Cryptographic Properties of Monotone Boolean Functions

DTIC Science & Technology

2016-01-01

Algebraic attacks on stream ciphers with linear feedback, in: Advances in Cryptology (Eurocrypt 2003), Lecture Notes in Comput. Sci. 2656, Springer, Berlin...spectrum, algebraic immu- nity MSC 2010: 06E30, 94C10, 94A60, 11T71, 05E99 || Communicated by: Carlo Blundo 1 Introduction Let F 2 be the prime eld of...7]. For the reader’s convenience, we recall some basic notions below. Any f ∈ Bn can be expressed in algebraic normal form (ANF) as f(x 1 , x 2

Intelligent machines in the twenty-first century: foundations of inference and inquiry.

PubMed

Knuth, Kevin H

2003-12-15

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

Intelligent machines in the twenty-first century: foundations of inference and inquiry

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2003-01-01

The last century saw the application of Boolean algebra to the construction of computing machines, which work by applying logical transformations to information contained in their memory. The development of information theory and the generalization of Boolean algebra to Bayesian inference have enabled these computing machines, in the last quarter of the twentieth century, to be endowed with the ability to learn by making inferences from data. This revolution is just beginning as new computational techniques continue to make difficult problems more accessible. Recent advances in our understanding of the foundations of probability theory have revealed implications for areas other than logic. Of relevance to intelligent machines, we recently identified the algebra of questions as the free distributive algebra, which will now allow us to work with questions in a way analogous to that which Boolean algebra enables us to work with logical statements. In this paper, we examine the foundations of inference and inquiry. We begin with a history of inferential reasoning, highlighting key concepts that have led to the automation of inference in modern machine-learning systems. We then discuss the foundations of inference in more detail using a modern viewpoint that relies on the mathematics of partially ordered sets and the scaffolding of lattice theory. This new viewpoint allows us to develop the logic of inquiry and introduce a measure describing the relevance of a proposed question to an unresolved issue. Last, we will demonstrate the automation of inference, and discuss how this new logic of inquiry will enable intelligent machines to ask questions. Automation of both inference and inquiry promises to allow robots to perform science in the far reaches of our solar system and in other star systems by enabling them not only to make inferences from data, but also to decide which question to ask, which experiment to perform, or which measurement to take given what they have learned and what they are designed to understand.

On the inherent competition between valid and spurious inductive inferences in Boolean data

NASA Astrophysics Data System (ADS)

Andrecut, M.

Inductive inference is the process of extracting general rules from specific observations. This problem also arises in the analysis of biological networks, such as genetic regulatory networks, where the interactions are complex and the observations are incomplete. A typical task in these problems is to extract general interaction rules as combinations of Boolean covariates, that explain a measured response variable. The inductive inference process can be considered as an incompletely specified Boolean function synthesis problem. This incompleteness of the problem will also generate spurious inferences, which are a serious threat to valid inductive inference rules. Using random Boolean data as a null model, here we attempt to measure the competition between valid and spurious inductive inference rules from a given data set. We formulate two greedy search algorithms, which synthesize a given Boolean response variable in a sparse disjunct normal form, and respectively a sparse generalized algebraic normal form of the variables from the observation data, and we evaluate numerically their performance.

Electrical Circuits in the Mathematics/Computer Science Classroom.

ERIC Educational Resources Information Center

McMillan, Robert D.

1988-01-01

Shows how, with little or no electrical background, students can apply Boolean algebra concepts to design and build integrated electrical circuits in the classroom that will reinforce important ideas in mathematics. (PK)

Deriving Laws from Ordering Relations

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.

2004-01-01

The effect of Richard T. Cox's contribution to probability theory was to generalize Boolean implication among logical statements to degrees of implication, which are manipulated using rules derived from consistency with Boolean algebra. These rules are known as the sum rule, the product rule and Bayes Theorem, and the measure resulting from this generalization is probability. In this paper, I will describe how Cox s technique can be further generalized to include other algebras and hence other problems in science and mathematics. The result is a methodology that can be used to generalize an algebra to a calculus by relying on consistency with order theory to derive the laws of the calculus. My goals are to clear up the mysteries as to why the same basic structure found in probability theory appears in other contexts, to better understand the foundations of probability theory, and to extend these ideas to other areas by developing new mathematics and new physics. The relevance of this methodology will be demonstrated using examples from probability theory, number theory, geometry, information theory, and quantum mechanics.

Steady state analysis of Boolean molecular network models via model reduction and computational algebra.

PubMed

Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard

2014-06-26

A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem.

Steady state analysis of Boolean molecular network models via model reduction and computational algebra

PubMed Central

2014-01-01

Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem. PMID:24965213

Lattice Theory, Measures and Probability

NASA Astrophysics Data System (ADS)

Knuth, Kevin H.

2007-11-01

In this tutorial, I will discuss the concepts behind generalizing ordering to measuring and apply these ideas to the derivation of probability theory. The fundamental concept is that anything that can be ordered can be measured. Since we are in the business of making statements about the world around us, we focus on ordering logical statements according to implication. This results in a Boolean lattice, which is related to the fact that the corresponding logical operations form a Boolean algebra. The concept of logical implication can be generalized to degrees of implication by generalizing the zeta function of the lattice. The rules of probability theory arise naturally as a set of constraint equations. Through this construction we are able to neatly connect the concepts of order, structure, algebra, and calculus. The meaning of probability is inherited from the meaning of the ordering relation, implication, rather than being imposed in an ad hoc manner at the start.

Phased-mission system analysis using Boolean algebraic methods

NASA Technical Reports Server (NTRS)

Somani, Arun K.; Trivedi, Kishor S.

1993-01-01

Most reliability analysis techniques and tools assume that a system is used for a mission consisting of a single phase. However, multiple phases are natural in many missions. The failure rates of components, system configuration, and success criteria may vary from phase to phase. In addition, the duration of a phase may be deterministic or random. Recently, several researchers have addressed the problem of reliability analysis of such systems using a variety of methods. A new technique for phased-mission system reliability analysis based on Boolean algebraic methods is described. Our technique is computationally efficient and is applicable to a large class of systems for which the failure criterion in each phase can be expressed as a fault tree (or an equivalent representation). Our technique avoids state space explosion that commonly plague Markov chain-based analysis. A phase algebra to account for the effects of variable configurations and success criteria from phase to phase was developed. Our technique yields exact (as opposed to approximate) results. The use of our technique was demonstrated by means of an example and present numerical results to show the effects of mission phases on the system reliability.

Topics for Mathematics Clubs.

ERIC Educational Resources Information Center

Dalton, LeRoy C., Ed.; Snyder, Henry D., Ed.

The ten chapters in this booklet cover topics not ordinarily discussed in the classroom: Fibonacci sequences, projective geometry, groups, infinity and transfinite numbers, Pascal's Triangle, topology, experiments with natural numbers, non-Euclidean geometries, Boolean algebras, and the imaginary and the infinite in geometry. Each chapter is…

Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models

NASA Astrophysics Data System (ADS)

Suga, Tetsuya; Iijima, Junichi

2018-03-01

Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.

Boolean Approaches in Digital Diagnosis

DTIC Science & Technology

1989-12-04

Automation Conference, pages 64-70, 1983. 16. Barry W. Johnson. Design and A nalysis of Fault-Tolerant Digital Systems. Addison- Wesley Publishing...Mitchell. On a new algebra of logic. In C.S. Peirce, edhitor, Studies in Logic. Little, Brown. Boston. 1883. 2:3. Roger S. Pressman . Softwrare Engineering

Observability of Boolean multiplex control networks

NASA Astrophysics Data System (ADS)

Wu, Yuhu; Xu, Jingxue; Sun, Xi-Ming; Wang, Wei

2017-04-01

Boolean multiplex (multilevel) networks (BMNs) are currently receiving considerable attention as theoretical arguments for modeling of biological systems and system level analysis. Studying control-related problems in BMNs may not only provide new views into the intrinsic control in complex biological systems, but also enable us to develop a method for manipulating biological systems using exogenous inputs. In this article, the observability of the Boolean multiplex control networks (BMCNs) are studied. First, the dynamical model and structure of BMCNs with control inputs and outputs are constructed. By using of Semi-Tensor Product (STP) approach, the logical dynamics of BMCNs is converted into an equivalent algebraic representation. Then, the observability of the BMCNs with two different kinds of control inputs is investigated by giving necessary and sufficient conditions. Finally, examples are given to illustrate the efficiency of the obtained theoretical results.

Probabilistic Relational Structures and Their Applications

ERIC Educational Resources Information Center

Domotor, Zoltan

The principal objects of the investigation reported were, first, to study qualitative probability relations on Boolean algebras, and secondly, to describe applications in the theories of probability logic, information, automata, and probabilistic measurement. The main contribution of this work is stated in 10 definitions and 20 theorems. The basic…

Fundamentals of Digital Logic.

ERIC Educational Resources Information Center

Noell, Monica L.

This course is designed to prepare electronics personnel for further training in digital techniques, presenting need to know information that is basic to any maintenance course on digital equipment. It consists of seven study units: (1) binary arithmetic; (2) boolean algebra; (3) logic gates; (4) logic flip-flops; (5) nonlogic circuits; (6)…

Cryptographic Properties of the Hidden Weighted Bit Function

DTIC Science & Technology

2013-12-23

valid OMB control number. 1. REPORT DATE 23 DEC 2013 2. REPORT TYPE 3. DATES COVERED 00-00-2013 to 00-00-2013 4. TITLE AND SUBTITLE...K. Feng, An Infinite Class of Balanced Vectorial Boolean Functions with Optimum Algebraic Immunity and Good Nonlinearity, in: IWCC 2009, In: LNCS

Questions Revisited: A Close Examination of Calculus of Inference and Inquiry

NASA Technical Reports Server (NTRS)

Knuth, Kevin H.; Koga, Dennis (Technical Monitor)

2003-01-01

In this paper I examine more closely the way in which probability theory, the calculus of inference, is derived from the Boolean lattice structure of logical assertions ordered by implication. I demonstrate how the duality between the logical conjunction and disjunction in Boolean algebra is lost when deriving the probability calculus. In addition, I look more closely at the other lattice identities to verify that they are satisfied by the probability calculus. Last, I look towards developing the calculus of inquiry demonstrating that there is a sum and product rule for the relevance measure as well as a Bayes theorem. Current difficulties in deriving the complete inquiry calculus will also be discussed.

Extending Clause Learning of SAT Solvers with Boolean Gröbner Bases

NASA Astrophysics Data System (ADS)

Zengler, Christoph; Küchlin, Wolfgang

We extend clause learning as performed by most modern SAT Solvers by integrating the computation of Boolean Gröbner bases into the conflict learning process. Instead of learning only one clause per conflict, we compute and learn additional binary clauses from a Gröbner basis of the current conflict. We used the Gröbner basis engine of the logic package Redlog contained in the computer algebra system Reduce to extend the SAT solver MiniSAT with Gröbner basis learning. Our approach shows a significant reduction of conflicts and a reduction of restarts and computation time on many hard problems from the SAT 2009 competition.

Crisp Sets and Boolean Algebra: A Research Strategy for Student Affairs

ERIC Educational Resources Information Center

Banning, James; Eversole, Barbara; Most, David; Kuk, Linda

2008-01-01

A review of student affairs journals clearly points out that most, if not all, research strategies within the field fall within traditional approaches based on quantitative methods and, more recently, qualitative methods. The purpose of this article is not to discourage use of these time honored research strategies, but to suggest the inclusion of…

An Investigation of the Mathematical Models of Piaget's Psychological Theory of Cognitive Learning. Final Report.

ERIC Educational Resources Information Center

Kalechofsky, Robert

This research paper proposes several mathematical models which help clarify Piaget's theory of cognition on the concrete and formal operational stages. Some modified lattice models were used for the concrete stage and a combined Boolean Algebra and group theory model was used for the formal stage. The researcher used experiments cited in the…

Discrete interference modeling via boolean algebra.

PubMed

Beckhoff, Gerhard

2011-01-01

Two types of boolean functions are considered, the locus function of n variables, and the interval function of ν = n - 1 variables. A 1-1 mapping is given that takes elements (cells) of the interval function to antidual pairs of elements in the locus function, and vice versa. A set of ν binary codewords representing the intervals are defined and used to generate the codewords of all genomic regions. Next a diallelic three-point system is reviewed in the light of boolean functions, which leads to redefining complete interference by a logic function. Together with the upper bound of noninterference already defined by a boolean function, it confines the region of interference. Extensions of these two functions to any finite number of ν are straightforward, but have been also made in terms of variables taken from the inclusion-exclusion principle (expressing "at least" and "exactly equal to" a decimal integer). Two coefficients of coincidence for systems with more than three loci are defined and discussed, one using the average of several individual coefficients and the other taking as coefficient a real number between zero and one. Finally, by way of a malfunction of the mod-2 addition, it is shown that a four-point system may produce two different functions, one of which exhibiting loss of a class of odd recombinants.

Generalized Flip-Flop Input Equations Based on a Four-Valued Boolean Algebra

NASA Technical Reports Server (NTRS)

Tucker, Jerry H.; Tapia, Moiez A.

1996-01-01

A procedure is developed for obtaining generalized flip-flop input equations, and a concise method is presented for representing these equations. The procedure is based on solving a four-valued characteristic equation of the flip-flop, and can encompass flip-flops that are too complex to approach intuitively. The technique is presented using Karnaugh maps, but could easily be implemented in software.

On Various Nonlinearity Measures for Boolean Functions*

PubMed Central

Boyar, Joan; Find, Magnus Gausdal; Peralta, René

2016-01-01

A necessary condition for the security of cryptographic functions is to be “sufficiently distant” from linear, and cryptographers have proposed several measures for this distance. In this paper, we show that six common measures, nonlinearity, algebraic degree, annihilator immunity, algebraic thickness, normality, and multiplicative complexity, are incomparable in the sense that for each pair of measures, μ1, μ2, there exist functions f1, f2 with f1 being more nonlinear than f2 according to μ1, but less nonlinear according to μ2. We also present new connections between two of these measures. Additionally, we give a lower bound on the multiplicative complexity of collision-free functions. PMID:27458499

Classification scheme and prevention measures for caught-in-between occupational fatalities.

PubMed

Chi, Chia-Fen; Lin, Syuan-Zih

2018-04-01

The current study analyzed 312 caught-in-between fatalities caused by machinery and vehicles. A comprehensive and mutually exclusive coding scheme was developed to analyze and code each caught-in-between fatality in terms of age, gender, experience of the victim, type of industry, source of injury, and causes for these accidents. Boolean algebra analysis was applied on these 312 caught-in-between fatalities to derive minimal cut set (MCS) causes associated with each source of injury. Eventually, contributing factors and common accident patterns associated with (1) special process machinery including textile, printing, packaging machinery, (2) metal, woodworking, and special material machinery, (3) conveyor, (4) vehicle, (5) crane, (6) construction machinery, and (7) elevator can be divided into three major groups through Boolean algebra and MCS analysis. The MCS causes associated with conveyor share the same primary causes as those of the special process machinery including textile, printing, packaging and metal, woodworking, and special material machinery. These fatalities can be eliminated by focusing on the prevention measures associated with lack of safeguards, working on a running machine or process, unintentional activation, unsafe posture or position, unsafe clothing, and defective safeguards. Other precise and effective intervention can be developed based on the identified groups of accident causes associated with each source of injury. Copyright © 2017 Elsevier Ltd. All rights reserved.

The phase topology of a special case of Goryachev integrability in rigid body dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryabov, P. E., E-mail: orelryabov@mail.ru

2014-07-31

The phase topology of a special case of Goryachev integrability in the problem of motion of a rigid body in a fluid is investigated using the method of Boolean functions, which was developed by Kharlamov for algebraically separated systems. The bifurcation diagram of the moment map is found and the Fomenko invariant, which classifies the systems up to rough Liouville equivalence, is specified. Bibliography: 15 titles. (paper)

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

DTIC Science & Technology

2012-03-01

and Budget, Paperwork Reduction Project (0704-0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2 . REPORT DATE March 2012 3. REPORT... CA 93943-5000 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING /MONITORING AGENCY NAME(S) AND ADDRESS(ES) N/A 10. SPONSORING...developed for this conversion. This reduced form requires many fewer gates and has ( )n delay versus ( 2 ) n delay for a full transeunt triangle

A real signal and its states

NASA Astrophysics Data System (ADS)

Basiladze, S. G.

2017-05-01

The paper describes the general physical theory of signals, carriers of information, which supplements Shannon's abstract classical theory and is applicable in much broader fields, including nuclear physics. It is shown that in the absence of classical noise its place should be taken by the physical threshold of signal perception for objects of both macrocosm and microcosm. The signal perception threshold allows the presence of subthreshold (virtual) signal states. For these states, Boolean algebra of logic ( A = 0/1) is transformed into the "algebraic logic" of probabilities (0 ≤ a ≤ 1). The similarity and difference of virtual states of macroand microsignals are elucidated. "Real" and "quantum" information for computers is considered briefly. The maximum information transmission rate is estimated based on physical constants.

Development of an optical parallel logic device and a half-adder circuit for digital optical processing

NASA Technical Reports Server (NTRS)

Athale, R. A.; Lee, S. H.

1978-01-01

The paper describes the fabrication and operation of an optical parallel logic (OPAL) device which performs Boolean algebraic operations on binary images. Several logic operations on two input binary images were demonstrated using an 8 x 8 device with a CdS photoconductor and a twisted nematic liquid crystal. Two such OPAL devices can be interconnected to form a half-adder circuit which is one of the essential components of a CPU in a digital signal processor.

MONOMIALS AND BASIN CYLINDERS FOR NETWORK DYNAMICS.

PubMed

Austin, Daniel; Dinwoodie, Ian H

We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks.

MONOMIALS AND BASIN CYLINDERS FOR NETWORK DYNAMICS

PubMed Central

AUSTIN, DANIEL; DINWOODIE, IAN H

2014-01-01

We describe methods to identify cylinder sets inside a basin of attraction for Boolean dynamics of biological networks. Such sets are used for designing regulatory interventions that make the system evolve towards a chosen attractor, for example initiating apoptosis in a cancer cell. We describe two algebraic methods for identifying cylinders inside a basin of attraction, one based on the Groebner fan that finds monomials that define cylinders and the other on primary decomposition. Both methods are applied to current examples of gene networks. PMID:25620893

An improved lambda-scheme for one-dimensional flows

NASA Technical Reports Server (NTRS)

Moretti, G.; Dipiano, M. T.

1983-01-01

A code for the calculation of one-dimensional flows is presented, which combines a simple and efficient version of the lambda-scheme with tracking of discontinuities. The latter is needed to identify points where minor departures from the basic integration scheme are applied to prevent infiltration of numerical errors. Such a tracking is obtained via a systematic application of Boolean algebra. It is, therefore, very efficient. Fifteen examples are presented and discussed in detail. The results are exceptionally good. All discontinuites are captured within one mesh interval.

Smart molecules at work--mimicking advanced logic operations.

PubMed

Andréasson, Joakim; Pischel, Uwe

2010-01-01

Molecular logic is an interdisciplinary research field, which has captured worldwide interest. This tutorial review gives a brief introduction into molecular logic and Boolean algebra. This serves as the basis for a discussion of the state-of-the-art and future challenges in the field. Representative examples from the most recent literature including adders/subtractors, multiplexers/demultiplexers, encoders/decoders, and sequential logic devices (keypad locks) are highlighted. Other horizons, such as the utility of molecular logic in bio-related applications, are discussed as well.

Toward Question-Asking Machines: The Logic of Questions and the Inquiry Calculus

NASA Technical Reports Server (NTRS)

Knuth,Kevin H.

2005-01-01

For over a century, the study of logic has focused on the algebra of logical statements. This work, first performed by George Boole, has led to the development of modern computers, and was shown by Richard T. Cox to be the foundation of Bayesian inference. Meanwhile the logic of questions has been much neglected. For our computing machines to be truly intelligent, they need to be able to ask relevant questions. In this paper I will show how the Boolean lattice of logical statements gives rise to the free distributive lattice of questions thus defining their algebra. Furthermore, there exists a quantity analogous to probability, called relevance, which quantifies the degree to which one question answers another. I will show that relevance is not only a natural generalization of information theory, but also forms its foundation.

The detection and stabilisation of limit cycle for deterministic finite automata

NASA Astrophysics Data System (ADS)

Han, Xiaoguang; Chen, Zengqiang; Liu, Zhongxin; Zhang, Qing

2018-04-01

In this paper, the topological structure properties of deterministic finite automata (DFA), under the framework of the semi-tensor product of matrices, are investigated. First, the dynamics of DFA are converted into a new algebraic form as a discrete-time linear system by means of Boolean algebra. Using this algebraic description, the approach of calculating the limit cycles of different lengths is given. Second, we present two fundamental concepts, namely, domain of attraction of limit cycle and prereachability set. Based on the prereachability set, an explicit solution of calculating domain of attraction of a limit cycle is completely characterised. Third, we define the globally attractive limit cycle, and then the necessary and sufficient condition for verifying whether all state trajectories of a DFA enter a given limit cycle in a finite number of transitions is given. Fourth, the problem of whether a DFA can be stabilised to a limit cycle by the state feedback controller is discussed. Criteria for limit cycle-stabilisation are established. All state feedback controllers which implement the minimal length trajectories from each state to the limit cycle are obtained by using the proposed algorithm. Finally, an illustrative example is presented to show the theoretical results.

Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

PubMed

Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

PubMed Central

Davies, Robin; Hodge, Terrell; Enyedi, Alexander

2010-01-01

We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

An algebra-based method for inferring gene regulatory networks.

PubMed

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 dynamic patterns present in the network. Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html.

Cellular Automata Generalized To An Inferential System

NASA Astrophysics Data System (ADS)

Blower, David J.

2007-11-01

Stephen Wolfram popularized elementary one-dimensional cellular automata in his book, A New Kind of Science. Among many remarkable things, he proved that one of these cellular automata was a Universal Turing Machine. Such cellular automata can be interpreted in a different way by viewing them within the context of the formal manipulation rules from probability theory. Bayes's Theorem is the most famous of such formal rules. As a prelude, we recapitulate Jaynes's presentation of how probability theory generalizes classical logic using modus ponens as the canonical example. We emphasize the important conceptual standing of Boolean Algebra for the formal rules of probability manipulation and give an alternative demonstration augmenting and complementing Jaynes's derivation. We show the complementary roles played in arguments of this kind by Bayes's Theorem and joint probability tables. A good explanation for all of this is afforded by the expansion of any particular logic function via the disjunctive normal form (DNF). The DNF expansion is a useful heuristic emphasized in this exposition because such expansions point out where relevant 0s should be placed in the joint probability tables for logic functions involving any number of variables. It then becomes a straightforward exercise to rely on Boolean Algebra, Bayes's Theorem, and joint probability tables in extrapolating to Wolfram's cellular automata. Cellular automata are seen as purely deductive systems, just like classical logic, which probability theory is then able to generalize. Thus, any uncertainties which we might like to introduce into the discussion about cellular automata are handled with ease via the familiar inferential path. Most importantly, the difficult problem of predicting what cellular automata will do in the far future is treated like any inferential prediction problem.

A Module Language for Typing by Contracts

NASA Technical Reports Server (NTRS)

Glouche, Yann; Talpin, Jean-Pierre; LeGuernic, Paul; Gautier, Thierry

2009-01-01

Assume-guarantee reasoning is a popular and expressive paradigm for modular and compositional specification of programs. It is becoming a fundamental concept in some computer-aided design tools for embedded system design. In this paper, we elaborate foundations for contract-based embedded system design by proposing a general-purpose module language based on a Boolean algebra allowing to define contracts. In this framework, contracts are used to negotiate the correctness of assumptions made on the definition of a component at the point where it is used and provides guarantees to its environment. We illustrate this presentation with the specification of a simplified 4-stroke engine model.

An algebra-based method for inferring gene regulatory networks

PubMed Central

2014-01-01

Background 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. Results 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 dynamic patterns present in the network. Conclusions Boolean polynomial dynamical systems provide a powerful modeling framework for the reverse engineering of gene regulatory networks, that enables a rich mathematical structure on the model search space. A C++ implementation of the method, distributed under LPGL license, is available, together with the source code, at http://www.paola-vera-licona.net/Software/EARevEng/REACT.html. PMID:24669835

Adaptiveness in monotone pseudo-Boolean optimization and stochastic neural computation.

PubMed

Grossi, Giuliano

2009-08-01

Hopfield neural network (HNN) is a nonlinear computational model successfully applied in finding near-optimal solutions of several difficult combinatorial problems. In many cases, the network energy function is obtained through a learning procedure so that its minima are states falling into a proper subspace (feasible region) of the search space. However, because of the network nonlinearity, a number of undesirable local energy minima emerge from the learning procedure, significantly effecting the network performance. In the neural model analyzed here, we combine both a penalty and a stochastic process in order to enhance the performance of a binary HNN. The penalty strategy allows us to gradually lead the search towards states representing feasible solutions, so avoiding oscillatory behaviors or asymptotically instable convergence. Presence of stochastic dynamics potentially prevents the network to fall into shallow local minima of the energy function, i.e., quite far from global optimum. Hence, for a given fixed network topology, the desired final distribution on the states can be reached by carefully modulating such process. The model uses pseudo-Boolean functions both to express problem constraints and cost function; a combination of these two functions is then interpreted as energy of the neural network. A wide variety of NP-hard problems fall in the class of problems that can be solved by the model at hand, particularly those having a monotonic quadratic pseudo-Boolean function as constraint function. That is, functions easily derived by closed algebraic expressions representing the constraint structure and easy (polynomial time) to maximize. We show the asymptotic convergence properties of this model characterizing its state space distribution at thermal equilibrium in terms of Markov chain and give evidence of its ability to find high quality solutions on benchmarks and randomly generated instances of two specific problems taken from the computational graph theory.

Alternative probability theories for cognitive psychology.

PubMed

Narens, Louis

2014-01-01

Various proposals for generalizing event spaces for probability functions have been put forth in the mathematical, scientific, and philosophic literatures. In cognitive psychology such generalizations are used for explaining puzzling results in decision theory and for modeling the influence of context effects. This commentary discusses proposals for generalizing probability theory to event spaces that are not necessarily boolean algebras. Two prominent examples are quantum probability theory, which is based on the set of closed subspaces of a Hilbert space, and topological probability theory, which is based on the set of open sets of a topology. Both have been applied to a variety of cognitive situations. This commentary focuses on how event space properties can influence probability concepts and impact cognitive modeling. Copyright © 2013 Cognitive Science Society, Inc.

ADAM: analysis of discrete models of biological systems using computer algebra.

PubMed

Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

2011-07-20

Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics.

GENERAL A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

NASA Astrophysics Data System (ADS)

Gerd, Niestegge

2010-12-01

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lüders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are: the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic (events) belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Attractor controllability of Boolean networks by flipping a subset of their nodes

NASA Astrophysics Data System (ADS)

Rafimanzelat, Mohammad Reza; Bahrami, Fariba

2018-04-01

The controllability analysis of Boolean networks (BNs), as models of biomolecular regulatory networks, has drawn the attention of researchers in recent years. In this paper, we aim at governing the steady-state behavior of BNs using an intervention method which can easily be applied to most real system, which can be modeled as BNs, particularly to biomolecular regulatory networks. To this end, we introduce the concept of attractor controllability of a BN by flipping a subset of its nodes, as the possibility of making a BN converge from any of its attractors to any other one, by one-time flipping members of a subset of BN nodes. Our approach is based on the algebraic state-space representation of BNs using semi-tensor product of matrices. After introducing some new matrix tools, we use them to derive necessary and sufficient conditions for the attractor controllability of BNs. A forward search algorithm is then suggested to identify the minimal perturbation set for attractor controllability of a BN. Next, a lower bound is derived for the cardinality of this set. Two new indices are also proposed for quantifying the attractor controllability of a BN and the influence of each network variable on the attractor controllability of the network and the relationship between them is revealed. Finally, we confirm the efficiency of the proposed approach by applying it to the BN models of some real biomolecular networks.

Modeling and simulation of reliability of unmanned intelligent vehicles

NASA Astrophysics Data System (ADS)

Singh, Harpreet; Dixit, Arati M.; Mustapha, Adam; Singh, Kuldip; Aggarwal, K. K.; Gerhart, Grant R.

2008-04-01

Unmanned ground vehicles have a large number of scientific, military and commercial applications. A convoy of such vehicles can have collaboration and coordination. For the movement of such a convoy, it is important to predict the reliability of the system. A number of approaches are available in literature which describes the techniques for determining the reliability of the system. Graph theoretic approaches are popular in determining terminal reliability and system reliability. In this paper we propose to exploit Fuzzy and Neuro-Fuzzy approaches for predicting the node and branch reliability of the system while Boolean algebra approaches are used to determine terminal reliability and system reliability. Hence a combination of intelligent approaches like Fuzzy, Neuro-Fuzzy and Boolean approaches is used to predict the overall system reliability of a convoy of vehicles. The node reliabilities may correspond to the collaboration of vehicles while branch reliabilities will determine the terminal reliabilities between different nodes. An algorithm is proposed for determining the system reliabilities of a convoy of vehicles. The simulation of the overall system is proposed. Such simulation should be helpful to the commander to take an appropriate action depending on the predicted reliability in different terrain and environmental conditions. It is hoped that results of this paper will lead to more important techniques to have a reliable convoy of vehicles in a battlefield.

Modeling formalisms in Systems Biology

PubMed Central

2011-01-01

Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future. PMID:22141422

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

NASA Astrophysics Data System (ADS)

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

State feedback control design for Boolean networks.

PubMed

Liu, Rongjie; Qian, Chunjiang; Liu, Shuqian; Jin, Yu-Fang

2016-08-26

Driving Boolean networks to desired states is of paramount significance toward our ultimate goal of controlling the progression of biological pathways and regulatory networks. Despite recent computational development of controllability of general complex networks and structural controllability of Boolean networks, there is still a lack of bridging the mathematical condition on controllability to real boolean operations in a network. Further, no realtime control strategy has been proposed to drive a Boolean network. In this study, we applied semi-tensor product to represent boolean functions in a network and explored controllability of a boolean network based on the transition matrix and time transition diagram. We determined the necessary and sufficient condition for a controllable Boolean network and mapped this requirement in transition matrix to real boolean functions and structure property of a network. An efficient tool is offered to assess controllability of an arbitrary Boolean network and to determine all reachable and non-reachable states. We found six simplest forms of controllable 2-node Boolean networks and explored the consistency of transition matrices while extending these six forms to controllable networks with more nodes. Importantly, we proposed the first state feedback control strategy to drive the network based on the status of all nodes in the network. Finally, we applied our reachability condition to the major switch of P53 pathway to predict the progression of the pathway and validate the prediction with published experimental results. This control strategy allowed us to apply realtime control to drive Boolean networks, which could not be achieved by the current control strategy for Boolean networks. Our results enabled a more comprehensive understanding of the evolution of Boolean networks and might be extended to output feedback control design.

The Boolean Is Dead, Long Live the Boolean! Natural Language versus Boolean Searching in Introductory Undergraduate Instruction

ERIC Educational Resources Information Center

Lowe, M. Sara; Maxson, Bronwen K.; Stone, Sean M.; Miller, Willie; Snajdr, Eric; Hanna, Kathleen

2018-01-01

Boolean logic can be a difficult concept for first-year, introductory students to grasp. This paper compares the results of Boolean and natural language searching across several databases with searches created from student research questions. Performance differences between databases varied. Overall, natural search language is at least as good as…

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

PubMed Central

2011-01-01

Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics. PMID:21774817

Computational complexity of Boolean functions

NASA Astrophysics Data System (ADS)

Korshunov, Aleksei D.

2012-02-01

Boolean functions are among the fundamental objects of discrete mathematics, especially in those of its subdisciplines which fall under mathematical logic and mathematical cybernetics. The language of Boolean functions is convenient for describing the operation of many discrete systems such as contact networks, Boolean circuits, branching programs, and some others. An important parameter of discrete systems of this kind is their complexity. This characteristic has been actively investigated starting from Shannon's works. There is a large body of scientific literature presenting many fundamental results. The purpose of this survey is to give an account of the main results over the last sixty years related to the complexity of computation (realization) of Boolean functions by contact networks, Boolean circuits, and Boolean circuits without branching. Bibliography: 165 titles.

Cryptographic Boolean Functions with Biased Inputs

DTIC Science & Technology

2015-07-31

theory of random graphs developed by Erdős and Rényi [2]. The graph properties in a random graph expressed as such Boolean functions are used by...distributed Bernoulli variates with the parameter p. Since our scope is within the area of cryptography , we initiate an analysis of cryptographic...Boolean functions with biased inputs, which we refer to as µp-Boolean functions, is a common generalization of Boolean functions which stems from the

Evolutionary Algorithms for Boolean Functions in Diverse Domains of Cryptography.

PubMed

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.

A Simple Blueprint for Automatic Boolean Query Processing.

ERIC Educational Resources Information Center

Salton, G.

1988-01-01

Describes a new Boolean retrieval environment in which an extended soft Boolean logic is used to automatically construct queries from original natural language formulations provided by users. Experimental results that compare the retrieval effectiveness of this method to conventional Boolean and vector processing are discussed. (27 references)…

Optimal stabilization of Boolean networks through collective influence

NASA Astrophysics Data System (ADS)

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.

Effect of memory in non-Markovian Boolean networks illustrated with a case study: A cell cycling process

NASA Astrophysics Data System (ADS)

Ebadi, H.; Saeedian, M.; Ausloos, M.; Jafari, G. R.

2016-11-01

The Boolean network is one successful model to investigate discrete complex systems such as the gene interacting phenomenon. The dynamics of a Boolean network, controlled with Boolean functions, is usually considered to be a Markovian (memory-less) process. However, both self-organizing features of biological phenomena and their intelligent nature should raise some doubt about ignoring the history of their time evolution. Here, we extend the Boolean network Markovian approach: we involve the effect of memory on the dynamics. This can be explored by modifying Boolean functions into non-Markovian functions, for example, by investigating the usual non-Markovian threshold function —one of the most applied Boolean functions. By applying the non-Markovian threshold function on the dynamical process of the yeast cell cycle network, we discover a power-law-like memory with a more robust dynamics than the Markovian dynamics.

Mining TCGA Data Using Boolean Implications

PubMed Central

Sinha, Subarna; Tsang, Emily K.; Zeng, Haoyang; Meister, Michela; Dill, David L.

2014-01-01

Boolean implications (if-then rules) provide a conceptually simple, uniform and highly scalable way to find associations between pairs of random variables. In this paper, we propose to use Boolean implications to find relationships between variables of different data types (mutation, copy number alteration, DNA methylation and gene expression) from the glioblastoma (GBM) and ovarian serous cystadenoma (OV) data sets from The Cancer Genome Atlas (TCGA). We find hundreds of thousands of Boolean implications from these data sets. A direct comparison of the relationships found by Boolean implications and those found by commonly used methods for mining associations show that existing methods would miss relationships found by Boolean implications. Furthermore, many relationships exposed by Boolean implications reflect important aspects of cancer biology. Examples of our findings include cis relationships between copy number alteration, DNA methylation and expression of genes, a new hierarchy of mutations and recurrent copy number alterations, loss-of-heterozygosity of well-known tumor suppressors, and the hypermethylation phenotype associated with IDH1 mutations in GBM. The Boolean implication results used in the paper can be accessed at http://crookneck.stanford.edu/microarray/TCGANetworks/. PMID:25054200

An algorithmic approach to solving polynomial equations associated with quantum circuits

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Zinin, M. V.

2009-12-01

In this paper we present two algorithms for reducing systems of multivariate polynomial equations over the finite field F 2 to the canonical triangular form called lexicographical Gröbner basis. This triangular form is the most appropriate for finding solutions of the system. On the other hand, the system of polynomials over F 2 whose variables also take values in F 2 (Boolean polynomials) completely describes the unitary matrix generated by a quantum circuit. In particular, the matrix itself can be computed by counting the number of solutions (roots) of the associated polynomial system. Thereby, efficient construction of the lexicographical Gröbner bases over F 2 associated with quantum circuits gives a method for computing their circuit matrices that is alternative to the direct numerical method based on linear algebra. We compare our implementation of both algorithms with some other software packages available for computing Gröbner bases over F 2.

Exploring hurdles to transfer : student experiences of applying knowledge across disciplines

NASA Astrophysics Data System (ADS)

Lappalainen, Jouni; Rosqvist, Juho

2015-04-01

This paper explores the ways students perceive the transfer of learned knowledge to new situations - often a surprisingly difficult prospect. The novel aspect compared to the traditional transfer studies is that the learning phase is not a part of the experiment itself. The intention was only to activate acquired knowledge relevant to the transfer target using a short primer immediately prior to the situation where the knowledge was to be applied. Eight volunteer students from either mathematics or computer science curricula were given a task of designing an adder circuit using logic gates: a new context in which to apply knowledge of binary arithmetic and Boolean algebra. The results of a phenomenographic classification of the views presented by the students in their post-experiment interviews are reported. The degree to which the students were conscious of the acquired knowledge they employed and how they applied it in a new context emerged as the differentiating factors.

Synchronization of coupled large-scale Boolean networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Fangfei, E-mail: li-fangfei@163.com

2014-03-15

This paper investigates the complete synchronization and partial synchronization of two large-scale Boolean networks. First, the aggregation algorithm towards large-scale Boolean network is reviewed. Second, the aggregation algorithm is applied to study the complete synchronization and partial synchronization of large-scale Boolean networks. Finally, an illustrative example is presented to show the efficiency of the proposed results.

State feedback controller design for the synchronization of Boolean networks with time delays

NASA Astrophysics Data System (ADS)

Li, Fangfei; Li, Jianning; Shen, Lijuan

2018-01-01

State feedback control design to make the response Boolean network synchronize with the drive Boolean network is far from being solved in the literature. Motivated by this, this paper studies the feedback control design for the complete synchronization of two coupled Boolean networks with time delays. A necessary condition for the existence of a state feedback controller is derived first. Then the feedback control design procedure for the complete synchronization of two coupled Boolean networks is provided based on the necessary condition. Finally, an example is given to illustrate the proposed design procedure.

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

PubMed

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.

BoolFilter: an R package for estimation and identification of partially-observed Boolean dynamical systems.

PubMed

Mcclenny, Levi D; Imani, Mahdi; Braga-Neto, Ulisses M

2017-11-25

Gene regulatory networks govern the function of key cellular processes, such as control of the cell cycle, response to stress, DNA repair mechanisms, and more. Boolean networks have been used successfully in modeling gene regulatory networks. In the Boolean network model, the transcriptional state of each gene is represented by 0 (inactive) or 1 (active), and the relationship among genes is represented by logical gates updated at discrete time points. However, the Boolean gene states are never observed directly, but only indirectly and incompletely through noisy measurements based on expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays. The Partially-Observed Boolean Dynamical System (POBDS) signal model is distinct from other deterministic and stochastic Boolean network models in removing the requirement of a directly observable Boolean state vector and allowing uncertainty in the measurement process, addressing the scenario encountered in practice in transcriptomic analysis. BoolFilter is an R package that implements the POBDS model and associated algorithms for state and parameter estimation. It allows the user to estimate the Boolean states, network topology, and measurement parameters from time series of transcriptomic data using exact and approximated (particle) filters, as well as simulate the transcriptomic data for a given Boolean network model. Some of its infrastructure, such as the network interface, is the same as in the previously published R package for Boolean Networks BoolNet, which enhances compatibility and user accessibility to the new package. We introduce the R package BoolFilter for Partially-Observed Boolean Dynamical Systems (POBDS). The BoolFilter package provides a useful toolbox for the bioinformatics community, with state-of-the-art algorithms for simulation of time series transcriptomic data as well as the inverse process of system identification from data obtained with various expression technologies such as cDNA microarrays, RNA-Seq, and cell imaging-based assays.

Development of Boolean calculus and its application

NASA Technical Reports Server (NTRS)

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.

Boolean integral calculus

NASA Technical Reports Server (NTRS)

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.

Modeling the Normal and Neoplastic Cell Cycle with 'Realistic Boolean Genetic Networks': Their Application for Understanding Carcinogenesis and Assessing Therapeutic Strategies

NASA Technical Reports Server (NTRS)

Szallasi, Zoltan; Liang, Shoudan

2000-01-01

In this paper we show how Boolean genetic networks could be used to address complex problems in cancer biology. First, we describe a general strategy to generate Boolean genetic networks that incorporate all relevant biochemical and physiological parameters and cover all of their regulatory interactions in a deterministic manner. Second, we introduce 'realistic Boolean genetic networks' that produce time series measurements very similar to those detected in actual biological systems. Third, we outline a series of essential questions related to cancer biology and cancer therapy that could be addressed by the use of 'realistic Boolean genetic network' modeling.

Automatic query formulations in information retrieval.

PubMed

Salton, G; Buckley, C; Fox, E A

1983-07-01

Modern information retrieval systems are designed to supply relevant information in response to requests received from the user population. In most retrieval environments the search requests consist of keywords, or index terms, interrelated by appropriate Boolean operators. Since it is difficult for untrained users to generate effective Boolean search requests, trained search intermediaries are normally used to translate original statements of user need into useful Boolean search formulations. Methods are introduced in this study which reduce the role of the search intermediaries by making it possible to generate Boolean search formulations completely automatically from natural language statements provided by the system patrons. Frequency considerations are used automatically to generate appropriate term combinations as well as Boolean connectives relating the terms. Methods are covered to produce automatic query formulations both in a standard Boolean logic system, as well as in an extended Boolean system in which the strict interpretation of the connectives is relaxed. Experimental results are supplied to evaluate the effectiveness of the automatic query formulation process, and methods are described for applying the automatic query formulation process in practice.

An Attractor-Based Complexity Measurement for Boolean Recurrent Neural Networks

PubMed Central

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

Quantum processes: A Whiteheadian interpretation of quantum field theory

NASA Astrophysics Data System (ADS)

Bain, Jonathan

Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field theory, and the third section consists of a translation between the first two sections. This review will concentrate on the first and third sections, with an eye on making explicit the essential characteristics of the H-W interpretation.

To Boolean or Not To Boolean.

ERIC Educational Resources Information Center

Hildreth, Charles R.

1983-01-01

This editorial addresses the issue of whether or not to provide free-text, keyword/boolean search capabilities in the information retrieval mechanisms of online public access catalogs and discusses online catalogs developed prior to 1980--keyword searching, phrase searching, and precoordination and postcoordination. (EJS)

Minimum energy control and optimal-satisfactory control of Boolean control network

NASA Astrophysics Data System (ADS)

Li, Fangfei; Lu, Xiwen

2013-12-01

In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floyd's algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.

Identifying a Probabilistic Boolean Threshold Network From Samples.

PubMed

Melkman, Avraham A; Cheng, Xiaoqing; Ching, Wai-Ki; Akutsu, Tatsuya

2018-04-01

This paper studies the problem of exactly identifying the structure of a probabilistic Boolean network (PBN) from a given set of samples, where PBNs are probabilistic extensions of Boolean networks. Cheng et al. studied the problem while focusing on PBNs consisting of pairs of AND/OR functions. This paper considers PBNs consisting of Boolean threshold functions while focusing on those threshold functions that have unit coefficients. The treatment of Boolean threshold functions, and triplets and -tuplets of such functions, necessitates a deepening of the theoretical analyses. It is shown that wide classes of PBNs with such threshold functions can be exactly identified from samples under reasonable constraints, which include: 1) PBNs in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2) PBNs consisting of pairs of threshold functions with different numbers of input variables. It is also shown that the problem of deciding the equivalence of two Boolean threshold functions is solvable in pseudopolynomial time but remains co-NP complete.

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

PubMed

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.

On the Run-Time Optimization of the Boolean Logic of a Program.

ERIC Educational Resources Information Center

Cadolino, C.; Guazzo, M.

1982-01-01

Considers problem of optimal scheduling of Boolean expression (each Boolean variable represents binary outcome of program module) on single-processor system. Optimization discussed consists of finding operand arrangement that minimizes average execution costs representing consumption of resources (elapsed time, main memory, number of…

Boolean integral calculus for digital systems

NASA Technical Reports Server (NTRS)

Tucker, J. H.; Tapia, M. A.; Bennett, A. W.

1985-01-01

The concept of Boolean integration is introduced and developed. When the changes in a desired function are specified in terms of changes in its arguments, then ways of 'integrating' (i.e., realizing) the function, if it exists, are presented. Boolean integral calculus has applications in design of logic circuits.

A Comparison of Two Methods for Boolean Query Relevancy Feedback.

ERIC Educational Resources Information Center

Salton, G.; And Others

1984-01-01

Evaluates and compares two recently proposed automatic methods for relevance feedback of Boolean queries (Dillon method, which uses probabilistic approach as basis, and disjunctive normal form method). Conclusions are drawn concerning the use of effective feedback methods in a Boolean query environment. Nineteen references are included. (EJS)

Health literacy and patient web portals.

PubMed

Coughlin, Steven S; Stewart, Jessica L; Young, Lufei; Heboyan, Vahé; De Leo, Gianluca

2018-05-01

There is limited evidence about the association between health literacy and use of patient web portals in patients with chronic illnesses. The objective of this review was to learn more about health literacy and use of patient web portals. Bibliographic searches were conducted in PubMed and CINAHL using relevant MeSH search terms and Boolean algebra commands. Qualitative studies and studies with a cross-sectional, cohort, or pre-/post-test design have shown that persons with limited health literacy are less likely to use patient web portals, although there is inconsistency in the association across studies. The conflicting findings may be partially due to racial and ethnic differences in health literacy or level of comfort in sharing private health information using mobile technologies. Several opportunities exist to improve the usability and acceptability of web portals for patients with limited health literacy including enhancements in the design of the portals, patient and provider education and training, and engagement of proxies such as caregivers and close family members. Copyright © 2018 Elsevier B.V. All rights reserved.

Application of fuzzy fault tree analysis based on modified fuzzy AHP and fuzzy TOPSIS for fire and explosion in the process industry.

PubMed

Yazdi, Mohammad; Korhan, Orhan; Daneshvar, Sahand

2018-05-09

This study aimed at establishing fault tree analysis (FTA) using expert opinion to compute the probability of an event. To find the probability of the top event (TE), all probabilities of the basic events (BEs) should be available when the FTA is drawn. In this case, employing expert judgment can be used as an alternative to failure data in an awkward situation. The fuzzy analytical hierarchy process as a standard technique is used to give a specific weight to each expert, and fuzzy set theory is engaged for aggregating expert opinion. In this regard, the probability of BEs will be computed and, consequently, the probability of the TE obtained using Boolean algebra. Additionally, to reduce the probability of the TE in terms of three parameters (safety consequences, cost and benefit), the importance measurement technique and modified TOPSIS was employed. The effectiveness of the proposed approach is demonstrated with a real-life case study.

A biochemical logic gate using an enzyme and its inhibitor. Part II: The logic gate.

PubMed

Sivan, Sarit; Tuchman, Samuel; Lotan, Noah

2003-06-01

Enzyme-Based Logic Gates (ENLOGs) are key components in bio-molecular systems for information processing. This report and the previous one in this series address the characterization of two bio-molecular switching elements, namely the alpha-chymotrypsin (alphaCT) derivative p-phenylazobenzoyl-alpha-chymotrypsin (PABalphaCT) and its inhibitor (proflavine), as well as their assembly into a logic gate. The experimental output of the proposed system is expressed in terms of enzymic activity and this was translated into logic output (i.e. "1" or "0") relative to a predetermined threshold value. We have found that an univalent link exists between the dominant isomers of PABalphaCT (cis or trans), the dominant form of either acridine (proflavine) or acridan and the logic output of the system. Thus, of all possible combinations, only the trans-PABalphaCT and the acridan lead to an enzymic activity that can be defined as logic output "1". The system operates under the rules of Boolean algebra and performs as an "AND" logic gate.

Boolean Classes and Qualitative Inquiry. WCER Working Paper No. 2006-3

ERIC Educational Resources Information Center

Nathan, Mitchell J.; Jackson, Kristi

2006-01-01

The prominent role of Boolean classes in qualitative data analysis software is viewed by some as an encroachment of logical positivism on qualitative research methodology. The authors articulate an embodiment perspective, in which Boolean classes are viewed as conceptual metaphors for apprehending and manipulating data, concepts, and categories in…

E-Referencer: Transforming Boolean OPACs to Web Search Engines.

ERIC Educational Resources Information Center

Khoo, Christopher S. G.; Poo, Danny C. C.; Toh, Teck-Kang; Hong, Glenn

E-Referencer is an expert intermediary system for searching library online public access catalogs (OPACs) on the World Wide Web. It is implemented as a proxy server that mediates the interaction between the user and Boolean OPACs. It transforms a Boolean OPAC into a retrieval system with many of the search capabilities of Web search engines.…

BEAT: A Web-Based Boolean Expression Fault-Based Test Case Generation Tool

ERIC Educational Resources Information Center

Chen, T. Y.; Grant, D. D.; Lau, M. F.; Ng, S. P.; Vasa, V. R.

2006-01-01

BEAT is a Web-based system that generates fault-based test cases from Boolean expressions. It is based on the integration of our several fault-based test case selection strategies. The generated test cases are considered to be fault-based, because they are aiming at the detection of particular faults. For example, when the Boolean expression is in…

Expected Number of Fixed Points in Boolean Networks with Arbitrary Topology.

PubMed

Mori, Fumito; Mochizuki, Atsushi

2017-07-14

Boolean network models describe genetic, neural, and social dynamics in complex networks, where the dynamics depend generally on network topology. Fixed points in a genetic regulatory network are typically considered to correspond to cell types in an organism. We prove that the expected number of fixed points in a Boolean network, with Boolean functions drawn from probability distributions that are not required to be uniform or identical, is one, and is independent of network topology if only a feedback arc set satisfies a stochastic neutrality condition. We also demonstrate that the expected number is increased by the predominance of positive feedback in a cycle.

SETS. Set Equation Transformation System

DOE Office of Scientific and Technical Information (OSTI.GOV)

Worrell, R.B.

1992-01-13

SETS is used for symbolic manipulation of Boolean equations, particularly the reduction of equations by the application of Boolean 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 noncoherent 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 throughmore » nullification of sensors in its protection system.« less

Monotone Boolean approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hulme, B.L.

1982-12-01

This report presents a theory of approximation of arbitrary Boolean functions by simpler, monotone functions. Monotone increasing functions can be expressed without the use of complements. Nonconstant monotone increasing functions are important in their own right since they model a special class of systems known as coherent systems. It is shown here that when Boolean expressions for noncoherent systems become too large to treat exactly, then monotone approximations are easily defined. The algorithms proposed here not only provide simpler formulas but also produce best possible upper and lower monotone bounds for any Boolean function. This theory has practical application formore » the analysis of noncoherent fault trees and event tree sequences.« less

On spectral techniques in analysis of Boolean networks

NASA Astrophysics Data System (ADS)

Kesseli, Juha; Rämö, Pauli; Yli-Harja, Olli

2005-06-01

In this work we present results that can be used for analysis of Boolean networks. The results utilize Fourier spectra of the functions in the network. An accurate formula is given for Derrida plots of networks of finite size N based on a result on Boolean functions presented in another context. Derrida plots are widely used to examine the stability issues of Boolean networks. For the limit N→∞, we give a computationally simple form that can be used as a good approximation for rather small networks as well. A formula for Derrida plots of random Boolean networks (RBNs) presented earlier in the literature is given an alternative derivation. It is shown that the information contained in the Derrida plot is equal to the average Fourier spectrum of the functions in the network. In the case of random networks the mean Derrida plot can be obtained from the mean spectrum of the functions. The method is applied to real data by using the Boolean functions found in genetic regulatory networks of eukaryotic cells in an earlier study. Conventionally, Derrida plots and stability analysis have been computed with statistical sampling resulting in poorer accuracy.

Automatic Screening for Perturbations in Boolean Networks.

PubMed

Schwab, Julian D; Kestler, Hans A

2018-01-01

A common approach to address biological questions in systems biology is to simulate regulatory mechanisms using dynamic models. Among others, Boolean networks can be used to model the dynamics of regulatory processes in biology. Boolean network models allow simulating the qualitative behavior of the modeled processes. A central objective in the simulation of Boolean networks is the computation of their long-term behavior-so-called attractors. These attractors are of special interest as they can often be linked to biologically relevant behaviors. Changing internal and external conditions can influence the long-term behavior of the Boolean network model. Perturbation of a Boolean network by stripping a component of the system or simulating a surplus of another element can lead to different attractors. Apparently, the number of possible perturbations and combinations of perturbations increases exponentially with the size of the network. Manually screening a set of possible components for combinations that have a desired effect on the long-term behavior can be very time consuming if not impossible. We developed a method to automatically screen for perturbations that lead to a user-specified change in the network's functioning. This method is implemented in the visual simulation framework ViSiBool utilizing satisfiability (SAT) solvers for fast exhaustive attractor search.

Inference of combinatorial Boolean rules of synergistic gene sets from cancer microarray datasets.

PubMed

Park, Inho; Lee, Kwang H; Lee, Doheon

2010-06-15

Gene set analysis has become an important tool for the functional interpretation of high-throughput gene expression datasets. Moreover, pattern analyses based on inferred gene set activities of individual samples have shown the ability to identify more robust disease signatures than individual gene-based pattern analyses. Although a number of approaches have been proposed for gene set-based pattern analysis, the combinatorial influence of deregulated gene sets on disease phenotype classification has not been studied sufficiently. We propose a new approach for inferring combinatorial Boolean rules of gene sets for a better understanding of cancer transcriptome and cancer classification. To reduce the search space of the possible Boolean rules, we identify small groups of gene sets that synergistically contribute to the classification of samples into their corresponding phenotypic groups (such as normal and cancer). We then measure the significance of the candidate Boolean rules derived from each group of gene sets; the level of significance is based on the class entropy of the samples selected in accordance with the rules. By applying the present approach to publicly available prostate cancer datasets, we identified 72 significant Boolean rules. Finally, we discuss several identified Boolean rules, such as the rule of glutathione metabolism (down) and prostaglandin synthesis regulation (down), which are consistent with known prostate cancer biology. Scripts written in Python and R are available at http://biosoft.kaist.ac.kr/~ihpark/. The refined gene sets and the full list of the identified Boolean rules are provided in the Supplementary Material. Supplementary data are available at Bioinformatics online.

Autonomous Modeling, Statistical Complexity and Semi-annealed Treatment of Boolean Networks

NASA Astrophysics Data System (ADS)

Gong, Xinwei

This dissertation presents three studies on Boolean networks. Boolean networks are a class of mathematical systems consisting of interacting elements with binary state variables. Each element is a node with a Boolean logic gate, and the presence of interactions between any two nodes is represented by directed links. Boolean networks that implement the logic structures of real systems are studied as coarse-grained models of the real systems. Large random Boolean networks are studied with mean field approximations and used to provide a baseline of possible behaviors of large real systems. This dissertation presents one study of the former type, concerning the stable oscillation of a yeast cell-cycle oscillator, and two studies of the latter type, respectively concerning the statistical complexity of large random Boolean networks and an extension of traditional mean field techniques that accounts for the presence of short loops. In the cell-cycle oscillator study, a novel autonomous update scheme is introduced to study the stability of oscillations in small networks. A motif that corrects pulse-growing perturbations and a motif that grows pulses are identified. A combination of the two motifs is capable of sustaining stable oscillations. Examining a Boolean model of the yeast cell-cycle oscillator using an autonomous update scheme yields evidence that it is endowed with such a combination. Random Boolean networks are classified as ordered, critical or disordered based on their response to small perturbations. In the second study, random Boolean networks are taken as prototypical cases for the evaluation of two measures of complexity based on a criterion for optimal statistical prediction. One measure, defined for homogeneous systems, does not distinguish between the static spatial inhomogeneity in the ordered phase and the dynamical inhomogeneity in the disordered phase. A modification in which complexities of individual nodes are calculated yields vanishing complexity values for networks in the ordered and critical phases and for highly disordered networks, peaking somewhere in the disordered phase. Individual nodes with high complexity have, on average, a larger influence on the system dynamics. Lastly, a semi-annealed approximation that preserves the correlation between states at neighboring nodes is introduced to study a social game-inspired network model in which all links are bidirectional and all nodes have a self-input. The technique developed here is shown to yield accurate predictions of distribution of players' states, and accounts for some nontrivial collective behavior of game theoretic interest.

Computing preimages of Boolean networks.

PubMed

Klotz, Johannes; Bossert, Martin; Schober, Steffen

2013-01-01

In this paper we present an algorithm based on the sum-product algorithm that finds elements in the preimage of a feed-forward Boolean networks given an output of the network. Our probabilistic method runs in linear time with respect to the number of nodes in the network. We evaluate our algorithm for randomly constructed Boolean networks and a regulatory network of Escherichia coli and found that it gives a valid solution in most cases.

Reliability analysis of the solar array based on Fault Tree Analysis

NASA Astrophysics Data System (ADS)

Jianing, Wu; Shaoze, Yan

2011-07-01

The solar array is an important device used in the spacecraft, which influences the quality of in-orbit operation of the spacecraft and even the launches. This paper analyzes the reliability of the mechanical system and certifies the most vital subsystem of the solar array. The fault tree analysis (FTA) model is established according to the operating process of the mechanical system based on DFH-3 satellite; the logical expression of the top event is obtained by Boolean algebra and the reliability of the solar array is calculated. The conclusion shows that the hinges are the most vital links between the solar arrays. By analyzing the structure importance(SI) of the hinge's FTA model, some fatal causes, including faults of the seal, insufficient torque of the locking spring, temperature in space, and friction force, can be identified. Damage is the initial stage of the fault, so limiting damage is significant to prevent faults. Furthermore, recommendations for improving reliability associated with damage limitation are discussed, which can be used for the redesigning of the solar array and the reliability growth planning.

Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2008-06-01

The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space). These investigations were started hundred of years ago by J. Boole (who invented Boolean algebras). The complete solution of the problem was obtained by Soviet mathematician Vorobjev in 60th. Surprisingly probabilists and statisticians obtained inequalities for probabilities and correlations among which one can find the famous Bell’s inequality and its generalizations. Such inequalities appeared simply as constraints for probabilistic compatibility. In this framework one can not see a priori any link to such problems as nonlocality and “death of reality” which are typically linked to Bell’s type inequalities in physical literature. We analyze the difference between positions of mathematicians and quantum physicists. In particular, we found that one of the most reasonable explanations of probabilistic incompatibility is mixing in Bell’s type inequalities statistical data from a number of experiments performed under different experimental contexts.

The use of mobile learning application to the fundament of digital electronics course

NASA Astrophysics Data System (ADS)

Rakhmawati, L.; Firdha, A.

2018-01-01

A new trend in e-learning is known as Mobile Learning. Learning through mobile phones have become part of the educative process. Thus, the purposes of this study are to develop a mobile application for the Fundament of Digital Electronics course that consists of number systems operation, logic gates, and Boolean Algebra, and to assess the readiness, perceptions, and effectiveness of students in the use of mobile devices for learning in the classroom. This research uses Research and Development (R&D) method. The design used in this research, by doing treatment in one class and observing by using Android-based mobile application instructional media. The result obtained from this research shows that the test has 80 % validity aspect, 82 % of the user from senior high school students gives a positive response in using the application of mobile learning, and based on the result of post-test, 90, 90% students passed the exam. At last, it can be concluded that the use of the mobile learning application makes the learning process more effective when it is used in the teaching-learning process.

Fuzzy tree automata and syntactic pattern recognition.

PubMed

Lee, E T

1982-04-01

An approach of representing patterns by trees and processing these trees by fuzzy tree automata is described. Fuzzy tree automata are defined and investigated. The results include that the class of fuzzy root-to-frontier recognizable ¿-trees is closed under intersection, union, and complementation. Thus, the class of fuzzy root-to-frontier recognizable ¿-trees forms a Boolean algebra. Fuzzy tree automata are applied to processing fuzzy tree representation of patterns based on syntactic pattern recognition. The grade of acceptance is defined and investigated. Quantitative measures of ``approximate isosceles triangle,'' ``approximate elongated isosceles triangle,'' ``approximate rectangle,'' and ``approximate cross'' are defined and used in the illustrative examples of this approach. By using these quantitative measures, a house, a house with high roof, and a church are also presented as illustrative examples. In addition, three fuzzy tree automata are constructed which have the capability of processing the fuzzy tree representations of ``fuzzy houses,'' ``houses with high roofs,'' and ``fuzzy churches,'' respectively. The results may have useful applications in pattern recognition, image processing, artificial intelligence, pattern database design and processing, image science, and pictorial information systems.

A network model for biofilm development in Escherichia coli K-12.

PubMed

Shalá, Andrew A; Restrepo, Silvia; González Barrios, Andrés F

2011-09-22

In nature, bacteria often exist as biofilms. Biofilms are communities of microorganisms attached to a surface. It is clear that biofilm-grown cells harbor properties remarkably distinct from planktonic cells. Biofilms frequently complicate treatments of infections by protecting bacteria from the immune system, decreasing antibiotic efficacy and dispersing planktonic cells to distant body sites. In this work, we employed enhanced Boolean algebra to model biofilm formation. The network obtained describes biofilm formation successfully, assuming - in accordance with the literature - that when the negative regulators (RscCD and EnvZ/OmpR) are off, the positive regulator (FlhDC) is on. The network was modeled under three different conditions through time with satisfactory outcomes. Each cluster was constructed using the K-means/medians Clustering Support algorithm on the basis of published Affymetrix microarray gene expression data from biofilm-forming bacteria and the planktonic state over four time points for Escherichia coli K-12. The different phenotypes obtained demonstrate that the network model of biofilm formation can simulate the formation or repression of biofilm efficiently in E. coli K-12.

Anthropomorphic robot for recognition and drawing generalized object images

NASA Astrophysics Data System (ADS)

Ginzburg, Vera M.

1998-10-01

The process of recognition, for instance, understanding the text, written by different fonts, consists in the depriving of the individual attributes of the letters in the particular font. It is shown that such process, in Nature and technique, can be provided by the narrowing the spatial frequency of the object's image by its defocusing. In defocusing images remain only areas, so-called Informative Fragments (IFs), which all together form the generalized (stylized) image of many identical objects. It is shown that the variety of shapes of IFs is restricted and can be presented by `Geometrical alphabet'. The `letters' for this alphabet can be created using two basic `genetic' figures: a stripe and round spot. It is known from physiology that the special cells of visual cortex response to these particular figures. The prototype of such `genetic' alphabet has been made using Boolean algebra (Venn's diagrams). The algorithm for drawing the letter's (`genlet's') shape in this alphabet and generalized images of objects (for example, `sleeping cat'), are given. A scheme of an anthropomorphic robot is shown together with results of model computer experiment of the robot's action--`drawing' the generalized image.

Cybernetic systems based on inductive logic

NASA Astrophysics Data System (ADS)

Fry, Robert L.

2001-05-01

Recent work in the area of inductive logic suggests that cybernetics might be quantified and reduced to engineering practice. If so, then there are considerable implications for engineering, science, and other fields. This paper attempts to capture the essential ideas of cybernetics cast in the light of inductive logic. The described inductive logic extends conventional logic by adding a conjugate logical domain of questions to the logical domain of assertions intrinsic to Boolean Algebra with which most are familiar. This was first posited and developed by Richard Cox. Interestingly enough, these two logical domains, one of questions and the other of assertions, only exist relative to one another with each possessing natural measures of entropy and probability, respectively. Examples are given that highlight the utility of cybernetic approaches to neuroscience, algorithm design, system engineering, and the design and understanding of defensive and offensive systems. For example, the application of cybernetic approaches to defense systems suggests that these systems possess a wavefunction which like quantum mechanics, collapses when we ``look'' through the eyes of the system sensors such as radars and optical sensors. .

Nonlinear secret image sharing scheme.

PubMed

Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young

2014-01-01

Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively.

Nonlinear Secret Image Sharing Scheme

PubMed Central

Shin, Sang-Ho; Yoo, Kee-Young

2014-01-01

Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2⁡m⌉ bit-per-pixel (bpp), respectively. PMID:25140334

Graphical fault tree analysis for fatal falls in the construction industry.

PubMed

Chi, Chia-Fen; Lin, Syuan-Zih; Dewi, Ratna Sari

2014-11-01

The current study applied a fault tree analysis to represent the causal relationships among events and causes that contributed to fatal falls in the construction industry. Four hundred and eleven work-related fatalities in the Taiwanese construction industry were analyzed in terms of age, gender, experience, falling site, falling height, company size, and the causes for each fatality. Given that most fatal accidents involve multiple events, the current study coded up to a maximum of three causes for each fall fatality. After the Boolean algebra and minimal cut set analyses, accident causes associated with each falling site can be presented as a fault tree to provide an overview of the basic causes, which could trigger fall fatalities in the construction industry. Graphical icons were designed for each falling site along with the associated accident causes to illustrate the fault tree in a graphical manner. A graphical fault tree can improve inter-disciplinary discussion of risk management and the communication of accident causation to first line supervisors. Copyright © 2014 Elsevier Ltd. All rights reserved.

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

PubMed Central

Dragović, Ivana; Turajlić, Nina; Pilčević, Dejan; Petrović, Bratislav; Radojević, Dragan

2015-01-01

Fuzzy inference systems (FIS) enable automated assessment and reasoning in a logically consistent manner akin to the way in which humans reason. However, since no conventional fuzzy set theory is in the Boolean frame, it is proposed that Boolean consistent fuzzy logic should be used in the evaluation of rules. The main distinction of this approach is that it requires the execution of a set of structural transformations before the actual values can be introduced, which can, in certain cases, lead to different results. While a Boolean consistent FIS could be used for establishing the diagnostic criteria for any given disease, in this paper it is applied for determining the likelihood of peritonitis, as the leading complication of peritoneal dialysis (PD). Given that patients could be located far away from healthcare institutions (as peritoneal dialysis is a form of home dialysis) the proposed Boolean consistent FIS would enable patients to easily estimate the likelihood of them having peritonitis (where a high likelihood would suggest that prompt treatment is indicated), when medical experts are not close at hand. PMID:27069500

Surface-confined assemblies and polymers for molecular logic.

PubMed

de Ruiter, Graham; van der Boom, Milko E

2011-08-16

Stimuli responsive materials are capable of mimicking the operation characteristics of logic gates such as AND, OR, NOR, and even flip-flops. Since the development of molecular sensors and the introduction of the first AND gate in solution by de Silva in 1993, Molecular (Boolean) Logic and Computing (MBLC) has become increasingly popular. In this Account, we present recent research activities that focus on MBLC with electrochromic polymers and metal polypyridyl complexes on a solid support. Metal polypyridyl complexes act as useful sensors to a variety of analytes in solution (i.e., H(2)O, Fe(2+/3+), Cr(6+), NO(+)) and in the gas phase (NO(x) in air). This information transfer, whether the analyte is present, is based on the reversible redox chemistry of the metal complexes, which are stable up to 200 °C in air. The concurrent changes in the optical properties are nondestructive and fast. In such a setup, the input is directly related to the output and, therefore, can be represented by one-input logic gates. These input-output relationships are extendable for mimicking the diverse functions of essential molecular logic gates and circuits within a set of Boolean algebraic operations. Such a molecular approach towards Boolean logic has yielded a series of proof-of-concept devices: logic gates, multiplexers, half-adders, and flip-flop logic circuits. MBLC is a versatile and, potentially, a parallel approach to silicon circuits: assemblies of these molecular gates can perform a wide variety of logic tasks through reconfiguration of their inputs. Although these developments do not require a semiconductor blueprint, similar guidelines such as signal propagation, gate-to-gate communication, propagation delay, and combinatorial and sequential logic will play a critical role in allowing this field to mature. For instance, gate-to-gate communication by chemical wiring of the gates with metal ions as electron carriers results in the integration of stand-alone systems: the output of one gate is used as the input for another gate. Using the same setup, we were able to display both combinatorial and sequential logic. We have demonstrated MBLC by coupling electrochemical inputs with optical readout, which resulted in various logic architectures built on a redox-active, functionalized surface. Electrochemically operated sequential logic systems such as flip-flops, multivalued logic, and multistate memory could enhance computational power without increasing spatial requirements. Applying multivalued digits in data storage could exponentially increase memory capacity. Furthermore, we evaluate the pros and cons of MBLC and identify targets for future research in this Account. © 2011 American Chemical Society

Exploiting Surroundedness for Saliency Detection: A Boolean Map Approach.

PubMed

Zhang, Jianming; Sclaroff, Stan

2016-05-01

We demonstrate the usefulness of surroundedness for eye fixation prediction by proposing a Boolean Map based Saliency model (BMS). In our formulation, an image is characterized by a set of binary images, which are generated by randomly thresholding the image's feature maps in a whitened feature space. Based on a Gestalt principle of figure-ground segregation, BMS computes a saliency map by discovering surrounded regions via topological analysis of Boolean maps. Furthermore, we draw a connection between BMS and the Minimum Barrier Distance to provide insight into why and how BMS can properly captures the surroundedness cue via Boolean maps. The strength of BMS is verified by its simplicity, efficiency and superior performance compared with 10 state-of-the-art methods on seven eye tracking benchmark datasets.

Network dynamics and systems biology

NASA Astrophysics Data System (ADS)

Norrell, Johannes A.

The physics of complex systems has grown considerably as a field in recent decades, largely due to improved computational technology and increased availability of systems level data. One area in which physics is of growing relevance is molecular biology. A new field, systems biology, investigates features of biological systems as a whole, a strategy of particular importance for understanding emergent properties that result from a complex network of interactions. Due to the complicated nature of the systems under study, the physics of complex systems has a significant role to play in elucidating the collective behavior. In this dissertation, we explore three problems in the physics of complex systems, motivated in part by systems biology. The first of these concerns the applicability of Boolean models as an approximation of continuous systems. Studies of gene regulatory networks have employed both continuous and Boolean models to analyze the system dynamics, and the two have been found produce similar results in the cases analyzed. We ask whether or not Boolean models can generically reproduce the qualitative attractor dynamics of networks of continuously valued elements. Using a combination of analytical techniques and numerical simulations, we find that continuous networks exhibit two effects---an asymmetry between on and off states, and a decaying memory of events in each element's inputs---that are absent from synchronously updated Boolean models. We show that in simple loops these effects produce exactly the attractors that one would predict with an analysis of the stability of Boolean attractors, but in slightly more complicated topologies, they can destabilize solutions that are stable in the Boolean approximation, and can stabilize new attractors. Second, we investigate ensembles of large, random networks. Of particular interest is the transition between ordered and disordered dynamics, which is well characterized in Boolean systems. Networks at the transition point, called critical, exhibit many of the features of regulatory networks, and recent studies suggest that some specific regulatory networks are indeed near-critical. We ask whether certain statistical measures of the ensemble behavior of large continuous networks are reproduced by Boolean models. We find that, in spite of the lack of correspondence between attractors observed in smaller systems, the statistical characterization given by the continuous and Boolean models show close agreement, and the transition between order and disorder known in Boolean systems can occur in continuous systems as well. One effect that is not present in Boolean systems, the failure of information to propagate down chains of elements of arbitrary length, is present in a class of continuous networks. In these systems, a modified Boolean theory that takes into account the collective effect of propagation failure on chains throughout the network gives a good description of the observed behavior. We find that propagation failure pushes the system toward greater order, resulting in a partial or complete suppression of the disordered phase. Finally, we explore a dynamical process of direct biological relevance: asymmetric cell division in A. thaliana. The long term goal is to develop a model for the process that accurately accounts for both wild type and mutant behavior. To contribute to this endeavor, we use confocal microscopy to image roots in a SHORT-ROOT inducible mutant. We compute correlation functions between the locations of asymmetrically divided cells, and we construct stochastic models based on a few simple assumptions that accurately predict the non-zero correlations. Our result shows that intracellular processes alone cannot be responsible for the observed divisions, and that an intercell signaling mechanism could account for the measured correlations.

"Antelope": a hybrid-logic model checker for branching-time Boolean GRN analysis

PubMed Central

2011-01-01

Background In Thomas' formalism for modeling gene regulatory networks (GRNs), branching time, where a state can have more than one possible future, plays a prominent role. By representing a certain degree of unpredictability, branching time can model several important phenomena, such as (a) asynchrony, (b) incompletely specified behavior, and (c) interaction with the environment. Introducing more than one possible future for a state, however, creates a difficulty for ordinary simulators, because infinitely many paths may appear, limiting ordinary simulators to statistical conclusions. Model checkers for branching time, by contrast, are able to prove properties in the presence of infinitely many paths. Results We have developed Antelope ("Analysis of Networks through TEmporal-LOgic sPEcifications", http://turing.iimas.unam.mx:8080/AntelopeWEB/), a model checker for analyzing and constructing Boolean GRNs. Currently, software systems for Boolean GRNs use branching time almost exclusively for asynchrony. Antelope, by contrast, also uses branching time for incompletely specified behavior and environment interaction. We show the usefulness of modeling these two phenomena in the development of a Boolean GRN of the Arabidopsis thaliana root stem cell niche. There are two obstacles to a direct approach when applying model checking to Boolean GRN analysis. First, ordinary model checkers normally only verify whether or not a given set of model states has a given property. In comparison, a model checker for Boolean GRNs is preferable if it reports the set of states having a desired property. Second, for efficiency, the expressiveness of many model checkers is limited, resulting in the inability to express some interesting properties of Boolean GRNs. Antelope tries to overcome these two drawbacks: Apart from reporting the set of all states having a given property, our model checker can express, at the expense of efficiency, some properties that ordinary model checkers (e.g., NuSMV) cannot. This additional expressiveness is achieved by employing a logic extending the standard Computation-Tree Logic (CTL) with hybrid-logic operators. Conclusions We illustrate the advantages of Antelope when (a) modeling incomplete networks and environment interaction, (b) exhibiting the set of all states having a given property, and (c) representing Boolean GRN properties with hybrid CTL. PMID:22192526

Theory and calculus of cubical complexes

NASA Technical Reports Server (NTRS)

Perlman, M.

1973-01-01

Combination switching networks with multiple outputs may be represented by Boolean functions. Report has been prepared which describes derivation and use of extraction algorithm that may be adapted to simplification of such simultaneous Boolean functions.

Total Parenteral Nutrition

MedlinePlus

... Boolean useRights, FileShare share, Int32 bufferSize, FileOptions options, SECURITY_ATTRIBUTES secAttrs, String msgPath, Boolean bFromProxy) at System.IO.FileStream..ctor(String path, FileMode mode, FileAccess ...

A genetic code Boolean structure. II. The genetic information system as a Boolean information system.

PubMed

Sanchez, Robersy; Grau, Ricardo

2005-09-01

A Boolean structure of the genetic code where Boolean deductions have biological and physicochemical meanings was discussed in a previous paper. Now, from these Boolean deductions we propose to define the value of amino acid information in order to consider the genetic information system as a communication system and to introduce the semantic content of information ignored by the conventional information theory. In this proposal, the value of amino acid information is proportional to the molecular weight of amino acids with a proportional constant of about 1.96 x 10(25) bits per kg. In addition to this, for the experimental estimations of the minimum energy dissipation in genetic logic operations, we present two postulates: (1) the energy Ei (i=1,2,...,20) of amino acids in the messages conveyed by proteins is proportional to the value of information, and (2) amino acids are distributed according to their energy Ei so the amino acid population in proteins follows a Boltzmann distribution. Specifically, in the genetic message carried by the DNA from the genomes of living organisms, we found that the minimum energy dissipation in genetic logic operations was close to kTLn(2) joules per bit.

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

PubMed

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.

Improving the quantum cost of reversible Boolean functions using reorder algorithm

NASA Astrophysics Data System (ADS)

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.

Volumetric T-spline Construction Using Boolean Operations

DTIC Science & Technology

2013-07-01

SUBTITLE Volumetric T-spline Construction Using Boolean Operations 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d...Acknowledgements The work of L. Liu and Y. Zhang was supported by ONR-YIP award N00014- 10-1-0698 and an ONR Grant N00014-08-1-0653. T. J.R. Hughes was sup- 16...T-spline Construction Using Boolean Operations 17 ported by ONR Grant N00014-08-1-0992, NSF GOALI CMI-0700807/0700204, NSF CMMI-1101007 and a SINTEF

Dynamic Network-Based Epistasis Analysis: Boolean Examples

PubMed Central

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 single-path assumption, but also by demonstrating the importance of considering temporal dynamics, and specifically introducing the usefulness of Boolean network models and also reviewing some key properties of network approaches. PMID:22645556

Acoustic logic gates and Boolean operation based on self-collimating acoustic beams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Ting; Xu, Jian-yi; Cheng, Ying, E-mail: chengying@nju.edu.cn

2015-03-16

The reveal of self-collimation effect in two-dimensional (2D) photonic or acoustic crystals has opened up possibilities for signal manipulation. In this paper, we have proposed acoustic logic gates based on the linear interference of self-collimated beams in 2D sonic crystals (SCs) with line-defects. The line defects on the diagonal of the 2D square SCs are actually functioning as a 3 dB splitter. By adjusting the phase difference between two input signals, the basic Boolean logic functions such as XOR, OR, AND, and NOT are achieved both theoretically and experimentally. Due to the non-diffracting property of self-collimation beams, more complex Boolean logicmore » and algorithms such as NAND, NOR, and XNOR can be realized by cascading the basic logic gates. The achievement of acoustic logic gates and Boolean operation provides a promising approach for acoustic signal computing and manipulations.« less

Boolean networks with veto functions

NASA Astrophysics Data System (ADS)

Ebadi, Haleh; Klemm, Konstantin

2014-08-01

Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expressions for the sensitivity of these functions and provide evidence for their role in natural systems. In an intracellular signal transduction network [Helikar et al., Proc. Natl. Acad. Sci. USA 105, 1913 (2008), 10.1073/pnas.0705088105], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. In Boolean networks for control of the yeast cell cycle [Li et al., Proc. Natl. Acad. Sci. USA 101, 4781 (2004), 10.1073/pnas.0305937101; Davidich et al., PLoS ONE 3, e1672 (2008), 10.1371/journal.pone.0001672], no or minimal changes to the wiring diagrams are necessary to formulate their dynamics in terms of the veto functions introduced here.

Data-Driven Sampling Matrix Boolean Optimization for Energy-Efficient Biomedical Signal Acquisition by Compressive Sensing.

PubMed

Wang, Yuhao; Li, Xin; Xu, Kai; Ren, Fengbo; Yu, Hao

2017-04-01

Compressive sensing is widely used in biomedical applications, and the sampling matrix plays a critical role on both quality and power consumption of signal acquisition. It projects a high-dimensional vector of data into a low-dimensional subspace by matrix-vector multiplication. An optimal sampling matrix can ensure accurate data reconstruction and/or high compression ratio. Most existing optimization methods can only produce real-valued embedding matrices that result in large energy consumption during data acquisition. In this paper, we propose an efficient method that finds an optimal Boolean sampling matrix in order to reduce the energy consumption. Compared to random Boolean embedding, our data-driven Boolean sampling matrix can improve the image recovery quality by 9 dB. Moreover, in terms of sampling hardware complexity, it reduces the energy consumption by 4.6× and the silicon area by 1.9× over the data-driven real-valued embedding.

Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

PubMed

Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

2013-06-01

A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

An efficient algorithm for computing fixed length attractors based on bounded model checking in synchronous Boolean networks with biochemical applications.

PubMed

Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N

2015-04-28

Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.

A transition calculus for Boolean functions. [logic circuit analysis

NASA Technical Reports Server (NTRS)

Tucker, J. H.; Bennett, A. W.

1974-01-01

A transition calculus is presented for analyzing the effect of input changes on the output of logic circuits. The method is closely related to the Boolean difference, but it is more powerful. Both differentiation and integration are considered.

Characterizing short-term stability for Boolean networks over any distribution of transfer functions

DOE PAGES

Seshadhri, C.; Smith, Andrew M.; Vorobeychik, Yevgeniy; ...

2016-07-05

Here we present a characterization of short-term stability of random Boolean networks under arbitrary distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula that decides whether short-term chaos (damage spreading) will happen. We provide a formal proof for this formula, and empirically show that its predictions are accurate. Previous work only works for special cases of balanced families. Finally, it has been observed that these characterizations fail for unbalanced families, yet such families are widespread in real biological networks.

Inferring Boolean network states from partial information

PubMed Central

2013-01-01

Networks of molecular interactions regulate key processes in living cells. Therefore, understanding their functionality is a high priority in advancing biological knowledge. Boolean networks are often used to describe cellular networks mathematically and are fitted to experimental datasets. The fitting often results in ambiguities since the interpretation of the measurements is not straightforward and since the data contain noise. In order to facilitate a more reliable mapping between datasets and Boolean networks, we develop an algorithm that infers network trajectories from a dataset distorted by noise. We analyze our algorithm theoretically and demonstrate its accuracy using simulation and microarray expression data. PMID:24006954

Quantum algorithms on Walsh transform and Hamming distance for Boolean functions

NASA Astrophysics Data System (ADS)

Xie, Zhengwei; Qiu, Daowen; Cai, Guangya

2018-06-01

Walsh spectrum or Walsh transform is an alternative description of Boolean functions. In this paper, we explore quantum algorithms to approximate the absolute value of Walsh transform W_f at a single point z0 (i.e., |W_f(z0)|) for n-variable Boolean functions with probability at least 8/π 2 using the number of O(1/|W_f(z_{0)|ɛ }) queries, promised that the accuracy is ɛ , while the best known classical algorithm requires O(2n) queries. The Hamming distance between Boolean functions is used to study the linearity testing and other important problems. We take advantage of Walsh transform to calculate the Hamming distance between two n-variable Boolean functions f and g using O(1) queries in some cases. Then, we exploit another quantum algorithm which converts computing Hamming distance between two Boolean functions to quantum amplitude estimation (i.e., approximate counting). If Ham(f,g)=t≠0, we can approximately compute Ham( f, g) with probability at least 2/3 by combining our algorithm and {Approx-Count(f,ɛ ) algorithm} using the expected number of Θ( √{N/(\\lfloor ɛ t\\rfloor +1)}+√{t(N-t)}/\\lfloor ɛ t\\rfloor +1) queries, promised that the accuracy is ɛ . Moreover, our algorithm is optimal, while the exact query complexity for the above problem is Θ(N) and the query complexity with the accuracy ɛ is O(1/ɛ 2N/(t+1)) in classical algorithm, where N=2n. Finally, we present three exact quantum query algorithms for two promise problems on Hamming distance using O(1) queries, while any classical deterministic algorithm solving the problem uses Ω(2n) queries.

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

NASA Technical Reports Server (NTRS)

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.

Advanced Feedback Methods in Information Retrieval.

ERIC Educational Resources Information Center

Salton, G.; And Others

1985-01-01

In this study, automatic feedback techniques are applied to Boolean query statements in online information retrieval to generate improved query statements based on information contained in previously retrieved documents. Feedback operations are carried out using conventional Boolean logic and extended logic. Experimental output is included to…

Compact universal logic gates realized using quantization of current in nanodevices.

PubMed

Zhang, Wancheng; Wu, Nan-Jian; Yang, Fuhua

2007-12-12

This paper proposes novel universal logic gates using the current quantization characteristics of nanodevices. In nanodevices like the electron waveguide (EW) and single-electron (SE) turnstile, the channel current is a staircase quantized function of its control voltage. We use this unique characteristic to compactly realize Boolean functions. First we present the concept of the periodic-threshold threshold logic gate (PTTG), and we build a compact PTTG using EW and SE turnstiles. We show that an arbitrary three-input Boolean function can be realized with a single PTTG, and an arbitrary four-input Boolean function can be realized by using two PTTGs. We then use one PTTG to build a universal programmable two-input logic gate which can be used to realize all two-input Boolean functions. We also build a programmable three-input logic gate by using one PTTG. Compared with linear threshold logic gates, with the PTTG one can build digital circuits more compactly. The proposed PTTGs are promising for future smart nanoscale digital system use.

Phase transition in NK-Kauffman networks and its correction for Boolean irreducibility

NASA Astrophysics Data System (ADS)

Zertuche, Federico

2014-05-01

In a series of articles published in 1986, Derrida and his colleagues studied two mean field treatments (the quenched and the annealed) for NK-Kauffman networks. Their main results lead to a phase transition curve Kc 2 pc(1-pc)=1 (0

Controllability and observability of Boolean networks arising from biology

NASA Astrophysics Data System (ADS)

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.

Solving a discrete model of the lac operon using Z3

NASA Astrophysics Data System (ADS)

Gutierrez, Natalia A.

2014-05-01

A discrete model for the Lcac Operon is solved using the SMT-solver Z3. Traditionally the Lac Operon is formulated in a continuous math model. This model is a system of ordinary differential equations. Here, it was considerated as a discrete model, based on a Boolean red. The biological problem of Lac Operon is enunciated as a problem of Boolean satisfiability, and it is solved using an STM-solver named Z3. Z3 is a powerful solver that allows understanding the basic dynamic of the Lac Operon in an easier and more efficient way. The multi-stability of the Lac Operon can be easily computed with Z3. The code that solves the Boolean red can be written in Python language or SMT-Lib language. Both languages were used in local version of the program as online version of Z3. For future investigations it is proposed to solve the Boolean red of Lac Operon using others SMT-solvers as cvc4, alt-ergo, mathsat and yices.

Mathematical models for space shuttle ground systems

NASA Technical Reports Server (NTRS)

Tory, E. G.

1985-01-01

Math models are a series of algorithms, comprised of algebraic equations and Boolean Logic. At Kennedy Space Center, math models for the Space Shuttle Systems are performed utilizing the Honeywell 66/80 digital computers, Modcomp II/45 Minicomputers and special purpose hardware simulators (MicroComputers). The Shuttle Ground Operations Simulator operating system provides the language formats, subroutines, queueing schemes, execution modes and support software to write, maintain and execute the models. The ground systems presented consist primarily of the Liquid Oxygen and Liquid Hydrogen Cryogenic Propellant Systems, as well as liquid oxygen External Tank Gaseous Oxygen Vent Hood/Arm and the Vehicle Assembly Building (VAB) High Bay Cells. The purpose of math modeling is to simulate the ground hardware systems and to provide an environment for testing in a benign mode. This capability allows the engineers to check out application software for loading and launching the vehicle, and to verify the Checkout, Control, & Monitor Subsystem within the Launch Processing System. It is also used to train operators and to predict system response and status in various configurations (normal operations, emergency and contingent operations), including untried configurations or those too dangerous to try under real conditions, i.e., failure modes.

Application of fault tree approach for the causation mechanism of urban haze in Beijing--Considering the risk events related with exhausts of coal combustion.

PubMed

Huang, Weiqing; Fan, Hongbo; Qiu, Yongfu; Cheng, Zhiyu; Qian, Yu

2016-02-15

Haze weather has become a serious environmental pollution problem which occurs in many Chinese cities. One of the most critical factors for the formation of haze weather is the exhausts of coal combustion, thus it is meaningful to figure out the causation mechanism between urban haze and the exhausts of coal combustion. Based on above considerations, the fault tree analysis (FAT) approach was employed for the causation mechanism of urban haze in Beijing by considering the risk events related with the exhausts of coal combustion for the first time. Using this approach, firstly the fault tree of the urban haze causation system connecting with coal combustion exhausts was established; consequently the risk events were discussed and identified; then, the minimal cut sets were successfully determined using Boolean algebra; finally, the structure, probability and critical importance degree analysis of the risk events were completed for the qualitative and quantitative assessment. The study results proved that the FTA was an effective and simple tool for the causation mechanism analysis and risk management of urban haze in China. Copyright © 2015 Elsevier B.V. All rights reserved.

History, Applications, and Philosophy in Mathematics Education: HAPh—A Use of Primary Sources

NASA Astrophysics Data System (ADS)

Jankvist, Uffe Thomas

2013-03-01

The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and philosophy of mathematics in unison by discussing and analyzing the different `whys' and `hows' of including these three dimensions in mathematics education. Based on the observation that a use of history, applications, and philosophy as a `goal' is best realized through a modules approach, the article goes on to discuss how to actually design such teaching modules. It is argued that a use of primary original sources through a so-called guided reading along with a use of student essay assignments, which are suitable for bringing out relevant meta-issues of mathematics, is a sensible way of realizing a design encompassing the three dimensions. Two concrete teaching modules on aspects of the history, applications, and philosophy of mathematics—HAPh-modules—are outlined and the mathematical cases of these, graph theory and Boolean algebra, are described. Excerpts of student groups' essays from actual implementations of these modules are displayed as illustrative examples of the possible effect such HAPh-modules may have on students' development of an awareness regarding history, applications, and philosophy in relation to mathematics as a (scientific) discipline.

Perturbation propagation in random and evolved Boolean networks

NASA Astrophysics Data System (ADS)

Fretter, Christoph; Szejka, Agnes; Drossel, Barbara

2009-03-01

In this paper, we investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and its modifications. We show that even small random Boolean networks agree well with the predictions of the annealed approximation, but nonrandom networks show a very different behaviour. We focus on networks that were evolved for high dynamical robustness. The most important conclusion is that the simple distinction between frozen, critical and chaotic networks is no longer useful, since such evolved networks can display the properties of all three types of networks. Furthermore, we evaluate a simplified empirical network and show how its specific state space properties are reflected in the modified Derrida plots.

Multilayer neural networks with extensively many hidden units.

PubMed

Rosen-Zvi, M; Engel, A; Kanter, I

2001-08-13

The information processing abilities of a multilayer neural network with a number of hidden units scaling as the input dimension are studied using statistical mechanics methods. The mapping from the input layer to the hidden units is performed by general symmetric Boolean functions, whereas the hidden layer is connected to the output by either discrete or continuous couplings. Introducing an overlap in the space of Boolean functions as order parameter, the storage capacity is found to scale with the logarithm of the number of implementable Boolean functions. The generalization behavior is smooth for continuous couplings and shows a discontinuous transition to perfect generalization for discrete ones.

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

EPA Science Inventory

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...

Boolean linear differential operators on elementary cellular automata

NASA Astrophysics Data System (ADS)

Martín Del Rey, Ángel

2014-12-01

In this paper, the notion of boolean linear differential operator (BLDO) on elementary cellular automata (ECA) is introduced and some of their more important properties are studied. Special attention is paid to those differential operators whose coefficients are the ECA with rule numbers 90 and 150.

Describing the What and Why of Students' Difficulties in Boolean Logic

ERIC Educational Resources Information Center

Herman, Geoffrey L.; Loui, Michael C.; Kaczmarczyk, Lisa; Zilles, Craig

2012-01-01

The ability to reason with formal logic is a foundational skill for computer scientists and computer engineers that scaffolds the abilities to design, debug, and optimize. By interviewing students about their understanding of propositional logic and their ability to translate from English specifications to Boolean expressions, we characterized…

Evolution of canalizing Boolean networks

NASA Astrophysics Data System (ADS)

Szejka, A.; Drossel, B.

2007-04-01

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk, which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having such a high degree of robustness, the evolved networks still share many features with “chaotic” networks.

Circulant Matrices and Affine Equivalence of Monomial Rotation Symmetric Boolean Functions

DTIC Science & Technology

2015-01-01

definitions , including monomial rotation symmetric (MRS) Boolean functions and affine equivalence, and a known result for such quadratic functions...degree of the MRS is, we have a similar result as [40, Theorem 1.1] for n = 4p (p prime), or squarefree integers n, which along with our Theorem 5.2

User Practices in Keyword and Boolean Searching on an Online Public Access Catalog.

ERIC Educational Resources Information Center

Ensor, Pat

1992-01-01

Discussion of keyword and Boolean searching techniques in online public access catalogs (OPACs) focuses on a study conducted at Indiana State University that examined users' attitudes toward searching on NOTIS (Northwestern Online Total Integrated System). Relevant literature is reviewed, and implications for library instruction are suggested. (17…

Using Vector and Extended Boolean Matching in an Expert System for Selecting Foster Homes.

ERIC Educational Resources Information Center

Fox, Edward A.; Winett, Sheila G.

1990-01-01

Describes FOCES (Foster Care Expert System), a prototype expert system for choosing foster care placements for children which integrates information retrieval techniques with artificial intelligence. The use of prototypes and queries in Prolog routines, extended Boolean matching, and vector correlation are explained, as well as evaluation by…

A Construction of Boolean Functions with Good Cryptographic Properties

DTIC Science & Technology

2014-01-01

be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT...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

Therapeutic target discovery using Boolean network attractors: improvements of kali

PubMed Central

Guziolowski, Carito

2018-01-01

In a previous article, an algorithm for identifying therapeutic targets in Boolean networks modelling pathological mechanisms was introduced. In the present article, the improvements made on this algorithm, named kali, are described. These improvements are (i) the possibility to work on asynchronous Boolean networks, (ii) a finer assessment of therapeutic targets and (iii) the possibility to use multivalued logic. kali assumes that the attractors of a dynamical system, such as a Boolean network, are associated with the phenotypes of the modelled biological system. Given a logic-based model of pathological mechanisms, kali searches for therapeutic targets able to reduce the reachability of the attractors associated with pathological phenotypes, thus reducing their likeliness. kali is illustrated on an example network and used on a biological case study. The case study is a published logic-based model of bladder tumorigenesis from which kali returns consistent results. However, like any computational tool, kali can predict but cannot replace human expertise: it is a supporting tool for coping with the complexity of biological systems in the field of drug discovery. PMID:29515890

3D Boolean operations in virtual surgical planning.

PubMed

Charton, Jerome; Laurentjoye, Mathieu; Kim, Youngjun

2017-10-01

Boolean operations in computer-aided design or computer graphics are a set of operations (e.g. intersection, union, subtraction) between two objects (e.g. a patient model and an implant model) that are important in performing accurate and reproducible virtual surgical planning. This requires accurate and robust techniques that can handle various types of data, such as a surface extracted from volumetric data, synthetic models, and 3D scan data. This article compares the performance of the proposed method (Boolean operations by a robust, exact, and simple method between two colliding shells (BORES)) and an existing method based on the Visualization Toolkit (VTK). In all tests presented in this article, BORES could handle complex configurations as well as report impossible configurations of the input. In contrast, the VTK implementations were unstable, do not deal with singular edges and coplanar collisions, and have created several defects. The proposed method of Boolean operations, BORES, is efficient and appropriate for virtual surgical planning. Moreover, it is simple and easy to implement. In future work, we will extend the proposed method to handle non-colliding components.

Generalization and capacity of extensively large two-layered perceptrons.

PubMed

Rosen-Zvi, Michal; Engel, Andreas; Kanter, Ido

2002-09-01

The generalization ability and storage capacity of a treelike two-layered neural network with a number of hidden units scaling as the input dimension is examined. The mapping from the input to the hidden layer is via Boolean functions; the mapping from the hidden layer to the output is done by a perceptron. The analysis is within the replica framework where an order parameter characterizing the overlap between two networks in the combined space of Boolean functions and hidden-to-output couplings is introduced. The maximal capacity of such networks is found to scale linearly with the logarithm of the number of Boolean functions per hidden unit. The generalization process exhibits a first-order phase transition from poor to perfect learning for the case of discrete hidden-to-output couplings. The critical number of examples per input dimension, alpha(c), at which the transition occurs, again scales linearly with the logarithm of the number of Boolean functions. In the case of continuous hidden-to-output couplings, the generalization error decreases according to the same power law as for the perceptron, with the prefactor being different.

Boolean network identification from perturbation time series data combining dynamics abstraction and logic programming.

PubMed

Ostrowski, M; Paulevé, L; Schaub, T; Siegel, A; Guziolowski, C

2016-11-01

Boolean networks (and more general logic models) are useful frameworks to study signal transduction across multiple pathways. Logic models can be learned from a prior knowledge network structure and multiplex phosphoproteomics data. However, most efficient and scalable training methods focus on the comparison of two time-points and assume that the system has reached an early steady state. In this paper, we generalize such a learning procedure to take into account the time series traces of phosphoproteomics data in order to discriminate Boolean networks according to their transient dynamics. To that end, we identify a necessary condition that must be satisfied by the dynamics of a Boolean network to be consistent with a discretized time series trace. Based on this condition, we use Answer Set Programming to compute an over-approximation of the set of Boolean networks which fit best with experimental data and provide the corresponding encodings. Combined with model-checking approaches, we end up with a global learning algorithm. Our approach is able to learn logic models with a true positive rate higher than 78% in two case studies of mammalian signaling networks; for a larger case study, our method provides optimal answers after 7min of computation. We quantified the gain in our method predictions precision compared to learning approaches based on static data. Finally, as an application, our method proposes erroneous time-points in the time series data with respect to the optimal learned logic models. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Identification of Boolean Network Models From Time Series Data Incorporating Prior Knowledge.

PubMed

Leifeld, Thomas; Zhang, Zhihua; Zhang, Ping

2018-01-01

Motivation: Mathematical models take an important place in science and engineering. A model can help scientists to explain dynamic behavior of a system and to understand the functionality of system components. Since length of a time series and number of replicates is limited by the cost of experiments, Boolean networks as a structurally simple and parameter-free logical model for gene regulatory networks have attracted interests of many scientists. In order to fit into the biological contexts and to lower the data requirements, biological prior knowledge is taken into consideration during the inference procedure. In the literature, the existing identification approaches can only deal with a subset of possible types of prior knowledge. Results: We propose a new approach to identify Boolean networks from time series data incorporating prior knowledge, such as partial network structure, canalizing property, positive and negative unateness. Using vector form of Boolean variables and applying a generalized matrix multiplication called the semi-tensor product (STP), each Boolean function can be equivalently converted into a matrix expression. Based on this, the identification problem is reformulated as an integer linear programming problem to reveal the system matrix of Boolean model in a computationally efficient way, whose dynamics are consistent with the important dynamics captured in the data. By using prior knowledge the number of candidate functions can be reduced during the inference. Hence, identification incorporating prior knowledge is especially suitable for the case of small size time series data and data without sufficient stimuli. The proposed approach is illustrated with the help of a biological model of the network of oxidative stress response. Conclusions: The combination of efficient reformulation of the identification problem with the possibility to incorporate various types of prior knowledge enables the application of computational model inference to systems with limited amount of time series data. The general applicability of this methodological approach makes it suitable for a variety of biological systems and of general interest for biological and medical research.

Interpolation of the Extended Boolean Retrieval Model.

ERIC Educational Resources Information Center

Zanger, Daniel Z.

2002-01-01

Presents an interpolation theorem for an extended Boolean information retrieval model. Results show that whenever two or more documents are similarly ranked at any two points for a query containing exactly two terms, then they are similarly ranked at all points in between; and that results can fail for queries with more than two terms. (Author/LRW)

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

ERIC Educational Resources Information Center

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…

Energy and criticality in random Boolean networks

NASA Astrophysics Data System (ADS)

Andrecut, M.; Kauffman, S. A.

2008-06-01

The central issue of the research on the Random Boolean Networks (RBNs) model is the characterization of the critical transition between ordered and chaotic phases. Here, we discuss an approach based on the ‘energy’ associated with the unsatisfiability of the Boolean functions in the RBNs model, which provides an upper bound estimation for the energy used in computation. We show that in the ordered phase the RBNs are in a ‘dissipative’ regime, performing mostly ‘downhill’ moves on the ‘energy’ landscape. Also, we show that in the disordered phase the RBNs have to ‘hillclimb’ on the ‘energy’ landscape in order to perform computation. The analytical results, obtained using Derrida's approximation method, are in complete agreement with numerical simulations.

Optical programmable Boolean logic unit.

PubMed

Chattopadhyay, Tanay

2011-11-10

Logic units are the building blocks of many important computational operations likes arithmetic, multiplexer-demultiplexer, radix conversion, parity checker cum generator, etc. Multifunctional logic operation is very much essential in this respect. Here a programmable Boolean logic unit is proposed that can perform 16 Boolean logical operations from a single optical input according to the programming input without changing the circuit design. This circuit has two outputs. One output is complementary to the other. Hence no loss of data can occur. The circuit is basically designed by a 2×2 polarization independent optical cross bar switch. Performance of the proposed circuit has been achieved by doing numerical simulations. The binary logical states (0,1) are represented by the absence of light (null) and presence of light, respectively.

Boolean Dynamic Modeling Approaches to Study Plant Gene Regulatory Networks: Integration, Validation, and Prediction.

PubMed

Velderraín, José Dávila; Martínez-García, Juan Carlos; Álvarez-Buylla, Elena R

2017-01-01

Mathematical models based on dynamical systems theory are well-suited tools for the integration of available molecular experimental data into coherent frameworks in order to propose hypotheses about the cooperative regulatory mechanisms driving developmental processes. Computational analysis of the proposed models using well-established methods enables testing the hypotheses by contrasting predictions with observations. Within such framework, Boolean gene regulatory network dynamical models have been extensively used in modeling plant development. Boolean models are simple and intuitively appealing, ideal tools for collaborative efforts between theorists and experimentalists. In this chapter we present protocols used in our group for the study of diverse plant developmental processes. We focus on conceptual clarity and practical implementation, providing directions to the corresponding technical literature.

Designing Networks that are Capable of Self-Healing and Adapting

DTIC Science & Technology

2017-04-01

from statistical mechanics, combinatorics, boolean networks, and numerical simulations, and inspired by design principles from biological networks, we... principles for self-healing networks, and applications, and construct an all-possible-paths model for network adaptation. 2015-11-16 UNIT CONVERSION...combinatorics, boolean networks, and numerical simulations, and inspired by design principles from biological networks, we will undertake the fol

Equilibrium and nonequilibrium properties of Boolean decision problems on scale-free graphs with competing interactions with external biases

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Andresen, Juan Carlos; Janzen, Katharina; Katzgraber, Helmut G.

2013-03-01

We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free graphs in a magnetic field. Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scale-free networks. When the exponent that describes the power-law decay of the connectivity of the network is strictly larger than 3, the system undergoes a spin-glass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for all temperatures. First we perform finite-temperature Monte Carlo simulations in a field to test the robustness of the spin-glass phase and show, in agreement with analytical calculations, that the system exhibits a de Almeida-Thouless line. Furthermore, we study avalanches in the system at zero temperature to see if the system displays self-organized criticality. This would suggest that damage (avalanches) can spread across the whole system with nonzero probability, i.e., that Boolean decision problems on scale-free networks with competing interactions are fragile when not in thermal equilibrium.

Implementing neural nets with programmable logic

NASA Technical Reports Server (NTRS)

Vidal, Jacques J.

1988-01-01

Networks of Boolean programmable logic modules are presented as one purely digital class of artificial neural nets. The approach contrasts with the continuous analog framework usually suggested. Programmable logic networks are capable of handling many neural-net applications. They avoid some of the limitations of threshold logic networks and present distinct opportunities. The network nodes are called dynamically programmable logic modules. They can be implemented with digitally controlled demultiplexers. Each node performs a Boolean function of its inputs which can be dynamically assigned. The overall network is therefore a combinational circuit and its outputs are Boolean global functions of the network's input variables. The approach offers definite advantages for VLSI implementation, namely, a regular architecture with limited connectivity, simplicity of the control machinery, natural modularity, and the support of a mature technology.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivera-Durón, R. R., E-mail: roberto.rivera@ipicyt.edu.mx; Campos-Cantón, E., E-mail: eric.campos@ipicyt.edu.mx; Campos-Cantón, I.

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 enablemore » 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.« less

Stabilizing Motifs in Autonomous Boolean Networks and the Yeast Cell Cycle Oscillator

NASA Astrophysics Data System (ADS)

Sevim, Volkan; Gong, Xinwei; Socolar, Joshua

2009-03-01

Synchronously updated Boolean networks are widely used to model gene regulation. Some properties of these model networks are known to be artifacts of the clocking in the update scheme. Autonomous updating is a less artificial scheme that allows one to introduce small timing perturbations and study stability of the attractors. We argue that the stabilization of a limit cycle in an autonomous Boolean network requires a combination of motifs such as feed-forward loops and auto-repressive links that can correct small fluctuations in the timing of switching events. A recently published model of the transcriptional cell-cycle oscillator in yeast contains the motifs necessary for stability under autonomous updating [1]. [1] D. A. Orlando, et al. Nature (London), 4530 (7197):0 944--947, 2008.

Interactive Web-based tutorials for teaching digital electronics

NASA Astrophysics Data System (ADS)

Bailey, Donald G.

2000-10-01

With a wide range of student abilities in a class, it is difficult to effectively teach and stimulate all students. A series of web based tutorials was designed to help weaker students and stretch the stronger students. The tutorials consist of a series of HTML web pages with embedded Java applets. This combination is particularly powerful for providing interactive demonstrations because any textual content may be easily provided within the web page. The applet is able to be a compete working program that dynamically illustrates the concept, or provides a working environment for the student to experiment and work through their solution. The applet is dynamic, and responds to the student through both mouse clicks and keyboard entry. These allow the student to adjust parameters, make selections, and affect the way the program is run or information is displayed. Such interaction allows each applet to provide a mini demonstration or experiment to help the student understand a particular concept or technique. The approach taken is illustrated with a tutorial that dynamically shows the relationships between a truth table, Karnaugh amp, logic circuit and Boolean algebra representations of a logic function, and dramatically illustrates the effect of minimization on the resultant circuit. Use of the tutorial has resulted in significant benefits, particularly with weaker students.

Topological methods for the comparison of structures using LDR-brachytherapy of the prostate as an example.

PubMed

Schiefer, H; von Toggenburg, F; Seelentag, W W; Plasswilm, L; Ries, G; Schmid, H-P; Leippold, T; Krusche, B; Roth, J; Engeler, D

2009-08-21

The dose coverage of low dose rate (LDR)-brachytherapy for localized prostate cancer is monitored 4-6 weeks after intervention by contouring the prostate on computed tomography and/or magnetic resonance imaging sets. Dose parameters for the prostate (V100, D90 and D80) provide information on the treatment quality. Those depend strongly on the delineation of the prostate contours. We therefore systematically investigated the contouring process for 21 patients with five examiners. The prostate structures were compared with one another using topological procedures based on Boolean algebra. The coincidence number C(V) measures the agreement between a set of structures. The mutual coincidence C(i, j) measures the agreement between two structures i and j, and the mean coincidence C(i) compares a selected structure i with the remaining structures in a set. All coincidence parameters have a value of 1 for complete coincidence of contouring and 0 for complete absence. The five patients with the lowest C(V) values were discussed, and rules for contouring the prostate have been formulated. The contouring and assessment were repeated after 3 months for the same five patients. All coincidence parameters have been improved after instruction. This shows objectively that training resulted in more consistent contouring across examiners.

A general-purpose approach to computer-aided dynamic analysis of a flexible helicopter

NASA Technical Reports Server (NTRS)

Agrawal, Om P.

1988-01-01

A general purpose mathematical formulation is described for dynamic analysis of a helicopter consisting of flexible and/or rigid bodies that undergo large translations and rotations. Rigid body and elastic sets of generalized coordinates are used. The rigid body coordinates define the location and the orientation of a body coordinate frame (global frame) with respect to an inertial frame. The elastic coordinates are introduced using a finite element approach in order to model flexible components. The compatibility conditions between two adjacent elements in a flexible body are imposed using a Boolean matrix, whereas the compatibility conditions between two adjacent bodies are imposed using the Lagrange multiplier approach. Since the form of the constraint equations depends upon the type of kinematic joint and involves only the generalized coordinates of the two participating elements, then a library of constraint elements can be developed to impose the kinematic constraint in an automated fashion. For the body constraints, the Lagrange multipliers yield the reaction forces and torques of the bodies at the joints. The virtual work approach is used to derive the equations of motion, which are a system of differential and algebraic equations that are highly nonlinear. The formulation presented is general and is compared with hard-wired formulations commonly used in helicopter analysis.

Contribution of sublinear and supralinear dendritic integration to neuronal computations

PubMed Central

Tran-Van-Minh, Alexandra; Cazé, Romain D.; Abrahamsson, Therése; Cathala, Laurence; Gutkin, Boris S.; DiGregorio, David A.

2015-01-01

Nonlinear dendritic integration is thought to increase the computational ability of neurons. Most studies focus on how supralinear summation of excitatory synaptic responses arising from clustered inputs within single dendrites result in the enhancement of neuronal firing, enabling simple computations such as feature detection. Recent reports have shown that sublinear summation is also a prominent dendritic operation, extending the range of subthreshold input-output (sI/O) transformations conferred by dendrites. Like supralinear operations, sublinear dendritic operations also increase the repertoire of neuronal computations, but feature extraction requires different synaptic connectivity strategies for each of these operations. In this article we will review the experimental and theoretical findings describing the biophysical determinants of the three primary classes of dendritic operations: linear, sublinear, and supralinear. We then review a Boolean algebra-based analysis of simplified neuron models, which provides insight into how dendritic operations influence neuronal computations. We highlight how neuronal computations are critically dependent on the interplay of dendritic properties (morphology and voltage-gated channel expression), spiking threshold and distribution of synaptic inputs carrying particular sensory features. Finally, we describe how global (scattered) and local (clustered) integration strategies permit the implementation of similar classes of computations, one example being the object feature binding problem. PMID:25852470

Derailment-based Fault Tree Analysis on Risk Management of Railway Turnout Systems

NASA Astrophysics Data System (ADS)

Dindar, Serdar; Kaewunruen, Sakdirat; An, Min; Gigante-Barrera, Ángel

2017-10-01

Railway turnouts are fundamental mechanical infrastructures, which allow a rolling stock to divert one direction to another. As those are of a large number of engineering subsystems, e.g. track, signalling, earthworks, these particular sub-systems are expected to induce high potential through various kind of failure mechanisms. This could be a cause of any catastrophic event. A derailment, one of undesirable events in railway operation, often results, albeit rare occurs, in damaging to rolling stock, railway infrastructure and disrupt service, and has the potential to cause casualties and even loss of lives. As a result, it is quite significant that a well-designed risk analysis is performed to create awareness of hazards and to identify what parts of the systems may be at risk. This study will focus on all types of environment based failures as a result of numerous contributing factors noted officially as accident reports. This risk analysis is designed to help industry to minimise the occurrence of accidents at railway turnouts. The methodology of the study relies on accurate assessment of derailment likelihood, and is based on statistical multiple factors-integrated accident rate analysis. The study is prepared in the way of establishing product risks and faults, and showing the impact of potential process by Boolean algebra.

Towards Symbolic Model Checking for Multi-Agent Systems via OBDDs

NASA Technical Reports Server (NTRS)

Raimondi, Franco; Lomunscio, Alessio

2004-01-01

We present an algorithm for model checking temporal-epistemic properties of multi-agent systems, expressed in the formalism of interpreted systems. We first introduce a technique for the translation of interpreted systems into boolean formulae, and then present a model-checking algorithm based on this translation. The algorithm is based on OBDD's, as they offer a compact and efficient representation for boolean formulae.

The computational core and fixed point organization in Boolean networks

NASA Astrophysics Data System (ADS)

Correale, L.; Leone, M.; Pagnani, A.; Weigt, M.; Zecchina, R.

2006-03-01

In this paper, we analyse large random Boolean networks in terms of a constraint satisfaction problem. We first develop an algorithmic scheme which allows us to prune simple logical cascades and underdetermined variables, returning thereby the computational core of the network. Second, we apply the cavity method to analyse the number and organization of fixed points. We find in particular a phase transition between an easy and a complex regulatory phase, the latter being characterized by the existence of an exponential number of macroscopically separated fixed point clusters. The different techniques developed are reinterpreted as algorithms for the analysis of single Boolean networks, and they are applied in the analysis of and in silico experiments on the gene regulatory networks of baker's yeast (Saccharomyces cerevisiae) and the segment-polarity genes of the fruitfly Drosophila melanogaster.

Boolean network representation of contagion dynamics during a financial crisis

NASA Astrophysics Data System (ADS)

Caetano, Marco Antonio Leonel; Yoneyama, Takashi

2015-01-01

This work presents a network model for representation of the evolution of certain patterns of economic behavior. More specifically, after representing the agents as points in a space in which each dimension associated to a relevant economic variable, their relative "motions" that can be either stationary or discordant, are coded into a boolean network. Patterns with stationary averages indicate the maintenance of status quo, whereas discordant patterns represent aggregation of new agent into the cluster or departure from the former policies. The changing patterns can be embedded into a network representation, particularly using the concept of autocatalytic boolean networks. As a case study, the economic tendencies of the BRIC countries + Argentina were studied. Although Argentina is not included in the cluster formed by BRIC countries, it tends to follow the BRIC members because of strong commercial ties.

Modeling stochasticity and robustness in gene regulatory networks.

PubMed

Garg, Abhishek; Mohanram, Kartik; Di Cara, Alessandro; De Micheli, Giovanni; Xenarios, Ioannis

2009-06-15

Understanding gene regulation in biological processes and modeling the robustness of underlying regulatory networks is an important problem that is currently being addressed by computational systems biologists. Lately, there has been a renewed interest in Boolean modeling techniques for gene regulatory networks (GRNs). However, due to their deterministic nature, it is often difficult to identify whether these modeling approaches are robust to the addition of stochastic noise that is widespread in gene regulatory processes. Stochasticity in Boolean models of GRNs has been addressed relatively sparingly in the past, mainly by flipping the expression of genes between different expression levels with a predefined probability. This stochasticity in nodes (SIN) model leads to over representation of noise in GRNs and hence non-correspondence with biological observations. In this article, we introduce the stochasticity in functions (SIF) model for simulating stochasticity in Boolean models of GRNs. By providing biological motivation behind the use of the SIF model and applying it to the T-helper and T-cell activation networks, we show that the SIF model provides more biologically robust results than the existing SIN model of stochasticity in GRNs. Algorithms are made available under our Boolean modeling toolbox, GenYsis. The software binaries can be downloaded from http://si2.epfl.ch/ approximately garg/genysis.html.

Boolean decision problems with competing interactions on scale-free networks: Equilibrium and nonequilibrium behavior in an external bias

NASA Astrophysics Data System (ADS)

Zhu, Zheng; Andresen, Juan Carlos; Moore, M. A.; Katzgraber, Helmut G.

2014-02-01

We study the equilibrium and nonequilibrium properties of Boolean decision problems with competing interactions on scale-free networks in an external bias (magnetic field). Previous studies at zero field have shown a remarkable equilibrium stability of Boolean variables (Ising spins) with competing interactions (spin glasses) on scale-free networks. When the exponent that describes the power-law decay of the connectivity of the network is strictly larger than 3, the system undergoes a spin-glass transition. However, when the exponent is equal to or less than 3, the glass phase is stable for all temperatures. First, we perform finite-temperature Monte Carlo simulations in a field to test the robustness of the spin-glass phase and show that the system has a spin-glass phase in a field, i.e., exhibits a de Almeida-Thouless line. Furthermore, we study avalanche distributions when the system is driven by a field at zero temperature to test if the system displays self-organized criticality. Numerical results suggest that avalanches (damage) can spread across the whole system with nonzero probability when the decay exponent of the interaction degree is less than or equal to 2, i.e., that Boolean decision problems on scale-free networks with competing interactions can be fragile when not in thermal equilibrium.

Exact Algorithms for Output Encoding, State Assignment and Four-Level Boolean Minimization

DTIC Science & Technology

1989-10-01

APPROVED FOR PUBLIC DISTRIBUTION • DTIC MASSACHUSETTS INTITUTE OF TECHNOLOGY M VLSI PUBLICATIONSJAN 17 1990 VLSI Memo No. 89-569 JN. 9October 1989...nunijize large funclions exacly within reasonable amocunt. of CPt targeting twro-level logic imnplemientations involve finding ap- time. However, thle ,, m ...0(NV!) m ~iimizations . n5 10 The inptut encoding problemt can be exactly solved using mrultiple-valued Boolean nimuization. We present an exact (a) (b

Boolean logic tree of graphene-based chemical system for molecular computation and intelligent molecular search query.

PubMed

Huang, Wei Tao; Luo, Hong Qun; Li, Nian Bing

2014-05-06

The most serious, and yet unsolved, problem of constructing molecular computing devices consists in connecting all of these molecular events into a usable device. This report demonstrates the use of Boolean logic tree for analyzing the chemical event network based on graphene, organic dye, thrombin aptamer, and Fenton reaction, organizing and connecting these basic chemical events. And this chemical event network can be utilized to implement fluorescent combinatorial logic (including basic logic gates and complex integrated logic circuits) and fuzzy logic computing. On the basis of the Boolean logic tree analysis and logic computing, these basic chemical events can be considered as programmable "words" and chemical interactions as "syntax" logic rules to construct molecular search engine for performing intelligent molecular search query. Our approach is helpful in developing the advanced logic program based on molecules for application in biosensing, nanotechnology, and drug delivery.

A single-layer platform for Boolean logic and arithmetic through DNA excision in mammalian cells

PubMed Central

Weinberg, Benjamin H.; Hang Pham, N. T.; Caraballo, Leidy D.; Lozanoski, Thomas; Engel, Adrien; Bhatia, Swapnil; Wong, Wilson W.

2017-01-01

Genetic circuits engineered for mammalian cells often require extensive fine-tuning to perform their intended functions. To overcome this problem, we present a generalizable biocomputing platform that can engineer genetic circuits which function in human cells with minimal optimization. We used our Boolean Logic and Arithmetic through DNA Excision (BLADE) platform to build more than 100 multi-input-multi-output circuits. We devised a quantitative metric to evaluate the performance of the circuits in human embryonic kidney and Jurkat T cells. Of 113 circuits analysed, 109 functioned (96.5%) with the correct specified behavior without any optimization. We used our platform to build a three-input, two-output Full Adder and six-input, one-output Boolean Logic Look Up Table. We also used BLADE to design circuits with temporal small molecule-mediated inducible control and circuits that incorporate CRISPR/Cas9 to regulate endogenous mammalian genes. PMID:28346402

An Automated Design Framework for Multicellular Recombinase Logic.

PubMed

Guiziou, Sarah; Ulliana, Federico; Moreau, Violaine; Leclere, Michel; Bonnet, Jerome

2018-05-18

Tools to systematically reprogram cellular behavior are crucial to address pressing challenges in manufacturing, environment, or healthcare. Recombinases can very efficiently encode Boolean and history-dependent logic in many species, yet current designs are performed on a case-by-case basis, limiting their scalability and requiring time-consuming optimization. Here we present an automated workflow for designing recombinase logic devices executing Boolean functions. Our theoretical framework uses a reduced library of computational devices distributed into different cellular subpopulations, which are then composed in various manners to implement all desired logic functions at the multicellular level. Our design platform called CALIN (Composable Asynchronous Logic using Integrase Networks) is broadly accessible via a web server, taking truth tables as inputs and providing corresponding DNA designs and sequences as outputs (available at http://synbio.cbs.cnrs.fr/calin ). We anticipate that this automated design workflow will streamline the implementation of Boolean functions in many organisms and for various applications.

Tracking perturbations in Boolean networks with spectral methods

NASA Astrophysics Data System (ADS)

Kesseli, Juha; Rämö, Pauli; Yli-Harja, Olli

2005-08-01

In this paper we present a method for predicting the spread of perturbations in Boolean networks. The method is applicable to networks that have no regular topology. The prediction of perturbations can be performed easily by using a presented result which enables the efficient computation of the required iterative formulas. This result is based on abstract Fourier transform of the functions in the network. In this paper the method is applied to show the spread of perturbations in networks containing a distribution of functions found from biological data. The advances in the study of the spread of perturbations can directly be applied to enable ways of quantifying chaos in Boolean networks. Derrida plots over an arbitrary number of time steps can be computed and thus distributions of functions compared with each other with respect to the amount of order they create in random networks.

Emergence of diversity in homogeneous coupled Boolean networks

NASA Astrophysics Data System (ADS)

Kang, Chris; Aguilar, Boris; Shmulevich, Ilya

2018-05-01

The origin of multicellularity in metazoa is one of the fundamental questions of evolutionary biology. We have modeled the generic behaviors of gene regulatory networks in isogenic cells as stochastic nonlinear dynamical systems—coupled Boolean networks with perturbation. Model simulations under a variety of dynamical regimes suggest that the central characteristic of multicellularity, permanent spatial differentiation (diversification), indeed can arise. Additionally, we observe that diversification is more likely to occur near the critical regime of Lyapunov stability.

Adaptive Neuro-Fuzzy Determination of the Effect of Experimental Parameters on Vehicle Agent Speed Relative to Vehicle Intruder.

PubMed

Shamshirband, Shahaboddin; Banjanovic-Mehmedovic, Lejla; Bosankic, Ivan; Kasapovic, Suad; Abdul Wahab, Ainuddin Wahid Bin

2016-01-01

Intelligent Transportation Systems rely on understanding, predicting and affecting the interactions between vehicles. The goal of this paper is to choose a small subset from the larger set so that the resulting regression model is simple, yet have good predictive ability for Vehicle agent speed relative to Vehicle intruder. The method of ANFIS (adaptive neuro fuzzy inference system) was applied to the data resulting from these measurements. The ANFIS process for variable selection was implemented in order to detect the predominant variables affecting the prediction of agent speed relative to intruder. This process includes several ways to discover a subset of the total set of recorded parameters, showing good predictive capability. The ANFIS network was used to perform a variable search. Then, it was used to determine how 9 parameters (Intruder Front sensors active (boolean), Intruder Rear sensors active (boolean), Agent Front sensors active (boolean), Agent Rear sensors active (boolean), RSSI signal intensity/strength (integer), Elapsed time (in seconds), Distance between Agent and Intruder (m), Angle of Agent relative to Intruder (angle between vehicles °), Altitude difference between Agent and Intruder (m)) influence prediction of agent speed relative to intruder. The results indicated that distance between Vehicle agent and Vehicle intruder (m) and angle of Vehicle agent relative to Vehicle Intruder (angle between vehicles °) is the most influential parameters to Vehicle agent speed relative to Vehicle intruder.

Using Common Table Expressions to Build a Scalable Boolean Query Generator for Clinical Data Warehouses

PubMed Central

Harris, Daniel R.; Henderson, Darren W.; Kavuluru, Ramakanth; Stromberg, Arnold J.; Johnson, Todd R.

2015-01-01

We present a custom, Boolean query generator utilizing common-table expressions (CTEs) that is capable of scaling with big datasets. The generator maps user-defined Boolean queries, such as those interactively created in clinical-research and general-purpose healthcare tools, into SQL. We demonstrate the effectiveness of this generator by integrating our work into the Informatics for Integrating Biology and the Bedside (i2b2) query tool and show that it is capable of scaling. Our custom generator replaces and outperforms the default query generator found within the Clinical Research Chart (CRC) cell of i2b2. In our experiments, sixteen different types of i2b2 queries were identified by varying four constraints: date, frequency, exclusion criteria, and whether selected concepts occurred in the same encounter. We generated non-trivial, random Boolean queries based on these 16 types; the corresponding SQL queries produced by both generators were compared by execution times. The CTE-based solution significantly outperformed the default query generator and provided a much more consistent response time across all query types (M=2.03, SD=6.64 vs. M=75.82, SD=238.88 seconds). Without costly hardware upgrades, we provide a scalable solution based on CTEs with very promising empirical results centered on performance gains. The evaluation methodology used for this provides a means of profiling clinical data warehouse performance. PMID:25192572

Boolean Modeling of Neural Systems with Point-Process Inputs and Outputs. Part I: Theory and Simulations

PubMed Central

Marmarelis, Vasilis Z.; Zanos, Theodoros P.; Berger, Theodore W.

2010-01-01

This paper presents a new modeling approach for neural systems with point-process (spike) inputs and outputs that utilizes Boolean operators (i.e. modulo 2 multiplication and addition that correspond to the logical AND and OR operations respectively, as well as the AND_NOT logical operation representing inhibitory effects). The form of the employed mathematical models is akin to a “Boolean-Volterra” model that contains the product terms of all relevant input lags in a hierarchical order, where terms of order higher than first represent nonlinear interactions among the various lagged values of each input point-process or among lagged values of various inputs (if multiple inputs exist) as they reflect on the output. The coefficients of this Boolean-Volterra model are also binary variables that indicate the presence or absence of the respective term in each specific model/system. Simulations are used to explore the properties of such models and the feasibility of their accurate estimation from short data-records in the presence of noise (i.e. spurious spikes). The results demonstrate the feasibility of obtaining reliable estimates of such models, with excitatory and inhibitory terms, in the presence of considerable noise (spurious spikes) in the outputs and/or the inputs in a computationally efficient manner. A pilot application of this approach to an actual neural system is presented in the companion paper (Part II). PMID:19517238

Inferring Toxicological Responses of HepG2 Cells from ...

EPA Pesticide Factsheets

Understanding the dynamic perturbation of cell states by chemicals can aid in for predicting their adverse effects. High-content imaging (HCI) was used to measure the state of HepG2 cells over three time points (1, 24, and 72 h) in response to 976 ToxCast chemicals for 10 different concentrations (0.39-200µM). Cell state was characterized by p53 activation (p53), c-Jun activation (SK), phospho-Histone H2A.x (OS), phospho-Histone H3 (MA), alpha tubulin (Mt), mitochondrial membrane potential (MMP), mitochondrial mass (MM), cell cycle arrest (CCA), nuclear size (NS) and cell number (CN). Dynamic cell state perturbations due to each chemical concentration were utilized to infer coarse-grained dependencies between cellular functions as Boolean networks (BNs). BNs were inferred from data in two steps. First, the data for each state variable were discretized into changed/active (> 1 standard deviation), and unchanged/inactive values. Second, the discretized data were used to learn Boolean relationships between variables. In our case, a BN is a wiring diagram between nodes that represent 10 previously described observable phenotypes. Functional relationships between nodes were represented as Boolean functions. We found that inferred BN show that HepG2 cell response is chemical and concentration specific. We observed presence of both point and cycle BN attractors. In addition, there are instances where Boolean functions were not found. We believe that this may be either

American College of Rheumatology/European League Against Rheumatism remission criteria for rheumatoid arthritis maintain reliable performance when evaluated in 44 joints.

PubMed

Kaneko, Yuko; Kondo, Harumi; Takeuchi, Tsutomu

2013-08-01

To investigate the performance of the new remission criteria for rheumatoid arthritis (RA) in daily clinical practice and the effect of possible misclassification of remission when 44 joints are assessed. Disease activity and remission rate were calculated according to the Disease Activity Score (DAS28), Simplified Disease Activity Index (SDAI), Clinical Disease Activity Index (CDAI), and a Boolean-based definition for 1402 patients with RA in Keio University Hospital. Characteristics of patients in remission were investigated, and the number of misclassified patients was determined--those classified as being in remission based on 28-joint count but as nonremission based on a 44-joint count for each definition criterion. Of all patients analyzed, 46.6%, 45.9%, 41.0%, and 31.5% were classified as in remission in the DAS28, SDAI, CDAI, and Boolean definitions, respectively. Patients classified into remission based only on the DAS28 showed relatively low erythrocyte sedimentation rates but greater swollen joint counts than those classified into remission based on the other definitions. In patients classified into remission based only on the Boolean criteria, the mean physician global assessment was greater than the mean patient global assessment. Although 119 patients had ≤ 1 involved joint in the 28-joint count but > 1 in the 44-joint count, only 34 of these 119 (2.4% of all subjects) were found to have been misclassified into remission. In practice, about half of patients with RA can achieve clinical remission within the DAS28, SDAI, and CDAI; and one-third according to the Boolean-based definition. Patients classified in remission based on a 28-joint count may have pain and swelling in the feet, but misclassification of remission was relatively rare and was seen in only 2.4% of patients under a Boolean definition. The 28-joint count can be sufficient for assessing clinical remission based on the new remission criteria.

Random Boolean networks for autoassociative memory: Optimization and sequential learning

NASA Astrophysics Data System (ADS)

Sherrington, D.; Wong, K. Y. M.

Conventional neural networks are based on synaptic storage of information, even when the neural states are discrete and bounded. In general, the set of potential local operations is much greater. Here we discuss some aspects of the properties of networks of binary neurons with more general Boolean functions controlling the local dynamics. Two specific aspects are emphasised; (i) optimization in the presence of noise and (ii) a simple model for short-term memory exhibiting primacy and recency in the recall of sequentially taught patterns.

Realization of a quantum Hamiltonian Boolean logic gate on the Si(001):H surface.

PubMed

Kolmer, Marek; Zuzak, Rafal; Dridi, Ghassen; Godlewski, Szymon; Joachim, Christian; Szymonski, Marek

2015-08-07

The design and construction of the first prototypical QHC (Quantum Hamiltonian Computing) atomic scale Boolean logic gate is reported using scanning tunnelling microscope (STM) tip-induced atom manipulation on an Si(001):H surface. The NOR/OR gate truth table was confirmed by dI/dU STS (Scanning Tunnelling Spectroscopy) tracking how the surface states of the QHC quantum circuit on the Si(001):H surface are shifted according to the input logical status.

Boolean gates on actin filaments

NASA Astrophysics Data System (ADS)

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.

PyBoolNet: a python package for the generation, analysis and visualization of boolean networks.

PubMed

Klarner, Hannes; Streck, Adam; Siebert, Heike

2017-03-01

The goal of this project is to provide a simple interface to working with Boolean networks. Emphasis is put on easy access to a large number of common tasks including the generation and manipulation of networks, attractor and basin computation, model checking and trap space computation, execution of established graph algorithms as well as graph drawing and layouts. P y B ool N et is a Python package for working with Boolean networks that supports simple access to model checking via N u SMV, standard graph algorithms via N etwork X and visualization via dot . In addition, state of the art attractor computation exploiting P otassco ASP is implemented. The package is function-based and uses only native Python and N etwork X data types. https://github.com/hklarner/PyBoolNet. hannes.klarner@fu-berlin.de. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Discrete dynamic modeling of cellular signaling networks.

PubMed

Albert, Réka; Wang, Rui-Sheng

2009-01-01

Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.

Origins of Chaos in Autonomous Boolean Networks

NASA Astrophysics Data System (ADS)

Socolar, Joshua; Cavalcante, Hugo; Gauthier, Daniel; Zhang, Rui

2010-03-01

Networks with nodes consisting of ideal Boolean logic gates are known to display either steady states, periodic behavior, or an ultraviolet catastrophe where the number of logic-transition events circulating in the network per unit time grows as a power-law. In an experiment, non-ideal behavior of the logic gates prevents the ultraviolet catastrophe and may lead to deterministic chaos. We identify certain non-ideal features of real logic gates that enable chaos in experimental networks. We find that short-pulse rejection and the asymmetry between the logic states tends to engender periodic behavior. On the other hand, a memory effect termed ``degradation'' can generate chaos. Our results strongly suggest that deterministic chaos can be expected in a large class of experimental Boolean-like networks. Such devices may find application in a variety of technologies requiring fast complex waveforms or flat power spectra. The non-ideal effects identified here also have implications for the statistics of attractors in large complex networks.

Phase diagram of restricted Boltzmann machines and generalized Hopfield networks with arbitrary priors.

PubMed

Barra, Adriano; Genovese, Giuseppe; Sollich, Peter; Tantari, Daniele

2018-02-01

Restricted Boltzmann machines are described by the Gibbs measure of a bipartite spin glass, which in turn can be seen as a generalized Hopfield network. This equivalence allows us to characterize the state of these systems in terms of their retrieval capabilities, both at low and high load, of pure states. We study the paramagnetic-spin glass and the spin glass-retrieval phase transitions, as the pattern (i.e., weight) distribution and spin (i.e., unit) priors vary smoothly from Gaussian real variables to Boolean discrete variables. Our analysis shows that the presence of a retrieval phase is robust and not peculiar to the standard Hopfield model with Boolean patterns. The retrieval region becomes larger when the pattern entries and retrieval units get more peaked and, conversely, when the hidden units acquire a broader prior and therefore have a stronger response to high fields. Moreover, at low load retrieval always exists below some critical temperature, for every pattern distribution ranging from the Boolean to the Gaussian case.

Experimental Clocking of Nanomagnets with Strain for Ultralow Power Boolean Logic.

PubMed

D'Souza, Noel; Salehi Fashami, Mohammad; Bandyopadhyay, Supriyo; Atulasimha, Jayasimha

2016-02-10

Nanomagnetic implementations of Boolean logic have attracted attention because of their nonvolatility and the potential for unprecedented overall energy-efficiency. Unfortunately, the large dissipative losses that occur when nanomagnets are switched with a magnetic field or spin-transfer-torque severely compromise the energy-efficiency. Recently, there have been experimental reports of utilizing the Spin Hall effect for switching magnets, and theoretical proposals for strain induced switching of single-domain magnetostrictive nanomagnets, that might reduce the dissipative losses significantly. Here, we experimentally demonstrate, for the first time that strain-induced switching of single-domain magnetostrictive nanomagnets of lateral dimensions ∼200 nm fabricated on a piezoelectric substrate can implement a nanomagnetic Boolean NOT gate and steer bit information unidirectionally in dipole-coupled nanomagnet chains. On the basis of the experimental results with bulk PMN-PT substrates, we estimate that the energy dissipation for logic operations in a reasonably scaled system using thin films will be a mere ∼1 aJ/bit.

Relationships between probabilistic Boolean networks and dynamic Bayesian networks as models of gene regulatory networks

PubMed Central

Lähdesmäki, Harri; Hautaniemi, Sampsa; Shmulevich, Ilya; Yli-Harja, Olli

2006-01-01

A significant amount of attention has recently been focused on modeling of gene regulatory networks. Two frequently used large-scale modeling frameworks are Bayesian networks (BNs) and Boolean networks, the latter one being a special case of its recent stochastic extension, probabilistic Boolean networks (PBNs). PBN is a promising model class that generalizes the standard rule-based interactions of Boolean networks into the stochastic setting. Dynamic Bayesian networks (DBNs) is a general and versatile model class that is able to represent complex temporal stochastic processes and has also been proposed as a model for gene regulatory systems. In this paper, we concentrate on these two model classes and demonstrate that PBNs and a certain subclass of DBNs can represent the same joint probability distribution over their common variables. The major benefit of introducing the relationships between the models is that it opens up the possibility of applying the standard tools of DBNs to PBNs and vice versa. Hence, the standard learning tools of DBNs can be applied in the context of PBNs, and the inference methods give a natural way of handling the missing values in PBNs which are often present in gene expression measurements. Conversely, the tools for controlling the stationary behavior of the networks, tools for projecting networks onto sub-networks, and efficient learning schemes can be used for DBNs. In other words, the introduced relationships between the models extend the collection of analysis tools for both model classes. PMID:17415411

Mathematics make microbes beautiful, beneficial, and bountiful.

PubMed

Jungck, John R

2012-01-01

Microbiology is a rich area for visualizing the importance of mathematics in terms of designing experiments, data mining, testing hypotheses, and visualizing relationships. Historically, Nobel Prizes have acknowledged the close interplay between mathematics and microbiology in such examples as the fluctuation test and mutation rates using Poisson statistics by Luria and Delbrück and the use of graph theory of polyhedra by Caspar and Klug. More and more contemporary microbiology journals feature mathematical models, computational algorithms and heuristics, and multidimensional visualizations. While revolutions in research have driven these initiatives, a commensurate effort needs to be made to incorporate much more mathematics into the professional preparation of microbiologists. In order not to be daunting to many educators, a Bloom-like "Taxonomy of Quantitative Reasoning" is shared with explicit examples of microbiological activities for engaging students in (a) counting, measuring, calculating using image analysis of bacterial colonies and viral infections on variegated leaves, measurement of fractal dimensions of beautiful colony morphologies, and counting vertices, edges, and faces on viral capsids and using graph theory to understand self assembly; (b) graphing, mapping, ordering by applying linear, exponential, and logistic growth models of public health and sanitation problems, revisiting Snow's epidemiological map of cholera with computational geometry, and using interval graphs to do complementation mapping, deletion mapping, food webs, and microarray heatmaps; (c) problem solving by doing gene mapping and experimental design, and applying Boolean algebra to gene regulation of operons; (d) analysis of the "Bacterial Bonanza" of microbial sequence and genomic data using bioinformatics and phylogenetics; (e) hypothesis testing-again with phylogenetic trees and use of Poisson statistics and the Luria-Delbrück fluctuation test; and (f) modeling of biodiversity by using game theory, of epidemics with algebraic models, bacterial motion by using motion picture analysis and fluid mechanics of motility in multiple dimensions through the physics of "Life at Low Reynolds Numbers," and pattern formation of quorum sensing bacterial populations. Through a developmental model for preprofessional education that emphasizes the beauty, utility, and diversity of microbiological systems, we hope to foster creativity as well as mathematically rigorous reasoning. Copyright © 2012 Elsevier Inc. All rights reserved.

Symbolic Boolean Manipulation with Ordered Binary Decision Diagrams

DTIC Science & Technology

1992-07-01

memories , where careful attention has been given to programming the memory management routines [Brace et al 19901. To extract maximum performance, it...OBDDs) represent Boolean functions as directed acyclic graphs. They form a canonical representation, making testing of functional properties such as...indicated 3 X X2 X3 f 000 0 0 01 0X22 0 10 0 0 11 1 d 1 0 0 0 X3 X 3X 1 01 1 1 10 0 - i"o11 10o 1 1 Figure 1: Truth Table and Decison Tree Repremmtatios

Generating probabilistic Boolean networks from a prescribed transition probability matrix.

PubMed

Ching, W-K; Chen, X; Tsing, N-K

2009-11-01

Probabilistic Boolean networks (PBNs) have received much attention in modeling genetic regulatory networks. A PBN can be regarded as a Markov chain process and is characterised by a transition probability matrix. In this study, the authors propose efficient algorithms for constructing a PBN when its transition probability matrix is given. The complexities of the algorithms are also analysed. This is an interesting inverse problem in network inference using steady-state data. The problem is important as most microarray data sets are assumed to be obtained from sampling the steady-state.

Consistent Correlations for Parameterised Boolean Equation Systems with Applications in Correctness Proofs for Manipulations

NASA Astrophysics Data System (ADS)

Willemse, Tim A. C.

We introduce the concept of consistent correlations for parameterised Boolean equation systems (PBESs), motivated largely by the laborious proofs of correctness required for most manipulations in this setting. Consistent correlations focus on relating the equations that occur in PBESs, rather than their solutions. For a fragment of PBESs, consistent correlations are shown to coincide with a recently introduced form of bisimulation. Finally, we show that bisimilarity on processes induces consistent correlations on PBESs encoding model checking problems. We apply our theory to two example manipulations from the literature.

A Parallel Approach in Computing Correlation Immunity up to Six Variables

DTIC Science & Technology

2015-03-10

their nonlinearity is divisible by 4. Let CI(n, k) (respectively, BCI (n, k)) be the number of exact order k correlation im- mune, (respectively...further balanced) n-variable Boolean functions. The notations CI(n, k, d), BCI (n, k, d) restricts the previous count to degree d Boolean functions...Theorem 3. The following are true: (i) BCI (n, n, 0) = 0, CI(n, n, 0) = 2, CI(n, k, 1) = BCI (n, k, 1) = 2 ( n k+1 ) , 0 ≤ k ≤ n− 1. (ii) BCI (n, n− 2) = 2

On Weak and Strong 2k- bent Boolean Functions

DTIC Science & Technology

2016-01-01

U.S.A. Email: pstanica@nps.edu Abstract—In this paper we introduce a sequence of discrete Fourier transforms and define new versions of bent...denotes the complex conjugate of z. An important tool in our analysis is the discrete Fourier transform , known in Boolean functions literature, as Walsh...Hadamard, or Walsh–Hadamard transform , which is the func- tion Wf : Fn2 → C, defined by Wf (u) = 2− n 2 ∑ x∈Vn (−1)f(x)⊕u·x. Any f ∈ Bn can be

Qubits and quantum Hamiltonian computing performances for operating a digital Boolean 1/2-adder

NASA Astrophysics Data System (ADS)

Dridi, Ghassen; Faizy Namarvar, Omid; Joachim, Christian

2018-04-01

Quantum Boolean (1 + 1) digits 1/2-adders are designed with 3 qubits for the quantum computing (Qubits) and 4 quantum states for the quantum Hamiltonian computing (QHC) approaches. Detailed analytical solutions are provided to analyse the time operation of those different 1/2-adder gates. QHC is more robust to noise than Qubits and requires about the same amount of energy for running its 1/2-adder logical operations. QHC is faster in time than Qubits but its logical output measurement takes longer.

Logic circuits from zero forcing.

PubMed

Burgarth, Daniel; Giovannetti, Vittorio; Hogben, Leslie; Severini, Simone; Young, Michael

We design logic circuits based on the notion of zero forcing on graphs; each gate of the circuits is a gadget in which zero forcing is performed. We show that such circuits can evaluate every monotone Boolean function. By using two vertices to encode each logical bit, we obtain universal computation. We also highlight a phenomenon of "back forcing" as a property of each function. Such a phenomenon occurs in a circuit when the input of gates which have been already used at a given time step is further modified by a computation actually performed at a later stage. Finally, we show that zero forcing can be also used to implement reversible computation. The model introduced here provides a potentially new tool in the analysis of Boolean functions, with particular attention to monotonicity. Moreover, in the light of applications of zero forcing in quantum mechanics, the link with Boolean functions may suggest a new directions in quantum control theory and in the study of engineered quantum spin systems. It is an open technical problem to verify whether there is a link between zero forcing and computation with contact circuits.

Boolean dynamics of genetic regulatory networks inferred from microarray time series data

DOE PAGES

Martin, Shawn; Zhang, Zhaoduo; Martino, Anthony; ...

2007-01-31

Methods available for the inference of genetic regulatory networks strive to produce a single network, usually by optimizing some quantity to fit the experimental observations. In this paper we investigate the possibility that multiple networks can be inferred, all resulting in similar dynamics. This idea is motivated by theoretical work which suggests that biological networks are robust and adaptable to change, and that the overall behavior of a genetic regulatory network might be captured in terms of dynamical basins of attraction. We have developed and implemented a method for inferring genetic regulatory networks for time series microarray data. Our methodmore » first clusters and discretizes the gene expression data using k-means and support vector regression. We then enumerate Boolean activation–inhibition networks to match the discretized data. In conclusion, the dynamics of the Boolean networks are examined. We have tested our method on two immunology microarray datasets: an IL-2-stimulated T cell response dataset and a LPS-stimulated macrophage response dataset. In both cases, we discovered that many networks matched the data, and that most of these networks had similar dynamics.« less

Verification and Optimal Control of Context-Sensitive Probabilistic Boolean Networks Using Model Checking and Polynomial Optimization

PubMed Central

Hiraishi, Kunihiko

2014-01-01

One of the significant topics in systems biology is to develop control theory of gene regulatory networks (GRNs). In typical control of GRNs, expression of some genes is inhibited (activated) by manipulating external stimuli and expression of other genes. It is expected to apply control theory of GRNs to gene therapy technologies in the future. In this paper, a control method using a Boolean network (BN) is studied. A BN is widely used as a model of GRNs, and gene expression is expressed by a binary value (ON or OFF). In particular, a context-sensitive probabilistic Boolean network (CS-PBN), which is one of the extended models of BNs, is used. For CS-PBNs, the verification problem and the optimal control problem are considered. For the verification problem, a solution method using the probabilistic model checker PRISM is proposed. For the optimal control problem, a solution method using polynomial optimization is proposed. Finally, a numerical example on the WNT5A network, which is related to melanoma, is presented. The proposed methods provide us useful tools in control theory of GRNs. PMID:24587766

A survey of SAT solver

NASA Astrophysics Data System (ADS)

Gong, Weiwei; Zhou, Xu

2017-06-01

In Computer Science, the Boolean Satisfiability Problem(SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. SAT is one of the first problems that was proven to be NP-complete, which is also fundamental to artificial intelligence, algorithm and hardware design. This paper reviews the main algorithms of the SAT solver in recent years, including serial SAT algorithms, parallel SAT algorithms, SAT algorithms based on GPU, and SAT algorithms based on FPGA. The development of SAT is analyzed comprehensively in this paper. Finally, several possible directions for the development of the SAT problem are proposed.

Modeling bidirectional reflectance of forests and woodlands using Boolean models and geometric optics

NASA Technical Reports Server (NTRS)

Strahler, Alan H.; Jupp, David L. B.

1990-01-01

Geometric-optical discrete-element mathematical models for forest canopies have been developed using the Boolean logic and models of Serra. The geometric-optical approach is considered to be particularly well suited to describing the bidirectional reflectance of forest woodland canopies, where the concentration of leaf material within crowns and the resulting between-tree gaps make plane-parallel, radiative-transfer models inappropriate. The approach leads to invertible formulations, in which the spatial and directional variance provides the means for remote estimation of tree crown size, shape, and total cover from remotedly sensed imagery.

A Parallel Approach in Computing Correlation Immunity up to Six Variables

DTIC Science & Technology

2015-07-24

nonlinearity is divisible by 4. Let CI(n, k) (respectively, BCI (n, k)) be the number of exact order k corre- lation immune, (respectively, further...balanced) n-variable Boolean functions. The notations CI(n, k, d), BCI (n, k, d) restricts the previous count to degree d Boolean functions. Theorem 3...The following are true: (i) BCI (n, n, 0) = 0, CI(n, n, 0) = 2, CI(n, k, 1) = BCI (n, k, 1) = 2 ( n k+1 ) , 0 ≤ k ≤ n− 1. (ii) BCI (n, n− 2) = 2 ( n n−1

High speed all optical logic gates based on quantum dot semiconductor optical amplifiers.

PubMed

Ma, Shaozhen; Chen, Zhe; Sun, Hongzhi; Dutta, Niloy K

2010-03-29

A scheme to realize all-optical Boolean logic functions AND, XOR and NOT using semiconductor optical amplifiers with quantum-dot active layers is studied. nonlinear dynamics including carrier heating and spectral hole-burning are taken into account together with the rate equations scheme. Results show with QD excited state and wetting layer serving as dual-reservoir of carriers, as well as the ultra fast carrier relaxation of the QD device, this scheme is suitable for high speed Boolean logic operations. Logic operation can be carried out up to speed of 250 Gb/s.

Continuum analogues of contragredient Lie algebras (Lie algebras with a Cartan operator and nonlinear dynamical systems)

NASA Astrophysics Data System (ADS)

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

1989-12-01

We present an axiomatic formulation of a new class of infinitedimensional 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.

Risk assessment techniques with applicability in marine engineering

NASA Astrophysics Data System (ADS)

Rudenko, E.; Panaitescu, F. V.; Panaitescu, M.

2015-11-01

Nowadays risk management is a carefully planned process. The task of risk management is organically woven into the general problem of increasing the efficiency of business. Passive attitude to risk and awareness of its existence are replaced by active management techniques. Risk assessment is one of the most important stages of risk management, since for risk management it is necessary first to analyze and evaluate risk. There are many definitions of this notion but in general case risk assessment refers to the systematic process of identifying the factors and types of risk and their quantitative assessment, i.e. risk analysis methodology combines mutually complementary quantitative and qualitative approaches. Purpose of the work: In this paper we will consider as risk assessment technique Fault Tree analysis (FTA). The objectives are: understand purpose of FTA, understand and apply rules of Boolean algebra, analyse a simple system using FTA, FTA advantages and disadvantages. Research and methodology: The main purpose is to help identify potential causes of system failures before the failures actually occur. We can evaluate the probability of the Top event.The steps of this analize are: the system's examination from Top to Down, the use of symbols to represent events, the use of mathematical tools for critical areas, the use of Fault tree logic diagrams to identify the cause of the Top event. Results: In the finally of study it will be obtained: critical areas, Fault tree logical diagrams and the probability of the Top event. These results can be used for the risk assessment analyses.

Pathways from marine protected area design and management to ecological success

PubMed Central

2015-01-01

Using an international dataset compiled from 121 sites in 87 marine protected areas (MPAs) globally (Edgar et al., 2014), I assessed how various configurations of design and management conditions affected MPA ecological performance, measured in terms of fish species richness and biomass. The set-theoretic approach used Boolean algebra to identify pathways that combined up to five ‘NEOLI’ (No-take, Enforced, Old, Large, Isolated) conditions and that were sufficient for achieving positive, and negative, ecological outcomes. Ecological isolation was overwhelming the most important condition affecting ecological outcomes but Old and Large were also conditions important for achieving high levels of biomass among large fishes (jacks, groupers, sharks). Solution coverage was uniformly low (<0.35) for all models of positive ecological performance suggesting the presence of numerous other conditions and pathways to ecological success that did not involve the NEOLI conditions. Solution coverage was higher (>0.50) for negative results (i.e., the absence of high biomass) among the large commercially-exploited fishes, implying asymmetries in how MPAs may rebuild populations on the one hand and, on the other, protect against further decline. The results revealed complex interactions involving MPA design, implementation, and management conditions that affect MPA ecological performance. In general terms, the presence of no-take regulations and effective enforcement were insufficient to ensure MPA effectiveness on their own. Given the central role of ecological isolation in securing ecological benefits from MPAs, site selection in the design phase appears critical for success. PMID:26644975

Development of a mathematical model of the human cardiovascular system: An educational perspective

NASA Astrophysics Data System (ADS)

Johnson, Bruce Allen

A mathematical model of the human cardiovascular system will be a useful educational tool in biological sciences and bioengineering classrooms. The goal of this project is to develop a mathematical model of the human cardiovascular system that responds appropriately to variations of significant physical variables. Model development is based on standard fluid statics and dynamics principles, pressure-volume characteristics of the cardiac cycle, and compliant behavior of blood vessels. Cardiac cycle phases provide the physical and logical model structure, and Boolean algebra links model sections. The model is implemented using VisSim, a highly intuitive and easily learned block diagram modeling software package. Comparisons of model predictions of key variables to published values suggest that the model reasonably approximates expected behavior of those variables. The model responds plausibly to variations of independent variables. Projected usefulness of the model as an educational tool is threefold: independent variables which determine heart function may be easily varied to observe cause and effect; the model is used in an interactive setting; and the relationship of governing equations to model behavior is readily viewable and intuitive. Future use of this model in classrooms may give a more reasonable indication of its value as an educational tool.* *This dissertation includes a CD that is multimedia (contains text and other applications that are not available in a printed format). The CD requires the following applications: CorelPhotoHouse, CorelWordPerfect, VisSinViewer (included on CD), Internet access.

Effect of remission definition on healthcare cost savings estimates for patients with rheumatoid arthritis treated with biologic therapies.

PubMed

Barnabe, Cheryl; Thanh, Nguyen Xuan; Ohinmaa, Arto; Homik, Joanne; Barr, Susan G; Martin, Liam; Maksymowych, Walter P

2014-08-01

Sustained remission in rheumatoid arthritis (RA) results in healthcare utilization cost savings. We evaluated the variation in estimates of savings when different definitions of remission [2011 American College of Rheumatology/European League Against Rheumatism Boolean Definition, Simplified Disease Activity Index (SDAI) ≤ 3.3, Clinical Disease Activity Index (CDAI) ≤ 2.8, and Disease Activity Score-28 (DAS28) ≤ 2.6] are applied. The annual mean healthcare service utilization costs were estimated from provincial physician billing claims, outpatient visits, and hospitalizations, with linkage to clinical data from the Alberta Biologics Pharmacosurveillance Program (ABioPharm). Cost savings in patients who had a 1-year continuous period of remission were compared to those who did not, using 4 definitions of remission. In 1086 patients, sustained remission rates were 16.1% for DAS28, 8.8% for Boolean, 5.5% for CDAI, and 4.2% for SDAI. The estimated mean annual healthcare cost savings per patient achieving remission (relative to not) were SDAI $1928 (95% CI 592, 3264), DAS28 $1676 (95% CI 987, 2365), and Boolean $1259 (95% CI 417, 2100). The annual savings by CDAI remission per patient were not significant at $423 (95% CI -1757, 2602). For patients in DAS28, Boolean, and SDAI remission, savings were seen both in costs directly related to RA and its comorbidities, and in costs for non-RA-related conditions. The magnitude of the healthcare cost savings varies according to the remission definition used in classifying patient disease status. The highest point estimate for cost savings was observed in patients attaining SDAI remission and the least with the CDAI; confidence intervals for these estimates do overlap. Future pharmacoeconomic analyses should employ all response definitions in assessing the influence of treatment.

Modeling and controlling the two-phase dynamics of the p53 network: a Boolean network approach

NASA Astrophysics Data System (ADS)

Lin, Guo-Qiang; Ao, Bin; Chen, Jia-Wei; Wang, Wen-Xu; Di, Zeng-Ru

2014-12-01

Although much empirical evidence has demonstrated that p53 plays a key role in tumor suppression, the dynamics and function of the regulatory network centered on p53 have not yet been fully understood. Here, we develop a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage. In particular, we map the fates of cells into two types of Boolean attractors, and we find that the apoptosis attractor does not exist for minor DNA damage, reflecting that the cell is reparable. As the amount of DNA damage increases, the basin of the repair attractor shrinks, accompanied by the rising of the apoptosis attractor and the expansion of its basin, indicating that the cell becomes more irreparable with more DNA damage. For severe DNA damage, the repair attractor vanishes, and the apoptosis attractor dominates the state space, accounting for the exclusive fate of death. Based on the Boolean network model, we explore the significance of links, in terms of the sensitivity of the two-phase dynamics, to perturbing the weights of links and removing them. We find that the links are either critical or ordinary, rather than redundant. This implies that the p53 network is irreducible, but tolerant of small mutations at some ordinary links, and this can be interpreted with evolutionary theory. We further devised practical control schemes for steering the system into the apoptosis attractor in the presence of DNA damage by pinning the state of a single node or perturbing the weight of a single link. Our approach offers insights into understanding and controlling the p53 network, which is of paramount importance for medical treatment and genetic engineering.

Transforming Boolean models to continuous models: methodology and application to T-cell receptor signaling

PubMed Central

Wittmann, Dominik M; Krumsiek, Jan; Saez-Rodriguez, Julio; Lauffenburger, Douglas A; Klamt, Steffen; Theis, Fabian J

2009-01-01

Background The understanding of regulatory and signaling networks has long been a core objective in Systems Biology. Knowledge about these networks is mainly of qualitative nature, which allows the construction of Boolean models, where the state of a component is either 'off' or 'on'. While often able to capture the essential behavior of a network, these models can never reproduce detailed time courses of concentration levels. Nowadays however, experiments yield more and more quantitative data. An obvious question therefore is how qualitative models can be used to explain and predict the outcome of these experiments. Results In this contribution we present a canonical way of transforming Boolean into continuous models, where the use of multivariate polynomial interpolation allows transformation of logic operations into a system of ordinary differential equations (ODE). The method is standardized and can readily be applied to large networks. Other, more limited approaches to this task are briefly reviewed and compared. Moreover, we discuss and generalize existing theoretical results on the relation between Boolean and continuous models. As a test case a logical model is transformed into an extensive continuous ODE model describing the activation of T-cells. We discuss how parameters for this model can be determined such that quantitative experimental results are explained and predicted, including time-courses for multiple ligand concentrations and binding affinities of different ligands. This shows that from the continuous model we may obtain biological insights not evident from the discrete one. Conclusion The presented approach will facilitate the interaction between modeling and experiments. Moreover, it provides a straightforward way to apply quantitative analysis methods to qualitatively described systems. PMID:19785753

The DAS28-ESR cutoff value necessary to achieve remission under the new Boolean-based remission criteria in patients receiving tocilizumab.

PubMed

Hirabayashi, Yasuhiko; Ishii, Tomonori

2013-01-01

To seek the cutoff value of the 28-joint disease activity score using erythrocyte sedimentation rate (DAS28-ESR) that is necessary to achieve remission under the new Boolean-based criteria, we analyzed the data for 285 patients with rheumatoid arthritis registered between May 2008 and November 2009 by the Michinoku Tocilizumab Study Group and observed for 1 year after receiving tocilizumab (TCZ) in real clinical practice. Remission rates under the DAS28-ESR criteria and the Boolean criteria were assessed every 6 months after the first TCZ dose. The DAS28-ESR cutoff value necessary to achieve remission under the new criteria was analyzed by receiver operating characteristic (ROC) analysis. Data were analyzed using last observation carried forward. After 12 months of TCZ use, remission was achieved in 164 patients (57.5 %) by DAS28-ESR and 71 patients (24.9 %) under the new criteria for clinical trials. CRP levels scarcely affected remission rates, and the difference between remission rates defined by DAS28-ESR and by the new criteria was mainly due to patient global assessment (PGA). Improvement of PGA was inversely related to disease duration. ROC analysis revealed that the DAS28-ESR cutoff value necessary to predict remission under the new criteria for clinical trials was 1.54, with a sensitivity of 88.7 %, specificity of 85.5 %, positive predictive value of 67.0 %, and negative predictive value of 95.8 %. A DAS28-ESR cutoff value of 1.54 may be reasonable to predict achievement of remission under the new Boolean-based criteria for clinical trials in patients receiving TCZ.

Diagnostic reasoning techniques for selective monitoring

NASA Technical Reports Server (NTRS)

Homem-De-mello, L. S.; Doyle, R. J.

1991-01-01

An architecture for using diagnostic reasoning techniques in selective monitoring is presented. Given the sensor readings and a model of the physical system, a number of assertions are generated and expressed as Boolean equations. The resulting system of Boolean equations is solved symbolically. Using a priori probabilities of component failure and Bayes' rule, revised probabilities of failure can be computed. These will indicate what components have failed or are the most likely to have failed. This approach is suitable for systems that are well understood and for which the correctness of the assertions can be guaranteed. Also, the system must be such that changes are slow enough to allow the computation.

Computer Program Development Specification for Ada Integrated Environment. Ada Compiler Phases B5-AIE (1). COMP (1).

DTIC Science & Technology

1982-11-05

routines required by the Back End. 3.3 Detailed Functional Requirements 3.3.1 Front End 3.3.1.1 DRIVER The DRIVER is the primary user interface to the...Main 2. Exam ple" !.i ,, , ,vari able • id -: go for B Boolean Ai ’ A" ’ I type d 1 I , for Boolean I (from Standard) i I - - for A function i fuction ...TN in. If a TN cannot be allocated to the primary area of storage it needs(such as a register) it is allocated to the spill area reserved in the local

Concept locator: a client-server application for retrieval of UMLS metathesaurus concepts through complex boolean query.

PubMed

Nadkarni, P M

1997-08-01

Concept Locator (CL) is a client-server application that accesses a Sybase relational database server containing a subset of the UMLS Metathesaurus for the purpose of retrieval of concepts corresponding to one or more query expressions supplied to it. CL's query grammar permits complex Boolean expressions, wildcard patterns, and parenthesized (nested) subexpressions. CL translates the query expressions supplied to it into one or more SQL statements that actually perform the retrieval. The generated SQL is optimized by the client to take advantage of the strengths of the server's query optimizer, and sidesteps its weaknesses, so that execution is reasonably efficient.

A comparison of Boolean-based retrieval to the WAIS system for retrieval of aeronautical information

NASA Technical Reports Server (NTRS)

Marchionini, Gary; Barlow, Diane

1994-01-01

An evaluation of an information retrieval system using a Boolean-based retrieval engine and inverted file architecture and WAIS, which uses a vector-based engine, was conducted. Four research questions in aeronautical engineering were used to retrieve sets of citations from the NASA Aerospace Database which was mounted on a WAIS server and available through Dialog File 108 which served as the Boolean-based system (BBS). High recall and high precision searches were done in the BBS and terse and verbose queries were used in the WAIS condition. Precision values for the WAIS searches were consistently above the precision values for high recall BBS searches and consistently below the precision values for high precision BBS searches. Terse WAIS queries gave somewhat better precision performance than verbose WAIS queries. In every case, a small number of relevant documents retrieved by one system were not retrieved by the other, indicating the incomplete nature of the results from either retrieval system. Relevant documents in the WAIS searches were found to be randomly distributed in the retrieved sets rather than distributed by ranks. Advantages and limitations of both types of systems are discussed.

Feedback topology and XOR-dynamics in Boolean networks with varying input structure

NASA Astrophysics Data System (ADS)

Ciandrini, L.; Maffi, C.; Motta, A.; Bassetti, B.; Cosentino Lagomarsino, M.

2009-08-01

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter γ . We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying γ , this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Intrinsic noise and deviations from criticality in Boolean gene-regulatory networks

NASA Astrophysics Data System (ADS)

Villegas, Pablo; Ruiz-Franco, José; Hidalgo, Jorge; Muñoz, Miguel A.

2016-10-01

Gene regulatory networks can be successfully modeled as Boolean networks. A much discussed hypothesis says that such model networks reproduce empirical findings the best if they are tuned to operate at criticality, i.e. at the borderline between their ordered and disordered phases. Critical networks have been argued to lead to a number of functional advantages such as maximal dynamical range, maximal sensitivity to environmental changes, as well as to an excellent tradeoff between stability and flexibility. Here, we study the effect of noise within the context of Boolean networks trained to learn complex tasks under supervision. We verify that quasi-critical networks are the ones learning in the fastest possible way -even for asynchronous updating rules- and that the larger the task complexity the smaller the distance to criticality. On the other hand, when additional sources of intrinsic noise in the network states and/or in its wiring pattern are introduced, the optimally performing networks become clearly subcritical. These results suggest that in order to compensate for inherent stochasticity, regulatory and other type of biological networks might become subcritical rather than being critical, all the most if the task to be performed has limited complexity.

On the number of different dynamics in Boolean networks with deterministic update schedules.

PubMed

Aracena, J; Demongeot, J; Fanchon, E; Montalva, M

2013-04-01

Deterministic Boolean networks are a type of discrete dynamical systems widely used in the modeling of genetic networks. The dynamics of such systems is characterized by the local activation functions and the update schedule, i.e., the order in which the nodes are updated. In this paper, we address the problem of knowing the different dynamics of a Boolean network when the update schedule is changed. We begin by proving that the problem of the existence of a pair of update schedules with different dynamics is NP-complete. However, we show that certain structural properties of the interaction diagraph are sufficient for guaranteeing distinct dynamics of a network. In [1] the authors define equivalence classes which have the property that all the update schedules of a given class yield the same dynamics. In order to determine the dynamics associated to a network, we develop an algorithm to efficiently enumerate the above equivalence classes by selecting a representative update schedule for each class with a minimum number of blocks. Finally, we run this algorithm on the well known Arabidopsis thaliana network to determine the full spectrum of its different dynamics. Copyright © 2013 Elsevier Inc. All rights reserved.

Feedback topology and XOR-dynamics in Boolean networks with varying input structure.

PubMed

Ciandrini, L; Maffi, C; Motta, A; Bassetti, B; Cosentino Lagomarsino, M

2009-08-01

We analyze a model of fixed in-degree random Boolean networks in which the fraction of input-receiving nodes is controlled by the parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR updating scheme. This scheme is interesting because it is accessible analytically and its phenomenology is at the same time under control and as rich as the one of general Boolean networks. We give analytical formulas for the dynamics on general graphs, showing that with a XOR-type evolution rule, dynamic features are direct consequences of the topological feedback structure, in analogy with the role of relevant components in Kauffman networks. Considering graphs with fixed in-degree, we characterize analytically and numerically the feedback regions using graph decimation algorithms (Leaf Removal). With varying gamma , this graph ensemble shows a phase transition that separates a treelike graph region from one in which feedback components emerge. Networks near the transition point have feedback components made of disjoint loops, in which each node has exactly one incoming and one outgoing link. Using this fact, we provide analytical estimates of the maximum period starting from topological considerations.

Boolean logic analysis for flow regime recognition of gas-liquid horizontal flow

NASA Astrophysics Data System (ADS)

Ramskill, Nicholas P.; Wang, Mi

2011-10-01

In order to develop a flowmeter for the accurate measurement of multiphase flows, it is of the utmost importance to correctly identify the flow regime present to enable the selection of the optimal method for metering. In this study, the horizontal flow of air and water in a pipeline was studied under a multitude of conditions using electrical resistance tomography but the flow regimes that are presented in this paper have been limited to plug and bubble air-water flows. This study proposes a novel method for recognition of the prevalent flow regime using only a fraction of the data, thus rendering the analysis more efficient. By considering the average conductivity of five zones along the central axis of the tomogram, key features can be identified, thus enabling the recognition of the prevalent flow regime. Boolean logic and frequency spectrum analysis has been applied for flow regime recognition. Visualization of the flow using the reconstructed images provides a qualitative comparison between different flow regimes. Application of the Boolean logic scheme enables a quantitative comparison of the flow patterns, thus reducing the subjectivity in the identification of the prevalent flow regime.

Virasoro algebra in the KN algebra; Bosonic string with fermionic ghosts on Riemann surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koibuchi, H.

1991-10-10

In this paper the bosonic string model with fermionic ghosts is considered in the framework of the KN algebra. The authors' attentions are paid to representations of KN algebra and a Clifford algebra of the ghosts. The authors show that a Virasoro-like algebra is obtained from KN algebra when KN algebra has certain antilinear anti-involution, and that it is isomorphic to the usual Virasoro algebra. The authors show that there is an expected relation between a central charge of this Virasoro-like algebra and an anomaly of the combined system.

Mathematical Modeling for Inherited Diseases.

PubMed

Anis, Saima; Khan, Madad; Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra.

Mathematical Modeling for Inherited Diseases

PubMed Central

Khan, Saqib

2017-01-01

We introduced a new nonassociative algebra, namely, left almost algebra, and discussed some of its genetic properties. We discussed the relation of this algebra with flexible algebra, Jordan algebra, and generalized Jordan algebra. PMID:28781606

Boolean function applied to Mimosa pudica movements.

PubMed

De Luccia, Thiago Paes de Barros; Friedman, Pedro

2011-09-01

Seismonastic or thigmonastic movements of Mimosa pudica L. is mostly because of the fast loss of water from swollen motor cells, resulting in temporary collapse of cells and quick curvature in the parts where these cells are located. Because of this, the plant has been much studied since the 18th century, leading us to think about the classical binomial stimulus-response (action-reaction) when compared to animals. Mechanic and electrical stimuli were used to investigate the analogy of mimosa branch with an artificial neuron model and to observe the action potential propagation through the mimosa branch. Boolean function applied to the mimosa branch in analogy with an artificial neuron model is one of the peculiarities of our hypothesis.

Nonvolatile “AND,” “OR,” and “NOT” Boolean logic gates based on phase-change memory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Y.; Zhong, Y. P.; Deng, Y. F.

2013-12-21

Electronic devices or circuits that can implement both logic and memory functions are regarded as the building blocks for future massive parallel computing beyond von Neumann architecture. Here we proposed phase-change memory (PCM)-based nonvolatile logic gates capable of AND, OR, and NOT Boolean logic operations verified in SPICE simulations and circuit experiments. The logic operations are parallel computing and results can be stored directly in the states of the logic gates, facilitating the combination of computing and memory in the same circuit. These results are encouraging for ultralow-power and high-speed nonvolatile logic circuit design based on novel memory devices.

Reservoir computing with a single time-delay autonomous Boolean node

NASA Astrophysics Data System (ADS)

Haynes, Nicholas D.; Soriano, Miguel C.; Rosin, David P.; Fischer, Ingo; Gauthier, Daniel J.

2015-02-01

We demonstrate reservoir computing with a physical system using a single autonomous Boolean logic element with time-delay feedback. The system generates a chaotic transient with a window of consistency lasting between 30 and 300 ns, which we show is sufficient for reservoir computing. We then characterize the dependence of computational performance on system parameters to find the best operating point of the reservoir. When the best parameters are chosen, the reservoir is able to classify short input patterns with performance that decreases over time. In particular, we show that four distinct input patterns can be classified for 70 ns, even though the inputs are only provided to the reservoir for 7.5 ns.

Optical reversible programmable Boolean logic unit.

PubMed

Chattopadhyay, Tanay

2012-07-20

Computing with reversibility is the only way to avoid dissipation of energy associated with bit erase. So, a reversible microprocessor is required for future computing. In this paper, a design of a simple all-optical reversible programmable processor is proposed using a polarizing beam splitter, liquid crystal-phase spatial light modulators, a half-wave plate, and plane mirrors. This circuit can perform 16 logical operations according to three programming inputs. Also, inputs can be easily recovered from the outputs. It is named the "reversible programmable Boolean logic unit (RPBLU)." The logic unit is the basic building block of many complex computational operations. Hence the design is important in sense. Two orthogonally polarized lights are defined here as two logical states, respectively.

A sparse matrix algorithm on the Boolean vector machine

NASA Technical Reports Server (NTRS)

Wagner, Robert A.; Patrick, Merrell L.

1988-01-01

VLSI technology is being used to implement a prototype Boolean Vector Machine (BVM), which is a large network of very small processors with equally small memories that operate in SIMD mode; these use bit-serial arithmetic, and communicate via cube-connected cycles network. The BVM's bit-serial arithmetic and the small memories of individual processors are noted to compromise the system's effectiveness in large numerical problem applications. Attention is presently given to the implementation of a basic matrix-vector iteration algorithm for space matrices of the BVM, in order to generate over 1 billion useful floating-point operations/sec for this iteration algorithm. The algorithm is expressed in a novel language designated 'BVM'.

Adaptation and survivors in a random Boolean network.

PubMed

Nakamura, Ikuo

2002-04-01

We introduce the competitive agent with imitation strategy in a random Boolean network, in which the agent plays a competitive game that rewards those in minority. After a long time interval, the worst performer changes its strategy to the one of the best and the process is repeated. The network, initially in a chaotic state, evolves to an intermittent state and finally reaches a frozen state. Time series of survived species (whose strategies are imitated by other agents) in the system depend on the connectivity of each agent. In a system with various connectivity groups, the low connectivity groups win the minority game over the high connectivity groups. We also compared the result with mutation strategy system.

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

ERIC Educational Resources Information Center

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)

Phase transition of Boolean networks with partially nested canalizing functions

NASA Astrophysics Data System (ADS)

Jansen, Kayse; Matache, Mihaela Teodora

2013-07-01

We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the critical condition for the sensitivity of the network under a non-ergodic scenario. We use the proposed mathematical model to determine parameter values for which phase transitions from order to chaos occur. We generate Derrida plots to show that the mathematical model matches the actual network dynamics. The phase transition diagrams indicate that both order and chaos can occur, and that certain parameters induce a larger range of values leading to order versus chaos. The edge-of-chaos curves are identified analytically and numerically. It is shown that the depth of canalization does not cause major dynamical changes once certain thresholds are reached; these thresholds are fairly small in comparison to the connectivity of the nodes.

Development of a computer-aided design software for dental splint in orthognathic surgery

NASA Astrophysics Data System (ADS)

Chen, Xiaojun; Li, Xing; Xu, Lu; Sun, Yi; Politis, Constantinus; Egger, Jan

2016-12-01

In the orthognathic surgery, dental splints are important and necessary to help the surgeon reposition the maxilla or mandible. However, the traditional methods of manual design of dental splints are difficult and time-consuming. The research on computer-aided design software for dental splints is rarely reported. Our purpose is to develop a novel special software named EasySplint to design the dental splints conveniently and efficiently. The design can be divided into two steps, which are the generation of initial splint base and the Boolean operation between it and the maxilla-mandibular model. The initial splint base is formed by ruled surfaces reconstructed using the manually picked points. Then, a method to accomplish Boolean operation based on the distance filed of two meshes is proposed. The interference elimination can be conducted on the basis of marching cubes algorithm and Boolean operation. The accuracy of the dental splint can be guaranteed since the original mesh is utilized to form the result surface. Using EasySplint, the dental splints can be designed in about 10 minutes and saved as a stereo lithography (STL) file for 3D printing in clinical applications. Three phantom experiments were conducted and the efficiency of our method was demonstrated.

Toward using games to teach fundamental computer science concepts

NASA Astrophysics Data System (ADS)

Edgington, Jeffrey Michael

Video and computer games have become an important area of study in the field of education. Games have been designed to teach mathematics, physics, raise social awareness, teach history and geography, and train soldiers in the military. Recent work has created computer games for teaching computer programming and understanding basic algorithms. We present an investigation where computer games are used to teach two fundamental computer science concepts: boolean expressions and recursion. The games are intended to teach the concepts and not how to implement them in a programming language. For this investigation, two computer games were created. One is designed to teach basic boolean expressions and operators and the other to teach fundamental concepts of recursion. We describe the design and implementation of both games. We evaluate the effectiveness of these games using before and after surveys. The surveys were designed to ascertain basic understanding, attitudes and beliefs regarding the concepts. The boolean game was evaluated with local high school students and students in a college level introductory computer science course. The recursion game was evaluated with students in a college level introductory computer science course. We present the analysis of the collected survey information for both games. This analysis shows a significant positive change in student attitude towards recursion and modest gains in student learning outcomes for both topics.

Development of a computer-aided design software for dental splint in orthognathic surgery

PubMed Central

Chen, Xiaojun; Li, Xing; Xu, Lu; Sun, Yi; Politis, Constantinus; Egger, Jan

2016-01-01

In the orthognathic surgery, dental splints are important and necessary to help the surgeon reposition the maxilla or mandible. However, the traditional methods of manual design of dental splints are difficult and time-consuming. The research on computer-aided design software for dental splints is rarely reported. Our purpose is to develop a novel special software named EasySplint to design the dental splints conveniently and efficiently. The design can be divided into two steps, which are the generation of initial splint base and the Boolean operation between it and the maxilla-mandibular model. The initial splint base is formed by ruled surfaces reconstructed using the manually picked points. Then, a method to accomplish Boolean operation based on the distance filed of two meshes is proposed. The interference elimination can be conducted on the basis of marching cubes algorithm and Boolean operation. The accuracy of the dental splint can be guaranteed since the original mesh is utilized to form the result surface. Using EasySplint, the dental splints can be designed in about 10 minutes and saved as a stereo lithography (STL) file for 3D printing in clinical applications. Three phantom experiments were conducted and the efficiency of our method was demonstrated. PMID:27966601

Development of a computer-aided design software for dental splint in orthognathic surgery.

PubMed

Chen, Xiaojun; Li, Xing; Xu, Lu; Sun, Yi; Politis, Constantinus; Egger, Jan

2016-12-14

In the orthognathic surgery, dental splints are important and necessary to help the surgeon reposition the maxilla or mandible. However, the traditional methods of manual design of dental splints are difficult and time-consuming. The research on computer-aided design software for dental splints is rarely reported. Our purpose is to develop a novel special software named EasySplint to design the dental splints conveniently and efficiently. The design can be divided into two steps, which are the generation of initial splint base and the Boolean operation between it and the maxilla-mandibular model. The initial splint base is formed by ruled surfaces reconstructed using the manually picked points. Then, a method to accomplish Boolean operation based on the distance filed of two meshes is proposed. The interference elimination can be conducted on the basis of marching cubes algorithm and Boolean operation. The accuracy of the dental splint can be guaranteed since the original mesh is utilized to form the result surface. Using EasySplint, the dental splints can be designed in about 10 minutes and saved as a stereo lithography (STL) file for 3D printing in clinical applications. Three phantom experiments were conducted and the efficiency of our method was demonstrated.

Bounds on the number of hidden neurons in three-layer binary neural networks.

PubMed

Zhang, Zhaozhi; Ma, Xiaomin; Yang, Yixian

2003-09-01

This paper investigates an important problem concerning the complexity of three-layer binary neural networks (BNNs) with one hidden layer. The neuron in the studied BNNs employs a hard limiter activation function with only integer weights and an integer threshold. The studies are focused on implementations of arbitrary Boolean functions which map from [0, 1]n into [0, 1]. A deterministic algorithm called set covering algorithm (SCA) is proposed for the construction of a three-layer BNN to implement an arbitrary Boolean function. The SCA is based on a unit sphere covering (USC) of the Hamming space (HS) which is chosen in advance. It is proved that for the implementation of an arbitrary Boolean function of n-variables (n > or = 3) by using SCA, [3L/2] hidden neurons are necessary and sufficient, where L is the number of unit spheres contained in the chosen USC of the n-dimensional HS. It is shown that by using SCA, the number of hidden neurons required is much less than that by using a two-parallel hyperplane method. In order to indicate the potential ability of three-layer BNNs, a lower bound on the required number of hidden neurons which is derived by using the method of estimating the Vapnik-Chervonenkis (VC) dimension is also given.

A note on derivations of Murray-von Neumann algebras.

PubMed

Kadison, Richard V; Liu, Zhe

2014-02-11

A Murray-von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray-von Neumann algebras. We show that the "extended derivations" of a Murray-von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray-von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer's seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements.

Banach Synaptic Algebras

NASA Astrophysics Data System (ADS)

Foulis, David J.; Pulmannov, Sylvia

2018-04-01

Using a representation theorem of Erik Alfsen, Frederic Schultz, and Erling Størmer for special JB-algebras, we prove that a synaptic algebra is norm complete (i.e., Banach) if and only if it is isomorphic to the self-adjoint part of a Rickart C∗-algebra. Also, we give conditions on a Banach synaptic algebra that are equivalent to the condition that it is isomorphic to the self-adjoint part of an AW∗-algebra. Moreover, we study some relationships between synaptic algebras and so-called generalized Hermitian algebras.

The value of less connected agents in Boolean networks

NASA Astrophysics Data System (ADS)

Epstein, Daniel; Bazzan, Ana L. C.

2013-11-01

In multiagent systems, agents often face binary decisions where one seeks to take either the minority or the majority side. Examples are minority and congestion games in general, i.e., situations that require coordination among the agents in order to depict efficient decisions. In minority games such as the El Farol Bar Problem, previous works have shown that agents may reach appropriate levels of coordination, mostly by looking at the history of past decisions. Not many works consider any kind of structure of the social network, i.e., how agents are connected. Moreover, when structure is indeed considered, it assumes some kind of random network with a given, fixed connectivity degree. The present paper departs from the conventional approach in some ways. First, it considers more realistic network topologies, based on preferential attachments. This is especially useful in social networks. Second, the formalism of random Boolean networks is used to help agents to make decisions given their attachments (for example acquaintances). This is coupled with a reinforcement learning mechanism that allows agents to select strategies that are locally and globally efficient. Third, we use agent-based modeling and simulation, a microscopic approach, which allows us to draw conclusions about individuals and/or classes of individuals. Finally, for the sake of illustration we use two different scenarios, namely the El Farol Bar Problem and a binary route choice scenario. With this approach we target systems that adapt dynamically to changes in the environment, including other adaptive decision-makers. Our results using preferential attachments and random Boolean networks are threefold. First we show that an efficient equilibrium can be achieved, provided agents do experimentation. Second, microscopic analysis show that influential agents tend to consider few inputs in their Boolean functions. Third, we have also conducted measurements related to network clustering and centrality that help to see how agents are organized.

Stabilization of perturbed Boolean network attractors through compensatory interactions

PubMed Central

2014-01-01

Background Understanding and ameliorating the effects of network damage are of significant interest, due in part to the variety of applications in which network damage is relevant. For example, the effects of genetic mutations can cascade through within-cell signaling and regulatory networks and alter the behavior of cells, possibly leading to a wide variety of diseases. The typical approach to mitigating network perturbations is to consider the compensatory activation or deactivation of system components. Here, we propose a complementary approach wherein interactions are instead modified to alter key regulatory functions and prevent the network damage from triggering a deregulatory cascade. Results We implement this approach in a Boolean dynamic framework, which has been shown to effectively model the behavior of biological regulatory and signaling networks. We show that the method can stabilize any single state (e.g., fixed point attractors or time-averaged representations of multi-state attractors) to be an attractor of the repaired network. We show that the approach is minimalistic in that few modifications are required to provide stability to a chosen attractor and specific in that interventions do not have undesired effects on the attractor. We apply the approach to random Boolean networks, and further show that the method can in some cases successfully repair synchronous limit cycles. We also apply the methodology to case studies from drought-induced signaling in plants and T-LGL leukemia and find that it is successful in both stabilizing desired behavior and in eliminating undesired outcomes. Code is made freely available through the software package BooleanNet. Conclusions The methodology introduced in this report offers a complementary way to manipulating node expression levels. A comprehensive approach to evaluating network manipulation should take an "all of the above" perspective; we anticipate that theoretical studies of interaction modification, coupled with empirical advances, will ultimately provide researchers with greater flexibility in influencing system behavior. PMID:24885780

Disparity between ultrasound and clinical findings in psoriatic arthritis.

PubMed

Husic, Rusmir; Gretler, Judith; Felber, Anja; Graninger, Winfried B; Duftner, Christina; Hermann, Josef; Dejaco, Christian

2014-08-01

To investigate the association between psoriatic arthritis (PsA)-specific clinical composite scores and ultrasound-verified pathology as well as comparison of clinical and ultrasound definitions of remission. We performed a prospective study on 70 consecutive PsA patients. Clinical assessments included components of Disease Activity Index for Psoriatic Arthritis (DAPSA) and the Composite Psoriatic Disease Activity Index (CPDAI). Minimal disease activity (MDA) and the following remission criteria were applied: CPDAI joint, entheses and dactylitis domains (CPDAI-JED)=0, DAPSA≤3.3, Boolean's remission definition and physician-judged remission (rem-phys). B-mode and power Doppler (PD-) ultrasound findings were semiquantitatively scored at 68 joints (evaluating synovia, peritendinous tissue, tendons and bony changes) and 14 entheses. Ultrasound remission and minimal ultrasound disease activity (MUDA) were defined as PD-score=0 and PD-score ≤1, respectively, at joints, peritendinous tissue, tendons and entheses. DAPSA but not CPDAI correlated with B-mode and PD-synovitis. Ultrasound signs of enthesitis, dactylitis, tenosynovitis and perisynovitis were not linked with clinical composites. Clinical remission or MDA was observed in 15.7% to 47.1% of PsA patients. Ultrasound remission and MUDA were present in 4.3% and 20.0% of patients, respectively. Joint and tendon-related PD-scores were higher in patients with active versus inactive disease according to CPDAI-JED, DAPSA, Boolean's and rem-phys, whereas no difference was observed regarding enthesitis and perisynovitis. DAPSA≤3.3 (OR 3.9, p=0.049) and Boolean's definition (OR 4.6, p=0.03) were more useful to predict MUDA than other remission criteria. PsA-specific composite scores partially reflect ultrasound findings. DAPSA and Boolean's remission definitions better identify MUDA patients than other clinical criteria. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

NASA Astrophysics Data System (ADS)

Zhang, Tianjie; Gao, Xing; Guo, Li

2016-10-01

The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

The Unitality of Quantum B-algebras

NASA Astrophysics Data System (ADS)

Han, Shengwei; Xu, Xiaoting; Qin, Feng

2018-02-01

Quantum B-algebras as a generalization of quantales were introduced by Rump and Yang, which cover the majority of implicational algebras and provide a unified semantic for a wide class of substructural logics. Unital quantum B-algebras play an important role in the classification of implicational algebras. The main purpose of this paper is to construct unital quantum B-algebras from non-unital quantum B-algebras.

Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm.

PubMed

Stoll, Gautier; Viara, Eric; Barillot, Emmanuel; Calzone, Laurence

2012-08-29

Mathematical modeling is used as a Systems Biology tool to answer biological questions, and more precisely, to validate a network that describes biological observations and predict the effect of perturbations. This article presents an algorithm for modeling biological networks in a discrete framework with continuous time. There exist two major types of mathematical modeling approaches: (1) quantitative modeling, representing various chemical species concentrations by real numbers, mainly based on differential equations and chemical kinetics formalism; (2) and qualitative modeling, representing chemical species concentrations or activities by a finite set of discrete values. Both approaches answer particular (and often different) biological questions. Qualitative modeling approach permits a simple and less detailed description of the biological systems, efficiently describes stable state identification but remains inconvenient in describing the transient kinetics leading to these states. In this context, time is represented by discrete steps. Quantitative modeling, on the other hand, can describe more accurately the dynamical behavior of biological processes as it follows the evolution of concentration or activities of chemical species as a function of time, but requires an important amount of information on the parameters difficult to find in the literature. Here, we propose a modeling framework based on a qualitative approach that is intrinsically continuous in time. The algorithm presented in this article fills the gap between qualitative and quantitative modeling. It is based on continuous time Markov process applied on a Boolean state space. In order to describe the temporal evolution of the biological process we wish to model, we explicitly specify the transition rates for each node. For that purpose, we built a language that can be seen as a generalization of Boolean equations. Mathematically, this approach can be translated in a set of ordinary differential equations on probability distributions. We developed a C++ software, MaBoSS, that is able to simulate such a system by applying Kinetic Monte-Carlo (or Gillespie algorithm) on the Boolean state space. This software, parallelized and optimized, computes the temporal evolution of probability distributions and estimates stationary distributions. Applications of the Boolean Kinetic Monte-Carlo are demonstrated for three qualitative models: a toy model, a published model of p53/Mdm2 interaction and a published model of the mammalian cell cycle. Our approach allows to describe kinetic phenomena which were difficult to handle in the original models. In particular, transient effects are represented by time dependent probability distributions, interpretable in terms of cell populations.

Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra

NASA Astrophysics Data System (ADS)

Caroca, Ricardo; Concha, Patrick; Rodríguez, Evelyn; Salgado-Rebolledo, Patricio

2018-03-01

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the bms3 algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite-dimensional lifts of the so-called Bk, Ck and Dk algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Kač-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suh, Uhi Rinn, E-mail: uhrisu1@math.snu.ac.kr

We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms ofmore » free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.« less

A note on derivations of Murray–von Neumann algebras

PubMed Central

Kadison, Richard V.; Liu, Zhe

2014-01-01

A Murray–von Neumann algebra is the algebra of operators affiliated with a finite von Neumann algebra. In this article, we first present a brief introduction to the theory of derivations of operator algebras from both the physical and mathematical points of view. We then describe our recent work on derivations of Murray–von Neumann algebras. We show that the “extended derivations” of a Murray–von Neumann algebra, those that map the associated finite von Neumann algebra into itself, are inner. In particular, we prove that the only derivation that maps a Murray–von Neumann algebra associated with a factor of type II1 into that factor is 0. Those results are extensions of Singer’s seminal result answering a question of Kaplansky, as applied to von Neumann algebras: The algebra may be noncommutative and may even contain unbounded elements. PMID:24469831

A double commutant theorem for Murray–von Neumann algebras

PubMed Central

Liu, Zhe

2012-01-01

Murray–von Neumann algebras are algebras of operators affiliated with finite von Neumann algebras. In this article, we study commutativity and affiliation of self-adjoint operators (possibly unbounded). We show that a maximal abelian self-adjoint subalgebra of the Murray–von Neumann algebra associated with a finite von Neumann algebra is the Murray–von Neumann algebra , where is a maximal abelian self-adjoint subalgebra of and, in addition, is . We also prove that the Murray–von Neumann algebra with the center of is the center of the Murray–von Neumann algebra . Von Neumann’s celebrated double commutant theorem characterizes von Neumann algebras as those for which , where , the commutant of , is the set of bounded operators on the Hilbert space that commute with all operators in . At the end of this article, we present a double commutant theorem for Murray–von Neumann algebras. PMID:22543165

Type and Location of Wearable Sensors for Monitoring Falls during Static and Dynamic Tasks in Healthy Elderly: A Review

PubMed Central

Sorriso, Antonietta; Liparoti, Marianna; Ferraioli, Giampaolo; Sorrentino, Pierpaolo

2018-01-01

In recent years, the meaning of successful living has moved from extending lifetime to improving the quality of aging, mainly in terms of high cognitive and physical functioning together with avoiding diseases. In healthy elderly, falls represent an alarming accident both in terms of number of events and the consequent decrease in the quality of life. Stability control is a key approach for studying the genesis of falls, for detecting the event and trying to develop methodologies to prevent it. Wearable sensors have proved to be very useful in monitoring and analyzing the stability of subjects. Within this manuscript, a review of the approaches proposed in the literature for fall risk assessment, fall prevention and fall detection in healthy elderly is provided. The review has been carried out by using the most adopted publication databases and by defining a search strategy based on keywords and boolean algebra constructs. The analysis aims at evaluating the state of the art of such kind of monitoring, both in terms of most adopted sensor technologies and of their location on the human body. The review has been extended to both dynamic and static analyses. In order to provide a useful tool for researchers involved in this field, the manuscript also focuses on the tests conducted in the analyzed studies, mainly in terms of characteristics of the population involved and of the tasks used. Finally, the main trends related to sensor typology, sensor location and tasks have been identified. PMID:29783647

Assessing Algebraic Solving Ability: A Theoretical Framework

ERIC Educational Resources Information Center

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…

On the intersection of irreducible components of the space of finite-dimensional Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gorbatsevich, Vladimir V

2012-07-31

The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra ismore » considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.« less

Duncan F. Gregory, William Walton and the development of British algebra: 'algebraical geometry', 'geometrical algebra', abstraction.

PubMed

Verburgt, Lukas M

2016-01-01

This paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on 'algebraical geometry' and 'geometrical algebra' in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the 'abstract algebra' and 'abstract geometry' of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to 'algebraical geometry' and 'geometrical algebra' of the second generation of 'scientific' symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s-1840s.

From simplicial Lie algebras and hypercrossed complexes to differential graded Lie algebras via 1-jets

NASA Astrophysics Data System (ADS)

Jurčo, Branislav

2012-12-01

Let g be a simplicial Lie algebra with Moore complex Ng of length k. Let G be the simplicial Lie group integrating g, such that each Gn is simply connected. We use the 1-jet of the classifying space W¯ G to construct, starting from g, a Lie k-algebra L. The so constructed Lie k-algebra L is actually a differential graded Lie algebra. The differential and the brackets are explicitly described in terms (of a part) of the corresponding k-hypercrossed complex structure of Ng. The result can be seen as a geometric interpretation of Quillen's (purely algebraic) construction of the adjunction between simplicial Lie algebras and dg-Lie algebras.

Boolean function applied to Mimosa pudica movements

PubMed Central

Friedman, Pedro

2011-01-01

Seismonastic or thigmonastic movements of Mimosa pudica L. is mostly because of the fast loss of water from swollen motor cells, resulting in temporary collapse of cells and quick curvature in the parts where these cells are located. Because of this, the plant has been much studied since the 18th century, leading us to think about the classical binomial stimulus-response (action-reaction) when compared to animals. Mechanic and electrical stimuli were used to investigate the analogy of mimosa branch with an artificial neuron model and to observe the action potential propagation through the mimosa branch. Boolean function applied to the mimosa branch in analogy with an artificial neuron model is one of the peculiarities of our hypothesis. PMID:21847029

Fisher information at the edge of chaos in random Boolean networks.

PubMed

Wang, X Rosalind; Lizier, Joseph T; Prokopenko, Mikhail

2011-01-01

We study the order-chaos phase transition in random Boolean networks (RBNs), which have been used as models of gene regulatory networks. In particular we seek to characterize the phase diagram in information-theoretic terms, focusing on the effect of the control parameters (activity level and connectivity). Fisher information, which measures how much system dynamics can reveal about the control parameters, offers a natural interpretation of the phase diagram in RBNs. We report that this measure is maximized near the order-chaos phase transitions in RBNs, since this is the region where the system is most sensitive to its parameters. Furthermore, we use this study of RBNs to clarify the relationship between Shannon and Fisher information measures.

Investigating Cell Criticality

NASA Astrophysics Data System (ADS)

Serra, R.; Villani, M.; Damiani, C.; Graudenzi, A.; Ingrami, P.; Colacci, A.

Random Boolean networks provide a way to give a precise meaning to the notion that living beings are in a critical state. Some phenomena which are observed in real biological systems (distribution of "avalanches" in gene knock-out experiments) can be modeled using random Boolean networks, and the results can be analytically proven to depend upon the Derrida parameter, which also determines whether the network is critical. By comparing observed and simulated data one can then draw inferences about the criticality of biological cells, although with some care because of the limited number of experimental observations. The relationship between the criticality of a single network and that of a set of interacting networks, which simulate a tissue or a bacterial colony, is also analyzed by computer simulations.

Programming Cell Adhesion for On-Chip Sequential Boolean Logic Functions.

PubMed

Qu, Xiangmeng; Wang, Shaopeng; Ge, Zhilei; Wang, Jianbang; Yao, Guangbao; Li, Jiang; Zuo, Xiaolei; Shi, Jiye; Song, Shiping; Wang, Lihua; Li, Li; Pei, Hao; Fan, Chunhai

2017-08-02

Programmable remodelling of cell surfaces enables high-precision regulation of cell behavior. In this work, we developed in vitro constructed DNA-based chemical reaction networks (CRNs) to program on-chip cell adhesion. We found that the RGD-functionalized DNA CRNs are entirely noninvasive when interfaced with the fluidic mosaic membrane of living cells. DNA toehold with different lengths could tunably alter the release kinetics of cells, which shows rapid release in minutes with the use of a 6-base toehold. We further demonstrated the realization of Boolean logic functions by using DNA strand displacement reactions, which include multi-input and sequential cell logic gates (AND, OR, XOR, and AND-OR). This study provides a highly generic tool for self-organization of biological systems.

Reliable computation from contextual correlations

NASA Astrophysics Data System (ADS)

Oestereich, André L.; Galvão, Ernesto F.

2017-12-01

An operational approach to the study of computation based on correlations considers black boxes with one-bit inputs and outputs, controlled by a limited classical computer capable only of performing sums modulo-two. In this setting, it was shown that noncontextual correlations do not provide any extra computational power, while contextual correlations were found to be necessary for the deterministic evaluation of nonlinear Boolean functions. Here we investigate the requirements for reliable computation in this setting; that is, the evaluation of any Boolean function with success probability bounded away from 1 /2 . We show that bipartite CHSH quantum correlations suffice for reliable computation. We also prove that an arbitrarily small violation of a multipartite Greenberger-Horne-Zeilinger noncontextuality inequality also suffices for reliable computation.

The pseudo-Boolean optimization approach to form the N-version software structure

NASA Astrophysics Data System (ADS)

Kovalev, I. V.; Kovalev, D. I.; Zelenkov, P. V.; Voroshilova, A. A.

2015-10-01

The problem of developing an optimal structure of N-version software system presents a kind of very complex optimization problem. This causes the use of deterministic optimization methods inappropriate for solving the stated problem. In this view, exploiting heuristic strategies looks more rational. In the field of pseudo-Boolean optimization theory, the so called method of varied probabilities (MVP) has been developed to solve problems with a large dimensionality. Some additional modifications of MVP have been made to solve the problem of N-version systems design. Those algorithms take into account the discovered specific features of the objective function. The practical experiments have shown the advantage of using these algorithm modifications because of reducing a search space.

A procedure concept for local reflex control of grasping

NASA Technical Reports Server (NTRS)

Fiorini, Paolo; Chang, Jeffrey

1989-01-01

An architecture is proposed for the control of robotic devices, and in particular of anthropomorphic hands, characterized by a hierarchical structure in which every level of the architecture contains data and control function with varying degree of abstraction. Bottom levels of the hierarchy interface directly with sensors and actuators, and process raw data and motor commands. Higher levels perform more symbolic types of tasks, such as application of boolean rules and general planning operations. Layers implementation has to be consistent with the type of operation and its requirements for real time control. It is proposed to implement the rule level with a Boolean Artificial Neural Network characterized by a response time sufficient for producing reflex corrective action at the actuator level.

Algebra: A Challenge at the Crossroads of Policy and Practice

ERIC Educational Resources Information Center

Stein, Mary Kay; Kaufman, Julia Heath; Sherman, Milan; Hillen, Amy F.

2011-01-01

The authors review what is known about early and universal algebra, including who is getting access to algebra and student outcomes associated with algebra course taking in general and specifically with universal algebra policies. The findings indicate that increasing numbers of students, some of whom are underprepared, are taking algebra earlier.…

Making Algebra Work: Instructional Strategies that Deepen Student Understanding, within and between Algebraic Representations

ERIC Educational Resources Information Center

Star, Jon R.; Rittle-Johnson, Bethany

2009-01-01

Competence in algebra is increasingly recognized as a critical milestone in students' middle and high school years. The transition from arithmetic to algebra is a notoriously difficult one, and improvements in algebra instruction are greatly needed (National Research Council, 2001). Algebra historically has represented students' first sustained…

Algebraic K-theory, K-regularity, and -duality of -stable C ∗-algebras

NASA Astrophysics Data System (ADS)

Mahanta, Snigdhayan

2015-12-01

We develop an algebraic formalism for topological -duality. More precisely, we show that topological -duality actually induces an isomorphism between noncommutative motives that in turn implements the well-known isomorphism between twisted K-theories (up to a shift). In order to establish this result we model topological K-theory by algebraic K-theory. We also construct an E ∞ -operad starting from any strongly self-absorbing C ∗-algebra . Then we show that there is a functorial topological K-theory symmetric spectrum construction on the category of separable C ∗-algebras, such that is an algebra over this operad; moreover, is a module over this algebra. Along the way we obtain a new symmetric spectra valued functorial model for the (connective) topological K-theory of C ∗-algebras. We also show that -stable C ∗-algebras are K-regular providing evidence for a conjecture of Rosenberg. We conclude with an explicit description of the algebraic K-theory of a x+ b-semigroup C ∗-algebras coming from number theory and that of -stabilized noncommutative tori.

Generalized Clifford Algebras as Algebras in Suitable Symmetric Linear Gr-Categories

NASA Astrophysics Data System (ADS)

Cheng, Tao; Huang, Hua-Lin; Yang, Yuping

2016-01-01

By viewing Clifford algebras as algebras in some suitable symmetric Gr-categories, Albuquerque and Majid were able to give a new derivation of some well known results about Clifford algebras and to generalize them. Along the same line, Bulacu observed that Clifford algebras are weak Hopf algebras in the aforementioned categories and obtained other interesting properties. The aim of this paper is to study generalized Clifford algebras in a similar manner and extend the results of Albuquerque, Majid and Bulacu to the generalized setting. In particular, by taking full advantage of the gauge transformations in symmetric linear Gr-categories, we derive the decomposition theorem and provide categorical weak Hopf structures for generalized Clifford algebras in a conceptual and simpler manner.

Dynamical systems defined on infinite dimensional lie algebras of the ''current algebra'' or ''Kac-Moody'' type

NASA Astrophysics Data System (ADS)

Hermann, Robert

1982-07-01

Recent work by Morrison, Marsden, and Weinstein has drawn attention to the possibility of utilizing the cosymplectic structure of the dual of the Lie algebra of certain infinite dimensional Lie groups to study hydrodynamical and plasma systems. This paper treats certain models arising in elementary particle physics, considered by Lee, Weinberg, and Zumino; Sugawara; Bardacki, Halpern, and Frishman; Hermann; and Dolan. The lie algebras involved are associated with the ''current algebras'' of Gell-Mann. This class of Lie algebras contains certain of the algebras that are called ''Kac-Moody algebras'' in the recent mathematics and mathematical physics literature.

Information processing in dendrites I. Input pattern generalisation.

PubMed

Gurney, K N

2001-10-01

In this paper and its companion, we address the question as to whether there are any general principles underlying information processing in the dendritic trees of biological neurons. In order to address this question, we make two assumptions. First, the key architectural feature of dendrites responsible for many of their information processing abilities is the existence of independent sub-units performing local non-linear processing. Second, any general functional principles operate at a level of abstraction in which neurons are modelled by Boolean functions. To accommodate these assumptions, we therefore define a Boolean model neuron-the multi-cube unit (MCU)-which instantiates the notion of the discrete functional sub-unit. We then use this model unit to explore two aspects of neural functionality: generalisation (in this paper) and processing complexity (in its companion). Generalisation is dealt with from a geometric viewpoint and is quantified using a new metric-the set of order parameters. These parameters are computed for threshold logic units (TLUs), a class of random Boolean functions, and MCUs. Our interpretation of the order parameters is consistent with our knowledge of generalisation in TLUs and with the lack of generalisation in randomly chosen functions. Crucially, the order parameters for MCUs imply that these functions possess a range of generalisation behaviour. We argue that this supports the general thesis that dendrites facilitate input pattern generalisation despite any local non-linear processing within functionally isolated sub-units.

Attractor-Based Obstructions to Growth in Homogeneous Cyclic Boolean Automata.

PubMed

Khan, Bilal; Cantor, Yuri; Dombrowski, Kirk

2015-11-01

We consider a synchronous Boolean organism consisting of N cells arranged in a circle, where each cell initially takes on an independently chosen Boolean value. During the lifetime of the organism, each cell updates its own value by responding to the presence (or absence) of diversity amongst its two neighbours' values. We show that if all cells eventually take a value of 0 (irrespective of their initial values) then the organism necessarily has a cell count that is a power of 2. In addition, the converse is also proved: if the number of cells in the organism is a proper power of 2, then no matter what the initial values of the cells are, eventually all cells take on a value of 0 and then cease to change further. We argue that such an absence of structure in the dynamical properties of the organism implies a lack of adaptiveness, and so is evolutionarily disadvantageous. It follows that as the organism doubles in size (say from m to 2m) it will necessarily encounter an intermediate size that is a proper power of 2, and suffers from low adaptiveness. Finally we show, through computational experiments, that one way an organism can grow to more than twice its size and still avoid passing through intermediate sizes that lack structural dynamics, is for the organism to depart from assumptions of homogeneity at the cellular level.

Evolution of a designless nanoparticle network into reconfigurable Boolean logic

NASA Astrophysics Data System (ADS)

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.

Integrating Multiple Data Sources for Combinatorial Marker Discovery: A Study in Tumorigenesis.

PubMed

Bandyopadhyay, Sanghamitra; Mallik, Saurav

2018-01-01

Identification of combinatorial markers from multiple data sources is a challenging task in bioinformatics. Here, we propose a novel computational framework for identifying significant combinatorial markers ( s) using both gene expression and methylation data. The gene expression and methylation data are integrated into a single continuous data as well as a (post-discretized) boolean data based on their intrinsic (i.e., inverse) relationship. A novel combined score of methylation and expression data (viz., ) is introduced which is computed on the integrated continuous data for identifying initial non-redundant set of genes. Thereafter, (maximal) frequent closed homogeneous genesets are identified using a well-known biclustering algorithm applied on the integrated boolean data of the determined non-redundant set of genes. A novel sample-based weighted support ( ) is then proposed that is consecutively calculated on the integrated boolean data of the determined non-redundant set of genes in order to identify the non-redundant significant genesets. The top few resulting genesets are identified as potential s. Since our proposed method generates a smaller number of significant non-redundant genesets than those by other popular methods, the method is much faster than the others. Application of the proposed technique on an expression and a methylation data for Uterine tumor or Prostate Carcinoma produces a set of significant combination of markers. We expect that such a combination of markers will produce lower false positives than individual markers.

Predictive computation of genomic logic processing functions in embryonic development

PubMed Central

Peter, Isabelle S.; Faure, Emmanuel; Davidson, Eric H.

2012-01-01

Gene regulatory networks (GRNs) control the dynamic spatial patterns of regulatory gene expression in development. Thus, in principle, GRN models may provide system-level, causal explanations of developmental process. To test this assertion, we have transformed a relatively well-established GRN model into a predictive, dynamic Boolean computational model. This Boolean model computes spatial and temporal gene expression according to the regulatory logic and gene interactions specified in a GRN model for embryonic development in the sea urchin. Additional information input into the model included the progressive embryonic geometry and gene expression kinetics. The resulting model predicted gene expression patterns for a large number of individual regulatory genes each hour up to gastrulation (30 h) in four different spatial domains of the embryo. Direct comparison with experimental observations showed that the model predictively computed these patterns with remarkable spatial and temporal accuracy. In addition, we used this model to carry out in silico perturbations of regulatory functions and of embryonic spatial organization. The model computationally reproduced the altered developmental functions observed experimentally. Two major conclusions are that the starting GRN model contains sufficiently complete regulatory information to permit explanation of a complex developmental process of gene expression solely in terms of genomic regulatory code, and that the Boolean model provides a tool with which to test in silico regulatory circuitry and developmental perturbations. PMID:22927416

Attractor-Based Obstructions to Growth in Homogeneous Cyclic Boolean Automata

PubMed Central

Khan, Bilal; Cantor, Yuri; Dombrowski, Kirk

2016-01-01

We consider a synchronous Boolean organism consisting of N cells arranged in a circle, where each cell initially takes on an independently chosen Boolean value. During the lifetime of the organism, each cell updates its own value by responding to the presence (or absence) of diversity amongst its two neighbours’ values. We show that if all cells eventually take a value of 0 (irrespective of their initial values) then the organism necessarily has a cell count that is a power of 2. In addition, the converse is also proved: if the number of cells in the organism is a proper power of 2, then no matter what the initial values of the cells are, eventually all cells take on a value of 0 and then cease to change further. We argue that such an absence of structure in the dynamical properties of the organism implies a lack of adaptiveness, and so is evolutionarily disadvantageous. It follows that as the organism doubles in size (say from m to 2m) it will necessarily encounter an intermediate size that is a proper power of 2, and suffers from low adaptiveness. Finally we show, through computational experiments, that one way an organism can grow to more than twice its size and still avoid passing through intermediate sizes that lack structural dynamics, is for the organism to depart from assumptions of homogeneity at the cellular level. PMID:27660398

The general symmetry algebra structure of the underdetermined equation ux=(vxx)2

NASA Astrophysics Data System (ADS)

Kersten, Paul H. M.

1991-08-01

In a recent paper, Anderson, Kamran, and Olver [``Interior, exterior, and generalized symmetries,'' preprint (1990)] obtained the first- and second-order generalized symmetry algebra for the system ux=(vxx)2, leading to the noncompact real form of the exceptional Lie algebra G2. Here, the structure of the general higher-order symmetry algebra is obtained. Moreover, the Lie algebra G2 is obtained as ordinary symmetry algebra of the associated first-order system. The general symmetry algebra for ux=f(u,v,vx,...,) is established also.

A calculus based on a q-deformed Heisenberg algebra

DOE PAGES

Cerchiai, B. L.; Hinterding, R.; Madore, J.; ...

1999-04-27

We show how one can construct a differential calculus over an algebra where position variables $x$ and momentum variables p have be defined. As the simplest example we consider the one-dimensional q-deformed Heisenberg algebra. This algebra has a subalgebra generated by cursive Greek chi and its inverse which we call the coordinate algebra. A physical field is considered to be an element of the completion of this algebra. We can construct a derivative which leaves invariant the coordinate algebra and so takes physical fields into physical fields. A generalized Leibniz rule for this algebra can be found. Based on thismore » derivative differential forms and an exterior differential calculus can be constructed.« less

Highest-weight representations of Brocherd`s algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slansky, R.

1997-01-01

General features of highest-weight representations of Borcherd`s algebras are described. to show their typical features, several representations of Borcherd`s extensions of finite-dimensional algebras are analyzed. Then the example of the extension of affine- su(2) to a Borcherd`s algebra is examined. These algebras provide a natural way to extend a Kac-Moody algebra to include the hamiltonian and number-changing operators in a generalized symmetry structure.

Identities of Finitely Generated Algebras Over AN Infinite Field

NASA Astrophysics Data System (ADS)

Kemer, A. R.

1991-02-01

It is proved that for each finitely generated associative PI-algebra U over an infinite field F, there is a finite-dimensional F-algebra C such that the ideals of identities of the algebras U and C coincide. This yields a positive solution to the local problem of Specht for algebras over an infinite field: A finitely generated free associative algebra satisfies the maximum condition for T-ideals.

Quantum cluster algebras and quantum nilpotent algebras.

PubMed

Goodearl, Kenneth R; Yakimov, Milen T

2014-07-08

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein-Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405-455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337-397] for the case of symmetric Kac-Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1-52] associated with double Bruhat cells coincide with the corresponding cluster algebras.

Quantum cluster algebras and quantum nilpotent algebras

PubMed Central

Goodearl, Kenneth R.; Yakimov, Milen T.

2014-01-01

A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding upper quantum cluster algebras. We also establish analogs of these results for a large class of Poisson nilpotent algebras. Many important families of coordinate rings are subsumed in the class we are covering, which leads to a broad range of applications of the general results to the above-mentioned types of problems. As a consequence, we prove the Berenstein–Zelevinsky conjecture [Berenstein A, Zelevinsky A (2005) Adv Math 195:405–455] for the quantized coordinate rings of double Bruhat cells and construct quantum cluster algebra structures on all quantum unipotent groups, extending the theorem of Geiß et al. [Geiß C, et al. (2013) Selecta Math 19:337–397] for the case of symmetric Kac–Moody groups. Moreover, we prove that the upper cluster algebras of Berenstein et al. [Berenstein A, et al. (2005) Duke Math J 126:1–52] associated with double Bruhat cells coincide with the corresponding cluster algebras. PMID:24982197

The Feigin Tetrahedron

NASA Astrophysics Data System (ADS)

Rupel, Dylan

2015-03-01

The first goal of this note is to extend the well-known Feigin homomorphisms taking quantum groups to quantum polynomial algebras. More precisely, we define generalized Feigin homomorphisms from a quantum shuffle algebra to quantum polynomial algebras which extend the classical Feigin homomorphisms along the embedding of the quantum group into said quantum shuffle algebra. In a recent work of Berenstein and the author, analogous extensions of Feigin homomorphisms from the dual Hall-Ringel algebra of a valued quiver to quantum polynomial algebras were defined. To relate these constructions, we establish a homomorphism, dubbed the quantum shuffle character, from the dual Hall-Ringel algebra to the quantum shuffle algebra which relates the generalized Feigin homomorphisms. These constructions can be compactly described by a commuting tetrahedron of maps beginning with the quantum group and terminating in a quantum polynomial algebra. The second goal in this project is to better understand the dual canonical basis conjecture for skew-symmetrizable quantum cluster algebras. In the symmetrizable types it is known that dual canonical basis elements need not have positive multiplicative structure constants, while this is still suspected to hold for skew-symmetrizable quantum cluster algebras. We propose an alternate conjecture for the symmetrizable types: the cluster monomials should correspond to irreducible characters of a KLR algebra. Indeed, the main conjecture of this note would establish this ''KLR conjecture'' for acyclic skew-symmetrizable quantum cluster algebras: that is, we conjecture that the images of rigid representations under the quantum shuffle character give irreducible characters for KLR algebras. We sketch a proof in the symmetric case giving an alternative to the proof of Kimura-Qin that all non-initial cluster variables in an acyclic skew-symmetric quantum cluster algebra are contained in the dual canonical basis. With these results in mind we interpret the cluster mutations directly in terms of the representation theory of the KLR algebra.

Form in Algebra: Reflecting, with Peacock, on Upper Secondary School Teaching.

ERIC Educational Resources Information Center

Menghini, Marta

1994-01-01

Discusses algebra teaching by looking back into the history of algebra and the work of George Peacock, who considered algebra from two points of view: symbolic and instrumental. Claims that, to be meaningful, algebra must be linked to real-world problems. (18 references) (MKR)

Design of a Nanoscale, CMOS-Integrable, Thermal-Guiding Structure for Boolean-Logic and Neuromorphic Computation.

PubMed

Loke, Desmond; Skelton, Jonathan M; Chong, Tow-Chong; Elliott, Stephen R

2016-12-21

One of the requirements for achieving faster CMOS electronics is to mitigate the unacceptably large chip areas required to steer heat away from or, more recently, toward the critical nodes of state-of-the-art devices. Thermal-guiding (TG) structures can efficiently direct heat by "meta-materials" engineering; however, some key aspects of the behavior of these systems are not fully understood. Here, we demonstrate control of the thermal-diffusion properties of TG structures by using nanometer-scale, CMOS-integrable, graphene-on-silica stacked materials through finite-element-methods simulations. It has been shown that it is possible to implement novel, controllable, thermally based Boolean-logic and spike-timing-dependent plasticity operations for advanced (neuromorphic) computing applications using such thermal-guide architectures.

Modeling gene regulatory networks: A network simplification algorithm

NASA Astrophysics Data System (ADS)

Ferreira, Luiz Henrique O.; de Castro, Maria Clicia S.; da Silva, Fabricio A. B.

2016-12-01

Boolean networks have been used for some time to model Gene Regulatory Networks (GRNs), which describe cell functions. Those models can help biologists to make predictions, prognosis and even specialized treatment when some disturb on the GRN lead to a sick condition. However, the amount of information related to a GRN can be huge, making the task of inferring its boolean network representation quite a challenge. The method shown here takes into account information about the interactome to build a network, where each node represents a protein, and uses the entropy of each node as a key to reduce the size of the network, allowing the further inferring process to focus only on the main protein hubs, the ones with most potential to interfere in overall network behavior.

Stability of Boolean multilevel networks.

PubMed

Cozzo, Emanuele; Arenas, Alex; Moreno, Yamir

2012-09-01

The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semiannealed approximation to study the stability properties of random Boolean networks in multiplex (multilayered) graphs. Our main finding is that the multilevel structure provides a mechanism for the stabilization of the dynamics of the whole system even when individual layers work on the chaotic regime, therefore identifying new ways of feedback between the structure and the dynamics of these systems. Our results point out the need for a conceptual transition from the physics of single-layered networks to the physics of multiplex networks. Finally, the fact that the coupling modifies the phase diagram and the critical conditions of the isolated layers suggests that interdependency can be used as a control mechanism.

Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

ERIC Educational Resources Information Center

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…

Constructing Meanings and Utilities within Algebraic Tasks

ERIC Educational Resources Information Center

Ainley, Janet; Bills, Liz; Wilson, Kirsty

2004-01-01

The Purposeful Algebraic Activity project aims to explore the potential of spreadsheets in the introduction to algebra and algebraic thinking. We discuss two sub-themes within the project: tracing the development of pupils' construction of meaning for variable from arithmetic-based activity, through use of spreadsheets, and into formal algebra,…

Equivariant Gromov-Witten Invariants of Algebraic GKM Manifolds

NASA Astrophysics Data System (ADS)

Liu, Chiu-Chu Melissa; Sheshmani, Artan

2017-07-01

An algebraic GKM manifold is a non-singular algebraic variety equipped with an algebraic action of an algebraic torus, with only finitely many torus fixed points and finitely many 1-dimensional orbits. In this expository article, we use virtual localization to express equivariant Gromov-Witten invariants of any algebraic GKM manifold (which is not necessarily compact) in terms of Hodge integrals over moduli stacks of stable curves and the GKM graph of the GKM manifold.

Asymptotic aspect of derivations in Banach algebras.

PubMed

Roh, Jaiok; Chang, Ick-Soon

2017-01-01

We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

Lie algebra of conformal Killing-Yano forms

NASA Astrophysics Data System (ADS)

Ertem, Ümit

2016-06-01

We provide a generalization of the Lie algebra of conformal Killing vector fields to conformal Killing-Yano forms. A new Lie bracket for conformal Killing-Yano forms that corresponds to slightly modified Schouten-Nijenhuis bracket of differential forms is proposed. We show that conformal Killing-Yano forms satisfy a graded Lie algebra in constant curvature manifolds. It is also proven that normal conformal Killing-Yano forms in Einstein manifolds also satisfy a graded Lie algebra. The constructed graded Lie algebras reduce to the graded Lie algebra of Killing-Yano forms and the Lie algebras of conformal Killing and Killing vector fields in special cases.

Generalized Galilean algebras and Newtonian gravity

NASA Astrophysics Data System (ADS)

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.

On the structure of quantum L∞ algebras

NASA Astrophysics Data System (ADS)

Blumenhagen, Ralph; Fuchs, Michael; Traube, Matthias

2017-10-01

It is believed that any classical gauge symmetry gives rise to an L∞ algebra. Based on the recently realized relation between classical W algebras and L∞ algebras, we analyze how this generalizes to the quantum case. Guided by the existence of quantum W algebras, we provide a physically well motivated definition of quantum L∞ algebras describing the consistency of global symmetries in quantum field theories. In this case we are restricted to only two non-trivial graded vector spaces X 0 and X -1 containing the symmetry variations and the symmetry generators. This quantum L∞ algebra structure is explicitly exemplified for the quantum W_3 algebra. The natural quantum product between fields is the normal ordered one so that, due to contractions between quantum fields, the higher L∞ relations receive off-diagonal quantum corrections. Curiously, these are not present in the loop L∞ algebra of closed string field theory.

On special Lie algebras having a faithful module with Krull dimension

NASA Astrophysics Data System (ADS)

Pikhtilkova, O. A.; Pikhtilkov, S. A.

2017-02-01

For special Lie algebras we prove an analogue of Markov's theorem on {PI}-algebras having a faithful module with Krull dimension: the solubility of the prime radical. We give an example of a semiprime Lie algebra that has a faithful module with Krull dimension but cannot be represented as a subdirect product of finitely many prime Lie algebras. We prove a criterion for a semiprime Lie algebra to be representable as such a subdirect product.

Algebra for Everyone.

ERIC Educational Resources Information Center

Edwards, Edgar L., Jr., Ed.

The fundamentals of algebra and algebraic thinking should be a part of the background of all citizens in society. The vast increase in the use of technology requires that school mathematics ensure the teaching of algebraic thinking as well as its use at both the elementary and secondary school levels. Algebra is a universal theme that runs through…

Chinese Algebra: Using Historical Problems to Think about Current Curricula

ERIC Educational Resources Information Center

Tillema, Erik

2005-01-01

The Chinese used the idea of generating equivalent expressions for solving problems where the problems from a historical Chinese text are studied to understand the ways in which the ideas can lead into algebraic calculations and help students to learn algebra. The texts unify algebraic problem solving through complex algebraic thought and afford…

Conceptualizing Routines of Practice That Support Algebraic Reasoning in Elementary Schools: A Constructivist Grounded Theory

ERIC Educational Resources Information Center

Store, Jessie Chitsanzo

2012-01-01

There is ample literature documenting that, for many decades, high school students view algebra as difficult and do not demonstrate understanding of algebraic concepts. Algebraic reasoning in elementary school aims at meaningfully introducing algebra to elementary school students in preparation for higher-level mathematics. While there is research…

Derive Workshop Matrix Algebra and Linear Algebra.

ERIC Educational Resources Information Center

Townsley Kulich, Lisa; Victor, Barbara

This document presents the course content for a workshop that integrates the use of the computer algebra system Derive with topics in matrix and linear algebra. The first section is a guide to using Derive that provides information on how to write algebraic expressions, make graphs, save files, edit, define functions, differentiate expressions,…

Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

ERIC Educational Resources Information Center

Ozgun-Koca, S. Ash

2010-01-01

Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

A Richer Understanding of Algebra

ERIC Educational Resources Information Center

Foy, Michelle

2008-01-01

Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number,…

A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.

PubMed

DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J

2016-12-01

Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.

Topics in elementary particle physics

NASA Astrophysics Data System (ADS)

Jin, Xiang

The author of this thesis discusses two topics in elementary particle physics: n-ary algebras and their applications to M-theory (Part I), and functional evolution and Renormalization Group flows (Part II). In part I, Lie algebra is extended to four different n-ary algebraic structure: generalized Lie algebra, Filippov algebra, Nambu algebra and Nambu-Poisson tensor; though there are still many other n-ary algebras. A natural property of Generalized Lie algebras — the Bremner identity, is studied, and proved with a totally different method from its original version. We extend Bremner identity to n-bracket cases, where n is an arbitrary odd integer. Filippov algebras do not focus on associativity, and are defined by the Fundamental identity. We add associativity to Filippov algebras, and give examples of how to construct Filippov algebras from su(2), bosonic oscillator, Virasoro algebra. We try to include fermionic charges into the ternary Virasoro-Witt algebra, but the attempt fails because fermionic charges keep generating new charges that make the algebra not closed. We also study the Bremner identity restriction on Nambu algebras and Nambu-Poisson tensors. So far, the only example 3-algebra being used in physics is the BLG model with 3-algebra A4, describing two M2-branes interactions. Its extension with Nambu algebra, BLG-NB model, is believed to describe infinite M2-branes condensation. Also, there is another propose for M2-brane interactions, the ABJM model, which is constructed by ordinary Lie algebra. We compare the symmetry properties between them, and discuss the possible approaches to include these three models into a grand unification theory. In Part II, we give an approximate solution for Schroeder's equations, based on series and conjugation methods. We use the logistic map as an example, and demonstrate that this approximate solution converges to known analytical solutions around the fixed point, around which the approximate solution is constructed. Although the closed-form solutions for Schroeder's equations can not always be approached analytically, by fitting the approximation solutions, one can still obtain closed-form solutions sometimes. Based on Schroeder's theory, approximate solutions for trajectories, velocities and potentials can also be constructed. The approximate solution is significantly useful to calculate the beta function in renormalization group trajectory. By "wrapping" the series solutions with the conjugations from different inverse functions, we generate different branches of the trajectory, and construct a counterexample for a folk theorem about limited cycles.

Application of polynomial su(1, 1) algebra to Pöschl-Teller potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Hong-Biao, E-mail: zhanghb017@nenu.edu.cn; Lu, Lu

2013-12-15

Two novel polynomial su(1, 1) algebras for the physical systems with the first and second Pöschl-Teller (PT) potentials are constructed, and their specific representations are presented. Meanwhile, these polynomial su(1, 1) algebras are used as an algebraic technique to solve eigenvalues and eigenfunctions of the Hamiltonians associated with the first and second PT potentials. The algebraic approach explores an appropriate new pair of raising and lowing operators K-circumflex{sub ±} of polynomial su(1, 1) algebra as a pair of shift operators of our Hamiltonians. In addition, two usual su(1, 1) algebras associated with the first and second PT potentials are derivedmore » naturally from the polynomial su(1, 1) algebras built by us.« less

Reduction by invariants and projection of linear representations of Lie algebras applied to the construction of nonlinear realizations

NASA Astrophysics Data System (ADS)

Campoamor-Stursberg, R.

2018-03-01

A procedure for the construction of nonlinear realizations of Lie algebras in the context of Vessiot-Guldberg-Lie algebras of first-order systems of ordinary differential equations (ODEs) is proposed. The method is based on the reduction of invariants and projection of lowest-dimensional (irreducible) representations of Lie algebras. Applications to the description of parameterized first-order systems of ODEs related by contraction of Lie algebras are given. In particular, the kinematical Lie algebras in (2 + 1)- and (3 + 1)-dimensions are realized simultaneously as Vessiot-Guldberg-Lie algebras of parameterized nonlinear systems in R3 and R4, respectively.

(Fuzzy) Ideals of BN-Algebras

PubMed Central

Walendziak, Andrzej

2015-01-01

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships between ideals and fuzzy ideals of a BN-algebra are established. The homomorphic properties of fuzzy ideals of a BN-algebra are provided. Finally, characterizations of Noetherian BN-algebras and Artinian BN-algebras via fuzzy ideals are obtained. PMID:26125050

Understanding genetic regulatory networks

NASA Astrophysics Data System (ADS)

Kauffman, Stuart

2003-04-01

Random Boolean networks (RBM) were introduced about 35 years ago as first crude models of genetic regulatory networks. RBNs are comprised of N on-off genes, connected by a randomly assigned regulatory wiring diagram where each gene has K inputs, and each gene is controlled by a randomly assigned Boolean function. This procedure samples at random from the ensemble of all possible NK Boolean networks. The central ideas are to study the typical, or generic properties of this ensemble, and see 1) whether characteristic differences appear as K and biases in Boolean functions are introducted, and 2) whether a subclass of this ensemble has properties matching real cells. Such networks behave in an ordered or a chaotic regime, with a phase transition, "the edge of chaos" between the two regimes. Networks with continuous variables exhibit the same two regimes. Substantial evidence suggests that real cells are in the ordered regime. A key concept is that of an attractor. This is a reentrant trajectory of states of the network, called a state cycle. The central biological interpretation is that cell types are attractors. A number of properties differentiate the ordered and chaotic regimes. These include the size and number of attractors, the existence in the ordered regime of a percolating "sea" of genes frozen in the on or off state, with a remainder of isolated twinkling islands of genes, a power law distribution of avalanches of gene activity changes following perturbation to a single gene in the ordered regime versus a similar power law distribution plus a spike of enormous avalanches of gene changes in the chaotic regime, and the existence of branching pathway of "differentiation" between attractors induced by perturbations in the ordered regime. Noise is serious issue, since noise disrupts attractors. But numerical evidence suggests that attractors can be made very stable to noise, and meanwhile, metaplasias may be a biological manifestation of noise. As we learn more about the wiring diagram and constraints on rules controlling real genes, we can build refined ensembles reflecting these properties, study the generic properties of the refined ensembles, and hope to gain insight into the dynamics of real cells.

The algebra of supertraces for 2+1 super de Sitter gravity

NASA Technical Reports Server (NTRS)

Urrutia, L. F.; Waelbroeck, H.; Zertuche, F.

1993-01-01

The algebra of the observables for 2+1 super de Sitter gravity, for one genus of the spatial surface is calculated. The algebra turns out to be an infinite Lie algebra subject to non-linear constraints. The constraints are solved explicitly in terms of five independent complex supertraces. These variables are the true degrees of freedom of the system and their quantized algebra generates a new structure which is referred to as a 'central extension' of the quantum algebra SU(2)q.

a Triangular Deformation of the Two-Dimensional POINCARÉ Algebra

NASA Astrophysics Data System (ADS)

Khorrami, M.; Shariati, A.; Abolhassani, M. R.; Aghamohammadi, A.

Contracting the h-deformation of SL(2, ℝ), we construct a new deformation of two-dimensional Poincaré's algebra, the algebra of functions on its group and its differential structure. It is seen that these dual Hopf algebras are isomorphic to each other. It is also shown that the Hopf algebra is triangular, and its universal R-matrix is also constructed explicitly. We then find a deformation map for the universal enveloping algebra, and at the end, give the deformed mass shells and Lorentz transformation.

Computer algebra and operators

NASA Technical Reports Server (NTRS)

Fateman, Richard; Grossman, Robert

1989-01-01

The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

An Arithmetic-Algebraic Work Space for the Promotion of Arithmetic and Algebraic Thinking: Triangular Numbers

ERIC Educational Resources Information Center

Hitt, Fernando; Saboya, Mireille; Cortés Zavala, Carlos

2016-01-01

This paper presents an experiment that attempts to mobilise an arithmetic-algebraic way of thinking in order to articulate between arithmetic thinking and the early algebraic thinking, which is considered a prelude to algebraic thinking. In the process of building this latter way of thinking, researchers analysed pupils' spontaneous production…

Spontaneous Meta-Arithmetic as a First Step toward School Algebra

ERIC Educational Resources Information Center

Caspi, Shai; Sfard, Anna

2012-01-01

Taking as the point of departure the vision of school algebra as a formalized meta-discourse of arithmetic, we have been following five pairs of 7th grade students as they progress in algebraic discourse during 24 months, from their informal algebraic talk to the formal algebraic discourse, as taught in school. Our analysis follows changes that…

Gender differences in algebraic thinking ability to solve mathematics problems

NASA Astrophysics Data System (ADS)

Kusumaningsih, W.; Darhim; Herman, T.; Turmudi

2018-05-01

This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.

Particle-like structure of coaxial Lie algebras

NASA Astrophysics Data System (ADS)

Vinogradov, A. M.

2018-01-01

This paper is a natural continuation of Vinogradov [J. Math. Phys. 58, 071703 (2017)] where we proved that any Lie algebra over an algebraically closed field or over R can be assembled in a number of steps from two elementary constituents, called dyons and triadons. Here we consider the problems of the construction and classification of those Lie algebras which can be assembled in one step from base dyons and triadons, called coaxial Lie algebras. The base dyons and triadons are Lie algebra structures that have only one non-trivial structure constant in a given basis, while coaxial Lie algebras are linear combinations of pairwise compatible base dyons and triadons. We describe the maximal families of pairwise compatible base dyons and triadons called clusters, and, as a consequence, we give a complete description of the coaxial Lie algebras. The remarkable fact is that dyons and triadons in clusters are self-organised in structural groups which are surrounded by casings and linked by connectives. We discuss generalisations and applications to the theory of deformations of Lie algebras.

The Growing Importance of Linear Algebra in Undergraduate Mathematics.

ERIC Educational Resources Information Center

Tucker, Alan

1993-01-01

Discusses the theoretical and practical importance of linear algebra. Presents a brief history of linear algebra and matrix theory and describes the place of linear algebra in the undergraduate curriculum. (MDH)

Representing k-graphs as Matrix Algebras

NASA Astrophysics Data System (ADS)

Rosjanuardi, R.

2018-05-01

For any commutative unital ring R and finitely aligned k-graph Λ with |Λ| < ∞ without cycles, we can realise Kumjian-Pask algebra KP R (Λ) as a direct sum of of matrix algebra over some vertices v with properties ν = νΛ, i.e: ⊕ νΛ=ν M |Λv|(R). When there is only a single vertex ν ∈ Λ° such that ν = νΛ, we can realise the Kumjian-Pask algebra as the matrix algebra M |ΛV|(R). Hence the matrix algebra M |vΛ|(R) can be regarded as a representation of the k-graph Λ. In this talk we will figure out the relation between finitely aligned k-graph and matrix algebra.

A description of pseudo-bosons in terms of nilpotent Lie algebras

NASA Astrophysics Data System (ADS)

Bagarello, Fabio; Russo, Francesco G.

2018-02-01

We show how the one-mode pseudo-bosonic ladder operators provide concrete examples of nilpotent Lie algebras of dimension five. It is the first time that an algebraic-geometric structure of this kind is observed in the context of pseudo-bosonic operators. Indeed we do not find the well known Heisenberg algebras, which are involved in several quantum dynamical systems, but different Lie algebras which may be decomposed into the sum of two abelian Lie algebras in a prescribed way. We introduce the notion of semidirect sum (of Lie algebras) for this scope and find that it describes very well the behavior of pseudo-bosonic operators in many quantum models.

The hopf algebra of vector fields on complex quantum groups

NASA Astrophysics Data System (ADS)

Drabant, Bernhard; Jurčo, Branislav; Schlieker, Michael; Weich, Wolfgang; Zumino, Bruno

1992-10-01

We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A n , B n , C n , and D n by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of the algebra of regular functionals.

Algorithms for computations of Loday algebras' invariants

NASA Astrophysics Data System (ADS)

Hussain, Sharifah Kartini Said; Rakhimov, I. S.; Basri, W.

2017-04-01

The paper is devoted to applications of some computer programs to study structural determination of Loday algebras. We present how these computer programs can be applied in computations of various invariants of Loday algebras and provide several computer programs in Maple to verify Loday algebras' identities, the isomorphisms between the algebras, as a special case, to describe the automorphism groups, centroids and derivations.

Algebra for All: The Effect of Algebra Coursework and Classroom Peer Academic Composition on Low-Achieving Students

ERIC Educational Resources Information Center

Nomi, Takako; Raudenbush, Stephen W.

2014-01-01

Algebra is often considered as a gateway for later achievement. A recent report by the Mathematics Advisory Panel (2008) underscores the importance of improving algebra learning in secondary school. Today, a growing number of states and districts require algebra for all students in ninth grade or earlier. Chicago is at the forefront of this…

Rupture or Continuity: The Arithmetico-Algebraic Thinking as an Alternative in a Modelling Process in a Paper and Pencil and Technology Environment

ERIC Educational Resources Information Center

Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés

2017-01-01

Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…

Derivation in INK-algebras

NASA Astrophysics Data System (ADS)

Kaviyarasu, M.; Indhira, K.

2018-04-01

In 2017 we introduced a new notion of algebra called IKN-algebra. Motivated by some result on derivations (rightleft)-derivation and (leftright)- derivation in ring. In this paper we introduce derivation in INK-Algebras and investigate some important result.

Topological Aspects of Information Retrieval.

ERIC Educational Resources Information Center

Egghe, Leo; Rousseau, Ronald

1998-01-01

Discusses topological aspects of theoretical information retrieval, including retrieval topology; similarity topology; pseudo-metric topology; document spaces as topological spaces; Boolean information retrieval as a subsystem of any topological system; and proofs of theorems. (LRW)

Combinatorial optimization in foundry practice

NASA Astrophysics Data System (ADS)

Antamoshkin, A. N.; Masich, I. S.

2016-04-01

The multicriteria mathematical model of foundry production capacity planning is suggested in the paper. The model is produced in terms of pseudo-Boolean optimization theory. Different search optimization methods were used to solve the obtained problem.

Defining of the BDX930 Assembly Language

NASA Technical Reports Server (NTRS)

Boyer, R. S.; Moore, J. S.

1983-01-01

A definition of the BDX930 assembly language is presented. Various definition problems and suggested solutions are included. A class of defined recognizers based on boolean valued nowrecursive functions is employed in preprocessing.

Contractions and deformations of quasiclassical Lie algebras preserving a nondegenerate quadratic Casimir operator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campoamor-Stursberg, R., E-mail: rutwig@mat.ucm.e

2008-05-15

By means of contractions of Lie algebras, we obtain new classes of indecomposable quasiclassical Lie algebras that satisfy the Yang-Baxter equations in its reformulation in terms of triple products. These algebras are shown to arise naturally from noncompact real simple algebras with nonsimple complexification, where we impose that a nondegenerate quadratic Casimir operator is preserved by the limiting process. We further consider the converse problem and obtain sufficient conditions on integrable cocycles of quasiclassical Lie algebras in order to preserve nondegenerate quadratic Casimir operators by the associated linear deformations.

Roughness in Lattice Ordered Effect Algebras

PubMed Central

Xin, Xiao Long; Hua, Xiu Juan; Zhu, Xi

2014-01-01

Many authors have studied roughness on various algebraic systems. In this paper, we consider a lattice ordered effect algebra and discuss its roughness in this context. Moreover, we introduce the notions of the interior and the closure of a subset and give some of their properties in effect algebras. Finally, we use a Riesz ideal induced congruence and define a function e(a, b) in a lattice ordered effect algebra E and build a relationship between it and congruence classes. Then we study some properties about approximation of lattice ordered effect algebras. PMID:25170523

D{sub {infinity}}-differential E{sub {infinity}}-algebras and spectral sequences of fibrations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lapin, Sergei V

2007-10-31

The notion of an E{sub {infinity}}-algebra with a filtration is introduced. The connections are established between E{sub {infinity}}-algebras with filtrations and the theory of D{sub {infinity}}-differential E{sub {infinity}}-algebras over fields. Based on the technique of D{sub {infinity}}-differential E{sub {infinity}}-algebras, the apparatus of spectral sequences is developed for E{sub {infinity}}-algebras with filtrations, and applications of this apparatus to the multiplicative cohomology spectral sequences of fibrations are given. Bibliography: 21 titles.

Application of a Discrete Nonlinear Spectral Model to Ideal Cases of Wind Wave Generation.

DTIC Science & Technology

1982-04-01

WRITE (6965)) bBD ODRM4T (IHII C SKI ’> 3 LINS i AND WRITE PLOT TITLE (IDOCHAR S PER LINE t 10 LINES AXI4CH-,(NClkR*9) /10 dRJTE (660) (TJL..EfI),I-I...A*CaGE.D.)JPP-J>P 𔃻 I F ( 8 D Do)) jpp-j P?+2 MiFPPeE)’i)&O TO 44 73 40JT-NPr(NIN,JPP) ;o TD (72, 14,7b,7BhNOUT 44 IF(A*3)q46q4b47 46 JPP-2 ;0 TO 73...EXTEZNAL FJNrI3N LAND IJS 13 THE BOOLEAN I.EoLDGICAL$ AND 01’ Td C FULLWORD INTEGCRS. C EXTEtNAL FJN:TION LOR, I,JS 1)7 THE BOOLEAN OR OF TWO FULLWORD

Analog Approach to Constraint Satisfaction Enabled by Spin Orbit Torque Magnetic Tunnel Junctions.

PubMed

Wijesinghe, Parami; Liyanagedera, Chamika; Roy, Kaushik

2018-05-02

Boolean satisfiability (k-SAT) is an NP-complete (k ≥ 3) problem that constitute one of the hardest classes of constraint satisfaction problems. In this work, we provide a proof of concept hardware based analog k-SAT solver, that is built using Magnetic Tunnel Junctions (MTJs). The inherent physics of MTJs, enhanced by device level modifications, is harnessed here to emulate the intricate dynamics of an analog satisfiability (SAT) solver. In the presence of thermal noise, the MTJ based system can successfully solve Boolean satisfiability problems. Most importantly, our results exhibit that, the proposed MTJ based hardware SAT solver is capable of finding a solution to a significant fraction (at least 85%) of hard 3-SAT problems, within a time that has a polynomial relationship with the number of variables(<50).

A Semiquantitative Framework for Gene Regulatory Networks: Increasing the Time and Quantitative Resolution of Boolean Networks

PubMed Central

Kerkhofs, Johan; Geris, Liesbet

2015-01-01

Boolean models have been instrumental in predicting general features of gene networks and more recently also as explorative tools in specific biological applications. In this study we introduce a basic quantitative and a limited time resolution to a discrete (Boolean) framework. Quantitative resolution is improved through the employ of normalized variables in unison with an additive approach. Increased time resolution stems from the introduction of two distinct priority classes. Through the implementation of a previously published chondrocyte network and T helper cell network, we show that this addition of quantitative and time resolution broadens the scope of biological behaviour that can be captured by the models. Specifically, the quantitative resolution readily allows models to discern qualitative differences in dosage response to growth factors. The limited time resolution, in turn, can influence the reachability of attractors, delineating the likely long term system behaviour. Importantly, the information required for implementation of these features, such as the nature of an interaction, is typically obtainable from the literature. Nonetheless, a trade-off is always present between additional computational cost of this approach and the likelihood of extending the model’s scope. Indeed, in some cases the inclusion of these features does not yield additional insight. This framework, incorporating increased and readily available time and semi-quantitative resolution, can help in substantiating the litmus test of dynamics for gene networks, firstly by excluding unlikely dynamics and secondly by refining falsifiable predictions on qualitative behaviour. PMID:26067297

Remission of rheumatoid arthritis and potential determinants: a national multi-center cross-sectional survey.

PubMed

Wang, Guan-Ying; Zhang, Sa-Li; Wang, Xiu-Ru; Feng, Min; Li, Chun; An, Yuan; Li, Xiao-Feng; Wang, Li-Zhi; Wang, Cai-Hong; Wang, Yong-Fu; Yang, Rong; Yan, Hui-Ming; Wang, Guo-Chun; Lu, Xin; Liu, Xia; Zhu, Ping; Chen, Li-Na; Jin, Hong-Tao; Liu, Jin-Ting; Guo, Hui-Fang; Chen, Hai-Ying; Xie, Jian-Li; Wei, Ping; Wang, Jun-Xiang; Liu, Xiang-Yuan; Sun, Lin; Cui, Liu-Fu; Shu, Rong; Liu, Bai-Lu; Yu, Ping; Zhang, Zhuo-Li; Li, Guang-Tao; Li, Zhen-Bin; Yang, Jing; Li, Jun-Fang; Jia, Bin; Zhang, Feng-Xiao; Tao, Jie-Mei; Lin, Jin-Ying; Wei, Mei-Qiu; Liu, Xiao-Min; Ke, Dan; Hu, Shao-Xian; Ye, Cong; Han, Shu-Ling; Yang, Xiu-Yan; Li, Hao; Huang, Ci-Bo; Gao, Ming; Lai, Bei; Cheng, Yong-Jing; Li, Xing-Fu; Song, Li-Jun; Yu, Xiao-Xia; Wang, Ai-Xue; Wu, Li-Jun; Wang, Yan-Hua; He, Lan; Sun, Wen-Wen; Gong, Lu; Wang, Xiao-Yuan; Wang, Yi; Zhao, Yi; Li, Xiao-Xia; Wang, Yan; Zhang, Yan; Su, Yin; Zhang, Chun-Fang; Mu, Rong; Li, Zhan-Guo

2015-02-01

The aim of this study is to investigate the remission rate of rheumatoid arthritis (RA) in China and identify its potential determinants. A multi-center cross-sectional study was conducted from July 2009 to January 2012. Data were collected by face-to-face interviews of the rheumatology outpatients in 28 tertiary hospitals in China. The remission rates were calculated in 486 RA patients according to different definitions of remission: the Disease Activity Score in 28 joints (DAS28), the Simplified Disease Activity Index (SDAI), the Clinical Disease Activity Index (CDAI), and the American College of Rheumatology/European League Against Rheumatism (ACR/EULAR) Boolean definition. Potential determinants of RA remission were assessed by univariate and multivariate analyses. The remission rates of RA from this multi-center cohort were 8.6% (DAS28), 8.4% (SDAI), 8.2% (CDAI), and 6.8% (Boolean), respectively. Favorable factors associated with remission were: low Health Assessment Questionnaire (HAQ) score, absence of rheumatoid factor (RF) and anti-cyclic citrullinated peptide (anti-CCP), and treatment of methotrexate (MTX) and hydroxychloroquine (HCQ). Younger age was also predictive for the DAS28 and the Boolean remission. Multivariate analyses revealed a low HAQ score, the absence of anti-CCP, and the treatment with HCQ as independent determinants of remission. The clinical remission rate of RA patients was low in China. A low HAQ score, the absence of anti-CCP, and HCQ were significant independent determinants for RA remission.

Form and function in gene regulatory networks: the structure of network motifs determines fundamental properties of their dynamical state space.

PubMed

Ahnert, S E; Fink, T M A

2016-07-01

Network motifs have been studied extensively over the past decade, and certain motifs, such as the feed-forward loop, play an important role in regulatory networks. Recent studies have used Boolean network motifs to explore the link between form and function in gene regulatory networks and have found that the structure of a motif does not strongly determine its function, if this is defined in terms of the gene expression patterns the motif can produce. Here, we offer a different, higher-level definition of the 'function' of a motif, in terms of two fundamental properties of its dynamical state space as a Boolean network. One is the basin entropy, which is a complexity measure of the dynamics of Boolean networks. The other is the diversity of cyclic attractor lengths that a given motif can produce. Using these two measures, we examine all 104 topologically distinct three-node motifs and show that the structural properties of a motif, such as the presence of feedback loops and feed-forward loops, predict fundamental characteristics of its dynamical state space, which in turn determine aspects of its functional versatility. We also show that these higher-level properties have a direct bearing on real regulatory networks, as both basin entropy and cycle length diversity show a close correspondence with the prevalence, in neural and genetic regulatory networks, of the 13 connected motifs without self-interactions that have been studied extensively in the literature. © 2016 The Authors.

Psychological state is related to the remission of the Boolean-based definition of patient global assessment in patients with rheumatoid arthritis.

PubMed

Fusama, Mie; Miura, Yasushi; Yukioka, Kumiko; Kuroiwa, Takanori; Yukioka, Chikako; Inoue, Miyako; Nakanishi, Tae; Murata, Norikazu; Takai, Noriko; Higashi, Kayoko; Kuritani, Taro; Maeda, Keiji; Sano, Hajime; Yukioka, Masao; Nakahara, Hideko

2015-09-01

To evaluate whether the psychological state is related to the Boolean-based definition of patient global assessment (PGA) remission in patients with rheumatoid arthritis (RA). Patients with RA who met the criteria of swollen joint count (SJC) ≤ 1, tender joint count (TJC) ≤ 1 and C-reactive protein (CRP) ≤ 1 were divided into two groups, PGA remission group (PGA ≤ 1 cm) and non-remission group (PGA > 1 cm). Anxiety was evaluated utilizing the Hospital Anxiety and Depression Scale-Anxiety (HADS-A), while depression was evaluated with HADS-Depression (HADS-D) and the Center for Epidemiologic Studies Depression Scale (CES-D). Comparison analyses were done between the PGA remission and non-remission groups in HADS-A, HADS-D and CES-D. Seventy-eight patients met the criteria for SJC ≤ 1, TJC ≤ 1 and CRP ≤ 1. There were no significant differences between the PGA remission group (n = 45) and the non-remission group (n = 33) in age, sex, disease duration and Steinbrocker's class and stage. HADS-A, HADS-D and CES-D scores were significantly lower in the PGA remission group. Patients with RA who did not meet the PGA remission criteria despite good disease condition were in a poorer psychological state than those who satisfied the Boolean-based definition of clinical remission. Psychological support might be effective for improvement of PGA, resulting in the attainment of true remission.

Visualization of Dietary Patterns and Their Associations With Age-Related Macular Degeneration.

PubMed

Chiu, Chung-Jung; Chang, Min-Lee; Li, Tricia; Gensler, Gary; Taylor, Allen

2017-03-01

We aimed to visualize the relationship of predominant dietary patterns and their associations with AMD. A total of 8103 eyes from 4088 participants in the baseline Age-Related Eye Disease Study (AREDS) were classified into three groups: control (n = 2739), early AMD (n = 4599), and advanced AMD (n = 765). Using principle component analysis, two major dietary patterns and eight minor dietary patterns were characterized. Applying logistic regression in our analysis, we related dietary patterns to the prevalence of AMD. Qualitative comparative analysis by operating Boolean algebra and drawing Venn diagrams was used to visualize our findings. In general, the eight minor patterns were subsets or extensions of either one of the two major dietary patterns (Oriental and Western patterns) and consisted of fewer characteristic foods than the two major dietary patterns. Unlike the two major patterns, which were more strongly associated with both early and advanced AMD, none of the eight minors were associated with early AMD and only four minor patterns, including the Steak pattern (odds ratio comparing the highest to lowest quintile of the pattern score = 1.73 [95% confidence interval: 1.24 to 2.41; Ptrend = 0.02]), the Breakfast pattern (0.60 [0.44 to 0.82]; Ptrend = 0.004]), the Caribbean pattern (0.64 [0.47 to 0.89; Ptrend = 0.009]), and the Peanut pattern (0.64 [0.46 to 0.89; Ptrend = 0.03]), were significantly associated with advanced AMD. Our data also suggested several potential beneficial (peanuts, pizza, coffee, and tea) and harmful (salad dressing) foods for AMD. Our data indicate that a diet of various healthy foods may be optimal for reducing AMD risk. The effects of some specific foods in the context of overall diet warrant further study.

Integration of Genetic Algorithms and Fuzzy Logic for Urban Growth Modeling

NASA Astrophysics Data System (ADS)

Foroutan, E.; Delavar, M. R.; Araabi, B. N.

2012-07-01

Urban growth phenomenon as a spatio-temporal continuous process is subject to spatial uncertainty. This inherent uncertainty cannot be fully addressed by the conventional methods based on the Boolean algebra. Fuzzy logic can be employed to overcome this limitation. Fuzzy logic preserves the continuity of dynamic urban growth spatially by choosing fuzzy membership functions, fuzzy rules and the fuzzification-defuzzification process. Fuzzy membership functions and fuzzy rule sets as the heart of fuzzy logic are rather subjective and dependent on the expert. However, due to lack of a definite method for determining the membership function parameters, certain optimization is needed to tune the parameters and improve the performance of the model. This paper integrates genetic algorithms and fuzzy logic as a genetic fuzzy system (GFS) for modeling dynamic urban growth. The proposed approach is applied for modeling urban growth in Tehran Metropolitan Area in Iran. Historical land use/cover data of Tehran Metropolitan Area extracted from the 1988 and 1999 Landsat ETM+ images are employed in order to simulate the urban growth. The extracted land use classes of the year 1988 include urban areas, street, vegetation areas, slope and elevation used as urban growth physical driving forces. Relative Operating Characteristic (ROC) curve as an fitness function has been used to evaluate the performance of the GFS algorithm. The optimum membership function parameter is applied for generating a suitability map for the urban growth. Comparing the suitability map and real land use map of 1999 gives the threshold value for the best suitability map which can simulate the land use map of 1999. The simulation outcomes in terms of kappa of 89.13% and overall map accuracy of 95.58% demonstrated the efficiency and reliability of the proposed model.

Theoretical aspects of diagnostics of car as mechatronic system

NASA Astrophysics Data System (ADS)

Goncharov, A. E.; Bondarenko, E. V.; Krasnoshtanov, S. Yu

2018-03-01

The article describes transformation of mechanical systems of automobiles into mechatronic ones due to application of electronic control systems. To assess the relationship of mechanical and electronic components of the mechatronic systems with regard to their technical states, the method of equivalent elements was employed. A mathematical model of changes in the technical state of equivalent elements was developed. It allowed us to present changes in operation capacity in a graphic form. The analytical model is used to ensure operating capacity potential stability for the mechatronic system. For this purpose, new resources were identified with regard to the information ‘field’. Therefore, a new approach to the systematization of knowledge about mechatronic transport systems (D-C-R-E system) is required. The D-C-R-E system is examined as a separate unit. The article describes Information unit formation based on the physical component of the D-C-R-E system and external information which is collected and processed in the Information Diagnostic Center (IDC). Using probability theory and Boolean algebra methods, the authors obtained a logistic model describing information relations between elements of the upgraded D-C-R-E system and contribution of each component to the road safety protection. The logistic model helped formulate main IDC tasks. Implementation of those tasks was transformed into the logical sequence of data collection and analysis in the IDC. That approach predetermined development of the multi-level diagnosing system which made it possible to put in order existing and improved image identification methods and algorithms and to create a diagnosing method for mechatronic systems of cars which reduces labor content and increases accuracy. That approach can help assess the technical state of vehicles with characteristics of mechatronic systems and their transport and environmental safety.

q-Derivatives, quantization methods and q-algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Twarock, Reidun

1998-12-15

Using the example of Borel quantization on S{sup 1}, we discuss the relation between quantization methods and q-algebras. In particular, it is shown that a q-deformation of the Witt algebra with generators labeled by Z is realized by q-difference operators. This leads to a discrete quantum mechanics. Because of Z, the discretization is equidistant. As an approach to a non-equidistant discretization of quantum mechanics one can change the Witt algebra using not the number field Z as labels but a quadratic extension of Z characterized by an irrational number {tau}. This extension is denoted as quasi-crystal Lie algebra, because thismore » is a relation to one-dimensional quasicrystals. The q-deformation of this quasicrystal Lie algebra is discussed. It is pointed out that quasicrystal Lie algebras can be considered also as a 'deformed' Witt algebra with a 'deformation' of the labeling number field. Their application to the theory is discussed.« less

Generalized conformal realizations of Kac-Moody algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmkvist, Jakob

2009-01-15

We present a construction which associates an infinite sequence of Kac-Moody algebras, labeled by a positive integer n, to one single Jordan algebra. For n=1, this reduces to the well known Kantor-Koecher-Tits construction. Our generalization utilizes a new relation between different generalized Jordan triple systems, together with their known connections to Jordan and Lie algebras. Applied to the Jordan algebra of Hermitian 3x3 matrices over the division algebras R, C, H, O, the construction gives the exceptional Lie algebras f{sub 4}, e{sub 6}, e{sub 7}, e{sub 8} for n=2. Moreover, we obtain their infinite-dimensional extensions for n{>=}3. In the casemore » of 2x2 matrices, the resulting Lie algebras are of the form so(p+n,q+n) and the concomitant nonlinear realization generalizes the conformal transformations in a spacetime of signature (p,q)« less

Filiform Lie algebras of order 3

DOE Office of Scientific and Technical Information (OSTI.GOV)

Navarro, R. M., E-mail: rnavarro@unex.es

2014-04-15

The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de lamore » variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.« less

Labeled trees and the efficient computation of derivations

NASA Technical Reports Server (NTRS)

Grossman, Robert; Larson, Richard G.

1989-01-01

The effective parallel symbolic computation of operators under composition is discussed. Examples include differential operators under composition and vector fields under the Lie bracket. Data structures consisting of formal linear combinations of rooted labeled trees are discussed. A multiplication on rooted labeled trees is defined, thereby making the set of these data structures into an associative algebra. An algebra homomorphism is defined from the original algebra of operators into this algebra of trees. An algebra homomorphism from the algebra of trees into the algebra of differential operators is then described. The cancellation which occurs when noncommuting operators are expressed in terms of commuting ones occurs naturally when the operators are represented using this data structure. This leads to an algorithm which, for operators which are derivations, speeds up the computation exponentially in the degree of the operator. It is shown that the algebra of trees leads naturally to a parallel version of the algorithm.

Differential calculus and gauge transformations on a deformed space

NASA Astrophysics Data System (ADS)

Wess, Julius

2007-08-01

We consider a formalism by which gauge theories can be constructed on noncommutative space time structures. The coordinates are supposed to form an algebra, restricted by certain requirements that allow us to realise the algebra in terms of star products. In this formulation it is useful to define derivatives and to extend the algebra of coordinates by these derivatives. The elements of this extended algebra are deformed differential operators. We then show that there is a morphism between these deformed differential operators and the usual higher order differential operators acting on functions of commuting coordinates. In this way we obtain deformed gauge transformations and a deformed version of the algebra of diffeomorphisms. The deformation of these algebras can be clearly seen in the category of Hopf algebras. The comultiplication will be twisted. These twisted algebras can be realised on noncommutative spaces and allow the construction of deformed gauge theories and deformed gravity theory.

I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2009

2009-01-01

The I CAN Learn[R] Education System is an interactive, self-paced, mastery-based software system that includes the I CAN Learn[R] Fundamentals of Math (5th-6th grade math) curriculum, the I CAN Learn[R] Pre-Algebra curriculum, and the I CAN Learn[R] Algebra curriculum. College algebra credit is also available to students in participating schools…

A Characterization of a Unified Notion of Mathematical Function: The Case of High School Function and Linear Transformation

ERIC Educational Resources Information Center

Zandieh, Michelle; Ellis, Jessica; Rasmussen, Chris

2017-01-01

As part of a larger study of student understanding of concepts in linear algebra, we interviewed 10 university linear algebra students as to their conceptions of functions from high school algebra and linear transformation from their study of linear algebra. An overarching goal of this study was to examine how linear algebra students see linear…

Simple nuclear C*-algebras not isomorphic to their opposites

PubMed Central

Hirshberg, Ilan

2017-01-01

We show that it is consistent with Zermelo–Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable C∗-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra O2 or of the canonical anticommutation relations (CAR) algebra. PMID:28559339

Implementation of Algebra I in Eighth Grade: An "Ex-Post Facto" Study on Student Achievement

ERIC Educational Resources Information Center

Realdine, Dorothy S.

2010-01-01

Only recently have school districts across the nation begun to offer Algebra I to all eighth grade students. Currently, most eighth grade Algebra I curriculum does not have a national consistent focus of topics or level of rigor. A key issue of implementing Algebra I in eighth grade is defining national Algebra I concepts and skills that students…

The Xs and Whys of Algebra: Key Ideas and Common Misconceptions

ERIC Educational Resources Information Center

Collins, Anne; Dacey, Linda

2011-01-01

In many ways, algebra can be as challenging for teachers as it is for students. With so much emphasis placed on procedural knowledge and the manipulations of variables and symbols, it can be easy to lose sight of the key ideas that underlie algebraic thinking and the relevance algebra has to the real world. In the The Xs and Whys of Algebra: Key…

The applications of a higher-dimensional Lie algebra and its decomposed subalgebras

PubMed Central

Yu, Zhang; Zhang, Yufeng

2009-01-01

With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 × 6 matrix Lie algebra sμ(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra sμ(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras sμ(6) and E is used to directly construct integrable couplings. PMID:20084092

The applications of a higher-dimensional Lie algebra and its decomposed subalgebras.

PubMed

Yu, Zhang; Zhang, Yufeng

2009-01-15

With the help of invertible linear transformations and the known Lie algebras, a higher-dimensional 6 x 6 matrix Lie algebra smu(6) is constructed. It follows a type of new loop algebra is presented. By using a (2 + 1)-dimensional partial-differential equation hierarchy we obtain the integrable coupling of the (2 + 1)-dimensional KN integrable hierarchy, then its corresponding Hamiltonian structure is worked out by employing the quadratic-form identity. Furthermore, a higher-dimensional Lie algebra denoted by E, is given by decomposing the Lie algebra smu(6), then a discrete lattice integrable coupling system is produced. A remarkable feature of the Lie algebras smu(6) and E is used to directly construct integrable couplings.

Schwarz maps of algebraic linear ordinary differential equations

NASA Astrophysics Data System (ADS)

Sanabria Malagón, Camilo

2017-12-01

A linear ordinary differential equation is called algebraic if all its solution are algebraic over its field of definition. In this paper we solve the problem of finding closed form solution to algebraic linear ordinary differential equations in terms of standard equations. Furthermore, we obtain a method to compute all algebraic linear ordinary differential equations with rational coefficients by studying their associated Schwarz map through the Picard-Vessiot Theory.

Spatial-Operator Algebra For Robotic Manipulators

NASA Technical Reports Server (NTRS)

Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

1991-01-01

Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

Difficulties in initial algebra learning in Indonesia

NASA Astrophysics Data System (ADS)

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-12-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

Automated Library System Specifications.

DTIC Science & Technology

1986-06-01

University), LIS (Georqetown Universitv Medical Center) 20 DiSTRI3UT!ON.. AVAILABILITY OF ABSTRACT 21 ABSTRACT SECURITY CLASSIFICATION :UNCLASSIFIED...Interface) acquisitions, patron access catalo. (Boolean search), authority Afiles, zana ~ezient reports. Serials control expected in 1985. INDIVIDUALIZATIOI

Algebraic special functions and SO(3,2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-06-15

A ladder structure of operators is presented for the associated Legendre polynomials and the sphericas harmonics. In both cases these operators belong to the irreducible representation of the Lie algebra so(3,2) with quadratic Casimir equals to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be homomorphic to the space of linear operators acting on the L{sup 2} functions defined on (−1,1)×Z and on the sphere S{sup 2}, respectively. The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining inmore » this way the “algebraic special functions” that are proposed to be the connection between Lie algebras and square-integrable functions so that the space of linear operators on the L{sup 2} functions is homomorphic to the universal enveloping algebra. The passage to the group, by means of the exponential map, shows that the associated Legendre polynomials and the spherical harmonics support the corresponding unitary irreducible representation of the group SO(3,2). -- Highlights: •The algebraic ladder structure is constructed for the associated Legendre polynomials (ALP). •ALP and spherical harmonics support a unitary irreducible SO(3,2)-representation. •A ladder structure is the condition to get a Lie group representation defining “algebraic special functions”. •The “algebraic special functions” connect Lie algebras and L{sup 2} functions.« less

Locally Compact Quantum Groups. A von Neumann Algebra Approach

NASA Astrophysics Data System (ADS)

Van Daele, Alfons

2014-08-01

In this paper, we give an alternative approach to the theory of locally compact quantum groups, as developed by Kustermans and Vaes. We start with a von Neumann algebra and a comultiplication on this von Neumann algebra. We assume that there exist faithful left and right Haar weights. Then we develop the theory within this von Neumann algebra setting. In [Math. Scand. 92 (2003), 68-92] locally compact quantum groups are also studied in the von Neumann algebraic context. This approach is independent of the original C^*-algebraic approach in the sense that the earlier results are not used. However, this paper is not really independent because for many proofs, the reader is referred to the original paper where the C^*-version is developed. In this paper, we give a completely self-contained approach. Moreover, at various points, we do things differently. We have a different treatment of the antipode. It is similar to the original treatment in [Ann. Sci. & #201;cole Norm. Sup. (4) 33 (2000), 837-934]. But together with the fact that we work in the von Neumann algebra framework, it allows us to use an idea from [Rev. Roumaine Math. Pures Appl. 21 (1976), 1411-1449] to obtain the uniqueness of the Haar weights in an early stage. We take advantage of this fact when deriving the other main results in the theory. We also give a slightly different approach to duality. Finally, we collect, in a systematic way, several important formulas. In an appendix, we indicate very briefly how the C^*-approach and the von Neumann algebra approach eventually yield the same objects. The passage from the von Neumann algebra setting to the C^*-algebra setting is more or less standard. For the other direction, we use a new method. It is based on the observation that the Haar weights on the C^*-algebra extend to weights on the double dual with central support and that all these supports are the same. Of course, we get the von Neumann algebra by cutting down the double dual with this unique support projection in the center. All together, we see that there are many advantages when we develop the theory of locally compact quantum groups in the von Neumann algebra framework, rather than in the C^*-algebra framework. It is not only simpler, the theory of weights on von Neumann algebras is better known and one needs very little to go from the C^*-algebras to the von Neumann algebras. Moreover, in many cases when constructing examples, the von Neumann algebra with the coproduct is constructed from the very beginning and the Haar weights are constructed as weights on this von Neumann algebra (using left Hilbert algebra theory). This paper is written in a concise way. In many cases, only indications for the proofs of the results are given. This information should be enough to see that these results are correct. We will give more details in forthcoming paper, which will be expository, aimed at non-specialists. See also [Bull. Kerala Math. Assoc. (2005), 153-177] for an 'expanded' version of the appendix.

Algebraic theory of molecules

NASA Technical Reports Server (NTRS)

Iachello, Franco

1995-01-01

An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

FRT presentation of the Onsager algebras

NASA Astrophysics Data System (ADS)

Baseilhac, Pascal; Belliard, Samuel; Crampé, Nicolas

2018-03-01

A presentation à la Faddeev-Reshetikhin-Takhtajan (FRT) of the Onsager, augmented Onsager and sl_2 -invariant Onsager algebras is given, using the framework of the nonstandard classical Yang-Baxter algebras. Associated current algebras are identified, and generating functions of mutually commuting quantities are obtained.

The BMS4 algebra at spatial infinity

NASA Astrophysics Data System (ADS)

Troessaert, Cédric

2018-04-01

We show how a global BMS4 algebra appears as part of the asymptotic symmetry algebra at spatial infinity. Using linearised theory, we then show that this global BMS4 algebra is the one introduced by Strominger as a symmetry of the S-matrix.

Post-Lie algebras and factorization theorems

NASA Astrophysics Data System (ADS)

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.

Comparison of the Effectiveness of a Traditional Intermediate Algebra Course With That of a Less Rigorous Intermediate Algebra Course in Preparing Students for Success in a Subsequent Mathematics Course

ERIC Educational Resources Information Center

Sworder, Steven C.

2007-01-01

An experimental two-track intermediate algebra course was offered at Saddleback College, Mission Viejo, CA, between the Fall, 2002 and Fall, 2005 semesters. One track was modeled after the existing traditional California community college intermediate algebra course and the other track was a less rigorous intermediate algebra course in which the…

Hom Gel'fand-Dorfman bialgebras and Hom-Lie conformal algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yuan, Lamei, E-mail: lmyuan@hit.edu.cn

2014-04-15

The aim of this paper is to introduce the notions of Hom Gel'fand-Dorfman bialgebra and Hom-Lie conformal algebra. In this paper, we give four constructions of Hom Gel'fand-Dorfman bialgebras. Also, we provide a general construction of Hom-Lie conformal algebras from Hom-Lie algebras. Finally, we prove that a Hom Gel'fand-Dorfman bialgebra is equivalent to a Hom-Lie conformal algebra of degree 2.

Internally connected graphs and the Kashiwara-Vergne Lie algebra

NASA Astrophysics Data System (ADS)

Felder, Matteo

2018-06-01

It is conjectured that the Kashiwara-Vergne Lie algebra \\widehat{krv}_2 is isomorphic to the direct sum of the Grothendieck-Teichmüller Lie algebra grt_1 and a one-dimensional Lie algebra. In this paper, we use the graph complex of internally connected graphs to define a nested sequence of Lie subalgebras of \\widehat{krv}_2 whose intersection is grt_1, thus giving a way to interpolate between these two Lie algebras.

Discrimination in a General Algebraic Setting

PubMed Central

Fine, Benjamin; 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. PMID:26171421

Generalized derivation extensions of 3-Lie algebras and corresponding Nambu-Poisson structures

NASA Astrophysics Data System (ADS)

Song, Lina; Jiang, Jun

2018-01-01

In this paper, we introduce the notion of a generalized derivation on a 3-Lie algebra. We construct a new 3-Lie algebra using a generalized derivation and call it the generalized derivation extension. We show that the corresponding Leibniz algebra on the space of fundamental objects is the double of a matched pair of Leibniz algebras. We also determine the corresponding Nambu-Poisson structures under some conditions.

Metric 3-Leibniz algebras and M2-branes

NASA Astrophysics Data System (ADS)

Méndez-Escobar, Elena

2010-08-01

This thesis is concerned with superconformal Chern-Simons theories with matter in 3 dimensions. The interest in these theories is two-fold. On the one hand, it is a new family of theories in which to test the AdS/CFT correspondence and on the other, they are important to study one of the main objects of M-theory (M2-branes). All these theories have something in common: they can be written in terms of 3-Leibniz algebras. Here we study the structure theory of such algebras, paying special attention to a subclass of them that gives rise to maximal supersymmetry and that was the first to appear in this context: 3-Lie algebras. In chapter 2, we review the structure theory of metric Lie algebras and their unitary representations. In chapter 3, we study metric 3-Leibniz algebras and show, by specialising a construction originally due to Faulkner, that they are in one to one correspondence with pairs of real metric Lie algebras and unitary representations of them. We also show a third characterisation for six extreme cases of 3-Leibniz algebras as graded Lie (super)algebras. In chapter 4, we study metric 3-Lie algebras in detail. We prove a structural result and also classify those with a maximally isotropic centre, which is the requirement that ensures unitarity of the corresponding conformal field theory. Finally, in chapter 5, we study the universal structure of superpotentials in this class of superconformal Chern-Simons theories with matter in three dimensions. We provide a uniform formulation for all these theories and establish the connection between the amount of supersymmetry preserved and the gauge Lie algebra and the appropriate unitary representation to be used to write down the Lagrangian. The conditions for supersymmetry enhancement are then expressed equivalently in the language of representation theory of Lie algebras or the language of 3-Leibniz algebras.

On Maximal Subalgebras and the Hypercentre of Lie Algebras.

ERIC Educational Resources Information Center

Honda, Masanobu

1997-01-01

Derives two sufficient conditions for a finitely generated Lie algebra to have the nilpotent hypercenter. Presents a relatively large class of generalized soluble Lie algebras. Proves that if a finitely generated Lie algebra has a nilpotent maximal subalgebra, the Fitting radical is nilpotent. (DDR)

An algebra of reversible computation.

PubMed

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.

On Weak-BCC-Algebras

PubMed Central

Thomys, Janus; Zhang, Xiaohong

2013-01-01

We describe weak-BCC-algebras (also called BZ-algebras) in which the condition (x∗y)∗z = (x∗z)∗y is satisfied only in the case when elements x, y belong to the same branch. We also characterize ideals, nilradicals, and nilpotent elements of such algebras. PMID:24311983

Macdonald index and chiral algebra

NASA Astrophysics Data System (ADS)

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.

Macdonald index and chiral algebra

DOE Office of Scientific and Technical Information (OSTI.GOV)

Song, Jaewon

For any 4dN = 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. Here, 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 2n) and (A 1, D 2n+1) where the chiral algebras are given by Virasoro andmore » $$ˆ\\atop{su}$$(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.« less

Macdonald index and chiral algebra

DOE PAGES

Song, Jaewon

2017-08-10

For any 4dN = 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. Here, 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 2n) and (A 1, D 2n+1) where the chiral algebras are given by Virasoro andmore » $$ˆ\\atop{su}$$(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.« less

Line defect Schur indices, Verlinde algebras and U(1) r fixed points

NASA Astrophysics Data System (ADS)

Neitzke, Andrew; Yan, Fei

2017-11-01

Given an N=2 superconformal field theory, we reconsider the Schur index ℐ L ( q) in the presence of a half line defect L. Recently Cordova-Gaiotto-Shao found that ℐ L ( q) admits an expansion in terms of characters of the chiral algebra A introduced by Beem et al., with simple coefficients υ L, β ( q). We report a puzzling new feature of this expansion: the q → 1 limit of the coefficients υ L, β ( q) is linearly related to the vacuum expectation values 〈 L〉 in U(1) r -invariant vacua of the theory compactified on S 1. This relation can be expressed algebraically as a commutative diagram involving three algebras: the algebra generated by line defects, the algebra of functions on U(1) r -invariant vacua, and a Verlindelike algebra associated to A . Our evidence is experimental, by direct computation in the Argyres-Douglas theories of type ( A 1, A 2), ( A 1, A 4), ( A 1, A 6), ( A 1, D 3) and ( A 1, D 5). In the latter two theories, which have flavor symmetries, the Verlinde-like algebra which appears is a new deformation of algebras previously considered.

Constraint-Referenced Analytics of Algebra Learning

ERIC Educational Resources Information Center

Sutherland, Scot M.; White, Tobin F.

2016-01-01

The development of the constraint-referenced analytics tool for monitoring algebra learning activities presented here came from the desire to firstly, take a more quantitative look at student responses in collaborative algebra activities, and secondly, to situate those activities in a more traditional introductory algebra setting focusing on…

Teaching Strategies to Improve Algebra Learning

ERIC Educational Resources Information Center

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"…

Preparing Elementary Prospective Teachers to Teach Early Algebra

ERIC Educational Resources Information Center

Hohensee, Charles

2017-01-01

Researchers have argued that integrating early algebra into elementary grades will better prepare students for algebra. However, currently little research exists to guide teacher preparation programs on how to prepare prospective elementary teachers to teach early algebra. This study examines the insights and challenges that prospective teachers…

Difficulties in Initial Algebra Learning in Indonesia

ERIC Educational Resources Information Center

Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

2014-01-01

Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was…

Visual Salience of Algebraic Transformations

ERIC Educational Resources Information Center

Kirshner, David; Awtry, Thomas

2004-01-01

Information processing researchers have assumed that algebra symbol skills depend on mastery of the abstract rules presented in the curriculum (Matz, 1980; Sleeman, 1986). Thus, students' ubiquitous algebra errors have been taken as indicating the need to embed algebra in rich contextual settings (Kaput, 1995; National Council of Teachers of…

Quantum walled Brauer algebra: commuting families, Baxterization, and representations

NASA Astrophysics Data System (ADS)

Semikhatov, A. M.; Tipunin, I. Yu

2017-02-01

For the quantum walled Brauer algebra, we construct its Specht modules and (for generic parameters of the algebra) seminormal modules. The latter construction yields the spectrum of a commuting family of Jucys-Murphy elements. We also propose a Baxterization prescription; it involves representing the quantum walled Brauer algebra in terms of morphisms in a braided monoidal category and introducing parameters into these morphisms, which allows constructing a ‘universal transfer matrix’ that generates commuting elements of the algebra.

Nonvolatile reconfigurable sequential logic in a HfO2 resistive random access memory array.

PubMed

Zhou, Ya-Xiong; Li, Yi; Su, Yu-Ting; Wang, Zhuo-Rui; Shih, Ling-Yi; Chang, Ting-Chang; Chang, Kuan-Chang; Long, Shi-Bing; Sze, Simon M; Miao, Xiang-Shui

2017-05-25

Resistive random access memory (RRAM) based reconfigurable logic provides a temporal programmable dimension to realize Boolean logic functions and is regarded as a promising route to build non-von Neumann computing architecture. In this work, a reconfigurable operation method is proposed to perform nonvolatile sequential logic in a HfO 2 -based RRAM array. Eight kinds of Boolean logic functions can be implemented within the same hardware fabrics. During the logic computing processes, the RRAM devices in an array are flexibly configured in a bipolar or complementary structure. The validity was demonstrated by experimentally implemented NAND and XOR logic functions and a theoretically designed 1-bit full adder. With the trade-off between temporal and spatial computing complexity, our method makes better use of limited computing resources, thus provides an attractive scheme for the construction of logic-in-memory systems.

Synthesizing Biomolecule-based Boolean Logic Gates

PubMed Central

Miyamoto, Takafumi; Razavi, Shiva; DeRose, Robert; Inoue, Takanari

2012-01-01

One fascinating recent avenue of study in the field of synthetic biology is the creation of biomolecule-based computers. The main components of a computing device consist of an arithmetic logic unit, the control unit, memory, and the input and output devices. Boolean logic gates are at the core of the operational machinery of these parts, hence to make biocomputers a reality, biomolecular logic gates become a necessity. Indeed, with the advent of more sophisticated biological tools, both nucleic acid- and protein-based logic systems have been generated. These devices function in the context of either test tubes or living cells and yield highly specific outputs given a set of inputs. In this review, we discuss various types of biomolecular logic gates that have been synthesized, with particular emphasis on recent developments that promise increased complexity of logic gate circuitry, improved computational speed, and potential clinical applications. PMID:23526588

Interconnect-free parallel logic circuits in a single mechanical resonator

PubMed Central

Mahboob, I.; Flurin, E.; Nishiguchi, K.; Fujiwara, A.; Yamaguchi, H.

2011-01-01

In conventional computers, wiring between transistors is required to enable the execution of Boolean logic functions. This has resulted in processors in which billions of transistors are physically interconnected, which limits integration densities, gives rise to huge power consumption and restricts processing speeds. A method to eliminate wiring amongst transistors by condensing Boolean logic into a single active element is thus highly desirable. Here, we demonstrate a novel logic architecture using only a single electromechanical parametric resonator into which multiple channels of binary information are encoded as mechanical oscillations at different frequencies. The parametric resonator can mix these channels, resulting in new mechanical oscillation states that enable the construction of AND, OR and XOR logic gates as well as multibit logic circuits. Moreover, the mechanical logic gates and circuits can be executed simultaneously, giving rise to the prospect of a parallel logic processor in just a single mechanical resonator. PMID:21326230

Interconnect-free parallel logic circuits in a single mechanical resonator.

PubMed

Mahboob, I; Flurin, E; Nishiguchi, K; Fujiwara, A; Yamaguchi, H

2011-02-15

In conventional computers, wiring between transistors is required to enable the execution of Boolean logic functions. This has resulted in processors in which billions of transistors are physically interconnected, which limits integration densities, gives rise to huge power consumption and restricts processing speeds. A method to eliminate wiring amongst transistors by condensing Boolean logic into a single active element is thus highly desirable. Here, we demonstrate a novel logic architecture using only a single electromechanical parametric resonator into which multiple channels of binary information are encoded as mechanical oscillations at different frequencies. The parametric resonator can mix these channels, resulting in new mechanical oscillation states that enable the construction of AND, OR and XOR logic gates as well as multibit logic circuits. Moreover, the mechanical logic gates and circuits can be executed simultaneously, giving rise to the prospect of a parallel logic processor in just a single mechanical resonator.

Calculating the bidirectional reflectance of natural vegetation covers using Boolean models and geometric optics

NASA Technical Reports Server (NTRS)

Strahler, Alan H.; Li, Xiao-Wen; Jupp, David L. B.

1991-01-01

The bidirectional radiance or reflectance of a forest or woodland can be modeled using principles of geometric optics and Boolean models for random sets in a three dimensional space. This model may be defined at two levels, the scene includes four components; sunlight and shadowed canopy, and sunlit and shadowed background. The reflectance of the scene is modeled as the sum of the reflectances of the individual components as weighted by their areal proportions in the field of view. At the leaf level, the canopy envelope is an assemblage of leaves, and thus the reflectance is a function of the areal proportions of sunlit and shadowed leaf, and sunlit and shadowed background. Because the proportions of scene components are dependent upon the directions of irradiance and exitance, the model accounts for the hotspot that is well known in leaf and tree canopies.

Synthesizing biomolecule-based Boolean logic gates.

PubMed

Miyamoto, Takafumi; Razavi, Shiva; DeRose, Robert; Inoue, Takanari

2013-02-15

One fascinating recent avenue of study in the field of synthetic biology is the creation of biomolecule-based computers. The main components of a computing device consist of an arithmetic logic unit, the control unit, memory, and the input and output devices. Boolean logic gates are at the core of the operational machinery of these parts, and hence to make biocomputers a reality, biomolecular logic gates become a necessity. Indeed, with the advent of more sophisticated biological tools, both nucleic acid- and protein-based logic systems have been generated. These devices function in the context of either test tubes or living cells and yield highly specific outputs given a set of inputs. In this review, we discuss various types of biomolecular logic gates that have been synthesized, with particular emphasis on recent developments that promise increased complexity of logic gate circuitry, improved computational speed, and potential clinical applications.

Simultaneous G-Quadruplex DNA Logic.

PubMed

Bader, Antoine; Cockroft, Scott L

2018-04-03

A fundamental principle of digital computer operation is Boolean logic, where inputs and outputs are described by binary integer voltages. Similarly, inputs and outputs may be processed on the molecular level as exemplified by synthetic circuits that exploit the programmability of DNA base-pairing. Unlike modern computers, which execute large numbers of logic gates in parallel, most implementations of molecular logic have been limited to single computing tasks, or sensing applications. This work reports three G-quadruplex-based logic gates that operate simultaneously in a single reaction vessel. The gates respond to unique Boolean DNA inputs by undergoing topological conversion from duplex to G-quadruplex states that were resolved using a thioflavin T dye and gel electrophoresis. The modular, addressable, and label-free approach could be incorporated into DNA-based sensors, or used for resolving and debugging parallel processes in DNA computing applications. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Satisfiability of logic programming based on radial basis function neural networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hamadneh, Nawaf; Sathasivam, Saratha; Tilahun, Surafel Luleseged

2014-07-10

In this paper, we propose a new technique to test the Satisfiability of propositional logic programming and quantified Boolean formula problem in radial basis function neural networks. For this purpose, we built radial basis function neural networks to represent the proportional logic which has exactly three variables in each clause. We used the Prey-predator algorithm to calculate the output weights of the neural networks, while the K-means clustering algorithm is used to determine the hidden parameters (the centers and the widths). Mean of the sum squared error function is used to measure the activity of the two algorithms. We appliedmore » the developed technique with the recurrent radial basis function neural networks to represent the quantified Boolean formulas. The new technique can be applied to solve many applications such as electronic circuits and NP-complete problems.« less

Altered Micro-RNA Degradation Promotes Tumor Heterogeneity: A Result from Boolean Network Modeling.

PubMed

Wu, Yunyi; Krueger, Gerhard R F; Wang, Guanyu

2016-02-01

Cancer heterogeneity may reflect differential dynamical outcomes of the regulatory network encompassing biomolecules at both transcriptional and post-transcriptional levels. In other words, differential gene-expression profiles may correspond to different stable steady states of a mathematical model for simulation of biomolecular networks. To test this hypothesis, we simplified a regulatory network that is important for soft-tissue sarcoma metastasis and heterogeneity, comprising of transcription factors, micro-RNAs, and signaling components of the NOTCH pathway. We then used a Boolean network model to simulate the dynamics of this network, and particularly investigated the consequences of differential miRNA degradation modes. We found that efficient miRNA degradation is crucial for sustaining a homogenous and healthy phenotype, while defective miRNA degradation may lead to multiple stable steady states and ultimately to carcinogenesis and heterogeneity. Copyright© 2016 International Institute of Anticancer Research (Dr. John G. Delinassios), All rights reserved.

A solution to the surface intersection problem. [Boolean functions in geometric modeling

NASA Technical Reports Server (NTRS)

Timer, H. G.

1977-01-01

An application-independent geometric model within a data base framework should support the use of Boolean operators which allow the user to construct a complex model by appropriately combining a series of simple models. The use of these operators leads to the concept of implicitly and explicitly defined surfaces. With an explicitly defined model, the surface area may be computed by simply summing the surface areas of the bounding surfaces. For an implicitly defined model, the surface area computation must deal with active and inactive regions. Because the surface intersection problem involves four unknowns and its solution is a space curve, the parametric coordinates of each surface must be determined as a function of the arc length. Various subproblems involved in the general intersection problem are discussed, and the mathematical basis for their solution is presented along with a program written in FORTRAN IV for implementation on the IBM 370 TSO system.

Graphene-based non-Boolean logic circuits

NASA Astrophysics Data System (ADS)

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.

Abstract Numeric Relations and the Visual Structure of Algebra

ERIC Educational Resources Information Center

Landy, David; Brookes, David; Smout, Ryan

2014-01-01

Formal algebras are among the most powerful and general mechanisms for expressing quantitative relational statements; yet, even university engineering students, who are relatively proficient with algebraic manipulation, struggle with and often fail to correctly deploy basic aspects of algebraic notation (Clement, 1982). In the cognitive tradition,…

Classical versus Computer Algebra Methods in Elementary Geometry

ERIC Educational Resources Information Center

Pech, Pavel

2005-01-01

Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

UCSMP Algebra. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2007

2007-01-01

"University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

Teacher Actions to Facilitate Early Algebraic Reasoning

ERIC Educational Resources Information Center

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…

Abstract Algebra to Secondary School Algebra: Building Bridges

ERIC Educational Resources Information Center

Christy, Donna; Sparks, Rebecca

2015-01-01

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

A Proposed Algebra Assessment for Use in a Problem-Analysis Framework

ERIC Educational Resources Information Center

Walick, Christopher M.; Burns, Matthew K.

2017-01-01

Algebra is critical to high school graduation and college success, but student achievement in algebra frequently falls significantly below expected proficiency levels. While existing research emphasizes the importance of quality algebra instruction, there is little research about how to conduct problem analysis for struggling secondary students.…

A Relational Algebra Query Language for Programming Relational Databases

ERIC Educational Resources Information Center

McMaster, Kirby; Sambasivam, Samuel; Anderson, Nicole

2011-01-01

In this paper, we describe a Relational Algebra Query Language (RAQL) and Relational Algebra Query (RAQ) software product we have developed that allows database instructors to teach relational algebra through programming. Instead of defining query operations using mathematical notation (the approach commonly taken in database textbooks), students…

Assessing Mathematics Automatically Using Computer Algebra and the Internet

ERIC Educational Resources Information Center

Sangwin, Chris

2004-01-01

This paper reports some recent developments in mathematical computer-aided assessment which employs computer algebra to evaluate students' work using the Internet. Technical and educational issues raised by this use of computer algebra are addressed. Working examples from core calculus and algebra which have been used with first year university…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 1. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the student text for part one of a three-part SMSG algebra course for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations;…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 1), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 1, Teacher's Commentary. Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part one of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables;…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2). Traduccion Preliminar de la Edicion Inglesa Revisada. (Mathematics for High School, First Course in Algebra, Part 2. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real numbers, subtraction and division…

Quiver W-algebras

NASA Astrophysics Data System (ADS)

Kimura, Taro; Pestun, Vasily

2018-06-01

For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds-Kac-Moody Lie algebras, their quantum affinizations and associated W-algebras.

An Algebraic Formulation of Level One Wess-Zumino Models

NASA Astrophysics Data System (ADS)

Böckenhauer, Jens

The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven.

Factors associated with sustained remission in patients with rheumatoid arthritis.

PubMed

Martire, María Victoria; Marino Claverie, Lucila; Duarte, Vanesa; Secco, Anastasia; Mammani, Marta

2015-01-01

To find out the factors that are associated with sustained remission measured by DAS28 and boolean ACR EULAR 2011 criteria at the time of diagnosis of rheumatoid arthritis. Medical records of patients with rheumatoid arthritis in sustained remission according to DAS28 were reviewed. They were compared with patients who did not achieved values of DAS28<2.6 in any visit during the first 3 years after diagnosis. We also evaluated if patients achieved the boolean ACR/EULAR criteria. Variables analyzed: sex, age, smoking, comorbidities, rheumatoid factor, anti-CCP, ESR, CRP, erosions, HAQ, DAS28, extra-articular manifestations, time to initiation of treatment, involvement of large joints, number of tender joints, number of swollen joints, pharmacological treatment. Forty five patients that achieved sustained remission were compared with 44 controls. The variables present at diagnosis that significantly were associated with remission by DAS28 were: lower values of DAS28, HAQ, ESR, NTJ, NSJ, negative CRP, absence of erosions, male sex and absence of involvement of large joints. Only 24.71% achieved the boolean criteria. The variables associated with sustained remission by these criteria were: lower values of DAS28, HAQ, ESR, number of tender joints and number of swollen joints, negative CRP and absence of erosions. The factors associated with sustained remission were the lower baseline disease activity, the low degree of functional disability and lower joint involvement. We consider it important to recognize these factors to optimize treatment. Copyright © 2014 Elsevier España, S.L.U. All rights reserved.

Jimena: efficient computing and system state identification for genetic regulatory networks.

PubMed

Karl, Stefan; Dandekar, Thomas

2013-10-11

Boolean networks capture switching behavior of many naturally occurring regulatory networks. For semi-quantitative modeling, interpolation between ON and OFF states is necessary. The high degree polynomial interpolation of Boolean genetic regulatory networks (GRNs) in cellular processes such as apoptosis or proliferation allows for the modeling of a wider range of node interactions than continuous activator-inhibitor models, but suffers from scaling problems for networks which contain nodes with more than ~10 inputs. Many GRNs from literature or new gene expression experiments exceed those limitations and a new approach was developed. (i) As a part of our new GRN simulation framework Jimena we introduce and setup Boolean-tree-based data structures; (ii) corresponding algorithms greatly expedite the calculation of the polynomial interpolation in almost all cases, thereby expanding the range of networks which can be simulated by this model in reasonable time. (iii) Stable states for discrete models are efficiently counted and identified using binary decision diagrams. As application example, we show how system states can now be sampled efficiently in small up to large scale hormone disease networks (Arabidopsis thaliana development and immunity, pathogen Pseudomonas syringae and modulation by cytokinins and plant hormones). Jimena simulates currently available GRNs about 10-100 times faster than the previous implementation of the polynomial interpolation model and even greater gains are achieved for large scale-free networks. This speed-up also facilitates a much more thorough sampling of continuous state spaces which may lead to the identification of new stable states. Mutants of large networks can be constructed and analyzed very quickly enabling new insights into network robustness and behavior.

Computing smallest intervention strategies for multiple metabolic networks in a boolean model.

PubMed

Lu, Wei; Tamura, Takeyuki; Song, Jiangning; Akutsu, Tatsuya

2015-02-01

This article considers the problem whereby, given two metabolic networks N1 and N2, a set of source compounds, and a set of target compounds, we must find the minimum set of reactions whose removal (knockout) ensures that the target compounds are not producible in N1 but are producible in N2. Similar studies exist for the problem of finding the minimum knockout with the smallest side effect for a single network. However, if technologies of external perturbations are advanced in the near future, it may be important to develop methods of computing the minimum knockout for multiple networks (MKMN). Flux balance analysis (FBA) is efficient if a well-polished model is available. However, that is not always the case. Therefore, in this article, we study MKMN in Boolean models and an elementary mode (EM)-based model. Integer linear programming (ILP)-based methods are developed for these models, since MKMN is NP-complete for both the Boolean model and the EM-based model. Computer experiments are conducted with metabolic networks of clostridium perfringens SM101 and bifidobacterium longum DJO10A, respectively known as bad bacteria and good bacteria for the human intestine. The results show that larger networks are more likely to have MKMN solutions. However, solving for these larger networks takes a very long time, and often the computation cannot be completed. This is reasonable, because small networks do not have many alternative pathways, making it difficult to satisfy the MKMN condition, whereas in large networks the number of candidate solutions explodes. Our developed software minFvskO is available online.

On Correspondence of BRST-BFV, Dirac, and Refined Algebraic Quantizations of Constrained Systems

NASA Astrophysics Data System (ADS)

Shvedov, O. Yu.

2002-11-01

The correspondence between BRST-BFV, Dirac, and refined algebraic (group averaging, projection operator) approaches to quantizing constrained systems is analyzed. For the closed-algebra case, it is shown that the component of the BFV wave function corresponding to maximal (minimal) value of number of ghosts and antighosts in the Schrodinger representation may be viewed as a wave function in the refined algebraic (Dirac) quantization approach. The Giulini-Marolf group averaging formula for the inner product in the refined algebraic quantization approach is obtained from the Batalin-Marnelius prescription for the BRST-BFV inner product, which should be generally modified due to topological problems. The considered prescription for the correspondence of states is observed to be applicable to the open-algebra case. The refined algebraic quantization approach is generalized then to the case of nontrivial structure functions. A simple example is discussed. The correspondence of observables for different quantization methods is also investigated.

Toward the classification of differential calculi on κ-Minkowski space and related field theories

NASA Astrophysics Data System (ADS)

Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel; Štrajn, Rina

2015-07-01

Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.

Eighth Grade Algebra Placement Policies: Promoting Equity, Achievement, and Access

ERIC Educational Resources Information Center

Wambsgans, Cynthia

2014-01-01

This study was an investigation of a standardized 8th grade Algebra I placement policy across multiple educational districts. Researchers have documented benefits of students' 8th grade Algebra I education, while others have detailed the consequences of algebra enrollment without necessary prerequisite skills. The purpose of this study was to…

Designing Virtual Worlds for Use in Mathematics Education: The Example of Experiential Algebra.

ERIC Educational Resources Information Center

Winn, William; Bricken, William

1992-01-01

Discussion of the use of virtual reality (VR) to help students learn highlights the use of VR with elementary algebra. Learning theory is examined, including knowledge construction; knowledge representation is discussed, including the symbol systems of algebra; and spatial algebra is described and illustrated. (34 references) (LRW)

Meanings Given to Algebraic Symbolism in Problem-Posing

ERIC Educational Resources Information Center

Cañadas, María C.; Molina, Marta; del Río, Aurora

2018-01-01

Some errors in the learning of algebra suggest that students might have difficulties giving meaning to algebraic symbolism. In this paper, we use problem posing to analyze the students' capacity to assign meaning to algebraic symbolism and the difficulties that students encounter in this process, depending on the characteristics of the algebraic…

Build an Early Foundation for Algebra Success

ERIC Educational Resources Information Center

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…

A Balancing Act: Making Sense of Algebra

ERIC Educational Resources Information Center

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…

Unifying the Algebra for All Movement

ERIC Educational Resources Information Center

Eddy, Colleen M.; Quebec Fuentes, Sarah; Ward, Elizabeth K.; Parker, Yolanda A.; Cooper, Sandi; Jasper, William A.; Mallam, Winifred A.; Sorto, M. Alejandra; Wilkerson, Trena L.

2015-01-01

There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the "Algebra for All" movement. In light of this…

A Meta-Analysis of Algebra Interventions for Learners with Disabilities and Struggling Learners

ERIC Educational Resources Information Center

Hughes, Elizabeth M.; Witzel, Bradley S.; Riccomini, Paul J.; Fries, Karen M.; Kanyongo, Gibbs Y.

2014-01-01

The need for global competence in mathematics is apparent. Algebra is considered a gateway course to prepare students for the demands of a competitive global market. Many students demonstrate low performance in algebra; this is especially true for students with disabilities. Effective algebra instruction is essential to increase algebra…

Effectiveness of Cognitive Tutor Algebra I at Scale

ERIC Educational Resources Information Center

Pane, John F.; Griffin, Beth Ann; McCaffrey, Daniel F.; Karam, Rita

2014-01-01

This article examines the effectiveness of a technology-based algebra curriculum in a wide variety of middle schools and high schools in seven states. Participating schools were matched into similar pairs and randomly assigned to either continue with the current algebra curriculum for 2 years or to adopt Cognitive Tutor Algebra I (CTAI), which…

Using Linguistics in the Teaching of Developmental and Remedial Algebra.

ERIC Educational Resources Information Center

Lesnak, Richard J.

Basic algebra at Robert Morris College (RMC) in Pittsburgh, Pennsylvania, is a remedial course for students with virtually no algebra background, and for students whose previous experiences with algebra have created math blocks and math anxiety. A study was conducted in an effort to measure quantitatively the benefits of using linguistic methods…

How Middle Grade Teachers Think about Algebraic Reasoning

ERIC Educational Resources Information Center

Glassmeyer, David; Edwards, Belinda

2016-01-01

Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…

Assessing Elementary Algebra with STACK

ERIC Educational Resources Information Center

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…

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

NASA Astrophysics Data System (ADS)

Aryani, F.; Amin, S. M.; Sulaiman, R.

2018-01-01

Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.

Asymptotic symmetries of Rindler space at the horizon and null infinity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chung, Hyeyoun

2010-08-15

We investigate the asymptotic symmetries of Rindler space at null infinity and at the event horizon using both systematic and ad hoc methods. We find that the approaches that yield infinite-dimensional asymptotic symmetry algebras in the case of anti-de Sitter and flat spaces only give a finite-dimensional algebra for Rindler space at null infinity. We calculate the charges corresponding to these symmetries and confirm that they are finite, conserved, and integrable, and that the algebra of charges gives a representation of the asymptotic symmetry algebra. We also use relaxed boundary conditions to find infinite-dimensional asymptotic symmetry algebras for Rindler spacemore » at null infinity and at the event horizon. We compute the charges corresponding to these symmetries and confirm that they are finite and integrable. We also determine sufficient conditions for the charges to be conserved on-shell, and for the charge algebra to give a representation of the asymptotic symmetry algebra. In all cases, we find that the central extension of the charge algebra is trivial.« less

A Note about Information Science Research.

ERIC Educational Resources Information Center

Salton, Gerard

1985-01-01

Discusses the relationship between information science research and practice and briefly describes current research on 10 topics in information retrieval literature: vector processing retrieval strategy, probabilistic retrieval models, inverted file procedures, relevance feedback, Boolean query formulations, front-end procedures, citation…

Bibliographic Instruction in the 21st Century.

ERIC Educational Resources Information Center

Poirier, Gayle

2000-01-01

Discusses bibliographic instruction in libraries. Topics include a history of bibliographic instruction; the Internet and electronic searching; librarians' use of technology; defining information needs; locating and accessing information, including classification systems and Boolean searching; evaluating information; using and communication…

The Dixmier Map for Nilpotent Super Lie Algebras

NASA Astrophysics Data System (ADS)

Herscovich, Estanislao

2012-07-01

In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by {Prim({U}({g}))} the set of (graded) primitive ideals of the enveloping algebra {{U}({g})} of a nilpotent Lie superalgebra {{g}} and {{A}d0} the adjoint group of {{g}0}, we prove that the usual Dixmier map for nilpotent Lie algebras can be naturally extended to the context of nilpotent super Lie algebras, i.e. there exists a bijective map I : {g}0^{*}/{A}d0 rightarrow Prim({U}({g})) defined by sending the equivalence class [ λ] of a functional λ to a primitive ideal I( λ) of {{U}({g})}, and which coincides with the Dixmier map in the case of nilpotent Lie algebras. Moreover, the construction of the previous map is explicit, and more or less parallel to the one for Lie algebras, a major difference with a previous approach ( cf. [18]). One key fact in the construction is the existence of polarizations for super Lie algebras, generalizing the concept defined for Lie algebras. As a corollary of the previous description, we obtain the isomorphism {{U}({g})/I(λ) ˜eq Cliffq(k) ⊗ Ap(k)}, where {(p,q) = (dim({g}0/{g}0^{λ})/2,dim({g}1/{g}1^{λ}))}, we get a direct construction of the maximal ideals of the underlying algebra of {{U}({g})} and also some properties of the stabilizers of the primitive ideals of {{U}({g})}.

Attributions for Success and Failure in Algebra of Samoan Community College Students: A Profile Analysis.

ERIC Educational Resources Information Center

Powers, Stephen; And Others

Sex differences in attributions for success and failure in algebra of Samoan community college students were examined and compared with attributions of a large group of mainland U.S. students. study included the Mathematics Attribution Scale: Algebra Version (MAS), which assessed students' attributions of achievement in algebra to their effort,…

Using CRA to Teach Algebra to Students with Math Difficulties in Inclusive Settings

ERIC Educational Resources Information Center

Witzel, Bradley S.

2005-01-01

The importance of algebra instruction has increased in the United States in the past few years. Thus, in most states, middle school students are required to take Algebra 1. Middle school students with math difficulties in inclusion algebra settings may require a different instructional approach. The purpose of this research was to compare student…

Learning to Apply Algebra in the Community for Adults with Intellectual Developmental Disabilities

ERIC Educational Resources Information Center

Rodriguez, Anthony M.

2016-01-01

Students with intellectual and developmental disabilities (IDD) are routinely excluded from algebra and other high-level mathematics courses. High school students with IDD take courses in arithmetic and life skills rather than having an opportunity to learn algebra. Yet algebra skills can support the learning of money and budgeting skills. This…

Capitalizing on Basic Brain Processes in Developmental Algebra--Part 2

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand its basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain processes…

Capitalizing on Basic Brain Processes in Developmental Algebra--Part One

ERIC Educational Resources Information Center

Laughbaum, Edward D.

2011-01-01

Basic brain function is not a mystery. Given that neuroscientists understand the brain's basic functioning processes, one wonders what their research suggests to teachers of developmental algebra. What if we knew how to teach so as to improve understanding of the algebra taught to developmental algebra students? What if we knew how the brain…

Reinventing Fractions and Division as They Are Used in Algebra: The Power of Preformal Productions

ERIC Educational Resources Information Center

Peck, Frederick; Matassa, Michael

2016-01-01

In this paper, we explore algebra students' mathematical realities around fractions and division, and the ways in which students reinvented mathematical productions involving fractions and division. We find that algebra students' initial realities do not include the fraction-as-quotient sub-construct. This can be problematic because in algebra,…

The Development of Children's Algebraic Thinking: The Impact of a Comprehensive Early Algebra Intervention in Third Grade

ERIC Educational Resources Information Center

Blanton, Maria; Stephens, Ana; Knuth, Eric; Gardiner, Angela Murphy; Isler, Isil; Kim, Jee-Seon

2015-01-01

This article reports results from a study investigating the impact of a sustained, comprehensive early algebra intervention in third grade. Participants included 106 students; 39 received the early algebra intervention, and 67 received their district's regularly planned mathematics instruction. We share and discuss students' responses to a written…

Algebra? A Gate! A Barrier! A Mystery!

ERIC Educational Resources Information Center

Mathematics Educatio Dialogues, 2000

2000-01-01

This issue of Mathematics Education Dialogues focuses on the nature and the role of algebra in the K-14 curriculum. Articles on this theme include: (1) "Algebra For All? Why?" (Nel Noddings); (2) "Algebra For All: It's a Matter of Equity, Expectations, and Effectiveness" (Dorothy S. Strong and Nell B. Cobb); (3) "Don't Delay: Build and Talk about…

Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2014-01-01

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

The State of the Gate: A Description of Instructional Practice in Algebra in Five Urban Districts

ERIC Educational Resources Information Center

Litke, Erica G.

2015-01-01

Algebra is considered a linchpin for success in secondary mathematics, serving as a gatekeeper to higher-level courses. Access to algebra is also considered an important lever for educational equity. Yet despite its prominence, large-scale examinations of algebra instruction are rare. In my dissertation, I endeavor to better understand what…

Relationships between Classroom Schedule Types and Performance on the Algebra I Criterion-Referenced Test

ERIC Educational Resources Information Center

Murray, Gregory V.; Moyer-Packenham, Patricia S.

2014-01-01

One option for length of individual mathematics class periods is the schedule type selected for Algebra I classes. This study examined the relationship between student achievement, as indicated by Algebra I Criterion-Referenced Test scores, and the schedule type for Algebra I classes. Data obtained from the Utah State Office of Education included…

Grade 11 Students' Interconnected Use of Conceptual Knowledge, Procedural Skills, and Strategic Competence in Algebra: A Mixed Method Study of Error Analysis

ERIC Educational Resources Information Center

Egodawatte, Gunawardena; Stoilescu, Dorian

2015-01-01

The purpose of this mixed-method study was to investigate grade 11 university/college stream mathematics students' difficulties in applying conceptual knowledge, procedural skills, strategic competence, and algebraic thinking in solving routine (instructional) algebraic problems. A standardized algebra test was administered to thirty randomly…

The Ideas of Algebra, K-12. 1988 Yearbook.

ERIC Educational Resources Information Center

Coxford, Arthur F., Ed.; Shulte, Albert P., Ed.

This volume is organized into six parts. Chapters 1-5, which make up Part 1, first discuss the forces impinging on algebra in the curriculum and suggest possible directions for change. Chapters 6-8, Part 2, concentrate on concepts and teaching possibilities available prior to the formal introduction of algebra. The notion that algebraic ideas are…

Solving the Unknown with Algebra: Poster/Teaching Guide for Pre-Algebra Students. Expect the Unexpected with Math[R

ERIC Educational Resources Information Center

Actuarial Foundation, 2013

2013-01-01

"Solving the Unknown with Algebra" is a new math program aligned with the National Council of Teachers of Mathematics (NCTM) standards and designed to help students practice pre-algebra skills including using formulas, solving for unknowns, and manipulating equations. Developed by The Actuarial Foundation with Scholastic, this program provides…

Developing "Algebraic Thinking": Two Key Ways to Establish Some Early Algebraic Ideas in Primary Classrooms

ERIC Educational Resources Information Center

Ormond, Christine

2012-01-01

Primary teachers play a key role in their students' future mathematical success in the early secondary years. While the word "algebra" may make some primary teachers feel uncomfortable or worried, the basic arithmetic ideas underlying algebra are vitally important for older primary students as they are increasingly required to use "algebraic…

Investigating Students' Modes of Thinking in Linear Algebra: The Case of Linear Independence

ERIC Educational Resources Information Center

Çelik, Derya

2015-01-01

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

Exploring Teacher Noticing of Student Algebraic Thinking in a Video Club

ERIC Educational Resources Information Center

Walkoe, Janet

2015-01-01

Learning algebra is critical for students in the USA today, yet many students in the USA struggle in algebra classes. Researchers claim that one reason for these difficulties is that algebra classes often focus on symbol manipulation and procedures above, and many times at the expense of, a more conceptual understanding of the content. Teaching…

Algebra and Algebraic Thinking in School Math: 70th YB

ERIC Educational Resources Information Center

National Council of Teachers of Mathematics, 2008

2008-01-01

Algebra is no longer just for college-bound students. After a widespread push by the National Council of Teachers of Mathematics (NCTM) and teachers across the country, algebra is now a required part of most curricula. However, students' standardized test scores are not at the level they should be. NCTM's seventieth yearbook takes a look at the…

Matematica Para La Escuela Secundaria, Primer Curso de Algebra (Parte 2), Comentario. Traduccion Preliminar de la Edicion en Ingles Revisada. (Mathematics for High School, First Course in Algebra, Part 2, Teacher's Commentary. Preliminary Translation of the Revised English Edition).

ERIC Educational Resources Information Center

Allen, Frank B.; And Others

This is the teacher's commentary for part two of a three-part SMSG algebra text for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include addition and multiplication of real…

Quantum superintegrable system with a novel chain structure of quadratic algebras

NASA Astrophysics Data System (ADS)

Liao, Yidong; Marquette, Ian; Zhang, Yao-Zhong

2018-06-01

We analyse the n-dimensional superintegrable Kepler–Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure and obtain the algebra relations satisfied by them and the corresponding Casimir operators. These quadratic sub-algebras are realized in terms of a chain of deformed oscillators with factorized structure functions. We construct the finite-dimensional unitary representations of the deformed oscillators, and give an algebraic derivation of the energy spectrum of the superintegrable system.

Literal algebra for satellite dynamics. [perturbation analysis

NASA Technical Reports Server (NTRS)

Gaposchkin, E. M.

1975-01-01

A description of the rather general class of operations available is given and the operations are related to problems in satellite dynamics. The implementation of an algebra processor is discussed. The four main categories of symbol processors are related to list processing, string manipulation, symbol manipulation, and formula manipulation. Fundamental required operations for an algebra processor are considered. It is pointed out that algebra programs have been used for a number of problems in celestial mechanics with great success. The advantage of computer algebra is its accuracy and speed.

Contractions from grading

NASA Astrophysics Data System (ADS)

Krishnan, Chethan; Raju, Avinash

2018-04-01

We note that large classes of contractions of algebras that arise in physics can be understood purely algebraically via identifying appropriate Zm-gradings (and their generalizations) on the parent algebra. This includes various types of flat space/Carroll limits of finite and infinite dimensional (A)dS algebras, as well as Galilean and Galilean conformal algebras. Our observations can be regarded as providing a natural context for the Grassmann approach of Krishnan et al. [J. High Energy Phys. 2014(3), 36]. We also introduce a related notion, which we call partial grading, that arises naturally in this context.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mozrzymas, Marek; Horodecki, Michał; Studziński, Michał

We consider the structure of algebra of operators, acting in n-fold tensor product space, which are partially transposed on the last term. Using purely algebraical methods we show that this algebra is semi-simple and then, considering its regular representation, we derive basic properties of the algebra. In particular, we describe all irreducible representations of the algebra of partially transposed operators and derive expressions for matrix elements of the representations. It appears that there are two kinds of irreducible representations of the algebra. The first one is strictly connected with the representations of the group S(n − 1) induced by irreduciblemore » representations of the group S(n − 2). The second kind is structurally connected with irreducible representations of the group S(n − 1)« less

Systems with outer constraints. Gupta-Bleuler electromagnetism as an algebraic field theory

NASA Astrophysics Data System (ADS)

Grundling, Hendrik

1988-03-01

Since there are some important systems which have constraints not contained in their field algebras, we develop here in a C*-context the algebraic structures of these. The constraints are defined as a group G acting as outer automorphisms on the field algebra ℱ, α: G ↦ Aut ℱ, α G ⊄ Inn ℱ, and we find that the selection of G-invariant states on ℱ is the same as the selection of states ω on M( G M(Gmathop × limits_α F) ℱ) by ω( U g)=1∨ g∈ G, where U g ∈ M ( G M(Gmathop × limits_α F) ℱ)/ℱ are the canonical elements implementing α g . These states are taken as the physical states, and this specifies the resulting algebraic structure of the physics in M( G M(Gmathop × limits_α F) ℱ), and in particular the maximal constraint free physical algebra ℛ. A nontriviality condition is given for ℛ to exist, and we extend the notion of a crossed product to deal with a situation where G is not locally compact. This is necessary to deal with the field theoretical aspect of the constraints. Next the C*-algebra of the CCR is employed to define the abstract algebraic structure of Gupta-Bleuler electromagnetism in the present framework. The indefinite inner product representation structure is obtained, and this puts Gupta-Bleuler electromagnetism on a rigorous footing. Finally, as a bonus, we find that the algebraic structures just set up, provide a blueprint for constructive quadratic algebraic field theory.

Developing Meaning for Algebraic Procedures: An Exploration of the Connections Undergraduate Students Make between Algebraic Rational Expressions and Basic Number Properties

ERIC Educational Resources Information Center

Yantz, Jennifer

2013-01-01

The attainment and retention of later algebra skills in high school has been identified as a factor significantly impacting the postsecondary success of students majoring in STEM fields. Researchers maintain that learners develop meaning for algebraic procedures by forming connections to the basic number system properties. The present study…

Curricula Alignment and Its Impact on End of Course Assessment Scores

ERIC Educational Resources Information Center

Burti, Neil, Jr.

2011-01-01

The purpose of this mixed methods study was to examine the alignment of the written, enacted, and tested Algebra I curricula in the Cherry Hill (NJ) Public School District. Furthermore, this QUAN-QUAL study sought to determine the impact of course selection (Algebra I, Enriched Algebra) on achievement as measured by the Algebra I End of Course…

The Impact of New State Accountability Standards on Algebra I Students

ERIC Educational Resources Information Center

Heath, Kyle G.

2013-01-01

The purpose of this quasi-experimental quantitative study was to determine if a new Algebra I curriculum resulted in improved student performance on the state Algebra I exam. The treatment group consisted of 383 9th grade Algebra I students who received the college-ready standards-based (CRSB) curricula. The control group consisted of 338 9th…

From No to Yes: The Impact of an Intervention on The Persistence of Algebraic Misconceptions among Secondary School Algebra Students

ERIC Educational Resources Information Center

Zielinski, Susan F.

2017-01-01

Many students enter high school with persistent algebraic misconceptions that limit their success in mathematics and, by extension, limit potential educational attainment and future earnings. The purpose of this study was to assess the effectiveness of a warm conceptual change based intervention on remediating algebraic misconceptions held by…

Card Games and Algebra Tic Tacmatics on Achievement of Junior Secondary II Students in Algebraic Expressions

ERIC Educational Resources Information Center

Okpube, Nnaemeka Michael; Anugwo, M. N.

2016-01-01

This study investigated the Card Games and Algebra tic-Tacmatics on Junior Secondary II Students' Achievement in Algebraic Expressions. Three research questions and three null hypotheses guided the study. The study adopted the pre-test, post-test control group design. A total of two hundred and forty (240) Junior Secondary School II students were…

A Study of Improving Eighth Graders' Learning Deficiency in Algebra by Applying a Realistic Context Instructional Design

ERIC Educational Resources Information Center

Chang, Yu-Liang; Huang, Yu-I

2014-01-01

The intention of this study was to improve the learning deficiency in algebraic learning and to enhance Taiwanese middle students' learning achievement and interest in algebra. By using a grade skipping experimental design, the research team intended to find out an effective way to benefit these students' leaning in abstract algebraic concepts.…

Effects of Comparison and Game-Challenge on Sixth Graders' Algebra Variable Learning Achievement, Learning Attitude, and Meta-Cognitive Awareness

ERIC Educational Resources Information Center

Sun Lin, Hong-Zheng; Chiou, Guey-Fa

2017-01-01

This study examined the effects of comparison and game-challenge strategies on sixth graders' learning achievement of algebra variable, learning attitude towards algebra variable learning, and meta-cognitive awareness of algebra variable learning. A 2 × 2 factorial design was used, and 86 students were invited to participate in the experimental…

Middle School Math Acceleration and Equitable Access to Eighth-Grade Algebra: Evidence from the Wake County Public School System

ERIC Educational Resources Information Center

Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.

2015-01-01

Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…

It's a Wonderful Life: Using Public Domain Cinema Clips To Teach Affective Objectives and Illustrate Real-World Algebra Applications.

ERIC Educational Resources Information Center

Palmer, Loretta

A basic algebra unit was developed at Utah Valley State College to emphasize applications of mathematical concepts in the work world, using video and computer-generated graphics to integrate textual material. The course was implemented in three introductory algebra sections involving 80 students and taught algebraic concepts using such areas as…

Linking Computer Algebra Systems and Paper-and-Pencil Techniques To Support the Teaching of Mathematics.

ERIC Educational Resources Information Center

van Herwaarden, Onno A.; Gielen, Joseph L. W.

2002-01-01

Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

Assessing non-uniqueness: An algebraic approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Vasco, Don W.

Geophysical inverse problems are endowed with a rich mathematical structure. When discretized, most differential and integral equations of interest are algebraic (polynomial) in form. Techniques from algebraic geometry and computational algebra provide a means to address questions of existence and uniqueness for both linear and non-linear inverse problem. In a sense, the methods extend ideas which have proven fruitful in treating linear inverse problems.

Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students. Educator's Practice Guide. What Works Clearinghouse.™ NCEE 2015-4010

ERIC Educational Resources Information Center

Star, Jon R.; Foegen, Anne; Larson, Matthew R.; McCallum, William G.; Porath, Jane; Zbiek, Rose Mary; Caronongan, Pia; Furgeson, Joshua,; Keating, Betsy; Lyskawa, Julia

2015-01-01

Mastering algebra is important for future math and postsecondary success. Educators will find practical recommendations for how to improve algebra instruction in the What Works Clearinghouse (WWC) practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students". The methods and examples included in…

Students’ Algebraic Thinking Process in Context of Point and Line Properties

NASA Astrophysics Data System (ADS)

Nurrahmi, H.; Suryadi, D.; Fatimah, S.

2017-09-01

Learning of schools algebra is limited to symbols and operating procedures, so students are able to work on problems that only require the ability to operate symbols but unable to generalize a pattern as one of part of algebraic thinking. The purpose of this study is to create a didactic design that facilitates students to do algebraic thinking process through the generalization of patterns, especially in the context of the property of point and line. This study used qualitative method and includes Didactical Design Research (DDR). The result is students are able to make factual, contextual, and symbolic generalization. This happen because the generalization arises based on facts on local terms, then the generalization produced an algebraic formula that was described in the context and perspective of each student. After that, the formula uses the algebraic letter symbol from the symbol t hat uses the students’ language. It can be concluded that the design has facilitated students to do algebraic thinking process through the generalization of patterns, especially in the context of property of the point and line. The impact of this study is this design can use as one of material teaching alternative in learning of school algebra.

A Geometric Construction of Cyclic Cocycles on Twisted Convolution Algebras

NASA Astrophysics Data System (ADS)

Angel, Eitan

2010-09-01

In this thesis we give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. In his seminal book, Connes constructs a map from the equivariant cohomology of a manifold carrying the action of a discrete group into the periodic cyclic cohomology of the associated convolution algebra. Furthermore, for proper étale groupoids, J.-L. Tu and P. Xu provide a map between the periodic cyclic cohomology of a gerbe twisted convolution algebra and twisted cohomology groups. Our focus will be the convolution algebra with a product defined by a gerbe over a discrete translation groupoid. When the action is not proper, we cannot construct an invariant connection on the gerbe; therefore to study this algebra, we instead develop simplicial notions related to ideas of J. Dupont to construct a simplicial form representing the Dixmier-Douady class of the gerbe. Then by using a JLO formula we define a morphism from a simplicial complex twisted by this simplicial Dixmier-Douady form to the mixed bicomplex of certain matrix algebras. Finally, we define a morphism from this complex to the mixed bicomplex computing the periodic cyclic cohomology of the twisted convolution algebras.

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics

PubMed Central

Simzar, Rahila M.; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics. PMID:26942210

On the homotopy equivalence of simple AI-algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aristov, O Yu

1999-02-28

Let A and B be simple unital AI-algebras (an AI-algebra is an inductive limit of C*-algebras of the form BigOplus{sub i}{sup k}C([0,1],M{sub N{sub i}}). It is proved that two arbitrary unital homomorphisms from A into B such that the corresponding maps K{sub 0}A{yields}K{sub 0}B coincide are homotopic. Necessary and sufficient conditions on the Elliott invariant for A and B to be homotopy equivalent are indicated. Moreover, two algebras in the above class having the same K-theory but not homotopy equivalent are constructed. A theorem on the homotopy of approximately unitarily equivalent homomorphisms between AI-algebras is used in the proof, whichmore » is deduced in its turn from a generalization to the case of AI-algebras of a theorem of Manuilov stating that a unitary matrix almost commuting with a self-adjoint matrix h can be joined to 1 by a continuous path consisting of unitary matrices almost commuting with h.« less

On the quantum symmetry of the chiral Ising model

NASA Astrophysics Data System (ADS)

Vecsernyés, Peter

1994-03-01

We introduce the notion of rational Hopf algebras that we think are able to describe the superselection symmetries of rational quantum field theories. As an example we show that a six-dimensional rational Hopf algebra H can reproduce the fusion rules, the conformal weights, the quantum dimensions and the representation of the modular group of the chiral Ising model. H plays the role of the global symmetry algebra of the chiral Ising model in the following sense: (1) a simple field algebra F and a representation π on Hπ of it is given, which contains the c = {1}/{2} unitary representations of the Virasoro algebra as subrepresentations; (2) the embedding U: H → B( Hπ) is such that the observable algebra π( A) - is the invariant subalgebra of B( Hπ) with respect to the left adjoint action of H and U(H) is the commutant of π( A); (3) there exist H-covariant primary fields in B( Hπ), which obey generalized Cuntz algebra properties and intertwine between the inequivalent sectors of the observables.

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

DOE PAGES

Günaydin, Murat; Lüst, Dieter; Malek, Emanuel

2016-11-07

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginarymore » octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s.« less

Non-associativity in non-geometric string and M-theory backgrounds, the algebra of octonions, and missing momentum modes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Günaydin, Murat; Lüst, Dieter; Malek, Emanuel

We propose a non-associative phase space algebra for M-theory backgrounds with locally non-geometric fluxes based on the non-associative algebra of octonions. Our proposal is based on the observation that the non-associative algebra of the non-geometric R-flux background in string theory can be obtained by a proper contraction of the simple Malcev algebra generated by imaginary octonions. Furthermore, by studying a toy model of a four-dimensional locally non-geometric M-theory background which is dual to a twisted torus, we show that the non-geometric background is “missing” a momentum mode. The resulting seven-dimensional phase space can thus be naturally identified with the imaginarymore » octonions. This allows us to interpret the full uncontracted algebra of imaginary octonions as the uplift of the string theory R-flux algebra to M-theory, with the contraction parameter playing the role of the string coupling constant g s.« less

Eighth Grade Algebra Course Placement and Student Motivation for Mathematics.

PubMed

Simzar, Rahila M; Domina, Thurston; Tran, Cathy

2016-01-01

This study uses student panel data to examine the association between Algebra placement and student motivation for mathematics. Changes in achievement goals, expectancy, and task value for students in eighth grade Algebra are compared with those of peers placed in lower-level mathematics courses (N = 3,306). In our sample, students placed in Algebra reported an increase in performance-avoidance goals as well as decreases in academic self-efficacy and task value. These relations were attenuated for students who had high mathematics achievement prior to Algebra placement. Whereas all students reported an overall decline in performance-approach goals over the course of eighth grade, previously high-achieving students reported an increase in these goals. Lastly, previously high-achieving students reported an increase in mastery goals. These findings suggest that while previously high-achieving students may benefit motivationally from eighth grade Algebra placement, placing previously average- and low-performing students in Algebra can potentially undermine their motivation for mathematics.

A natural history of mathematics: George Peacock and the making of English algebra.

PubMed

Lambert, Kevin

2013-06-01

In a series of papers read to the Cambridge Philosophical Society through the 1820s, the Cambridge mathematician George Peacock laid the foundation for a natural history of arithmetic that would tell a story of human progress from counting to modern arithmetic. The trajectory of that history, Peacock argued, established algebraic analysis as a form of universal reasoning that used empirically warranted operations of mind to think with symbols on paper. The science of counting would suggest arithmetic, arithmetic would suggest arithmetical algebra, and, finally, arithmetical algebra would suggest symbolic algebra. This philosophy of suggestion provided the foundation for Peacock's "principle of equivalent forms," which justified the practice of nineteenth-century English symbolic algebra. Peacock's philosophy of suggestion owed a considerable debt to the early Cambridge Philosophical Society culture of natural history. The aim of this essay is to show how that culture of natural history was constitutively significant to the practice of nineteenth-century English algebra.

Situating the Debate on "Geometrical Algebra" within the Framework of Premodern Algebra.

PubMed

Sialaros, Michalis; Christianidis, Jean

2016-06-01

Argument The aim of this paper is to employ the newly contextualized historiographical category of "premodern algebra" in order to revisit the arguably most controversial topic of the last decades in the field of Greek mathematics, namely the debate on "geometrical algebra." Within this framework, we shift focus from the discrepancy among the views expressed in the debate to some of the historiographical assumptions and methodological approaches that the opposing sides shared. Moreover, by using a series of propositions related to Elem. II.5 as a case study, we discuss Euclid's geometrical proofs, the so-called "semi-algebraic" alternative demonstrations attributed to Heron of Alexandria, as well as the solutions given by Diophantus, al-Sulamī, and al-Khwārizmī to the corresponding numerical problem. This comparative analysis offers a new reading of Heron's practice, highlights the significance of contextualizing "premodern algebra," and indicates that the origins of algebraic reasoning should be sought in the problem-solving practice, rather than in the theorem-proving tradition.

Visualizing the inner product space ℝm×n in a MATLAB-assisted linear algebra classroom

NASA Astrophysics Data System (ADS)

Caglayan, Günhan

2018-05-01

This linear algebra note offers teaching and learning ideas in the treatment of the inner product space ? in a technology-supported learning environment. Classroom activities proposed in this note demonstrate creative ways of integrating MATLAB technology into various properties of Frobenius inner product as visualization tools that complement the algebraic approach. As implemented in linear algebra lessons in a university in the Unites States, the article also incorporates algebraic and visual work of students who experienced these activities with MATLAB software. The connection between the Frobenius norm and the Euclidean norm is also emphasized.

Spatial-Operator Algebra For Flexible-Link Manipulators

NASA Technical Reports Server (NTRS)

Jain, Abhinandan; Rodriguez, Guillermo

1994-01-01

Method of computing dynamics of multiple-flexible-link robotic manipulators based on spatial-operator algebra, which originally applied to rigid-link manipulators. Aspects of spatial-operator-algebra approach described in several previous articles in NASA Tech Briefs-most recently "Robot Control Based on Spatial-Operator Algebra" (NPO-17918). In extension of spatial-operator algebra to manipulators with flexible links, each link represented by finite-element model: mass of flexible link apportioned among smaller, lumped-mass rigid bodies, coupling of motions expressed in terms of vibrational modes. This leads to operator expression for modal-mass matrix of link.

Graph C ∗-algebras and Z2-quotients of quantum spheres

NASA Astrophysics Data System (ADS)

Hajac, Piotr M.; Matthes, Rainer; Szymański, Wojciech

2003-06-01

We consider two Z2-actions on the Podleś generic quantum spheres. They yield, as noncommutative quotient spaces, the Klimek-Lesmewski q-disc and the quantum real projective space, respectively. The C ∗-algebas of all these quantum spaces are described as graph C ∗-algebras. The K-groups of the thus presented C ∗-algebras are then easily determined from the general theory of graph C ∗-algebas. For the quantum real projective space, we also recall the classification of the classes of irreducible ∗-representations of its algebra and give a linear basis for this algebra.

Quiver elliptic W-algebras

NASA Astrophysics Data System (ADS)

Kimura, Taro; Pestun, Vasily

2018-06-01

We define elliptic generalization of W-algebras associated with arbitrary quiver using our construction (Kimura and Pestun in Quiver W-algebras, 2015. arXiv:1512.08533 [hep-th]) with six-dimensional gauge theory.

Hurwitz Algebras and the Octonion Algebra

NASA Astrophysics Data System (ADS)

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.

Computer Program For Linear Algebra

NASA Technical Reports Server (NTRS)

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.

The effects of an integrated Algebra 1/physical science curriculum on student achievement in Algebra 1, proportional reasoning and graphing abilities

NASA Astrophysics Data System (ADS)

Lawrence, Lettie Carol

1997-08-01

The purpose of this investigation was to determine if an integrated curriculum in algebra 1/physical science facilitates acquisition of proportional reasoning and graphing abilities better than a non-integrated, traditional, algebra 1 curriculum. Also, this study was to ascertain if the integrated algebra 1/physical science curriculum resulted in greater student achievement in algebra 1. The curriculum used in the experimental class was SAM 9 (Science and Mathematics 9), an investigation-based curriculum that was written to integrate physical science and basic algebra content. The experiment was conducted over one school year. The subjects in the study were 61 ninth grade students. The experimental group consisted of one class taught concurrently by a mathematics teacher and a physical science teacher. The control group consisted of three classes of algebra 1 students taught by one mathematics teacher and taking physical science with other teachers in the school who were not participating in the SAM 9 program. This study utilized a quasi-experimental non-randomized control group pretest-posttest design. The investigator obtained end-of-algebra 1 scores from student records. The written open-ended graphing instruments and the proportional reasoning instrument were administered to both groups as pretests and posttests. The graphing instruments were also administered as a midtest. A two sample t-test for independent means was used to determine significant differences in achievement on the end-of-course algebra 1 test. Quantitative data from the proportional reasoning and graphing instruments were analyzed using a repeated measures analysis of variance to determine differences in scores over time for the experimental and control groups. The findings indicate no significant difference between the experimental and control groups on the end-of-course algebra 1 test. Results also indicate no significant differences in proportional reasoning and graphing abilities between the two groups over time. However, all subjects (experimental and control groups) made significant improvement in graphing abilities over one school year. In this study, students participating in an investigation-based curriculum integrating algebra 1 and physical science performed as well on the instruments as the students in the traditional curriculum. Therefore, an argument can be made that instruction using an integrated curriculum (algebra l/physical science) is a viable alternative to instruction using a more traditional algebra 1 curriculum. Finally, the integrated curriculum adheres to the constructivist theoretical perspective (Krupnik-Gotlieb, 1995) and is more consistent with recommendations in the NCTM Standards (1992) than the traditional curriculum.

The Great Debate: Should All 8th Graders Take Algebra?

ERIC Educational Resources Information Center

McKibben, Sarah

2009-01-01

While 8th grade algebra was once reserved as a course for the gifted, today, more U.S. 8th graders take algebra than any other math course. This article discusses a report from the Brookings Institution which chronicles the history of the 8th-grade algebra surge and its impact on today's low-performing students. The report indicates that many of…

Characterizing the Nature of Students' Feature Noticing-and-Using with Respect to Mathematical Symbols across Different Levels of Algebra Exposure

ERIC Educational Resources Information Center

Sullivan, Patrick

2013-01-01

The purpose of this study is to examine the nature of what students notice about symbols and use as they solve unfamiliar algebra problems based on familiar algebra concepts and involving symbolic inscriptions. The researcher conducted a study of students at three levels of algebra exposure: (a) students enrolled in a high school pre-calculus…

The Effects of Teacher Collective Responsibility on the Mathematics Achievement of Students Who Repeat Algebra

ERIC Educational Resources Information Center

Morales-Chicas, Jessica; Agger, Charlotte

2017-01-01

In this article, the authors use the national High School Longitudinal Study of 2009 (HSLS:09) dataset to explore (a) if repeating algebra in the eighth grade was associated with overall mathematics grades and course-taking patterns by twelfth grade, (b) if repeating algebra in the eighth grade was associated with students' final grade in algebra,…

Quantum mechanics on periodic and non-periodic lattices and almost unitary Schwinger operators

NASA Astrophysics Data System (ADS)

Arik, Metin; Ildes, Medine

2018-05-01

In this work, we uncover the mathematical structure of the Schwinger algebra and introduce almost unitary Schwinger operators which are derived by considering translation operators on a finite lattice. We calculate mathematical relations between these algebras and show that the almost unitary Schwinger operators are equivalent to the Schwinger algebra. We introduce new representations for MN(C) in terms of these algebras.

Those Do What? Connecting Eigenvectors and Eigenvalues to the Rest of Linear Algebra: Using Visual Enhancements to Help Students Connect Eigenvectors to the Rest of Linear Algebra

ERIC Educational Resources Information Center

Nyman, Melvin A.; Lapp, Douglas A.; St. John, Dennis; Berry, John S.

2010-01-01

This paper discusses student difficulties in grasping concepts from Linear Algebra--in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student…

Change in Peer Ability as a Mediator and Moderator of the Effect of the Algebra-For-All Policy on Ninth Graders' Math Outcomes

ERIC Educational Resources Information Center

Hong, Guanglei; Nomi, Takako

2011-01-01

A recent report by the Mathematics Advisory Panel referred to algebra as a "gateway" to later achievement (National Mathematics Advisory Panel, 2008). To address the problem of low academic performance in algebra, an increasing number of states and districts have started to implement a policy of requiring algebra for all students in…

The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

ERIC Educational Resources Information Center

O'Hanlon, Angela L.

2011-01-01

The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…

Associative Algebraic Approach to Logarithmic CFT in the Bulk: The Continuum Limit of the {gl(1|1)} Periodic Spin Chain, Howe Duality and the Interchiral Algebra

NASA Astrophysics Data System (ADS)

Gainutdinov, A. M.; Read, N.; Saleur, H.

2016-01-01

We develop in this paper the principles of an associative algebraic approach to bulk logarithmic conformal field theories (LCFTs). We concentrate on the closed {gl(1|1)} spin-chain and its continuum limit—the {c=-2} symplectic fermions theory—and rely on two technical companion papers, Gainutdinov et al. (Nucl Phys B 871:245-288, 2013) and Gainutdinov et al. (Nucl Phys B 871:289-329, 2013). Our main result is that the algebra of local Hamiltonians, the Jones-Temperley-Lieb algebra JTL N , goes over in the continuum limit to a bigger algebra than {V}, the product of the left and right Virasoro algebras. This algebra, {S}—which we call interchiral, mixes the left and right moving sectors, and is generated, in the symplectic fermions case, by the additional field {S(z,bar{z})≡ S_{αβ} ψ^α(z)bar{ψ}^β(bar{z})}, with a symmetric form {S_{αβ}} and conformal weights (1,1). We discuss in detail how the space of states of the LCFT (technically, a Krein space) decomposes onto representations of this algebra, and how this decomposition is related with properties of the finite spin-chain. We show that there is a complete correspondence between algebraic properties of finite periodic spin chains and the continuum limit. An important technical aspect of our analysis involves the fundamental new observation that the action of JTL N in the {gl(1|1)} spin chain is in fact isomorphic to an enveloping algebra of a certain Lie algebra, itself a non semi-simple version of {sp_{N-2}}. The semi-simple part of JTL N is represented by {U sp_{N-2}}, providing a beautiful example of a classical Howe duality, for which we have a non semi-simple version in the full JTL N image represented in the spin-chain. On the continuum side, simple modules over {S} are identified with "fundamental" representations of {sp_∞}.

Deformed twistors and higher spin conformal (super-)algebras in four dimensions

DOE PAGES

Govil, Karan; Gunaydin, Murat

2015-03-05

Massless conformal scalar field in d = 4 corresponds to the minimal unitary representation (minrep) of the conformal group SU(2, 2) which admits a one-parameter family of deformations that describe massless fields of arbitrary helicity. The minrep and its deformations were obtained by quantization of the nonlinear realization of SU(2, 2) as a quasiconformal group in arXiv:0908.3624. We show that the generators of SU(2,2) for these unitary irreducible representations can be written as bilinears of deformed twistorial oscillators which transform nonlinearly under the Lorentz group and apply them to define and study higher spin algebras and superalgebras in AdS 5.more » The higher spin (HS) algebra of Fradkin-Vasiliev type in AdS 5 is simply the enveloping algebra of SU(2, 2) quotiented by a two-sided ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph ideal vanishes identically for the quasiconformal realization of the minrep and its enveloping algebra leads directly to the HS algebra in AdS 5. Furthermore, the enveloping algebras of the deformations of the minrep define a one parameter family of HS algebras in AdS 5 for which certain 4d covariant deformations of the Joseph ideal vanish identically. These results extend to superconformal algebras SU(2, 2|N) and we find a one parameter family of HS superalgebras as enveloping algebras of the minimal unitary supermultiplet and its deformations. Our results suggest the existence of a family of (supersymmetric) HS theories in AdS 5 which are dual to free (super)conformal field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in 4d. We also discuss the corresponding picture in HS algebras in AdS 4 where the corresponding 3d conformal group Sp(4,R) admits only two massless representations (minreps), namely the scalar and spinor singletons.« less

Combinatorial Formulas for Characteristic Classes, and Localization of Secondary Topological Invariants.

NASA Astrophysics Data System (ADS)

Smirnov, Mikhail

1995-01-01

The problems solved in this thesis originated from combinatorial formulas for characteristic classes. This thesis deals with Chern-Simons classes, their generalizations and related algebraic and analytic problems. (1) In this thesis, I describe a new class of algebras whose elements contain Chern and generalized Chern -Simons classes. There is a Poisson bracket in these algebras, similar to the bracket in Kontsevich's noncommutative symplectic geometry (Kon). I prove that the Poisson bracket gives rise to a graded Lie algebra containing differential forms representing Chern and Chern-Simons classes. This is a new result. I describe algebraic analogs of the dilogarithm and higher polylogarithms in the algebra corresponding to Chern-Simons classes. (2) I study the properties of this bracket. It is possible to write the exterior differential and other operations in the algebra using this bracket. The bracket of any two Chern classes is zero and the bracket of a Chern class and a Chern-Simons class is d-closed. The construction developed here easily gives explicit formulas for known secondary classes and makes it possible to construct new ones. (3) I develop an algebraic model for the action of the gauge group and describe how elements of algebra corresponding to the secondary characteristic classes change under this action (see theorem 3 page xi). (4) It is possible give new explicit formulas for cocycles on a gauge group of a bundle and for the corresponding cocycles on the Lie algebra of the gauge group. I use formulas for secondary characteristic classes and an algebraic approach developed in chapter 1. I also use the work of Faddeev, Reiman and Semyonov-Tian-Shanskii (FRS) on cocycles as quantum anomalies. (5) I apply the methods of differential geometry of formal power series to construct universal characteristic and secondary characteristic classes. Given a pair of gauge equivalent connections using local formulas I obtain dilogarithmic and trilogarithmic analogs of Chern-Simons classes.

Simulating Quantitative Cellular Responses Using Asynchronous Threshold Boolean Network Ensembles

EPA Science Inventory

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 t...