

    CERN Document Server

    Hazewinkel, M

    2008-01-01

    Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it i

  3. New examples of continuum graded Lie algebras

    International Nuclear Information System (INIS)

    Savel'ev, M.V.

    1989-01-01

    Several new examples of continuum graded Lie algebras which provide an additional elucidation of these algebras are given. Here, in particular, the Kac-Moody algebras, the algebra S 0 Diff T 2 of infinitesimal area-preserving diffeomorphisms of the torus T 2 , the Fairlie, Fletcher and Zachos sine-algebras, etc., are described as special cases of the cross product Lie algebras. 8 refs

  4. Fractional supersymmetry and infinite dimensional lie algebras

    International Nuclear Information System (INIS)

    Rausch de Traubenberg, M.

    2001-01-01

    In an earlier work extensions of supersymmetry and super Lie algebras were constructed consistently starting from any representation D of any Lie algebra g. Here it is shown how infinite dimensional Lie algebras appear naturally within the framework of fractional supersymmetry. Using a differential realization of g this infinite dimensional Lie algebra, containing the Lie algebra g as a sub-algebra, is explicitly constructed

  5. Graded associative conformal algebras of finite type

    OpenAIRE

    Kolesnikov, Pavel

    2011-01-01

    In this paper, we consider graded associative conformal algebras. The class of these objects includes pseudo-algebras over non-cocommutative Hopf algebras of regular functions on some linear algebraic groups. In particular, an associative conformal algebra which is graded by a finite group $\\Gamma $ is a pseudo-algebra over the coordinate Hopf algebra of a linear algebraic group $G$ such that the identity component $G^0$ is the affine line and $G/G^0\\simeq \\Gamma $. A classification of simple...

  6. Galois Connections for Flow Algebras

    DEFF Research Database (Denmark)

    Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis

    2011-01-01

    to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...

  7. Ultraproducts of von Neumann algebras

    DEFF Research Database (Denmark)

    Ando, Hiroshi; Haagerup, Uffe

    2014-01-01

    We study several notions of ultraproducts of von Neumann algebras from a unified viewpoint. In particular, we show that for a sigma-finite von Neumann algebra M  , the ultraproduct MωMω introduced by Ocneanu is a corner of the ultraproduct ∏ωM∏ωM introduced by Groh and Raynaud. Using...

  8. Orthogonal symmetries and Clifford algebras

    Indian Academy of Sciences (India)

    a universal property of the even Clifford algebra in §3. ..... symmetry if σ2 = id. In the literature, such maps are sometimes also called “orthogonal involutions” (cf. Ch. III, §5 of [4]). We have, however, preferred to use the former ...... [7] Helmstetter J and Micali A, Quadratic mappings and Clifford algebras (Basel: Birkhäuser.

  9. Six Lectures on Commutative Algebra

    CERN Document Server

    Elias, J; Miro-Roig, Rosa Maria; Zarzuela, Santiago

    2009-01-01

    Interest in commutative algebra has surged over the years. In order to survey and highlight the developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. This title offers a synthesis of the lectures presented at the Summer School

  10. Templates for Linear Algebra Problems

    NARCIS (Netherlands)

    Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der

    1995-01-01

    The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and

  11. Linear Algebra and Image Processing

    Science.gov (United States)

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  12. Smarandache hyper BCC-algebra

    OpenAIRE

    Ahadpanah, A.; Borumand Saeid, A.

    2011-01-01

    In this paper, we define the Smarandache hyper BCC-algebra, and Smarandache hyper BCC-ideals of type 1, 2, 3 and 4. We state and prove some theorems in Smarandache hyper BCC -algebras, and then we determine the relationships between these hyper ideals.

  13. The Algebra of Complex Numbers.

    Science.gov (United States)

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  14. Modular specifications in process algebra

    NARCIS (Netherlands)

    R.J. van Glabbeek (Rob); F.W. Vaandrager (Frits)

    1987-01-01

    textabstractIn recent years a wide variety of process algebras has been proposed in the literature. Often these process algebras are closely related: they can be viewed as homomorphic images, submodels or restrictions of each other. The aim of this paper is to show how the semantical reality,

  15. Linear Algebra and Linear Models

    Indian Academy of Sciences (India)

    Linear Algebra and Linear. Models. Kalyan Das. Linear Algebra and linear Models. (2nd Edn) by R P Bapat. Hindustan Book Agency, 1999 pp.xiii+180, Price: Rs.135/-. This monograph provides an introduction to the basic aspects of the theory oflinear estima- tion and that of testing linear hypotheses. The primary objective ...

  16. Quantum Observables and Effect Algebras

    Science.gov (United States)

    Dvurečenskij, Anatolij

    2017-11-01

    We study observables on monotone σ-complete effect algebras. We find conditions when a spectral resolution implies existence of the corresponding observable. We characterize sharp observables of a monotone σ-complete homogeneous effect algebra using its orthoalgebraic skeleton. In addition, we study compatibility in orthoalgebras and we show that every orthoalgebra satisfying RIP is an orthomodular poset.

  17. Algebraic study of chiral anomalies

    Indian Academy of Sciences (India)

    2012-06-14

    Jun 14, 2012 ... Abstract. The algebraic structure of chiral anomalies is made globally valid on non-trivial bundles ... Editor's Note: †Reproduced with kind permission from Springer Science+Business Media: Algebraic study of chiral anoma- ..... We shall see in the sequel several examples in which this ambiguity helps.

  18. Practical algebraic renormalization

    International Nuclear Information System (INIS)

    Grassi, Pietro Antonio; Hurth, Tobias; Steinhauser, Matthias

    2001-01-01

    A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the standard model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustrated for two processes of phenomenological interest: QCD corrections to the decay of the Higgs boson into two photons and two-loop electroweak corrections to the process B→X s γ

  19. 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

  20. Unlimited multistability and Boolean logic in microbial signalling.

    Science.gov (United States)

    Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S

    2015-07-06

    The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology.

  1. Structures and Boolean Dynamics in Gene Regulatory Networks

    Science.gov (United States)

    Szedlak, Anthony

    This dissertation discusses the topological and dynamical properties of GRNs in cancer, and is divided into four main chapters. First, the basic tools of modern complex network theory are introduced. These traditional tools as well as those developed by myself (set efficiency, interset efficiency, and nested communities) are crucial for understanding the intricate topological properties of GRNs, and later chapters recall these concepts. Second, the biology of gene regulation is discussed, and a method for disease-specific GRN reconstruction developed by our collaboration is presented. This complements the traditional exhaustive experimental approach of building GRNs edge-by-edge by quickly inferring the existence of as of yet undiscovered edges using correlations across sets of gene expression data. This method also provides insight into the distribution of common mutations across GRNs. Third, I demonstrate that the structures present in these reconstructed networks are strongly related to the evolutionary histories of their constituent genes. Investigation of how the forces of evolution shaped the topology of GRNs in multicellular organisms by growing outward from a core of ancient, conserved genes can shed light upon the ''reverse evolution'' of normal cells into unicellular-like cancer states. Next, I simulate the dynamics of the GRNs of cancer cells using the Hopfield model, an infinite range spin-glass model designed with the ability to encode Boolean data as attractor states. This attractor-driven approach facilitates the integration of gene expression data into predictive mathematical models. Perturbations representing therapeutic interventions are applied to sets of genes, and the resulting deviations from their attractor states are recorded, suggesting new potential drug targets for experimentation. Finally, I extend the Hopfield model to modular networks, cyclic attractors, and complex attractors, and apply these concepts to simulations of the cell cycle

  2. Waterloo Workshop on Computer Algebra

    CERN Document Server

    Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday

    2018-01-01

    This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016.   This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

  3. Invariants of triangular Lie algebras

    International Nuclear Information System (INIS)

    Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

    2007-01-01

    Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

  4. Elements of algebraic coding systems

    CERN Document Server

    Cardoso da Rocha, Jr, Valdemar

    2014-01-01

    Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...

  5. Representations of affine Hecke algebras

    CERN Document Server

    Xi, Nanhua

    1994-01-01

    Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest

  6. A parallel attractor-finding algorithm based on Boolean satisfiability for genetic regulatory networks.

    Science.gov (United States)

    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.

  7. The spruce budworm and forest: a qualitative comparison of ODE and Boolean models

    Directory of Open Access Journals (Sweden)

    Raina Robeva

    2016-01-01

    Full Text Available Boolean and polynomial models of biological systems have emerged recently as viable companions to differential equations models. It is not immediately clear however whether such models are capable of capturing the multi-stable behaviour of certain biological systems: this behaviour is often sensitive to changes in the values of the model parameters, while Boolean and polynomial models are qualitative in nature. In the past few years, Boolean models of gene regulatory systems have been shown to capture multi-stability at the molecular level, confirming that such models can be used to obtain information about the system’s qualitative dynamics when precise information regarding its parameters may not be available. In this paper, we examine Boolean approximations of a classical ODE model of budworm outbreaks in a forest and show that these models exhibit a qualitative behaviour consistent with that derived from the ODE models. In particular, we demonstrate that these models can capture the bistable nature of insect population outbreaks, thus showing that Boolean models can be successfully utilized beyond the molecular level.

  8. An algebra-based method for inferring gene regulatory networks.

    Science.gov (United States)

    Vera-Licona, Paola; Jarrah, Abdul; Garcia-Puente, Luis David; McGee, John; Laubenbacher, Reinhard

    2014-03-26

    The inference of gene regulatory networks (GRNs) from experimental observations is at the heart of systems biology. This includes the inference of both the network topology and its dynamics. While there are many algorithms available to infer the network topology from experimental data, less emphasis has been placed on methods that infer network dynamics. Furthermore, since the network inference problem is typically underdetermined, it is essential to have the option of incorporating into the inference process, prior knowledge about the network, along with an effective description of the search space of dynamic models. Finally, it is also important to have an understanding of how a given inference method is affected by experimental and other noise in the data used. This paper contains a novel inference algorithm using the algebraic framework of Boolean polynomial dynamical systems (BPDS), meeting all these requirements. The algorithm takes as input time series data, including those from network perturbations, such as knock-out mutant strains and RNAi experiments. It allows for the incorporation of prior biological knowledge while being robust to significant levels of noise in the data used for inference. It uses an evolutionary algorithm for local optimization with an encoding of the mathematical models as BPDS. The BPDS framework allows an effective representation of the search space for algebraic dynamic models that improves computational performance. The algorithm is validated with both simulated and experimental microarray expression profile data. Robustness to noise is tested using a published mathematical model of the segment polarity gene network in Drosophila melanogaster. Benchmarking of the algorithm is done by comparison with a spectrum of state-of-the-art network inference methods on data from the synthetic IRMA network to demonstrate that our method has good precision and recall for the network reconstruction task, while also predicting several of the

  9. Rota-Baxter algebras and the Hopf algebra of renormalization

    International Nuclear Information System (INIS)

    Ebrahimi-Fard, K.

    2006-06-01

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  10. Rota-Baxter algebras and the Hopf algebra of renormalization

    Energy Technology Data Exchange (ETDEWEB)

    Ebrahimi-Fard, K.

    2006-06-15

    Recently, the theory of renormalization in perturbative quantum field theory underwent some exciting new developments. Kreimer discovered an organization of Feynman graphs into combinatorial Hopf algebras. The process of renormalization is captured by a factorization theorem for regularized Hopf algebra characters. Hereby the notion of Rota-Baxter algebras enters the scene. In this work we develop in detail several mathematical aspects of Rota-Baxter algebras as they appear also in other sectors closely related to perturbative renormalization, to wit, for instance multiple-zeta-values and matrix differential equations. The Rota-Baxter picture enables us to present the algebraic underpinning for the Connes-Kreimer Birkhoff decomposition in a concise way. This is achieved by establishing a general factorization theorem for filtered algebras. Which in turn follows from a new recursion formula based on the Baker-Campbell-Hausdorff formula. This allows us to generalize a classical result due to Spitzer to non-commutative Rota-Baxter algebras. The Baker-Campbell-Hausdorff based recursion turns out to be a generalization of Magnus' expansion in numerical analysis to generalized integration operators. We will exemplify these general results by establishing a simple representation of the combinatorics of renormalization in terms of triangular matrices. We thereby recover in the presence of a Rota-Baxter operator the matrix representation of the Birkhoff decomposition of Connes and Kreimer. (orig.)

  11. Universal enveloping Lie Rota-Baxter algebra of preLie and post-Lie algebras

    OpenAIRE

    Gubarev, Vsevolod

    2017-01-01

    Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras are constructed. It is proved that the pairs of varieties (Lie Rota-Baxter algebras of zero weight,preLie algebras) and (Lie Rota-Baxter algebras of nonzero weight,post-Lie algebras) are PBW-pairs and the variety of Lie Rota-Baxter algebras is not Schreier.

  12. Lie algebra in quantum physics by means of computer algebra

    OpenAIRE

    Kikuchi, Ichio; Kikuchi, Akihito

    2017-01-01

    This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...

  13. Head First Algebra A Learner's Guide to Algebra I

    CERN Document Server

    Pilone, Tracey

    2008-01-01

    Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials. Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive i

  14. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    Science.gov (United States)

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  15. TESTING HISTOLOGICAL IMAGES OF MAMMARY TISSUES ON COMPATIBILITY WITH THE BOOLEAN MODEL OF RANDOM SETS

    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.

  16. Polynomial-Time Algorithm for Controllability Test of a Class of Boolean Biological Networks

    Directory of Open Access Journals (Sweden)

    Koichi Kobayashi

    2010-01-01

    Full Text Available In recent years, Boolean-network-model-based approaches to dynamical analysis of complex biological networks such as gene regulatory networks have been extensively studied. One of the fundamental problems in control theory of such networks is the problem of determining whether a given substance quantity can be arbitrarily controlled by operating the other substance quantities, which we call the controllability problem. This paper proposes a polynomial-time algorithm for solving this problem. Although the algorithm is based on a sufficient condition for controllability, it is easily computable for a wider class of large-scale biological networks compared with the existing approaches. A key to this success in our approach is to give up computing Boolean operations in a rigorous way and to exploit an adjacency matrix of a directed graph induced by a Boolean network. By applying the proposed approach to a neurotransmitter signaling pathway, it is shown that it is effective.

  17. Mechanical system reliability analysis using a combination of graph theory and Boolean function

    International Nuclear Information System (INIS)

    Tang, J.

    2001-01-01

    A new method based on graph theory and Boolean function for assessing reliability of mechanical systems is proposed. The procedure for this approach consists of two parts. By using the graph theory, the formula for the reliability of a mechanical system that considers the interrelations of subsystems or components is generated. Use of the Boolean function to examine the failure interactions of two particular elements of the system, followed with demonstrations of how to incorporate such failure dependencies into the analysis of larger systems, a constructive algorithm for quantifying the genuine interconnections between the subsystems or components is provided. The combination of graph theory and Boolean function provides an effective way to evaluate the reliability of a large, complex mechanical system. A numerical example demonstrates that this method an effective approaches in system reliability analysis

  18. Current algebra for parafields

    International Nuclear Information System (INIS)

    Palev, Ch.D.

    1976-01-01

    Within the framework of the Lagrangean QFT a generalization of canonical commutation and anticommutation relations in terms of three-linear commutation relations, corresponding to the parastatistics, s discussed. A detailed derivation of these three-linear relations for a set of parafermi fields is presented. Then for a Lagrangean, depending of a family of parabose fields and a family of paraferm fields, is shown that the fundamental hypothesis of current algebra is valid. In other words, the currents corresponding to the linear gauge transformations are found to meet the commutation relation: [Jsub(f)sup(0)(x), Jsub(g)sup(0)]sub(x 0 =y 0 ) = -idelta(x vector - y vector)Jsub([f,g])sup(0) (x), where Jsub(f)sup(0) is a time component of the current, corresponding to transformation f. (S.P.)

  19. Space-time algebra

    CERN Document Server

    Hestenes, David

    2015-01-01

    This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, a...

  20. Algebraic Multigrid Benchmark

    Energy Technology Data Exchange (ETDEWEB)

    2017-08-01

    AMG is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the BoomerAMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL and is very similar to the AMG2013 benchmark with additional optimizations. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem with a 27-point stencil, which can be scaled up and is designed to solve a very large problem. A second problem simulates a time dependent problem, in which successively various smnllcr systems are solved.

  1. Applications of computer algebra

    CERN Document Server

    1985-01-01

    Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in­ creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa­ tion and obtains a closed for...

  2. Macdonald index and chiral algebra

    Science.gov (United States)

    Song, Jaewon

    2017-08-01

    For any 4d N = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type ( A 1 , A 2 n ) and ( A 1 , D 2 n+1) where the chiral algebras are given by Virasoro and \\widehat{su}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

  3. Quantum algebra of N superspace

    International Nuclear Information System (INIS)

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-01-01

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the κ-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra

  4. Vertex algebras and mirror symmetry

    International Nuclear Information System (INIS)

    Borisov, L.A.

    2001-01-01

    Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)

  5. Semiprojectivity of universal -algebras generated by algebraic elements

    DEFF Research Database (Denmark)

    Shulman, Tatiana

    2012-01-01

    Let be a polynomial in one variable whose roots all have multiplicity more than 1. It is shown that the universal -algebra of a relation , , is semiprojective and residually finite-dimensional. Applications to polynomially compact operators are given....

  6. Topological Ã-algebras with CÃ-enveloping algebras II

    Indian Academy of Sciences (India)

    subalgebra and contained in the crossed product *-algebra *(, , ) satisfies ()=*(, , ). If G = R , if is an -invariant dense Frechet ∗-subalgebra of such that () = , and if the action on is -tempered, smooth and by continuous ...

  7. Coxeter groups and Hopf algebras

    CERN Document Server

    Aguiar, Marcelo

    2011-01-01

    An important idea in the work of G.-C. Rota is that certain combinatorial objects give rise to Hopf algebras that reflect the manner in which these objects compose and decompose. Recent work has seen the emergence of several interesting Hopf algebras of this kind, which connect diverse subjects such as combinatorics, algebra, geometry, and theoretical physics. This monograph presents a novel geometric approach using Coxeter complexes and the projection maps of Tits for constructing and studying many of these objects as well as new ones. The first three chapters introduce the necessary backgrou

  8. Linear operators in Clifford algebras

    International Nuclear Information System (INIS)

    Laoues, M.

    1991-01-01

    We consider the real vector space structure of the algebra of linear endomorphisms of a finite-dimensional real Clifford algebra (2, 4, 5, 6, 7, 8). A basis of that space is constructed in terms of the operators M eI,eJ defined by x→e I .x.e J , where the e I are the generators of the Clifford algebra and I is a multi-index (3, 7). In particular, it is shown that the family (M eI,eJ ) is exactly a basis in the even case. (orig.)

  9. Homology theory on algebraic varieties

    CERN Document Server

    Wallace, Andrew H

    1958-01-01

    Homology Theory on Algebraic Varieties, Volume 6 deals with the principles of homology theory in algebraic geometry and includes the main theorems first formulated by Lefschetz, one of which is interpreted in terms of relative homology and another concerns the Poincaré formula. The actual details of the proofs of these theorems are introduced by geometrical descriptions, sometimes aided with diagrams. This book is comprised of eight chapters and begins with a discussion on linear sections of an algebraic variety, with emphasis on the fibring of a variety defined over the complex numbers. The n

  10. Clifford algebraic symmetries in physics

    International Nuclear Information System (INIS)

    Salingaros, N.

    1986-01-01

    This paper reviews the following appearances of Clifford algebras in theoretical physics: statistical mechanics; general relativity; quantum electrodynamics; internal symmetries; the vee product; classical electrodynamics; charged-particle motion; and the Lorentz group. It is concluded that the power of the Clifford-algebraic description resides in its ability to perform representation-free calculations which are generalizations of the traditional vector algebra and that this considerable computational asset, in combination with the intrinsic symmetry, provides a practical framework for much of theoretical physics. 5 references

  11. Test bank for college algebra

    CERN Document Server

    Kolman, Bernard; Levitan, Michael L

    1985-01-01

    Test Bank for College Algebra, Second Edition is a supplementary material for the text, College Algebra, Second Edition. The book is intended for use by mathematics teachers.The book contains standard tests for each chapter in the textbook. Each set of test aims to evaluate the level of understanding the student has achieved during the course. The answers for each chapter test and the final exam are found at the end of the book.Mathematics teachers teaching college algebra will find the book very useful.

  12. Introduction to applied algebraic systems

    CERN Document Server

    Reilly, Norman R

    2009-01-01

    This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as

  13. Introduction to algebra and trigonometry

    CERN Document Server

    Kolman, Bernard

    1981-01-01

    Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry.This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are

  14. Study guide for college algebra

    CERN Document Server

    Snow, James W; Shapiro, Arnold

    1981-01-01

    Study Guide for College Algebra is a supplemental material for the basic text, College Algebra. Its purpose is to make the learning of college algebra and trigonometry easier and enjoyable.The book provides detailed solutions to exercises found in the text. Students are encouraged to use the study guide as a learning tool during the duration of the course, a reviewer prior to an exam, a reference book, and as a quick overview before studying a section of the text. The Study Guide and Solutions Manual consists of four major components: basic concepts that should be learned from each unit, what

  15. Planar algebra of the subgroup-subfactor

    Indian Academy of Sciences (India)

    G in terms of operator matrices. We also obtain an identification between the planar algebra of the fixed algebra sub- factor RG ⊂ RH and the G-invariant planar subalgebra of the planar algebra of the 'flip' of ⋆n. Keywords. Planar algebras; subfactors; standard invariant. 1. Introduction. For every pair H ⊂ G of finite groups, ...

  16. Abstract algebra an introduction with applications

    CERN Document Server

    Robinson, Derek JS

    2015-01-01

    This is the second edition of the introduction to abstract algebra. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. There is ample material here for a two semester course in abstract algebra.

  17. Homomorphisms of certain Banach function algebras

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    . } < ∞ is denoted by Lipα(X, d). These algebras are called Lipschitz algebras of order α and were first studied by Sherbert. The Lipschitz algebras Lipα(X, d) for α ≤ 1 are natural. Banach function algebras on X under the norm f α = f X + pα(f ) ...

  18. Particle-like structure of Lie algebras

    Science.gov (United States)

    Vinogradov, A. M.

    2017-07-01

    If a Lie algebra structure 𝔤 on a vector space is the sum of a family of mutually compatible Lie algebra structures 𝔤i's, we say that 𝔤 is simply assembled from the 𝔤i's. Repeating this procedure with a number of Lie algebras, themselves simply assembled from the 𝔤i's, one obtains a Lie algebra assembled in two steps from 𝔤i's, and so on. We describe the process of modular disassembling of a Lie algebra into a unimodular and a non-unimodular part. We then study two inverse questions: which Lie algebras can be assembled from a given family of Lie algebras, and from which Lie algebras can a given Lie algebra be assembled. We develop some basic assembling and disassembling techniques that constitute the elements of a new approach to the general theory of Lie algebras. The main result of our theory is that any finite-dimensional Lie algebra over an algebraically closed field of characteristic zero or over R can be assembled in a finite number of steps from two elementary constituents, which we call dyons and triadons. Up to an abelian summand, a dyon is a Lie algebra structure isomorphic to the non-abelian 2-dimensional Lie algebra, while a triadon is isomorphic to the 3-dimensional Heisenberg Lie algebra. As an example, we describe constructions of classical Lie algebras from triadons.

  19. Contraction of graded su(2) algebra

    International Nuclear Information System (INIS)

    Patra, M.K.; Tripathy, K.C.

    1989-01-01

    The Inoenu-Wigner contraction scheme is extended to Lie superalgebras. The structure and representations of extended BRS algebra are obtained from contraction of the graded su(2) algebra. From cohomological consideration, we demonstrate that the graded su(2) algebra is the only superalgebra which, on contraction, yields the full BRS algebra. (orig.)

  20. Ordinary differential equations and Boolean networks in application to modelling of 6-mercaptopurine metabolism.

    Science.gov (United States)

    Lavrova, Anastasia I; Postnikov, Eugene B; Zyubin, Andrey Yu; Babak, Svetlana V

    2017-04-01

    We consider two approaches to modelling the cell metabolism of 6-mercaptopurine, one of the important chemotherapy drugs used for treating acute lymphocytic leukaemia: kinetic ordinary differential equations, and Boolean networks supplied with one controlling node, which takes continual values. We analyse their interplay with respect to taking into account ATP concentration as a key parameter of switching between different pathways. It is shown that the Boolean networks, which allow avoiding the complexity of general kinetic modelling, preserve the possibility of reproducing the principal switching mechanism.

  1. Improving the quantum cost of reversible Boolean functions using reorder algorithm

    Science.gov (United States)

    Ahmed, Taghreed; Younes, Ahmed; Elsayed, Ashraf

    2018-05-01

    This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed-Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decrease the quantum cost of the reversible circuit. The paper achieves a decrease in the quantum cost and/or the circuit length, on average, when compared with relevant work in the literature.

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

    Directory of Open Access Journals (Sweden)

    Le Yu

    2007-05-01

    Full Text Available The inference of gene regulatory networks is a key issue for genomic signal processing. This paper addresses the inference of probabilistic Boolean networks (PBNs from observed temporal sequences of network states. Since a PBN is composed of a finite number of Boolean networks, a basic observation is that the characteristics of a single Boolean network without perturbation may be determined by its pairwise transitions. Because the network function is fixed and there are no perturbations, a given state will always be followed by a unique state at the succeeding time point. Thus, a transition counting matrix compiled over a data sequence will be sparse and contain only one entry per line. If the network also has perturbations, with small perturbation probability, then the transition counting matrix would have some insignificant nonzero entries replacing some (or all of the zeros. If a data sequence is sufficiently long to adequately populate the matrix, then determination of the functions and inputs underlying the model is straightforward. The difficulty comes when the transition counting matrix consists of data derived from more than one Boolean network. We address the PBN inference procedure in several steps: (1 separate the data sequence into “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

  3. Boolean Matching Filters Based on Row and Column Weights of Reed–Muller Polarity Coefficient Matrix

    Directory of Open Access Journals (Sweden)

    Chip-Hong Chang

    2002-01-01

    Full Text Available In this article, we have shown, by means of the EXOR Ternary Decision Diagram that the number of literals and product terms of the Fixed Polarity Reed–Muller (FPRM expansions can be used to fully classify all Boolean functions in NP equivalent class and NPN equivalent class, respectively. Efficient graph based algorithms to compute the complete weight vectors have been presented. The proof and computation method has led to the derivation of a set of characteristic signatures that has low probability of aliasing when used as the Boolean matching filters in library mapping.

  4. 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

  5. AT -algebras and extensions of AT-algebras

    Indian Academy of Sciences (India)

    and E has real rank zero, then E is an AT-algebra if and only if the index maps are both zero. Accordingly, in this ... It is well-known that two extensions with the same index are isomorphic as C. ∗. -algebras. We call these .... where each Bi = I (Ei) is a direct sum of K. By Lemma 2.3, I (E) = B. Without loss of generality, we may ...

  6. Lectures on algebraic quantum field theory and operator algebras

    International Nuclear Information System (INIS)

    Schroer, Bert

    2001-04-01

    In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as why mathematicians are/should be interested in algebraic quantum field theory would be equally fitting. besides a presentation of the framework and the main results of local quantum physics these notes may serve as a guide to frontier research problems in mathematical. (author)

  7. Topological أ-algebras with Cأ-enveloping algebras II

    Indian Academy of Sciences (India)

    A with the locally convex inductive limit topology t is a locally m-convex Q-algebra satisfying EًKnc. A ق ¼ EًKAق ¼ A. (3) If A has a countable bounded approximate identity, then ًKnc. A ; tق is an LFQ-algebra. In general KA 6¼ Knc. A , though KA Knc. A . Now KA has been interpreted as a non- commutative analogue of CcًXق.

  8. Pre-Algebra Essentials For Dummies

    CERN Document Server

    Zegarelli, Mark

    2010-01-01

    Many students worry about starting algebra. Pre-Algebra Essentials For Dummies provides an overview of critical pre-algebra concepts to help new algebra students (and their parents) take the next step without fear. Free of ramp-up material, Pre-Algebra Essentials For Dummies contains content focused on key topics only. It provides discrete explanations of critical concepts taught in a typical pre-algebra course, from fractions, decimals, and percents to scientific notation and simple variable equations. This guide is also a perfect reference for parents who need to review critical pre-algebra

  9. Lukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems

    Directory of Open Access Journals (Sweden)

    James F. Glazebrook

    2010-06-01

    Full Text Available The fundamentals of Lukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the SchrÄodinger representation, with both initial and boundary conditions in space-time. A new theorem is proven which states that the category of quantum automata and automata-homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R-Systems which are open, dynamic biosystem networks [4] with de¯ned biological relations that represent physiological functions of primordial(s, single cells and the simpler organisms. A new category of quantum computers is also defined in terms of reversible quantum automata with quantum state spaces represented by topological groupoids that admit a local characterization through unique, quantum Lie algebroids. On the other hand, the category of n-Lukasiewicz algebras has a subcategory of centered n-Lukasiewicz algebras (as proven in ref. [2] which can be employed to design and construct subcategories of quantum automata based on n-Lukasiewicz diagrams of existing VLSI. Furthermore, as shown in ref. [2] the category of centered n-Lukasiewicz algebras and the category of Boolean algebras are naturally equivalent. A `no-go' conjecture is also proposed which states that Generalized (M

  10. Connections between algebra, combinatorics, and geometry

    CERN Document Server

    Sather-Wagstaff, Sean

    2014-01-01

    Commutative algebra, combinatorics, and algebraic geometry are thriving areas of mathematical research with a rich history of interaction. Connections Between Algebra, Combinatorics, and Geometry contains lecture notes, along with exercises and solutions, from the Workshop on Connections Between Algebra and Geometry held at the University of Regina from May 29-June 1, 2012. It also contains research and survey papers from academics invited to participate in the companion Special Session on Interactions Between Algebraic Geometry and Commutative Algebra, which was part of the CMS Summer Meeting at the University of Regina held June 2–3, 2012, and the meeting Further Connections Between Algebra and Geometry, which was held at the North Dakota State University, February 23, 2013. This volume highlights three mini-courses in the areas of commutative algebra and algebraic geometry: differential graded commutative algebra, secant varieties, and fat points and symbolic powers. It will serve as a useful resou...

  11. Ada Linear-Algebra Program

    Science.gov (United States)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  12. Cartooning in Algebra and Calculus

    Science.gov (United States)

    Moseley, L. Jeneva

    2014-01-01

    This article discusses how teachers can create cartoons for undergraduate math classes, such as college algebra and basic calculus. The practice of cartooning for teaching can be helpful for communication with students and for students' conceptual understanding.

  13. Lie-Algebras. Pt. 1

    International Nuclear Information System (INIS)

    Baeuerle, G.G.A.; Kerf, E.A. de

    1990-01-01

    The structure of the laws in physics is largely based on symmetries. This book is on Lie algebras, the mathematics of symmetry. It gives a thorough mathematical treatment of finite dimensional Lie algebras and Kac-Moody algebras. Concepts such as Cartan matrix, root system, Serre's construction are carefully introduced. Although the book can be read by an undergraduate with only an elementary knowledge of linear algebra, the book will also be of use to the experienced researcher. Experience has shown that students who followed the lectures are well-prepared to take on research in the realms of string-theory, conformal field-theory and integrable systems. 48 refs.; 66 figs.; 3 tabs

  14. Classical theory of algebraic numbers

    CERN Document Server

    Ribenboim, Paulo

    2001-01-01

    Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...

  15. Computational linear and commutative algebra

    CERN Document Server

    Kreuzer, Martin

    2016-01-01

    This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...

  16. Completeness of algebraic CPS simulations

    Directory of Open Access Journals (Sweden)

    Ali Assaf

    2012-07-01

    Full Text Available The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the differential lambda calculus, the latter is a candidate lambda calculus for quantum computation. They differ in the handling of application arguments and algebraic rules. The two languages can simulate each other using an algebraic extension of the well-known call-by-value and call-by-name CPS translations. These simulations are sound, in that they preserve reductions. In this paper, we prove that the simulations are actually complete, strengthening the connection between the two languages.

  17. Cluster algebras in mathematical physics

    International Nuclear Information System (INIS)

    Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

    2014-01-01

    This special issue of Journal of Physics A: Mathematical and Theoretical contains reviews and original research articles on cluster algebras and their applications to mathematical physics. Cluster algebras were introduced by S Fomin and A Zelevinsky around 2000 as a tool for studying total positivity and dual canonical bases in Lie theory. Since then the theory has found diverse applications in mathematics and mathematical physics. Cluster algebras are axiomatically defined commutative rings equipped with a distinguished set of generators (cluster variables) subdivided into overlapping subsets (clusters) of the same cardinality subject to certain polynomial relations. A cluster algebra of rank n can be viewed as a subring of the field of rational functions in n variables. Rather than being presented, at the outset, by a complete set of generators and relations, it is constructed from the initial seed via an iterative procedure called mutation producing new seeds successively to generate the whole algebra. A seed consists of an n-tuple of rational functions called cluster variables and an exchange matrix controlling the mutation. Relations of cluster algebra type can be observed in many areas of mathematics (Plücker and Ptolemy relations, Stokes curves and wall-crossing phenomena, Feynman integrals, Somos sequences and Hirota equations to name just a few examples). The cluster variables enjoy a remarkable combinatorial pattern; in particular, they exhibit the Laurent phenomenon: they are expressed as Laurent polynomials rather than more general rational functions in terms of the cluster variables in any seed. These characteristic features are often referred to as the cluster algebra structure. In the last decade, it became apparent that cluster structures are ubiquitous in mathematical physics. Examples include supersymmetric gauge theories, Poisson geometry, integrable systems, statistical mechanics, fusion products in infinite dimensional algebras, dilogarithm

  18. A characterisation of algebraic exactness

    OpenAIRE

    Garner, Richard

    2011-01-01

    An algebraically exact category in one that admits all of the limits and colimits which every variety of algebras possesses and every forgetful functor between varieties preserves, and which verifies the same interactions between these limits and colimits as hold in any variety. Such categories were studied by Ad\\'amek, Lawvere and Rosick\\'y: they characterised them as the categories with small limits and sifted colimits for which the functor taking sifted colimits is continuous. They conject...

  19. Distribution theory of algebraic numbers

    CERN Document Server

    Yang, Chung-Chun

    2008-01-01

    The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.

  20. Nineteen papers on algebraic semigroups

    CERN Document Server

    Aizenshtat, A Ya; Podran, N E; Ponizovskii, IS; Shain, BM

    1988-01-01

    This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.

  1. Algebras with actions and automata

    Directory of Open Access Journals (Sweden)

    W. Kühnel

    1982-01-01

    Full Text Available In the present paper we want to give a common structure theory of left action, group operations, R-modules and automata of different types defined over various kinds of carrier objects: sets, graphs, presheaves, sheaves, topological spaces (in particular: compactly generated Hausdorff spaces. The first section gives an axiomatic approach to algebraic structures relative to a base category B, slightly more powerful than that of monadic (tripleable functors. In section 2 we generalize Lawveres functorial semantics to many-sorted algebras over cartesian closed categories. In section 3 we treat the structures mentioned in the beginning as many-sorted algebras with fixed “scalar” or “input” object and show that they still have an algebraic (or monadic forgetful functor (theorem 3.3 and hence the general theory of algebraic structures applies. These structures were usually treated as one-sorted in the Lawvere-setting, the action being expressed by a family of unary operations indexed over the scalars. But this approach cannot, as the one developed here, describe continuity of the action (more general: the action to be a B-morphism, which is essential for the structures mentioned above, e.g. modules for a sheaf of rings or topological automata. Finally we discuss consequences of theorem 3.3 for the structure theory of various types of automata. The particular case of algebras with fixed “natural numbers object” has been studied by the authors in [23].

  2. Algebraic Systems and Pushdown Automata

    Science.gov (United States)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  3. Algebras in genetics

    CERN Document Server

    Wörz-Busekros, Angelika

    1980-01-01

    The purpose of these notes is to give a rather complete presentation of the mathematical theory of algebras in genetics and to discuss in detail many applications to concrete genetic situations. Historically, the subject has its origin in several papers of Etherington in 1939- 1941. Fundamental contributions have been given by Schafer, Gonshor, Holgate, Reiers¢l, Heuch, and Abraham. At the moment there exist about forty papers in this field, one survey article by Monique Bertrand from 1966 based on four papers of Etherington, a paper by Schafer and Gonshor's first paper. Furthermore Ballonoff in the third section of his book "Genetics and Social Structure" has included four papers by Etherington and Reiers¢l's paper. Apparently a complete review, in par­ ticular one comprising more recent results was lacking, and it was difficult for students to enter this field of research. I started to write these notes in spring 1978. A first german version was finished at the end of that year. Further revision and tran...

  4. Esercizi scelti di algebra

    CERN Document Server

    Chirivì, Rocco; Dvornicich, Roberto

    2017-01-01

    Questo libro – primo di due volumi -  presenta oltre 250 esercizi scelti di algebra ricavati dai compiti d'esame dei corsi di Aritmetica tenuti dagli autori all'Università di Pisa. Ogni esercizio viene presentato con una o più soluzioni accuratamente redatte con linguaggio e notazioni uniformi. Caratteristica distintiva del libro è che gli esercizi proposti sono tutti diversi uno dall'altro e le soluzioni richiedono sempre una piccola idea originale; ciò rende il libro unico nel genere. Gli argomenti di questo primo volume sono: principio d'induzione, combinatoria, congruenze, gruppi abeliani, anelli commutativi, polinomi, estensioni di campi, campi finiti. Il libro contiene inoltre una dettagliata sezione di richiami teorici e può essere usato come libro di riferimento per lo studio. Una serie di esercizi preliminari introduce le tecniche principali da usare per confrontarsi con i testi d'esame proposti. Il volume è rivolto a tutti gli studenti del primo anno dei corsi di laur ea in Matematica e Inf...

  5. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    OpenAIRE

    Bugeaud, Yann; Evertse, Jan-Hendrik

    2007-01-01

    We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

  6. A Boolean Consistent Fuzzy Inference System for Diagnosing Diseases and Its Application for Determining Peritonitis Likelihood

    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.

  7. Toxicological Tipping Points: Learning Boolean Networks from High-Content Imaging Data. (BOSC meeting)

    Science.gov (United States)

    The objective of this work is to elucidate biological networks underlying cellular tipping points using time-course data. We discretized the high-content imaging (HCI) data and inferred Boolean networks (BNs) that could accurately predict dynamic cellular trajectories. We found t...

  8. Yes/No/Maybe: A Boolean attempt at feedback | Louw | Journal for ...

    African Journals Online (AJOL)

    This paper describes an experiment in which Boolean feedback (a kind of checklist) was used to provide feedback on the paragraph structures of first year students in an Academic Literacy course. We begin by introducing the major problems with feedback on L2 writing and establishing why a focus on paragraph structures ...

  9. The Concept of the "Imploded Boolean Search": A Case Study with Undergraduate Chemistry Students

    Science.gov (United States)

    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…

  10. 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.

  11. An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks

    Science.gov (United States)

    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

  12. Analysis and control of Boolean networks a semi-tensor product approach

    CERN Document Server

    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.

  13. Comparison of Detection and Classification Algorithms Using Boolean and Fuzzy Techniques

    Directory of Open Access Journals (Sweden)

    Rahul Dixit

    2012-01-01

    Full Text Available Modern military ranging, tracking, and classification systems are capable of generating large quantities of data. Conventional “brute-force” computational techniques, even with Moore’s law for processors, present a prohibitive computational challenge, and often, the system either fails to “lock onto” a target of interest within the available duty cycle, or the data stream is simply discarded because the system runs out of processing power or time. In searching for high-fidelity convergence, researchers have experimented with various reduction techniques, often using logic diagrams to make inferences from related signal data. Conventional Boolean and fuzzy logic systems generate a very large number of rules, which often are difficult to handle due to limitations in the processors. Published research has shown that reasonable approximations of the target are preferred over incomplete computations. This paper gives a figure of merit for comparing various logic analysis methods and presents results for a hypothetical target classification scenario. Novel multiquantization Boolean approaches also reduce the complexity of these multivariate analyses, making it possible to better use the available data to approximate target classification. This paper shows how such preprocessing can reasonably preserve result confidence and compares the results between Boolean, multi-quantization Boolean, and fuzzy techniques.

  14. Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras

    Directory of Open Access Journals (Sweden)

    Ilwoo Cho

    2016-01-01

    Full Text Available In this paper, by establishing free-probabilistic models on the Hecke algebras \\(\\mathcal{H}\\left(GL_{2}(\\mathbb{Q}_{p}\\right\\ induced by \\(p\\-adic number fields \\(\\mathbb{Q}_{p}\\, we construct free probability spaces for all primes \\(p\\. Hilbert-space representations are induced by such free-probabilistic structures. We study \\(C^{*}\\-algebras induced by certain partial isometries realized under the representations.

  15. Homological methods, representation theory, and cluster algebras

    CERN Document Server

    Trepode, Sonia

    2018-01-01

    This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, wh...

  16. Extended Kac-Moody algebras and applications

    International Nuclear Information System (INIS)

    Ragoucy, E.; Sorba, P.

    1991-04-01

    The notion of a Kac-Moody algebra defined on the S 1 circle is extended to super Kac-Moody algebras defined on MxG N , M being a smooth closed compact manifold of dimension greater than one, and G N the Grassman algebra with N generators. All the central extensions of these algebras are computed. Then, for each such algebra the derivation algebra constructed from the MxG N diffeomorphism is determined. The twists of such super Kac-Moody algebras as well as the generalization to non-compact surfaces are partially studied. Finally, the general construction is applied to the study of conformal and superconformal algebras, as well as area-preserving diffeomorphisms algebra and its supersymmetric extension. (author) 65 refs

  17. Infinite dimension algebra and conformal symmetry

    International Nuclear Information System (INIS)

    Ragoucy-Aubezon, E.

    1991-04-01

    A generalisation of Kac-Moody algebras (current algebras defined on a circle) to algebras defined on a compact supermanifold of any dimension and with any number of supersymmetries is presented. For such a purpose, we compute all the central extensions of loop algebras defined on this supermanifold, i.e. all the cohomology classes of these loop algebras. Then, we try to extend the relation (i.e. semi-direct sum) that exists between the two dimensional conformal algebras (called Virasoro algebra) and the usual Kac-Moody algebras, by considering the derivation algebra of our extended Kac-Moody algebras. The case of superconformal algebras (used in superstrings theories) is treated, as well as the cases of area-preserving diffeomorphisms (used in membranes theories), and Krichever-Novikov algebras (used for interacting strings). Finally, we present some generalizations of the Sugawara construction to the cases of extended Kac-Moody algebras, and Kac-Moody of superalgebras. These constructions allow us to get new realizations of the Virasoro, and Ramond, Neveu-Schwarz algebras

  18. Finite-dimensional division algebras over fields

    CERN Document Server

    Jacobson, Nathan

    2009-01-01

    Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called 'multiplication algebras of Riemann matrices'. The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of parti

  19. Principles of linear algebra with Mathematica

    CERN Document Server

    Shiskowski, Kenneth M

    2013-01-01

    A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings,

  20. Double-partition Quantum Cluster Algebras

    DEFF Research Database (Denmark)

    Jakobsen, Hans Plesner; Zhang, Hechun

    2012-01-01

    A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double parti- tions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping...... together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of one broken line to another. Compatible pairs can be written down. The algebras are equal to their upper cluster algebras. The variables of the quantum seeds are given by elements of the dual canonical basis....

  1. Discrete event systems in dioid algebra and conventional algebra

    CERN Document Server

    Declerck, Philippe

    2013-01-01

    This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i

  2. Dynamical systems of algebraic origin

    CERN Document Server

    Schmidt, Klaus

    1995-01-01

    Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting...

  3. Algebraic geometry and effective lagrangians

    International Nuclear Information System (INIS)

    Martinec, E.J.; Chicago Univ., IL

    1989-01-01

    N=2 supersymmetric Landau-Ginsburg fixed points describe nonlinear models whose target spaces are algebraic varieties in certain generalized projective spaces; the defining equation is precisely the zero set of the superpotential, considered as a condition in the projective space. The ADE classification of modular invariants arises as the classification of projective descriptions of P 1 ; in general, the hierarchy of fixed points is conjectured to be isomorphic to the classification of quasihomogeneous singularities. The condition of vanishing first Chern class is an integrality condition on the Virasoro central charge; the central charge is determined by the superpotential. The operator algebra is given by the algebra of Wick contractions of perturbations of the superpotential. (orig.)

  4. Logarithmic exotic conformal Galilean algebras

    Energy Technology Data Exchange (ETDEWEB)

    Henkel, Malte, E-mail: Malte.henkel@univ-lorraine.fr [Groupe de Physique Statistique, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex (France); Hosseiny, Ali, E-mail: al_hosseiny@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G.C. Evin, Tehran 19839 (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Rouhani, Shahin, E-mail: rouhani@ipm.ir [Department of Physics, Sharif University of Technology, P.O. Box 11165-9161, Tehran (Iran, Islamic Republic of); School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of)

    2014-02-15

    Logarithmic representations of the conformal Galilean algebra (CGA) and the Exotic Conformal Galilean algebra (ECGA) are constructed. This can be achieved by non-decomposable representations of the scaling dimensions or the rapidity indices, specific to conformal Galilean algebras. Logarithmic representations of the non-exotic CGA lead to the expected constraints on scaling dimensions and rapidities and also on the logarithmic contributions in the co-variant two-point functions. On the other hand, the ECGA admits several distinct situations which are distinguished by different sets of constraints and distinct scaling forms of the two-point functions. Two distinct realisations for the spatial rotations are identified as well. This is the first concrete example of a reducible, but non-decomposable representation, without logarithmic terms. Such cases had been anticipated before.

  5. Visualizing automorphisms of graph algebras

    DEFF Research Database (Denmark)

    Avery, James Emil; Johansen, Rune; Szymanski, Wojciech

    2018-01-01

    Graph C*-algebras have been celebrated as C*-algebras that can be seen, because many important properties may be determined by looking at the underlying graph. This paper introduces the permutation graph for a permutative endomorphism of a graph C*-algebra as a labeled directed multigraph...... that gives a visual representation of the endomorphism and facilitates computations. Combinatorial criteria have previously been developed for deciding when such an endomorphism is an automorphism, but here the question is reformulated in terms of the permutation graph and new proofs are given. Furthermore......, it is shown how to use permutation graphs to efficiently generate exhaustive collections of permutative automorphisms. Permutation graphs provide a natural link to the textile systems representing induced endomorphisms on the edge shift of the given graph, and this allows the powerful tools of the theory...

  6. Topics in quaternion linear algebra

    CERN Document Server

    Rodman, Leiba

    2014-01-01

    Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses...

  7. Zorn algebra in general relativity

    International Nuclear Information System (INIS)

    Oliveira, C.G.; Maia, M.D.

    The covariant differential properties of the split Cayley subalgebra of local real quaternion tetrads is considered. Referred to this local quaternion tetrad several geometrical objects are given in terms of Zorn-Weyl matrices. Associated to a pair of real null vectors we define two-component spinor fields over the curved space and the associated Zorn-Weyl matrices which satisfy the Dirac equation written in terms of the Zorn algebra. The formalism is generalized by considering a field of complex tetrads defining a Hermitian second rank tensor. The real part of this tensor describes the gravitational potentials and the imaginary part the electromagnetic potentials in the Lorentz gauge. The motion of a charged spin zero test body is considered. The Zorn-Weyl algebra associated to this generalized formalism has elements belonging to the full octonion algebra [pt

  8. Evolution algebras generated by Gibbs measures

    International Nuclear Information System (INIS)

    Rozikov, Utkir A.; Tian, Jianjun Paul

    2009-03-01

    In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure μ. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces have a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures are assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras. (author)

  9. ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS

    OpenAIRE

    KANEKO, HAJIME

    2010-01-01

    Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little is known about this problem. We improve the lower bounds for the number of digit changes in the binary expansions of algebraic irrational numbers.

  10. Current algebra, baryons and quark confinement

    International Nuclear Information System (INIS)

    Witten, E.

    1983-01-01

    It is shown that ordinary baryons can be understood as solitons in current algebra effective lagrangiangs. The formation of color flux tubes can also be seen in current algebra, under certain conditions. (orig.)

  11. Hopf algebra structures in particle physics

    International Nuclear Information System (INIS)

    Weinzierl, Stefan

    2004-01-01

    In the recent years, Hopf algebras have been introduced to describe certain combinatorial properties of quantum field theories. I give a basic introduction to these algebras and review some occurrences in particle physics. (orig.)

  12. Generalized Galilean algebras and Newtonian gravity

    Science.gov (United States)

    González, N.; Rubio, G.; Salgado, P.; Salgado, S.

    2016-04-01

    The non-relativistic versions of the generalized Poincaré algebras and generalized AdS-Lorentz algebras are obtained. These non-relativistic algebras are called, generalized Galilean algebras of type I and type II and denoted by GBn and GLn respectively. Using a generalized Inönü-Wigner contraction procedure we find that the generalized Galilean algebras of type I can be obtained from the generalized Galilean algebras type II. The S-expansion procedure allows us to find the GB5 algebra from the Newton Hooke algebra with central extension. The procedure developed in Ref. [1] allows us to show that the nonrelativistic limit of the five dimensional Einstein-Chern-Simons gravity is given by a modified version of the Poisson equation. The modification could be compatible with the effects of Dark Matter, which leads us to think that Dark Matter can be interpreted as a non-relativistic limit of Dark Energy.

  13. Comments on N=4 superconformal algebras

    International Nuclear Information System (INIS)

    Rasmussen, J.

    2001-01-01

    We present a new and asymmetric N=4 superconformal algebra for arbitrary central charge, thus completing our recent work on its classical analogue with vanishing central charge. Besides the Virasoro generator and 4 supercurrents, the algebra consists of an internal SU(2)xU(1) Kac-Moody algebra in addition to two spin 1/2 fermions and a bosonic scalar. The algebra is shown to be invariant under a linear twist of the generators, except for a unique value of the continuous twist parameter. At this value, the invariance is broken and the algebra collapses to the small N=4 superconformal algebra. The asymmetric N=4 superconformal algebra may be seen as induced by an affine SL(2 vertical bar 2) current superalgebra. Replacing SL(2 vertical bar 2) with the coset SL(2 vertical bar 2)/U(1), results directly in the small N=4 superconformal algebra

  14. Generalized NLS hierarchies from rational W algebras

    International Nuclear Information System (INIS)

    Toppan, F.

    1993-11-01

    Finite rational W algebras are very natural structures appearing in coset constructions when a Kac-Moody subalgebra is factored out. The problem of relating these algebras to integrable hierarchies of equations is studied by showing how to associate to a rational W algebra its corresponding hierarchy. Two examples are worked out, the sl(2)/U(1) coset, leading to the Non-Linear Schroedinger hierarchy, and the U(1) coset of the Polyakov-Bershadsky W algebra, leading to a 3-field representation of the KP hierarchy already encountered in the literature. In such examples a rational algebra appears as algebra of constraints when reducing a KP hierarchy to a finite field representation. This fact arises the natural question whether rational algebras are always associated to such reductions and whether a classification of rational algebras can lead to a classification of the integrable hierarchies. (author). 19 refs

  15. Applied matrix algebra in the statistical sciences

    CERN Document Server

    Basilevsky, Alexander

    2005-01-01

    This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.

  16. Quantum Groupoids Acting on Semiprime Algebras

    Directory of Open Access Journals (Sweden)

    Inês Borges

    2011-01-01

    Full Text Available Following Linchenko and Montgomery's arguments we show that the smash product of an involutive weak Hopf algebra and a semiprime module algebra, satisfying a polynomial identity, is semiprime.

  17. Introduction to algebraic quantum field theory

    International Nuclear Information System (INIS)

    Horuzhy, S.S.

    1990-01-01

    This volume presents a systematic introduction to the algebraic approach to quantum field theory. The structure of the contents corresponds to the way the subject has advanced. It is shown how the algebraic approach has developed from the purely axiomatic theory of observables via superselection rules into the dynamical formalism of fields and observables. Chapter one discusses axioms and their consequences -many of which are now classical theorems- and deals, in general, with the axiomatic theory of local observable algebras. The absence of field concepts makes this theory incomplete and, in chapter two, superselection rules are shown to be the key to the reconstruction of fields from observables. Chapter three deals with the algebras of Wightman fields, first unbounded operator algebras, then Von Neumann field algebras (with a special section on wedge region algebras) and finally local algebras of free and generalised free fields. (author). 447 refs.; 4 figs

  18. Invariants of generalized Lie algebras

    International Nuclear Information System (INIS)

    Agrawala, V.K.

    1981-01-01

    Invariants and invariant multilinear forms are defined for generalized Lie algebras with arbitrary grading and commutation factor. Explicit constructions of invariants and vector operators are given by contracting invariant forms with basic elements of the generalized Lie algebra. The use of the matrix of a linear map between graded vector spaces is emphasized. With the help of this matrix, the concept of graded trace of a linear operator is introduced, which is a rich source of multilinear forms of degree zero. To illustrate the use of invariants, a characteristic identity similar to that of Green is derived and a few Racah coefficients are evaluated in terms of invariants

  19. Introduction to computational linear algebra

    CERN Document Server

    Nassif, Nabil; Erhel, Jocelyne

    2015-01-01

    Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s

  20. Computational triadic algebras of signs

    Energy Technology Data Exchange (ETDEWEB)

    Zadrozny, W. [T.J. Watson Research Center, Yorktown Heights, NY (United States)

    1996-12-31

    We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.

  1. Entropic Forms and Related Algebras

    Directory of Open Access Journals (Sweden)

    Antonio Maria Scarfone

    2013-02-01

    Full Text Available Starting from a very general trace-form entropy, we introduce a pair of algebraic structures endowed by a generalized sum and a generalized product. These algebras form, respectively, two Abelian fields in the realm of the complex numbers isomorphic each other. We specify our results to several entropic forms related to distributions recurrently observed in social, economical, biological and physical systems including the stretched exponential, the power-law and the interpolating Bosons-Fermions distributions. Some potential applications in the study of complex systems are advanced.

  2. Algebraic geometry and theta functions

    CERN Document Server

    Coble, Arthur B

    1929-01-01

    This book is the result of extending and deepening all questions from algebraic geometry that are connected to the central problem of this book: the determination of the tritangent planes of a space curve of order six and genus four, which the author treated in his Colloquium Lecture in 1928 at Amherst. The first two chapters recall fundamental ideas of algebraic geometry and theta functions in such fashion as will be most helpful in later applications. In order to clearly present the state of the central problem, the author first presents the better-known cases of genus two (Chapter III) and

  3. The planar algebra associated to a Kac algebra

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    and not just the plane). ..... We will need the following facts from [L], which we state as a proposition for conve- nience of reference. PROPOSITION 3.3. Suppose P (L; R) is an exchange relation planar algebra. Then,. (i) dimPn(L; R) < ∞ ∀n;.

  4. AT-algebras and extensions of AT-algebras

    Indian Academy of Sciences (India)

    Home; Journals; Proceedings – Mathematical Sciences; Volume 120; Issue 2. A T -Algebras and Extensions of A T ... School of Science, Nanjing University of Science and Technology, Nanjing 210014, People's Republic of China; Department of Mathematics, Tongji University, Shanghai 200092, People's Republic of China ...

  5. Parts of the Whole: An Algebra Lesson

    Directory of Open Access Journals (Sweden)

    Dorothy Wallace

    2011-07-01

    Full Text Available This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.

  6. Discrimination in a General Algebraic Setting

    Directory of Open Access Journals (Sweden)

    Benjamin Fine

    2015-01-01

    Full Text Available Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.

  7. Discrimination in a General Algebraic Setting.

    Science.gov (United States)

    Fine, Benjamin; Gaglione, Anthony; Lipschutz, Seymour; Spellman, Dennis

    2015-01-01

    Discriminating groups were introduced by G. Baumslag, A. Myasnikov, and V. Remeslennikov as an outgrowth of their theory of algebraic geometry over groups. Algebraic geometry over groups became the main method of attack on the solution of the celebrated Tarski conjectures. In this paper we explore the notion of discrimination in a general universal algebra context. As an application we provide a different proof of a theorem of Malcev on axiomatic classes of Ω-algebras.

  8. Post-Lie algebras and factorization theorems

    Science.gov (United States)

    Ebrahimi-Fard, Kurusch; Mencattini, Igor; Munthe-Kaas, Hans

    2017-09-01

    In this note we further explore the properties of universal enveloping algebras associated to a post-Lie algebra. Emphasizing the role of the Magnus expansion, we analyze the properties of group like-elements belonging to (suitable completions of) those Hopf algebras. Of particular interest is the case of post-Lie algebras defined in terms of solutions of modified classical Yang-Baxter equations. In this setting we will study factorization properties of the aforementioned group-like elements.

  9. Quantized Matrix Algebras and Quantum Seeds

    DEFF Research Database (Denmark)

    Jakobsen, Hans Plesner; Pagani, Chiara

    2015-01-01

    We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees.......We determine explicitly quantum seeds for classes of quantized matrix algebras. Furthermore, we obtain results on centres and block diagonal forms of these algebras. In the case where is an arbitrary root of unity, this further determines the degrees....

  10. Simple Lie algebras and Dynkin diagrams

    International Nuclear Information System (INIS)

    Buccella, F.

    1983-01-01

    The following theorem is studied: in a simple Lie algebra of rank p there are p positive roots such that all the other n-3p/2 positive roots are linear combinations of them with integer non negative coefficients. Dykin diagrams are built by representing the simple roots with circles and drawing a junction between the roots. Five exceptional algebras are studied, focusing on triple junction algebra, angular momentum algebra, weights of the representation, antisymmetric tensors, and subalgebras

  11. The large N=4 superconformal W∞ algebra

    International Nuclear Information System (INIS)

    Beccaria, Matteo; Candu, Constantin; Gaberdiel, Matthias R.

    2014-01-01

    The most general large N=4 superconformal W ∞ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the W ∞ algebra is uniquely determined by the levels of the two su(2) algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.

  12. Algebra success in 20 minutes a day

    CERN Document Server

    LearningExpress, LLC

    2014-01-01

    Stripped of unnecessary math jargon but bursting with algebra essentials, this handy guide covers vital algebra skills that apply to real-world scenarios. Whether you're new to algebra or just looking for a refresher, Algebra Success in 20 Minutes a Day offers a lesson plan that provides quick and thorough instruction in practical, critical skills. All lessons can be completed in just 20 minutes a day, for a manageable and non-intimidating learning experience.

  13. Chomology of Heisenberg Hom-Lie algebras

    OpenAIRE

    Nejib, Saadaoui

    2017-01-01

    In this paper, we define the Heisenberg Hom-Lie algebra. We determine the minimal dimension of faithful representation for Heisenberg Hom-Lie algebra.We study the adjoint representation, the trivial representation and the faithful representation of Heisenberg Hom-Lie algebra.

  14. Quantum groups and double quiver algebras

    International Nuclear Information System (INIS)

    Huang Hualin; Yang Shilin

    2004-07-01

    For a finite dimensional sernisimple Lie algebra g and a root q of unity in a field k we associate to these data a double quiver Q-bar. It is shown that a restricted version of the quantized enveloping algebras U q (g) is a quotient of the double quiver algebra kQ-bar. (author)

  15. Algebra in Dutch education, 1600-2000

    NARCIS (Netherlands)

    Krüger, Jenneke

    2015-01-01

    Algebra became part of mathematics education in the Netherlands in course of the seventeenth century. At first in the form of cossic algebra, but by the end of the century, the influence of the notation of Descartes was noticeable. In the eighteenth century, algebra was part of the basic curriculum

  16. Feature-Oriented Programming with Object Algebras

    NARCIS (Netherlands)

    B.C.d.S. Oliveira (Bruno); T. van der Storm (Tijs); A. Loh; W.R. Cook

    2013-01-01

    htmlabstractObject algebras are a new programming technique that enables a simple solution to basic extensibility and modularity issues in programming languages. While object algebras excel at defining modular features, the composition mechanisms for object algebras (and features) are still

  17. Classifying bicrossed products of two Taft algebras

    OpenAIRE

    Agore, A. L.

    2016-01-01

    We classify all Hopf algebras which factorize through two Taft algebras $\\mathbb{T}_{n^{2}}(\\bar{q})$ and respectively $T_{m^{2}}(q)$. To start with, all possible matched pairs between the two Taft algebras are described: if $\\bar{q} \

  18. Fractional superLie algebras and groups

    Energy Technology Data Exchange (ETDEWEB)

    Ahmedov, H. [Feza Gursey Institute, Cengelkoy, Istanbul (Turkey)]. E-mail: hagi@gursey.gov.tr; Yildiz, A. [ Feza Gursey Institute, Cengelkoy, Istanbul (Turkey); Ucan, Y. [Yildiz Technical University, Department of Mathematics, Besiktas, Istanbul (Turkey)

    2001-08-24

    The nth root of a Lie algebra and its dual (that is the fractional supergroup) based on the permutation group S{sub n} invariant forms is formulated in the Hopf algebra formalism. Detailed discussion of S{sub 3}-graded sl(2) algebras is performed. (author)

  19. (L,M-Fuzzy σ-Algebras

    Directory of Open Access Journals (Sweden)

    Fu-Gui Shi

    2010-01-01

    Full Text Available The notion of (L,M-fuzzy σ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzy σ-algebras. In our definition of (L,M-fuzzy σ-algebras, each L-fuzzy subset can be regarded as an L-measurable set to some degree.

  20. Teaching Strategies to Improve Algebra Learning

    Science.gov (United States)

    Zbiek, Rose Mary; Larson, Matthew R.

    2015-01-01

    Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

  1. Geometry of Spin: Clifford Algebraic Approach

    Indian Academy of Sciences (India)

    of Pauli matrices follow from the underlying algebra. Clif- ford algebraic approach provides a geometrical and hence intuitive way to understand quantum theory of spin, and is a natural formalism to study spin. Clifford algebraic formal- ism has lot of applications in every field where spin plays an important role. Introduction.

  2. New family of Maxwell like algebras

    Energy Technology Data Exchange (ETDEWEB)

    Concha, P.K., E-mail: patillusion@gmail.com [Departamento de Ciencias, Facultad de Artes y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia (Chile); Durka, R., E-mail: remigiuszdurka@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Merino, N., E-mail: nemerino@gmail.com [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso (Chile); Rodríguez, E.K., E-mail: everodriguezd@gmail.com [Departamento de Ciencias, Facultad de Artes y Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Casilla 567, Valdivia (Chile)

    2016-08-10

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  3. Coherent state quantization of paragrassmann algebras

    Energy Technology Data Exchange (ETDEWEB)

    El Baz, M; Hassouni, Y [Laboratoire de Physique Theorique, LPT-URAC 13, Faculte des Sciences, Universite Mohamed V, Av.Ibn Battouta, BP 1014 Agdal Rabat (Morocco); Fresneda, R [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo (Brazil); Gazeau, J P, E-mail: elbaz@fsr.ac.m, E-mail: fresneda@gmail.co, E-mail: gazeau@apc.univ-paris7.f, E-mail: y-hassou@fsr.ac.m [Laboratoire APC, Universite Paris Diderot (Paris 7), 10, rue A Domon et L Duquet 75205 Paris Cedex 13 (France)

    2010-09-24

    By using a coherent state quantization of paragrassmann variables, operators are constructed in finite Hilbert spaces. We thus obtain in a straightforward way a matrix representation of the paragrassmann algebra. This algebra of finite matrices realizes a deformed Weyl-Heisenberg algebra. The study of mean values in coherent states of some of these operators leads to interesting conclusions.

  4. A Balancing Act: Making Sense of Algebra

    Science.gov (United States)

    Gavin, M. Katherine; Sheffield, Linda Jensen

    2015-01-01

    For most students, algebra seems like a totally different subject than the number topics they studied in elementary school. In reality, the procedures followed in arithmetic are actually based on the properties and laws of algebra. Algebra should be a logical next step for students in extending the proficiencies they developed with number topics…

  5. New family of Maxwell like algebras

    International Nuclear Information System (INIS)

    Concha, P.K.; Durka, R.; Merino, N.; Rodríguez, E.K.

    2016-01-01

    We introduce an alternative way of closing Maxwell like algebras. We show, through a suitable change of basis, that resulting algebras are given by the direct sums of the AdS and the Maxwell algebras already known in the literature. Casting the result into the S-expansion method framework ensures the straightaway construction of the gravity theories based on a found enlargement.

  6. Banana Algebra: Compositional Syntactic Language Extension

    DEFF Research Database (Denmark)

    Andersen, Jacob; Brabrand, Claus; Christiansen, David Raymond

    2013-01-01

    algebra as presented in the paper is implemented as the Banana Algebra Tool which may be used to syntactically extend languages in an incremental and modular fashion via algebraic composition of previously defined languages and transformations. We demonstrate and evaluate the tool via several kinds...

  7. Build an Early Foundation for Algebra Success

    Science.gov (United States)

    Knuth, Eric; Stephens, Ana; Blanton, Maria; Gardiner, Angela

    2016-01-01

    Research tells us that success in algebra is a factor in many other important student outcomes. Emerging research also suggests that students who are started on an algebra curriculum in the earlier grades may have greater success in the subject in secondary school. What's needed is a consistent, algebra-infused mathematics curriculum all…

  8. Teacher Actions to Facilitate Early Algebraic Reasoning

    Science.gov (United States)

    Hunter, Jodie

    2015-01-01

    In recent years there has been an increased emphasis on integrating the teaching of arithmetic and algebra in primary school classrooms. This requires teachers to develop links between arithmetic and algebra and use pedagogical actions that facilitate algebraic reasoning. Drawing on findings from a classroom-based study, this paper provides an…

  9. On Elementary and Algebraic Cellular Automata

    Science.gov (United States)

    Gulak, Yuriy

    In this paper we study elementary cellular automata from an algebraic viewpoint. The goal is to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures. We introduce algebraic cellular automata as a natural generalization of elementary ones and discuss their applications as generic models of complex systems.

  10. Implementing the Standards: Teaching Informal Algebra.

    Science.gov (United States)

    Schultz, James E.

    1991-01-01

    Presents suggestions for developing algebraic concepts beginning in the early grades to develop a gradual building from informal to formal algebraic concepts that progresses over the K-12 curriculum. Includes suggestions for representing relationships, solving equations, employing meaningful applications of algebra, and using of technology. (MDH)

  11. Role of associativity in Ramsey algebras

    Indian Academy of Sciences (India)

    Andrew Rajah

    2017-11-02

    Nov 2, 2017 ... to understand the role associativity plays in a binary system being a Ramsey algebra. Specifically, we show that the nonassociative Moufang loop of octonions is not a Ramsey algebra. Keywords. Binary systems; Ramsey algebras; octonions; semigroups; associativity; nonassociative Moufang loops ...

  12. Yang-Mills and some related algebras

    OpenAIRE

    Connes, Alain; Dubois-Violette, Michel

    2004-01-01

    15 pages. Contribution to the Proceedings of Rigorous Quantum Field Theory in the honour of Jacques Bros.; International audience; After a short introduction on the theory of homogeneous algebras we describe the application of this theory to the analysis of the cubic Yang-Mills algebra, the quadratic self-duality algebras, their \\"super\\" versions as well as to some generalization.

  13. Computations in finite-dimensional Lie algebras

    NARCIS (Netherlands)

    Cohen, A.M.; Graaf, W.A. de; Rónyai, L.

    1997-01-01

    This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP. A first sketch of the packagecan be found in Cohen and de Graaf[1]. Since then, in a collaborative

  14. Algebraic treatment of three-body problems

    International Nuclear Information System (INIS)

    Bijker, R.; Leviatan, A.

    1998-01-01

    We discuss an algebraic treatment of three-body systems in terms of a U(7) spectrum-generating algebra. In particular, we develop the formalism for nonilnear configurations and present an algebraic description of vibrational and rotational excitations of, symmetric (X 3 ) and asymmetric tops (XY 2 and XYZ). The relevant point-group symmetry is incorporated exactly. (author)

  15. Algebraic scattering theory and heavy ion scattering

    International Nuclear Information System (INIS)

    Allen, L.J.; Amos, K.; Berge, L.; Fiedeldey, H.

    1993-01-01

    Algebraic scattering theory is used to analyze elastic scattering cross-sections from heavy ion collisions. Collisions epitomized by strong absorption lead to algebraic potentials that can be described by simple exponential forms. But for collisions that are 'transparent', while asymptotically the algebraic potentials are exponential, their actual form (for low 1-values) is quite complex. 7 refs., 4 figs

  16. A GA-P algorithm to automatically formulate extended Boolean queries for a fuzzy information retrieval system

    OpenAIRE

    Cordón García, Oscar; Moya Anegón, Félix de; Zarco Fernández, Carmen

    2000-01-01

    [ES] Although the fuzzy retrieval model constitutes a powerful extension of the boolean one, being able to deal with the imprecision and subjectivity existing in the Information Retrieval process, users are not usually able to express their query requirements in the form of an extended boolean query including weights. To solve this problem, different tools to assist the user in the query formulation have been proposed. In this paper, the genetic algorithm-programming technique is considered t...

  17. CIRCUIT IMPLEMENTATION OF VHDL-DESCRIPTIONS OF SYSTEMS OF PARTIAL BOOLEAN FUNCTIONS

    Directory of Open Access Journals (Sweden)

    P. N. Bibilo

    2016-01-01

    Full Text Available Method for description of incompletely specified (partial Boolean functions in VHDL is proposed. Examples of synthesized VHDL models of partial Boolean functions are presented; and the results of experiments on circuit implementation of VHDL descriptions of systems of partial functions. The realizability of original partial functions in logical circuits was verified by formal verification. The results of the experiments show that the preliminary minimization in DNF class and in the class of BDD representations for pseudo-random systems of completely specified functions does not improve practically (and in the case of BDD sometimes worsens the results of the subsequent synthesis in the basis of FPGA unlike the significant efficiency of these procedures for the synthesis of benchmark circuits taken from the practice of the design.

  18. Hypercontractive inequality for pseudo-Boolean functions of bounded Fourier width

    DEFF Research Database (Denmark)

    Gutin, Gregory; Yeo, Anders

    2012-01-01

    A function f: -1,1n→R is called pseudo-Boolean. It is well-known that each pseudo-Boolean function f can be written as f(x)=∑ I∈Ff̂(I) χI(x), where F⊆I:I⊆[n], [n]=1,2,...,n, χI(x)= ∏ i∈I xi and f̂(I) are non-zero reals. The degree of f is max|I|:I∈F and the width of f is the minimum integer ρ suc...... for each q>papplications, we prove a stronger inequality: || f||4≤( 2ρ+1)14|| f||2....

  19. In Defence of Geometrical Algebra

    NARCIS (Netherlands)

    Blasjo, V.N.E.

    The geometrical algebra hypothesis was once the received interpretation of Greek mathematics. In recent decades, however, it has become anathema to many. I give a critical review of all arguments against it and offer a consistent rebuttal case against the modern consensus. Consequently, I find that

  20. Algebraic Methods in Plane Geometry

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 10. Algebraic Methods in Plane Geometry - The Use of Conic Sections. Shailesh A Shirali. General Article Volume 13 Issue 10 October 2008 pp 916-928. Fulltext. Click here to view fulltext PDF. Permanent link: