Mathematical Induction: Deductive Logic Perspective
ERIC Educational Resources Information Center
Dogan, Hamide
2016-01-01
Many studies mentioned the deductive nature of Mathematical Induction (MI) proofs but almost all fell short in explaining its potential role in the formation of the misconceptions reported in the literature. This paper is the first of its kind looking at the misconceptions from the perspective of the abstract of the deductive logic from one's…
Calculator Logic Systems and Mathematical Understandings.
ERIC Educational Resources Information Center
Burrows, Enid R.
This monograph is aimed at helping the reader understand the built-in logic of various calculator operating systems. It is an outgrowth of workshop contacts with in-service and pre-service teachers of mathematics and is in response to their request for a book on the subject of calculator logic systems and calculator algorithms. The mathematical…
Can Mathematics be Justified by Natural Logic?
NASA Astrophysics Data System (ADS)
Schreiber, Lothar; Sommer, Hanns
2010-11-01
Charles Darwin claimed that the forms and the behaviour of living beings can be explained from their will to survive. But what are the consequences of this idea for humans knowledge, their theories of nature and their mathematics?. We discuss the view that even Plato's objective world of mathematical objects does not exist absolutely, without the intentions of mathematicians. Using Husserl's Phenomenological Method, cognition can be understood as a process by which meaning is deduced from empirical data relative to intentions. Thereby the essential structure of any cognition process can be detected and this structure is mirrored in logic. A natural logic becomes the direct result of cognition. Only in a second step, mathematics is obtained by abstraction from natural logic. In this way mathematics gains a well-defined foundation and is no longer part of a dubious 'a-priori knowledge' (Kant). This access to mathematics offers a new look on many old problems, e.g. the Petersburg problem and the problem 'P = NP?'. We demonstrate that this new justification of mathematics has also important applications in Artificial Intelligence. Our method provides a procedure to construct an adequate logic to solve most efficiently the problems of a given problem class. Thus, heuristics can be tailor-made for the necessities of applications.
Rebuilding mathematics on a quantum logical foundation
NASA Astrophysics Data System (ADS)
DeJonghe, Richard J., III
We construct a rich first-order quantum logic which generalizes the standard classical predicate logic used in the development of virtually all of modern mathematics, and we use this quantum logic to build the foundations of a new quantum mathematics. First, we prove both soundness and completeness for the quantum logic we develop, and also prove a powerful new completeness result which heretofore had been known to hold for classical, but not quantum, first-order logic. We then use our quantum logic to develop multiple areas of mathematics, including abstract algebra, axiomatic set theory, and arithmetic. In some preliminary investigations into quantum mathematics, Dunn found that the Peano axioms for arithmetic yield the same theorems using either classical or quantum logic. We prove a similar result for certain classes of abstract algebras, and then show that Dunn's result is not generic by presenting examples of quantum monoids, groups, lattices, vector spaces, and operator algebras, all which differ from their classical counterparts. Moreover, we find natural classes of quantum lattices, vector spaces, and operator algebras which all have a beautiful inter-relationship, and make some preliminary investigations into using these structures as a basis for a new mathematical formulation of quantum mechanics. We also develop a quantum set theory (equivalent to ZFC under classical logic) which is far more tractable than quantum set theory previously developed. We then use this set theory to construct a quantum version of the natural numbers, and develop an arithmetic of these numbers based upon an alternative to Peano's axioms (which avoids Dunn's theorem). Surprisingly, we find that these "quantum natural numbers" satisfy our arithmetical axioms if and only if the underlying truth values form a modular lattice, giving a new arithmetical characterization of this important lattice-theoretic property. Finally, we show that these numbers have a natural interpretation as
NASA Astrophysics Data System (ADS)
Jetli, Priyedarshi
Modern logic begins with Boole's The Mathematical Analysis of Logic when the algebra of logic was developed so that classical logic syllogisms were proven as algebraic equations and the turn from the logic of classes to propositional logic was suggested. The emergence was incomplete as Boole algebraised classical logic. Frege in Begriffsschrift replaced Aristotelian subject-predicate propositions by function and argument and displaced syllogisms with an axiomatic propositional calculus using conditionals, modus ponens and the law of substitution. Further Frege provided the breakthrough to lay down the groundwork for the development of quantified logic as well as the logic of relations. He achieved all of this through his innovative formal notations which have remained underrated. Frege hence completed the emergence of modern logic. Both Boole and Frege mathematised logic, but Frege's goal was to logicise mathematics. However the emergence of modern logic in Frege should be detached from his logicism.
EXPERIMENTAL TEACHING OF MATHEMATICAL LOGIC IN THE ELEMENTARY SCHOOL.
ERIC Educational Resources Information Center
BINFORD, FREDERICK; SUPPES, PATRICK
STUDY OBJECTIVES WERE DEVELOPED AROUND THE IDEA THAT DELIBERATE AND PLANNED TEACHING OF FORMAL SYMBOLIC LOGIC WILL BENEFIT THE STUDENT AT ANY AGE BY ENLARGING HIS SCOPE AND PROVIDING FOR A DEEPER AND MORE PENETRATING STUDY OF MATHEMATICS AND OTHER DEDUCTIVELY FORMULATED DISCIPLINES. IT WAS HYPOTHESIZED THAT THE ABLE STUDENT IN ELEMENTARY SCHOOL IS…
Reasoning with Computer Code: a new Mathematical Logic
NASA Astrophysics Data System (ADS)
Pissanetzky, Sergio
2013-01-01
A logic is a mathematical model of knowledge used to study how we reason, how we describe the world, and how we infer the conclusions that determine our behavior. The logic presented here is natural. It has been experimentally observed, not designed. It represents knowledge as a causal set, includes a new type of inference based on the minimization of an action functional, and generates its own semantics, making it unnecessary to prescribe one. This logic is suitable for high-level reasoning with computer code, including tasks such as self-programming, objectoriented analysis, refactoring, systems integration, code reuse, and automated programming from sensor-acquired data. A strong theoretical foundation exists for the new logic. The inference derives laws of conservation from the permutation symmetry of the causal set, and calculates the corresponding conserved quantities. The association between symmetries and conservation laws is a fundamental and well-known law of nature and a general principle in modern theoretical Physics. The conserved quantities take the form of a nested hierarchy of invariant partitions of the given set. The logic associates elements of the set and binds them together to form the levels of the hierarchy. It is conjectured that the hierarchy corresponds to the invariant representations that the brain is known to generate. The hierarchies also represent fully object-oriented, self-generated code, that can be directly compiled and executed (when a compiler becomes available), or translated to a suitable programming language. The approach is constructivist because all entities are constructed bottom-up, with the fundamental principles of nature being at the bottom, and their existence is proved by construction. The new logic is mathematically introduced and later discussed in the context of transformations of algorithms and computer programs. We discuss what a full self-programming capability would really mean. We argue that self
The Contribution of Logical Reasoning to the Learning of Mathematics in Primary School
ERIC Educational Resources Information Center
Nunes, Terezinha; Bryant, Peter; Evans, Deborah; Bell, Daniel; Gardner, Selina; Gardner, Adelina; Carraher, Julia
2007-01-01
It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6-year-old children's logical abilities…
ERIC Educational Resources Information Center
Seltman, Muriel; Seltman, P. E. J.
1978-01-01
The authors stress the importance of bringing together the causal logic of history and the formal logic of mathematics in order to humanize mathematics and make it more accessible. An example of such treatment is given in a discussion of the centrality of Euclid and the Euclidean system to mathematics development. (MN)
[Influence of music on a decision of mathematical logic tasks].
Pavlygina, R A; Karamysheva, N N; Sakharov, D S; Davydov, V I
2012-01-01
Accompaniment of a decision of mathematical logical tasks by music (different style and power) influenced on the time of the decision. Classical music 35 and 65 dB and roc-music 65 and 85 dB decreased the time of the decision. More powerful classical music (85 dB) did not effect like that. The decision without the musical accompaniment led to increasing of coherent values especially in beta1, beta2, gamma frequency ranges in EEG of occipital cortex. The intrahemispheric and the interhemispheric coherences of frontal EEG increased and EEG asymmetry (in a number of Coh-connections in left and right hemispheres) arose during the tasks decision accompanied by music. Application of classical music 35 and 65 dB caused left-side asymmetry in EEG. Using of more powerful classical or rock music led to prevalence of quantity of Coh-connections in a right hemisphere. PMID:23101361
Five Departures in Logic, Mathematics, and thus—Whether We Like It, or Not—in Physics as Well...
NASA Astrophysics Data System (ADS)
Rosinger, Elemér E.
2015-07-01
Physics depends on "physical intuition", much of which is formulated in terms of Mathematics. Mathematics itself depends on Logic. The paper presents three latest novelties in Logic which have major consequences in Mathematics. Further, it presents two possible significant departures in Mathematics itself. These five departures can have major implications in Physics. Some of them are indicated, among them in Quantum Mechanics and Relativity.
Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles
ERIC Educational Resources Information Center
Cigas, John; Hsin, Wen-Jung
2005-01-01
Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…
ERIC Educational Resources Information Center
Crestani, Fabio; Dominich, Sandor; Lalmas, Mounia; van Rijsbergen, Cornelis Joost
2003-01-01
Discusses the importance of research on the use of mathematical, logical, and formal methods in information retrieval to help enhance retrieval effectiveness and clarify underlying concepts of information retrieval. Highlights include logic; probability; spaces; and future research needs. (Author/LRW)
ERIC Educational Resources Information Center
Retzer, Kenneth Albert
Reported are the results of a study designed to test the effects of a programed unit in fundamentals of logic on the ability of college capable junior high school students to verbalize mathematical generalizations. The independent variables were the presence or absence of study of the logic unit, and ability level being college capable (I.Q.…
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
NASA Astrophysics Data System (ADS)
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
NASA Astrophysics Data System (ADS)
de Andrade, Thales Haddad Novaes; Vilela, Denise Silva
2013-09-01
In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of interlocutions and pose a dialogue between the field of mathematics education in Brazil and the sociology of science proposed by David Bloor. The main point of Bloor's theory is that logical-mathematical knowledge is far from being true and universal and is socially conditioned. In particular we will be discussing the first principle of the strong program, which deals with conditions that generate beliefs promoted by education policies in Brazil, such as the MEC/USAID treaties. In this case the "naturalization of logic" was stimulated by a widespread diffusion of both Piaget studies and the Modern Mathematics Movement.
ERIC Educational Resources Information Center
Novaes de Andrade, Thales Haddad; Vilela, Denise Silva
2013-01-01
In Brazil, mathematics education was associated with Jean Piaget's theory. Scholars in the field of education appropriated Piaget's work in different ways, but usually emphasized logical aspects of thought, which probably lead to an expansion of mathematics education influenced by psychology. This study attempts to extend the range of…
Elements of Mathematics, Book 2: Logic and Sets.
ERIC Educational Resources Information Center
Exner, Robert; And Others
One of 12 books developed for use with the core material (Book O) of the Elements of Mathematics Program, this text covers material well beyond the scope of the usual secondary mathematics sequences. These materials are designed for highly motivated students with strong verbal abilities; mathematical theories and ideas are developed through…
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate.
Dridi, G; Julien, R; Hliwa, M; Joachim, C
2015-08-28
The mathematics behind the quantum Hamiltonian computing (QHC) approach of designing Boolean logic gates with a quantum system are given. Using the quantum eigenvalue repulsion effect, the QHC AND, NAND, OR, NOR, XOR, and NXOR Hamiltonian Boolean matrices are constructed. This is applied to the construction of a QHC half adder Hamiltonian matrix requiring only six quantum states to fullfil a half Boolean logical truth table. The QHC design rules open a nano-architectronic way of constructing Boolean logic gates inside a single molecule or atom by atom at the surface of a passivated semi-conductor. PMID:26234709
The mathematics of a quantum Hamiltonian computing half adder Boolean logic gate
NASA Astrophysics Data System (ADS)
Dridi, G.; Julien, R.; Hliwa, M.; Joachim, C.
2015-08-01
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.
A Generalized Instructional System for Elementary Mathematical Logic.
ERIC Educational Resources Information Center
Goldberg, Adele
A computer-based instructional system for teaching the notion of mathematical proof is described. The system is capable of handling formalizations of the full predicate calculus with identity and, with minor work, definite description. Designed as an instructional device, the program is also the basis for a number of research projects involving…
ERIC Educational Resources Information Center
Yilmaz, Ismail
2014-01-01
This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…
Science-Technology Coupling: The Case of Mathematical Logic and Computer Science.
ERIC Educational Resources Information Center
Wagner-Dobler, Roland
1997-01-01
In the history of science, there have often been periods of sudden rapprochements between pure science and technology-oriented branches of science. Mathematical logic as pure science and computer science as technology-oriented science have experienced such a rapprochement, which is studied in this article in a bibliometric manner. (Author)
The Role of Logic in the Validation of Mathematical Proofs. Technical Report. No. 1999-1
ERIC Educational Resources Information Center
Selden, Annie; Selden, John
1999-01-01
Mathematics departments rarely require students to study very much logic before working with proofs. Normally, the most they will offer is contained in a small portion of a "bridge" course designed to help students move from more procedurally-based lower-division courses (e.g., abstract algebra and real analysis). What accounts for this seeming…
ERIC Educational Resources Information Center
Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri
2013-01-01
This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
Mathematical modeling of the lambda switch: a fuzzy logic approach.
Laschov, Dmitriy; Margaliot, Michael
2009-10-21
Gene regulation plays a central role in the development and functioning of living organisms. Gaining a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch. PMID:19589343
A Safety Conundrum Illustrated: Logic, Mathematics, and Science Are Not Enough
NASA Technical Reports Server (NTRS)
Holloway, C. M.; Johnson, C. W.; Collins, Kristine R.
2010-01-01
In an ideal world, conversations about whether a particular system is safe, or whether a particular method or tool enhances safety, would be emotion-free discussions concentrating on the level of safety required, available evidence, and coherent logical, mathematical, or scientific arguments based on that evidence. In the real world, discussions about safety are often not emotion-free. Political and economic arguments may play a bigger role than logical, mathematical, and scientific arguments, and psychological factors may be as important, or even more important, than purely technical factors. This paper illustrates the conundrum that can result from this clash of the ideal and the real by means of an imagined conversation among a collection of fictional characters representing various types of people who may be participating in a safety discussion.
Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szűcs, Dénes
2013-07-01
This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized that the development of mathematical skills is closely related to the development of logical abilities, a domain-general skill. In particular, we expected a close link between mathematical skills and the ability to reason independently of one's beliefs. Our results showed that this was indeed the case, with children with DD performing more poorly than controls, and high maths ability children showing outstanding skills in logical reasoning about belief-laden problems. Nevertheless, all groups performed poorly on structurally equivalent problems with belief-neutral content. This is in line with suggestions that abstract reasoning skills (i.e. the ability to reason about content without real-life referents) develops later than the ability to reason about belief-inconsistent fantasy content.A video abstract of this article can be viewed at http://www.youtube.com/watch?v=90DWY3O4xx8. PMID:23786472
NASA Astrophysics Data System (ADS)
Lanzalaco, Felix; Pissanetzky, Sergio
2013-12-01
A recent theory of physical information based on the fundamental principles of causality and thermodynamics has proposed that a large number of observable life and intelligence signals can be described in terms of the Causal Mathematical Logic (CML), which is proposed to encode the natural principles of intelligence across any physical domain and substrate. We attempt to expound the current definition of CML, the "Action functional" as a theory in terms of its ability to possess a superior explanatory power for the current neuroscientific data we use to measure the mammalian brains "intelligence" processes at its most general biophysical level. Brain simulation projects define their success partly in terms of the emergence of "non-explicitly programmed" complex biophysical signals such as self-oscillation and spreading cortical waves. Here we propose to extend the causal theory to predict and guide the understanding of these more complex emergent "intelligence Signals". To achieve this we review whether causal logic is consistent with, can explain and predict the function of complete perceptual processes associated with intelligence. Primarily those are defined as the range of Event Related Potentials (ERP) which include their primary subcomponents; Event Related Desynchronization (ERD) and Event Related Synchronization (ERS). This approach is aiming for a universal and predictive logic for neurosimulation and AGi. The result of this investigation has produced a general "Information Engine" model from translation of the ERD and ERS. The CML algorithm run in terms of action cost predicts ERP signal contents and is consistent with the fundamental laws of thermodynamics. A working substrate independent natural information logic would be a major asset. An information theory consistent with fundamental physics can be an AGi. It can also operate within genetic information space and provides a roadmap to understand the live biophysical operation of the phenotype
The evolution of the human mind and logic--mathematics structures.
Yunes, Rosendo A
2005-09-01
The evolution of the human mind is discussed based on: (i) the fact that living beings interchange matter, energy and information with their environment, (ii) an ontological interpretation of the "reality" of the quantum world, of which logic-mathematics structures are considered constitutive parts, (iii) recent theories according to which living beings are considered as dynamic complex systems organized by information, and (iv) the fact that the evolution of living beings is guided by information about the environment and by intrinsic information on living systems (auto-organization). Assuming the evolution of vision as a model we observe that the driving forces that directed the evolution of the eyes, as dynamic complex systems, are the information about the environment supplied by sunlight and the intrinsic information-gaining mechanism of living organisms. Thus, there exists a convergence toward a visual system with the greatest ability to obtain light information, like the human eye, and also a divergence that leads to the development of specific qualities in some species. As in the case of vision the evolution of the human mind-brain cannot be a consequence of factors unrelated to the object of its own functioning. The human mind was structured for the acquisition from reality of the logic-mathematics structures that underlie the whole universe and consequently of an internal representation of the external world and of its own self. Thus, these structures are, together with the intrinsic capacity for auto-organization of the human brain, the predominant driving force of the human mind evolution. Both factors are complementary. PMID:15967187
NASA Astrophysics Data System (ADS)
Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina
2013-06-01
In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."
ERIC Educational Resources Information Center
Stanford Univ., CA. School Mathematics Study Group.
One chapter in the fourteenth unit of this SMSG series deals with logic; simple and compound statements, truth tables, logical equivalence, rules of a logical argument, proof, quantifiers, and negations are the topics covered. The second chapter of the unit discusses applications of probability and statistics, including random sampling,…
NASA Astrophysics Data System (ADS)
Li, Jing; Ma, Sujuan; Ma, Linqing
Firstly, in this article, we expound the theory of the educational games and multiple intelligence and analyze the relationship between them. Then, further, we elaborate educational games' effect on the development of students' multiple intelligence, taking logic-mathematics intelligence for example. Also, we discuss the strategies of using educational games to improve students' intelligence. In a word, we can use the computer games to develop the students' multi-intelligence.
Black-box Brain Experiments, Causal Mathematical Logic, and the Thermodynamics of Intelligence
NASA Astrophysics Data System (ADS)
Pissanetzky, Sergio; Lanzalaco, Felix
2013-12-01
Awareness of the possible existence of a yet-unknown principle of Physics that explains cognition and intelligence does exist in several projects of emulation, simulation, and replication of the human brain currently under way. Brain simulation projects define their success partly in terms of the emergence of non-explicitly programmed biophysical signals such as self-oscillation and spreading cortical waves. We propose that a recently discovered theory of Physics known as Causal Mathematical Logic (CML) that links intelligence with causality and entropy and explains intelligent behavior from first principles, is the missing link. We further propose the theory as a roadway to understanding more complex biophysical signals, and to explain the set of intelligence principles. The new theory applies to information considered as an entity by itself. The theory proposes that any device that processes information and exhibits intelligence must satisfy certain theoretical conditions irrespective of the substrate where it is being processed. The substrate can be the human brain, a part of it, a worm's brain, a motor protein that self-locomotes in response to its environment, a computer. Here, we propose to extend the causal theory to systems in Neuroscience, because of its ability to model complex systems without heuristic approximations, and to predict emerging signals of intelligence directly from the models. The theory predicts the existence of a large number of observables (or "signals"), all of which emerge and can be directly and mathematically calculated from non-explicitly programmed detailed causal models. This approach is aiming for a universal and predictive language for Neuroscience and AGI based on causality and entropy, detailed enough to describe the finest structures and signals of the brain, yet general enough to accommodate the versatility and wholeness of intelligence. Experiments are focused on a black-box as one of the devices described above of which
ERIC Educational Resources Information Center
Gazit, Avikam
2012-01-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th…
NASA Astrophysics Data System (ADS)
Bektasli, Behzat
Graphs have a broad use in science classrooms, especially in physics. In physics, kinematics is probably the topic for which graphs are most widely used. The participants in this study were from two different grade-12 physics classrooms, advanced placement and calculus-based physics. The main purpose of this study was to search for the relationships between student spatial ability, logical thinking, mathematical achievement, and kinematics graphs interpretation skills. The Purdue Spatial Visualization Test, the Middle Grades Integrated Process Skills Test (MIPT), and the Test of Understanding Graphs in Kinematics (TUG-K) were used for quantitative data collection. Classroom observations were made to acquire ideas about classroom environment and instructional techniques. Factor analysis, simple linear correlation, multiple linear regression, and descriptive statistics were used to analyze the quantitative data. Each instrument has two principal components. The selection and calculation of the slope and of the area were the two principal components of TUG-K. MIPT was composed of a component based upon processing text and a second component based upon processing symbolic information. The Purdue Spatial Visualization Test was composed of a component based upon one-step processing and a second component based upon two-step processing of information. Student ability to determine the slope in a kinematics graph was significantly correlated with spatial ability, logical thinking, and mathematics aptitude and achievement. However, student ability to determine the area in a kinematics graph was only significantly correlated with student pre-calculus semester 2 grades. Male students performed significantly better than female students on the slope items of TUG-K. Also, male students performed significantly better than female students on the PSAT mathematics assessment and spatial ability. This study found that students have different levels of spatial ability, logical thinking
Zadeh, L.A.
1988-01-01
The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived. 7 references.
NASA Technical Reports Server (NTRS)
Le Balleur, J. C.
1988-01-01
The applicability of conventional mathematical analysis (based on the combination of two-valued logic and probability theory) to problems in which human judgment, perception, or emotions play significant roles is considered theoretically. It is shown that dispositional logic, a branch of fuzzy logic, has particular relevance to the common-sense reasoning typical of human decision-making. The concepts of dispositionality and usuality are defined analytically, and a dispositional conjunctive rule and dispositional modus ponens are derived.
ERIC Educational Resources Information Center
Morsanyi, Kinga; Devine, Amy; Nobes, Alison; Szucs, Denes
2013-01-01
This study examined performance on transitive inference problems in children with developmental dyscalculia (DD), typically developing controls matched on IQ, working memory and reading skills, and in children with outstanding mathematical abilities. Whereas mainstream approaches currently consider DD as a domain-specific deficit, we hypothesized…
Exploring Logical Reasoning and Mathematical Proof in Grade 6 Elementary School Students
ERIC Educational Resources Information Center
Flegas, Konstantinos; Charalampos, Lemonidis
2013-01-01
Research and classroom experience reveal that the construction of mathematical proofs is difficult for all students. While many contemporary mathematics curricula recognize the importance of teaching reasoning and proof, in Greece these concepts are introduced at the secondary education level. In this study, we will attempt to investigate a group…
ERIC Educational Resources Information Center
Hogan, David; Chan, Melvin; Rahim, Ridzuan; Kwek, Dennis; Aye, Khin Maung; Loo, Siok Chen; Sheng, Yee Zher; Luo, Wenshu
2013-01-01
By any measure, Singapore's educational system has generated an extraordinary record of achievement over the past two or three decades. In this article, we report on one key component of a broader three year investigation into why Singapore has done so well, and explore the logic, strength, resilience and limits of the underlying pedagogical…
NASA Astrophysics Data System (ADS)
Platz, M.; Rapp, J.; Groessler, M.; Niehaus, E.; Babu, A.; Soman, B.
2014-11-01
A Spatial Decision Support System (SDSS) provides support for decision makers and should not be viewed as replacing human intelligence with machines. Therefore it is reasonable that decision makers are able to use a feature to analyze the provided spatial decision support in detail to crosscheck the digital support of the SDSS with their own expertise. Spatial decision support is based on risk and resource maps in a Geographic Information System (GIS) with relevant layers e.g. environmental, health and socio-economic data. Spatial fuzzy logic allows the representation of spatial properties with a value of truth in the range between 0 and 1. Decision makers can refer to the visualization of the spatial truth of single risk variables of a disease. Spatial fuzzy logic rules that support the allocation of limited resources according to risk can be evaluated with measure theory on topological spaces, which allows to visualize the applicability of this rules as well in a map. Our paper is based on the concept of a spatial fuzzy logic on topological spaces that contributes to the development of an adaptive Early Warning And Response System (EWARS) providing decision support for the current or future spatial distribution of a disease. It supports the decision maker in testing interventions based on available resources and apply risk mitigation strategies and provide guidance tailored to the geo-location of the user via mobile devices. The software component of the system would be based on open source software and the software developed during this project will also be in the open source domain, so that an open community can build on the results and tailor further work to regional or international requirements and constraints. A freely available EWARS Spatial Fuzzy Logic Demo was developed wich enables a user to visualize risk and resource maps based on individual data in several data formats.
The Fallacy of Composition: Prospective Mathematics Teachers' Use of Logical Fallacies
ERIC Educational Resources Information Center
Chernoff, Egan J.; Russell, Gale L.
2012-01-01
The purpose of this article is to address the lack of research on teachers' knowledge of probability. As has been the case in prior research, we asked prospective mathematics teachers to determine which of the presented sequences of coin flips was least likely to occur. However, instead of using the traditional perspectives of heuristic and…
Cooper, D.K.; Cooper, J.A.; Ferson, S.
1999-01-21
Calculating safety and reliability probabilities with functions of uncertain variables can yield incorrect or misleading results if some precautions are not taken. One important consideration is the application of constrained mathematics for calculating probabilities for functions that contain repeated variables. This paper includes a description of the problem and develops a methodology for obtaining an accurate solution.
ERIC Educational Resources Information Center
Horn, Ilana Seidel; Kane, Britnie Delinger; Wilson, Jonee
2015-01-01
In the accountability era, educators are pressed to use evidence-based practice. In this comparative case study, we examine the learning opportunities afforded by teachers' data use conversations. Using situated discourse analysis, we compare two middle school mathematics teacher workgroups interpreting data from the same district assessment.…
ERIC Educational Resources Information Center
Korkmaz, Özgen
2016-01-01
The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
ERIC Educational Resources Information Center
Laupa, Marta; Becker, Joe
2004-01-01
Arithmetic algorithms include two types of rules: conventional rules that may be changed by authority, and may legitimately vary from one classroom or country to another (e.g. putting the sum below, rather than above, the numbers added) and logical rules that involve the logic of the algorithm. Changes in the logical rules produce incorrect…
Logic via Computer Programming.
ERIC Educational Resources Information Center
Wieschenberg, Agnes A.
This paper proposed the question "How do we teach logical thinking and sophisticated mathematics to unsophisticated college students?" One answer among many is through the writing of computer programs. The writing of computer algorithms is mathematical problem solving and logic in disguise and it may attract students who would otherwise stop…
ERIC Educational Resources Information Center
Tularam, Gurudeo Anand; Hulsman, Kees
2015-01-01
This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…
ERIC Educational Resources Information Center
Falsetti, Marcela; Alvarez, Marisa
2015-01-01
We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…
Foundations of logic programming
Lloyd, J.W.
1987-01-01
This is the second edition of the first book to give an account of the mathematical foundations of Logic Programming. Its purpose is to collect the basic theoretical results of Logic Programming, which have previously only been available in widely scattered research papers. In addition to presenting the technical results, the book also contains many illustrative examples. Many of the examples and problems are part of the folklore of Logic Programming and are not easily obtainable elsewhere.
ERIC Educational Resources Information Center
Yopp, David
2010-01-01
Understanding logical necessity is an important component of proof and reasoning for teachers of grades K-8. The ability to determine exactly where young students' arguments are faulty offers teachers the chance to give youngsters feedback as they progress toward writing mathematically valid deductive proofs. As defined, logical necessity is the…
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
Introducing Exclusion Logic as a Deontic Logic
NASA Astrophysics Data System (ADS)
Evans, Richard
This paper introduces Exclusion Logic - a simple modal logic without negation or disjunction. We show that this logic has an efficient decision procedure. We describe how Exclusion Logic can be used as a deontic logic. We compare this deontic logic with Standard Deontic Logic and with more syntactically restricted logics.
NASA Astrophysics Data System (ADS)
Rohrlich, Fritz
2011-12-01
Classical and the quantum mechanical sciences are in essential need of mathematics. Only thus can the laws of nature be formulated quantitatively permitting quantitative predictions. Mathematics also facilitates extrapolations. But classical and quantum sciences differ in essential ways: they follow different laws of logic, Aristotelian and non-Aristotelian logics, respectively. These are explicated.
ERIC Educational Resources Information Center
Dyrud, Marilyn A.
To make introducing logic to college students in speech and expository writing classes more interesting, letters to the editor can be used to teach logical fallacies. Letters to the editor are particularly useful because they give students a sense of the community they live in (issues, concerns, and the spectrum of opinion), they are easily…
Leveraging Structure: Logical Necessity in the Context of Integer Arithmetic
ERIC Educational Resources Information Center
Bishop, Jessica Pierson; Lamb, Lisa L.; Philipp, Randolph A.; Whitacre, Ian; Schappelle, Bonnie P.
2016-01-01
Looking for, recognizing, and using underlying mathematical structure is an important aspect of mathematical reasoning. We explore the use of mathematical structure in children's integer strategies by developing and exemplifying the construct of logical necessity. Students in our study used logical necessity to approach and use numbers in a…
NASA Astrophysics Data System (ADS)
Baader, Franz
Description Logics (DLs) are a well-investigated family of logic-based knowledge representation formalisms, which can be used to represent the conceptual knowledge of an application domain in a structured and formally well-understood way. They are employed in various application domains, such as natural language processing, configuration, and databases, but their most notable success so far is the adoption of the DL-based language OWL as standard ontology language for the semantic web.
NASA Astrophysics Data System (ADS)
Pascal, Robert; Pross, Addy
2016-04-01
In this paper we propose a logical connection between the physical and biological worlds, one resting on a broader understanding of the stability concept. We propose that stability manifests two facets - time and energy, and that stability's time facet, expressed as persistence, is more general than its energy facet. That insight leads to the logical formulation of the Persistence Principle, which describes the general direction of material change in the universe, and which can be stated most simply as: nature seeks persistent forms. Significantly, the principle is found to express itself in two mathematically distinct ways: in the replicative world through Malthusian exponential growth, and in the `regular' physical/chemical world through Boltzmann's probabilistic considerations. By encompassing both `regular' and replicative worlds, the principle appears to be able to help reconcile two of the major scientific theories of the 19th century - the Second Law of Thermodynamics and Darwin's theory of evolution - within a single conceptual framework.
A Mathematics Software Database Update.
ERIC Educational Resources Information Center
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
NASA Technical Reports Server (NTRS)
Zadeh, Lofti A.
1988-01-01
The author presents a condensed exposition of some basic ideas underlying fuzzy logic and describes some representative applications. The discussion covers basic principles; meaning representation and inference; basic rules of inference; and the linguistic variable and its application to fuzzy control.
NASA Astrophysics Data System (ADS)
Merkle, Ralph C.; Drexler, K. Eric
1996-12-01
Helical logic is a theoretical proposal for a future computing technology using the presence or absence of individual electrons (or holes) to encode 1s and 0s. The electrons are constrained to move along helical paths, driven by a rotating electric field in which the entire circuit is immersed. The electric field remains roughly orthogonal to the major axis of the helix and confines each charge carrier to a fraction of a turn of a single helical loop, moving it like water in an Archimedean screw. Each loop could in principle hold an independent carrier, permitting high information density. One computationally universal logic operation involves two helices, one of which splits into two `descendant' helices. At the point of divergence, differences in the electrostatic potential resulting from the presence or absence of a carrier in the adjacent helix controls the direction taken by a carrier in the splitting helix. The reverse of this sequence can be used to merge two initially distinct helical paths into a single outgoing helical path without forcing a dissipative transition. Because these operations are both logically and thermodynamically reversible, energy dissipation can be reduced to extremely low levels. This is the first proposal known to the authors that combines thermodynamic reversibility with the use of single charge carriers. It is important to note that this proposal permits a single electron to switch another single electron, and does not require that many electrons be used to switch one electron. The energy dissipated per logic operation can very likely be reduced to less than 0957-4484/7/4/004/img5 at a temperature of 1 K and a speed of 10 GHz, though further analysis is required to confirm this. Irreversible operations, when required, can be easily implemented and should have a dissipation approaching the fundamental limit of 0957-4484/7/4/004/img6.
NASA Astrophysics Data System (ADS)
Giordano, P.
2010-06-01
We introduce a ring of the so-called Fermat reals, which is an extension of the real field containing nilpotent infinitesimals. The construction is inspired by Smooth Infinitesimal Analysis (SIA) and provides a powerful theory of actual infinitesimals without any background in mathematical logic. In particular, in contrast to SIA, which admits models in intuitionistic logic only, the theory of Fermat reals is consistent with the classical logic. We face the problem of deciding whether or not a product of powers of nilpotent infinitesimals vanishes, study the identity principle for polynomials, and discuss the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order-preserving geometrical representation. Using nilpotent infinitesimals, every smooth function becomes a polynomial because the remainder in Taylor’s formulas is now zero. Finally, we present several applications to informal classical calculations used in physics, and all these calculations now become rigorous, and at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, which clarifies how to formalize the approximations tied with Hooke’s law using the language of nilpotent infinitesimals.
Indeterminacy, linguistic semantics and fuzzy logic
Novak, V.
1996-12-31
In this paper, we discuss the indeterminacy phenomenon which has two distinguished faces, namely uncertainty modeled especially by the probability theory and vagueness, modeled by fuzzy logic. Other important mathematical model of vagueness is provided by the Alternative Set Theory. We focus on some of the basic concepts of these theories in connection with mathematical modeling of the linguistic semantics.
Cognitive Correlates of Performance in Advanced Mathematics
ERIC Educational Resources Information Center
Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin
2012-01-01
Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…
Philosophy and mathematics: interactions.
Rashed, Roshdi
From Plato to the beginnings of the last century, mathematics provided philosophers with methods of exposition, procedures of demonstration, and instruments of analysis. The unprecedented development of mathematics on the one hand, and the mathematicians' appropriation of Logic from the philosophers on the other hand, have given rise to two problems with which the philosophers have to contend: (1) Is there still a place for the philosophy of mathematics? and (2) To what extent is a philosophy of mathematics still possible? This article offers some reflections on these questions, which have preoccupied a good many philosophers and continue to do so. PMID:25029825
Mythical systems: mathematic and logical theory
NASA Astrophysics Data System (ADS)
Nescolarde-Selva, J.; Usó-Doménech, J. L.; Lloret-Climent, M.
2015-01-01
The process of elaboration of the symbolic universe leads to exciting insights regarding the search for human emotional security. The symbols end up as explanatory axes of universal reality and on them are constructed myths that form a superstructure for belief systems. Human society is a multi-level system with a material structure (society), an ideological superstructure (belief systems, values, etc.) and a super superstructure with two parts: mythical (origin and justification) and utopic (final goal). All mythical belief systems have a numinous-religious nature.
Automated deduction for first-order logic with equality
Energy Science and Technology Software Center (ESTSC)
2001-06-01
Otter 3.2 is the current version of ANL's automated deduction system designed to search for proofs and countermodels of conjectures stated in first-order logic with equality. It is used mostly for research in mathematics and logic and also for various applications requiring deductive data processing.
Automated deduction for first-order logic with equality
Energy Science and Technology Software Center (ESTSC)
2003-09-01
Otter 3.3 is the current version of ANL's automated deduction system designed to search for proofs and countermodels of conjectures stated in first-order logic with equality. It is used mostly for research in mathematics and logic and also for various applications requiring deductive data processing.
Pre-Service Primary School Teachers' Logical Reasoning Skills
ERIC Educational Resources Information Center
Marchis, Iuliana
2013-01-01
Logical reasoning skills are important for a successful mathematical learning and in students' future career. These skills are essential for a primary school teacher, because they need to explain solving methods and solutions to their pupils. In this research we studied pre-service primary school teachers' logical reasoning skills. The results…
Preservice Elementary Teachers' Understanding of Logical Inference
ERIC Educational Resources Information Center
Hauk, Shandy; Judd, April Brown; Tsay, Jenq Jong; Barzilai, Harel; Austin, Homer
2009-01-01
This article reports on the logical reasoning efforts of five prospective elementary school teachers as they responded to interview prompts involving nonsense, natural, and mathematical representations of conditional statements. The interview participants evinced various levels of reliance on personal relevance, linguistic contextualization, and…
From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics
ERIC Educational Resources Information Center
Gavalas, Dimitris
2007-01-01
Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…
The Assessment of Mathematical Abilities.
ERIC Educational Resources Information Center
Osborn, Herbert H.
1983-01-01
A test was given to 322 secondary students to develop a profile of mathematical ability based on four components: computation, pattern recognition, logical reasoning, and symbolic manipulation. These profiles were compared to mathematics test scores; the results verified hypotheses about individual differences in mental processes and knowledge…
Audiovisual Materials in Mathematics.
ERIC Educational Resources Information Center
Raab, Joseph A.
This pamphlet lists five thousand current, readily available audiovisual materials in mathematics. These are grouped under eighteen subject areas: Advanced Calculus, Algebra, Arithmetic, Business, Calculus, Charts, Computers, Geometry, Limits, Logarithms, Logic, Number Theory, Probability, Soild Geometry, Slide Rule, Statistics, Topology, and…
Fuzzy logic controller optimization
Sepe, Jr., Raymond B; Miller, John Michael
2004-03-23
A method is provided for optimizing a rotating induction machine system fuzzy logic controller. The fuzzy logic controller has at least one input and at least one output. Each input accepts a machine system operating parameter. Each output produces at least one machine system control parameter. The fuzzy logic controller generates each output based on at least one input and on fuzzy logic decision parameters. Optimization begins by obtaining a set of data relating each control parameter to at least one operating parameter for each machine operating region. A model is constructed for each machine operating region based on the machine operating region data obtained. The fuzzy logic controller is simulated with at least one created model in a feedback loop from a fuzzy logic output to a fuzzy logic input. Fuzzy logic decision parameters are optimized based on the simulation.
NASA Astrophysics Data System (ADS)
Chiara, Maria Luisa Dalla; Giuntini, Roberto
1989-07-01
Paraconsistent quantum logics are weak forms of quantum logic, where the noncontradiction and the excluded-middle laws are violated. These logics find interesting applications in the operational approach to quantum mechanics. In this paper, we present an axiomatization, a Kripke-style, and an algebraic semantical characterization for two forms of paraconsistent quantum logic. Further developments are contained in Giuntini and Greuling's paper in this issue.
OncoLogic^{TM} - A Computer System to Evaluate the Carcinogenic Potential of Chemicals
OncoLogic^{TM} is a software program that evaluates the likelihood that a chemical may cause cancer. OncoLogic^{TM} has been peer reviewed and is being rele...
Mathematical Texts as Narrative: Rethinking Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2013-01-01
This paper proposes a framework for reading mathematics texts as narratives. Building from a narrative framework of Meike Bal, a reader's experience with the mathematical content as it unfolds in the text (the "mathematical story") is distinguished from his or her logical reconstruction of the content beyond the text (the…
Unified Modern Mathematics, Course 2, Part 1.
ERIC Educational Resources Information Center
Secondary School Mathematics Curriculum Improvement Study, New York, NY.
This is Part 1 of the second course in a series which focuses on building fundamental mathematical structures. Topics considered in this book include: an introduction to mathematical logic and mathematical proof, a continuation of the study of groups, an introduction to axiomatic affine geometry, fields, the real number system, and coordinate…
Designing a Software Tool for Fuzzy Logic Programming
NASA Astrophysics Data System (ADS)
Abietar, José M.; Morcillo, Pedro J.; Moreno, Ginés
2007-12-01
Fuzzy Logic Programming is an interesting and still growing research area that agglutinates the efforts for introducing fuzzy logic into logic programming (LP), in order to incorporate more expressive resources on such languages for dealing with uncertainty and approximated reasoning. The multi-adjoint logic programming approach is a recent and extremely flexible fuzzy logic paradigm for which, unfortunately, we have not found practical tools implemented so far. In this work, we describe a prototype system which is able to directly translate fuzzy logic programs into Prolog code in order to safely execute these residual programs inside any standard Prolog interpreter in a completely transparent way for the final user. We think that the development of such fuzzy languages and programing tools might play an important role in the design of advanced software applications for computational physics, chemistry, mathematics, medicine, industrial control and so on.
NASA Technical Reports Server (NTRS)
Preston, K., Jr.
1972-01-01
The characteristics of the holographic logic computer are discussed. The holographic operation is reviewed from the Fourier transform viewpoint, and the formation of holograms for use in performing digital logic are described. The operation of the computer with an experiment in which the binary identity function is calculated is discussed along with devices for achieving real-time performance. An application in pattern recognition using neighborhood logic is presented.
Digital Microfluidic Logic Gates
NASA Astrophysics Data System (ADS)
Zhao, Yang; Xu, Tao; Chakrabarty, Krishnendu
Microfluidic computing is an emerging application for microfluidics technology. We propose microfluidic logic gates based on digital microfluidics. Using the principle of electrowetting-on-dielectric, AND, OR, NOT and XOR gates are implemented through basic droplet-handling operations such as transporting, merging and splitting. The same input-output interpretation enables the cascading of gates to create nontrivial computing systems. We present a potential application for microfluidic logic gates by implementing microfluidic logic operations for on-chip HIV test.
Electrically reconfigurable logic array
NASA Technical Reports Server (NTRS)
Agarwal, R. K.
1982-01-01
To compose the complicated systems using algorithmically specialized logic circuits or processors, one solution is to perform relational computations such as union, division and intersection directly on hardware. These relations can be pipelined efficiently on a network of processors having an array configuration. These processors can be designed and implemented with a few simple cells. In order to determine the state-of-the-art in Electrically Reconfigurable Logic Array (ERLA), a survey of the available programmable logic array (PLA) and the logic circuit elements used in such arrays was conducted. Based on this survey some recommendations are made for ERLA devices.
NASA Technical Reports Server (NTRS)
Howard, Ayanna
2005-01-01
The Fuzzy Logic Engine is a software package that enables users to embed fuzzy-logic modules into their application programs. Fuzzy logic is useful as a means of formulating human expert knowledge and translating it into software to solve problems. Fuzzy logic provides flexibility for modeling relationships between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. In addition, linguistic fuzzy sets and conditional statements allow systems to make decisions based on imprecise and incomplete information. The user of the Fuzzy Logic Engine need not be an expert in fuzzy logic: it suffices to have a basic understanding of how linguistic rules can be applied to the user's problem. The Fuzzy Logic Engine is divided into two modules: (1) a graphical-interface software tool for creating linguistic fuzzy sets and conditional statements and (2) a fuzzy-logic software library for embedding fuzzy processing capability into current application programs. The graphical- interface tool was developed using the Tcl/Tk programming language. The fuzzy-logic software library was written in the C programming language.
Ferrite logic reliability study
NASA Technical Reports Server (NTRS)
Baer, J. A.; Clark, C. B.
1973-01-01
Development and use of digital circuits called all-magnetic logic are reported. In these circuits the magnetic elements and their windings comprise the active circuit devices in the logic portion of a system. The ferrite logic device belongs to the all-magnetic class of logic circuits. The FLO device is novel in that it makes use of a dual or bimaterial ferrite composition in one physical ceramic body. This bimaterial feature, coupled with its potential for relatively high speed operation, makes it attractive for high reliability applications. (Maximum speed of operation approximately 50 kHz.)
Meaning and Process in Mathematics and Programming.
ERIC Educational Resources Information Center
Grogono, Peter
1989-01-01
Trends in computer programing language design are described and children's difficulties in learning to write programs for mathematics problems are considered. Languages are compared under the headings of imperative programing, functional programing, logic programing, and pictures. (DC)
Programmable Logic Controllers.
ERIC Educational Resources Information Center
Insolia, Gerard; Anderson, Kathleen
This document contains a 40-hour course in programmable logic controllers (PLC), developed for a business-industry technology resource center for firms in eastern Pennsylvania by Northampton Community College. The 10 units of the course cover the following: (1) introduction to programmable logic controllers; (2) DOS primer; (3) prerequisite…
AROUSAL AND LOGICAL INFERENCE.
ERIC Educational Resources Information Center
KOEN, FRANK
THE PURPOSE OF THE EXPERIMENT WAS TO DETERMINE THE DEGREE TO WHICH PHYSIOLOGICAL AROUSAL, AS INDEXED BY THE GRASON STADLER TYPE OPERANT CONDITIONING APPARATUS (GSR), IS RELATED TO THE ACCURACY OF LOGICAL REASONING. THE STIMULI WERE 12 SYLLOGISMS, THREE OF EACH OF FOUR DIFFERENT LOGICAL FORMS. THE 14 SUBJECTS (SS) INDICATED THEIR AGREEMENT OR…
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)…
NASA Astrophysics Data System (ADS)
Malhas, Othman Qasim
1993-10-01
The concept of “abacus logic” has recently been developed by the author (Malhas, n.d.). In this paper the relation of abacus logic to the concept of fuzziness is explored. It is shown that if a certain “regularity” condition is met, concepts from fuzzy set theory arise naturally within abacus logics. In particular it is shown that every abacus logic then has a “pre-Zadeh orthocomplementation”. It is also shown that it is then possible to associate a fuzzy set with every proposition of abacus logic and that the collection of all such sets satisfies natural conditions expected in systems of fuzzy logic. Finally, the relevance to quantum mechanics is discussed.
Microelectromechanical reprogrammable logic device
Hafiz, M. A. A.; Kosuru, L.; Younis, M. I.
2016-01-01
In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme. PMID:27021295
Microelectromechanical reprogrammable logic device.
Hafiz, M A A; Kosuru, L; Younis, M I
2016-01-01
In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme. PMID:27021295
Microelectromechanical reprogrammable logic device
NASA Astrophysics Data System (ADS)
Hafiz, M. A. A.; Kosuru, L.; Younis, M. I.
2016-03-01
In modern computing, the Boolean logic operations are set by interconnect schemes between the transistors. As the miniaturization in the component level to enhance the computational power is rapidly approaching physical limits, alternative computing methods are vigorously pursued. One of the desired aspects in the future computing approaches is the provision for hardware reconfigurability at run time to allow enhanced functionality. Here we demonstrate a reprogrammable logic device based on the electrothermal frequency modulation scheme of a single microelectromechanical resonator, capable of performing all the fundamental 2-bit logic functions as well as n-bit logic operations. Logic functions are performed by actively tuning the linear resonance frequency of the resonator operated at room temperature and under modest vacuum conditions, reprogrammable by the a.c.-driving frequency. The device is fabricated using complementary metal oxide semiconductor compatible mass fabrication process, suitable for on-chip integration, and promises an alternative electromechanical computing scheme.
Regulatory Conformance Checking: Logic and Logical Form
ERIC Educational Resources Information Center
Dinesh, Nikhil
2010-01-01
We consider the problem of checking whether an organization conforms to a body of regulation. Conformance is studied in a runtime verification setting. The regulation is translated to a logic, from which we synthesize monitors. The monitors are evaluated as the state of an organization evolves over time, raising an alarm if a violation is…
Uncertainty, energy, and multiple-valued logics
Hayes, J.P.
1986-02-01
The multiple-valued logics obtained by introducing uncertainty and energy considerations into classical switching theory are studied in this paper. First, the nature of uncertain or unknown signals is examined, and two general uncertainty types called U-values and P-values are identified. It is shown that multiple-valued logics composed of U/P-values can be systematically derived from 2-valued Boolean algebra. These are useful for timing and hazard analysis, and provide a rigorous framework for designing gate-level logic simulation programs. Next, signals of the form (..nu..,S) are considered where ..nu.. and S denote logic level and strength, respectively, and the product vs corresponds to energy flow or power. It is shown that these signals from a type of lattice called a Pseudo-Boolean algebra. Such algebras characterize the behavior of digital circuits at a level (the switch level) intermediate between the conventional analog and logical levels. They provide the mathematical basis for an efficient new class of switch-level simulation programs used in MOS VLSI design.
Fuzzy logic based robotic controller
NASA Technical Reports Server (NTRS)
Attia, F.; Upadhyaya, M.
1994-01-01
Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.
Zargham, M.R.
1995-06-01
Recently, fuzzy logic has been applied to many areas, such as process control, image understanding, robots, expert systems, and decision support systems. This paper will explain the basic concepts of fuzzy logic and its application in different fields. The steps to design a control system will be explained in detail. Fuzzy control is the first successful industrial application of fuzzy logic. A fuzzy controller is able to control systems which previously could only be controlled by skilled operators. In recent years Japan has achieved significant progress in this area and has applied it to variety of products such as cruise control for cars, video cameras, rice cookers, washing machines, etc.
Tanida, J.; Ichioka, Y.
1983-01-01
A simple method for optically implementing digital logic gates in parallel has been developed. Parallel logic gates can be achieved by using a lensless shadow-casting system with a light emitting diode array as an incoherent light source. All the sixteen logic functions for two binary variables, which are the fundamental computations of Boolean algebra, can be simply realised in parallel with these gates by changing the switching modes of a led array. Parallel computation structures of the developed optical digital array processor are demonstrated by implementing pattern logics for two binary images with high space-bandwidth product. Applications of the proposed method to parallel shift operation of the image, differentiation, and processing of gray-level image are shown. 9 references.
Beyond Numbers: The Mathematics Literature Connection.
ERIC Educational Resources Information Center
Madison, John P.; Seidenstein, Roslynn
This document is a collection of activities designed to use children's literature to introduce, reinforce or broaden mathematics skills and concepts. The mathematical topics that are addressed include: time; problem solving; logic; measurement; comparison; sets; one-to-one correspondence; fraction concepts; division; counting; averages; infinity;…
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Mechanical passive logic module
NASA Astrophysics Data System (ADS)
Chattopadhyay, Tanay; Caulfield, H. John
2015-02-01
Nothing from nothing gives simple simile, but something from nothing is an interesting and challenging task. Adolf Lohmann once proposed 'do nothing machine' in optics, which only copies input to output. Passive logic module (PALM) is a special type of 'do nothing machine' which can converts inputs into one of 16 possible binary outputs. This logic module is not like the conventional irreversible one. It is a simple type of reversible Turing machine. In this manuscript we discussed and demonstrated PALM using mechanical movement of plane mirrors. Also we discussed the theoretical model of micro electro mechanical system (MEMS) based PALM in this manuscript. It may have several valuable properties such as passive operation (no need for nonlinear elements as other logic device require) and modular logic (one device implementing any Boolean logic function with simple internal changes). The result is obtained from the demonstration by only looking up the output. No calculation is required to get the result. Not only that, PALM is a simple type of the famous 'billiard ball machine', which also discussed in this manuscript.
Diagnosable structured logic array
NASA Technical Reports Server (NTRS)
Whitaker, Sterling (Inventor); Miles, Lowell (Inventor); Gambles, Jody (Inventor); Maki, Gary K. (Inventor)
2009-01-01
A diagnosable structured logic array and associated process is provided. A base cell structure is provided comprising a logic unit comprising a plurality of input nodes, a plurality of selection nodes, and an output node, a plurality of switches coupled to the selection nodes, where the switches comprises a plurality of input lines, a selection line and an output line, a memory cell coupled to the output node, and a test address bus and a program control bus coupled to the plurality of input lines and the selection line of the plurality of switches. A state on each of the plurality of input nodes is verifiably loaded and read from the memory cell. A trusted memory block is provided. The associated process is provided for testing and verifying a plurality of truth table inputs of the logic unit.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806
Group Solutions, Too! More Cooperative Logic Activities for Grades K-4. Teacher's Guide. LHS GEMS.
ERIC Educational Resources Information Center
Goodman, Jan M.; Kopp, Jaine
There is evidence that structured cooperative logic is an effective way to introduce or reinforce mathematics concepts, explore thinking processes basic to both math and science, and develop the important social skills of cooperative problem-solving. This book contains a number of cooperative logic activities for grades K-4 in order to improve…
Twenty-Five Years of the Fuzzy Factor: Fuzzy Logic, the Courts, and Student Press Law.
ERIC Educational Resources Information Center
Plopper, Bruce L.; McCool, Lauralee
A study applied the structure of fuzzy logic, a fairly modern development in mathematical set theory, to judicial opinions concerning non-university, public school student publications, from 1975 to 1999. The study examined case outcomes (19 cases generated 27 opinions) as a function of fuzzy logic, and it evaluated interactions between fuzzy…
Context-Based Exercises in Logic: To Park or Not to Park, 'Tis the Question
ERIC Educational Resources Information Center
Munakata, Mika
2011-01-01
In this article, ambiguous street and park signs are analysed and deciphered using symbolic logic. These examples showcase the ways in which instructors of undergraduate mathematics courses can blend their students' everyday exposure to logical reasoning with classroom experiences. (Contains 4 tables and 6 figures.)
Benchmarking emerging logic devices
NASA Astrophysics Data System (ADS)
Nikonov, Dmitri
2014-03-01
As complementary metal-oxide-semiconductor field-effect transistors (CMOS FET) are being scaled to ever smaller sizes by the semiconductor industry, the demand is growing for emerging logic devices to supplement CMOS in various special functions. Research directions and concepts of such devices are overviewed. They include tunneling, graphene based, spintronic devices etc. The methodology to estimate future performance of emerging (beyond CMOS) devices and simple logic circuits based on them is explained. Results of benchmarking are used to identify more promising concepts and to map pathways for improvement of beyond CMOS computing.
NASA Technical Reports Server (NTRS)
Agarwal, R. K.
1983-01-01
The source code for the SPICE 2 program was deblocked in order to isolate and compile the subroutine in an effort to provide a software simulation of discrete and combinatorial electronic components. Incompatibilities between the UNIVAC 1180 FORTRAN and the Sigma V CP-V FORTRAN 4 were resolved. The SPICE 2 model is to be used to determine gate and fan-out delays, logic state conditions, and signal race conditions for transistor array elements and circuit logic to be patterned in the (SPI) 7101 CMOS silicon gate semicustom array. The simulator is to be operable from the CP-V time sharing terminals.
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition
ERIC Educational Resources Information Center
Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon
2016-01-01
A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…
Reprint Series: What is Contemporary Mathematics. RS-3.
ERIC Educational Resources Information Center
Schaaf, William L., Ed.
This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the nature of mathematics; (2) mathematical inutility and the advance of science; and (3) logic. (MP)
Logic production systems: Analysis and synthesis
Donskoi, V.I.
1995-03-01
Many applied systems can be described in the following terms: given is a certain number of objects and a set of rules to construct new object from the original objects and from previously constructed objects. Mathematicians call such systems deductive, or calculi. Artificial intelligence scientists subsequently improved and elaborated the notion of production, retaining the Post operator A {yields} B as a basic element or a core. Production models are generally regarded as lacking a rigorous theory and governed by heuristics. Maslov noted: {open_quotes}We may assume that the language of calculi will become in the near future as natural and as widespread in new applications of discrete mathematics as, for instance, the language of graph theory is today.{close_quotes} Studies whose results are surveyed below were triggered by the development of applications of production systems in dual expert systems and focus around the following topics: (1) formalization of logic production systems (Pospelov has noted that results in the theory of production systems can be obtained by restricting the notion of productions and production systems); (2) analysis of completeness of logic production systems as a tool for realization of Boolean functions; (3) construction of a universal algorithmic model based on a logic production system; (4) construction of algorithms that synthesize the domain of deductive derivability of a given goal fact and analysis of algorithmic complexity of the corresponding problem. It is important to note that the results obtained so far relate to a strictly defined subclass - the subclass of logic production systems and machines. They do not pretend to cover the wider domain of applicability of the apparatus of deductive systems. Classical concepts and propositions of discrete mathematics used in this paper without further explanation are defined in existing literature.
Radiation tolerant combinational logic cell
NASA Technical Reports Server (NTRS)
Maki, Gary R. (Inventor); Gambles, Jody W. (Inventor); Whitaker, Sterling (Inventor)
2009-01-01
A system has a reduced sensitivity to Single Event Upset and/or Single Event Transient(s) compared to traditional logic devices. In a particular embodiment, the system includes an input, a logic block, a bias stage, a state machine, and an output. The logic block is coupled to the input. The logic block is for implementing a logic function, receiving a data set via the input, and generating a result f by applying the data set to the logic function. The bias stage is coupled to the logic block. The bias stage is for receiving the result from the logic block and presenting it to the state machine. The state machine is coupled to the bias stage. The state machine is for receiving, via the bias stage, the result generated by the logic block. The state machine is configured to retain a state value for the system. The state value is typically based on the result generated by the logic block. The output is coupled to the state machine. The output is for providing the value stored by the state machine. Some embodiments of the invention produce dual rail outputs Q and Q'. The logic block typically contains combinational logic and is similar, in size and transistor configuration, to a conventional CMOS combinational logic design. However, only a very small portion of the circuits of these embodiments, is sensitive to Single Event Upset and/or Single Event Transients.
Temporal logics meet telerobotics
NASA Technical Reports Server (NTRS)
Rutten, Eric; Marce, Lionel
1989-01-01
The specificity of telerobotics being the presence of a human operator, decision assistance tools are necessary for the operator, especially in hostile environments. In order to reduce execution hazards due to a degraded ability for quick and efficient recovery of unexpected dangerous situations, it is of importance to have the opportunity, amongst others, to simulate the possible consequences of a plan before its actual execution, in order to detect these problematic situations. Hence the idea of providing the operator with a simulator enabling him to verify the temporal and logical coherence of his plans. Therefore, the power of logical formalisms is used for representation and deduction purposes. Starting from the class of situations that are represented, a STRIPS (the STanford Research Institute Problem Solver)-like formalism and its underlying logic are adapted to the simulation of plans of actions in time. The choice of a temporal logic enables to build a world representation, on which the effects of plans, grouping actions into control structures, will be transcribed by the simulation, resulting in a verdict and information about the plan's coherence.
Quantum probabilistic logic programming
NASA Astrophysics Data System (ADS)
Balu, Radhakrishnan
2015-05-01
We describe a quantum mechanics based logic programming language that supports Horn clauses, random variables, and covariance matrices to express and solve problems in probabilistic logic. The Horn clauses of the language wrap random variables, including infinite valued, to express probability distributions and statistical correlations, a powerful feature to capture relationship between distributions that are not independent. The expressive power of the language is based on a mechanism to implement statistical ensembles and to solve the underlying SAT instances using quantum mechanical machinery. We exploit the fact that classical random variables have quantum decompositions to build the Horn clauses. We establish the semantics of the language in a rigorous fashion by considering an existing probabilistic logic language called PRISM with classical probability measures defined on the Herbrand base and extending it to the quantum context. In the classical case H-interpretations form the sample space and probability measures defined on them lead to consistent definition of probabilities for well formed formulae. In the quantum counterpart, we define probability amplitudes on Hinterpretations facilitating the model generations and verifications via quantum mechanical superpositions and entanglements. We cast the well formed formulae of the language as quantum mechanical observables thus providing an elegant interpretation for their probabilities. We discuss several examples to combine statistical ensembles and predicates of first order logic to reason with situations involving uncertainty.
ERIC Educational Resources Information Center
Straumanis, Joan
A major problem in teaching symbolic logic is that of providing individualized and early feedback to students who are learning to do proofs. To overcome this difficulty, a computer program was developed which functions as a line-by-line proof checker in Sentential Calculus. The program, DEMON, first evaluates any statement supplied by the student…
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
2000-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will start a series of notes concentrating on analysis techniques with this issues section discussing worst-case analysis requirements.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard; Day, John H. (Technical Monitor)
2001-01-01
This report will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter will continue a series of notes concentrating on analysis techniques with this issue's section discussing the use of Root-Sum-Square calculations for digital delays.
NASA Astrophysics Data System (ADS)
Stefaneas, Petros; Vandoulakis, Ioannis M.
2015-12-01
This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.
Sandia ATM SONET Interface Logic
Energy Science and Technology Software Center (ESTSC)
1994-07-21
SASIL is used to program the EPLD's (Erasable Programmable Logic Devices) and PAL's (Programmable Array Logic) that make up a large percentage of the Sandia ATM SONET Interface (OC3 version) for the INTEL Paragon.
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
Active structural control by fuzzy logic rules: An introduction
Tang, Yu; Wu, Kung C.
1996-12-31
A zeroth level introduction to fuzzy logic control applied to the active structural control to reduce the dynamic response of structures subjected to earthquake excitations is presented. It is hoped that this presentation will increase the attractiveness of the methodology to structural engineers in research as well as in practice. The basic concept of the fuzzy logic control are explained by examples and by diagrams with a minimum of mathematics. The effectiveness and simplicity of the fuzzy logic control is demonstrated by a numerical example in which the response of a single- degree-of-freedom system subjected to earthquake excitations is controlled by making use of the fuzzy logic controller. In the example, the fuzzy rules are first learned from the results obtained from linear control theory; then they are fine tuned to improve their performance. It is shown that the performance of fuzzy logic control surpasses that of the linear control theory. The paper shows that linear control theory provides experience for fuzzy logic control, and fuzzy logic control can provide better performance; therefore, two controllers complement each other.
Active structural control by fuzzy logic rules: An introduction
Tang, Y.
1995-07-01
An introduction to fuzzy logic control applied to the active structural control to reduce the dynamic response of structures subjected to earthquake excitations is presented. It is hoped that this presentation will increase the attractiveness of the methodology to structural engineers in research as well as in practice. The basic concept of the fuzzy logic control are explained by examples and by diagrams with a minimum of mathematics. The effectiveness and simplicity of the fuzzy logic control is demonstrated by a numerical example in which the response of a single-degree-of-freedom system subjected to earthquake excitations is controlled by making use of the fuzzy logic controller. In the example, the fuzzy rules are first learned from the results obtained from linear control theory; then they are fine tuned to improve their performance. It is shown that the performance of fuzzy logic control surpasses that of the linear control theory. The paper shows that linear control theory provides experience for fuzzy logic control, and fuzzy logic control can provide better performance; therefore, two controllers complement each other.
The mysterious connection between mathematics and physics.
Kauffman, Louis H; Ul-Haq, Rukhsan
2015-12-01
The essay is in the form of a dialogue between the two authors. We take John Wheeler's idea of "It from Bit" as an essential clue and we rework the structure of the bit not to the qubit, but to a logical particle that is its own anti-particle, a logical Marjorana particle. This is our key example of the amphibian nature of mathematics and the external world. We emphasize that mathematics is a combination of calculation and concept. At the conceptual level, mathematics is structured to be independent of time and multiplicity. Mathematics in this way occurs before number and counting. From this timeless domain, mathematics and mathematicians can explore worlds of multiplicity and infinity beyond the apparent limitations of the physical world and see that among these possible worlds there are coincidences with what is observed. PMID:26278645
Conditional Logic and Primary Children.
ERIC Educational Resources Information Center
Ennis, Robert H.
Conditional logic, as interpreted in this paper, means deductive logic characterized by "if-then" statements. This study sought to investigate the knowledge of conditional logic possessed by primary children and to test their readiness to learn such concepts. Ninety students were designated the experimental group and participated in a 15-week…
Logic of infinite quantum systems
NASA Astrophysics Data System (ADS)
Mundici, Daniele
1993-10-01
Limits of sequences of finite-dimensional (AF) C *-algebras, such as the CAR algebra for the ideal Fermi gas, are a standard mathematical tool to describe quantum statistical systems arising as thermodynamic limits of finite spin systems. Only in the infinite-volume limit one can, for instance, describe phase transitions as singularities in the thermodynamic potentials, and handle the proliferation of physically inequivalent Hilbert space representations of a system with infinitely many degrees of freedom. As is well known, commutative AF C *-algebras correspond to countable Boolean algebras, i.e., algebras of propositions in the classical two-valued calculus. We investigate the noncommutative logic properties of general AF C *-algebras, and their corresponding systems. We stress the interplay between Gödel incompleteness and quotient structures in the light of the “nature does not have ideals” program, stating that there are no quotient structures in physics. We interpret AF C *-algebras as algebras of the infinite-valued calculus of Lukasiewicz, i.e., algebras of propositions in Ulam's “ twenty questions” game with lies.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
1998-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter's column will include some announcements and some recent radiation test results and evaluations of interest. Specifically, the following topics will be covered: the Military and Aerospace Applications of Programmable Devices and Technologies Conference to be held at GSFC in September, 1998, proton test results, heavy ion test results, and some total dose results.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
1998-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter's column will include some announcements and some recent radiation test results and evaluations of interest. Specifically, the following topics will be covered: the Military and Aerospace Applications of Programmable Devices and Technologies Conference to be held at GSFC in September, 1998, proton test results, and some total dose results.
Kompa, K. L.; Levine, R. D.
2001-01-01
We propose a scheme for molecule-based information processing by combining well-studied spectroscopic techniques and recent results from chemical dynamics. Specifically it is discussed how optical transitions in single molecules can be used to rapidly perform classical (Boolean) logical operations. In the proposed way, a restricted number of states in a single molecule can act as a logical gate equivalent to at least two switches. It is argued that the four-level scheme can also be used to produce gain, because it allows an inversion, and not only a switching ability. The proposed scheme is quantum mechanical in that it takes advantage of the discrete nature of the energy levels but, we here discuss the temporal evolution, with the use of the populations only. On a longer time range we suggest that the same scheme could be extended to perform quantum logic, and a tentative suggestion, based on an available experiment, is discussed. We believe that the pumping can provide a partial proof of principle, although this and similar experiments were not interpreted thus far in our terms. PMID:11209046
Mathematics--Is It Any of Your Business?
ERIC Educational Resources Information Center
Mansfield, Ralph
1975-01-01
In this paper, the first section of a three-part article, the author discusses applications of mathematical theories in business situations. He explores the use of logic and networks in counting and accounting problems. (SD)
A Logical Analysis of Majorana's Papers on Theoretical Physics
NASA Astrophysics Data System (ADS)
Drago, A.; Esposito, S.
2006-05-01
We study two celebrated Majorana's papers through a method of investigation which relies upon the recently recognized distinction between classical logic and several kinds of non-classical logics, i.e. the failure of the double negation law. This law fails when a double negated sentence is not equivalent to the corresponding positive sentence, owing to the lack of scientific evidence of the latter one. All recognized double negated sentences inside the text of each paper are listed; the mere sequence of such sentences giving the logical thread of Majorana's arguing. This one is recognized to be of the Lagrangian kind, which mixes logical arguing and mathematical calculation; i.e. the author puts a fundamental problem which is solved by anticipating the mathematical hypothesis able to solve it, and then by drawing from this hypothesis the mathematical consequences in order to reach to desired result. Furthermore the rethoric of presentation used by Majorana results to be a juridical one, owing to his style of presenting the laws to which an ideal theoretical physicist has to conform his mind in order to solve the problem at issue.
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Formal verification of mathematical software
NASA Technical Reports Server (NTRS)
Sutherland, D.
1984-01-01
Methods are investigated for formally specifying and verifying the correctness of mathematical software (software which uses floating point numbers and arithmetic). Previous work in the field was reviewed. A new model of floating point arithmetic called the asymptotic paradigm was developed and formalized. Two different conceptual approaches to program verification, the classical Verification Condition approach and the more recently developed Programming Logic approach, were adapted to use the asymptotic paradigm. These approaches were then used to verify several programs; the programs chosen were simplified versions of actual mathematical software.
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Adaptive parallel logic networks
NASA Technical Reports Server (NTRS)
Martinez, Tony R.; Vidal, Jacques J.
1988-01-01
Adaptive, self-organizing concurrent systems (ASOCS) that combine self-organization with massive parallelism for such applications as adaptive logic devices, robotics, process control, and system malfunction management, are presently discussed. In ASOCS, an adaptive network composed of many simple computing elements operating in combinational and asynchronous fashion is used and problems are specified by presenting if-then rules to the system in the form of Boolean conjunctions. During data processing, which is a different operational phase from adaptation, the network acts as a parallel hardware circuit.
Flexible programmable logic module
Robertson, Perry J.; Hutchinson, Robert L.; Pierson, Lyndon G.
2001-01-01
The circuit module of this invention is a VME board containing a plurality of programmable logic devices (PLDs), a controlled impedance clock tree, and interconnecting buses. The PLDs are arranged to permit systolic processing of a problem by offering wide data buses and a plurality of processing nodes. The board contains a clock reference and clock distribution tree that can drive each of the PLDs with two critically timed clock references. External clock references can be used to drive additional circuit modules all operating from the same synchronous clock reference.
Programmable Logic Application Notes
NASA Technical Reports Server (NTRS)
Katz, Richard
1999-01-01
This column will be provided each quarter as a source for reliability, radiation results, NASA capabilities, and other information on programmable logic devices and related applications. This quarter the focus is on some experimental data on low voltage drop out regulators to support mixed 5 and 3.3 volt systems. A discussion of the Small Explorer WIRE spacecraft will also be given. Lastly, we show take a first look at robust state machines in Hardware Description Languages (VHDL) and their use in critical systems. If you have information that you would like to submit or an area you would like discussed or researched, please give me a call or e-mail.
A mathematical model of a computational problem solving system
NASA Astrophysics Data System (ADS)
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Adaptive parallel logic networks
Martinez, T.R.; Vidal, J.J.
1988-02-01
This paper presents a novel class of special purpose processors referred to as ASOCS (adaptive self-organizing concurrent systems). Intended applications include adaptive logic devices, robotics, process control, system malfunction management, and in general, applications of logic reasoning. ASOCS combines massive parallelism with self-organization to attain a distributed mechanism for adaptation. The ASOCS approach is based on an adaptive network composed of many simple computing elements (nodes) which operate in a combinational and asynchronous fashion. Problem specification (programming) is obtained by presenting to the system if-then rules expressed as Boolean conjunctions. New rules are added incrementally. In the current model, when conflicts occur, precedence is given to the most recent inputs. With each rule, desired network response is simply presented to the system, following which the network adjusts itself to maintain consistency and parsimony of representation. Data processing and adaptation form two separate phases of operation. During processing, the network acts as a parallel hardware circuit. Control of the adaptive process is distributed among the network nodes and efficiently exploits parallelism.
NASA Technical Reports Server (NTRS)
Canaris, J.
1991-01-01
A new logic family, which is immune to single event upsets, is described. Members of the logic family are capable of recovery, regardless of the shape of the upsetting event. Glitch propagation from an upset node is also blocked. Logic diagrams for an Inverter, Nor, Nand, and Complex Gates are provided. The logic family can be implemented in a standard, commercial CMOS process with no additional masks. DC, transient, static power, upset recovery and layout characteristics of the new family, based on a commercial 1 micron CMOS N-Well process, are described.
Barriers in Concurrent Separation Logic
NASA Astrophysics Data System (ADS)
Hobor, Aquinas; Gherghina, Cristian
We develop and prove sound a concurrent separation logic for Pthreads-style barriers. Although Pthreads barriers are widely used in systems, and separation logic is widely used for verification, there has not been any effort to combine the two. Unlike locks and critical sections, Pthreads barriers enable simultaneous resource redistribution between multiple threads and are inherently stateful, leading to significant complications in the design of the logic and its soundness proof. We show how our logic can be applied to a specific example program in a modular way. Our proofs are machine-checked in Coq.
Fuzzy logic and coarse coding using programmable logic devices
NASA Astrophysics Data System (ADS)
Brooks, Geoffrey
2009-05-01
Naturally-occurring sensory signal processing algorithms, such as those that inspired fuzzy-logic control, can be integrated into non-naturally-occurring high-performance technology, such as programmable logic devices, to realize novel bio-inspired designs. Research is underway concerning an investigation into using field programmable logic devices (FPLD's) to implement fuzzy logic sensory processing. A discussion is provided concerning the commonality between bio-inspired fuzzy logic algorithms and coarse coding that is prevalent in naturally-occurring sensory systems. Undergraduate design projects using fuzzy logic for an obstacle-avoidance robot has been accomplished at our institution and other places; numerous other successful fuzzy logic applications can be found as well. The long-term goal is to leverage such biomimetic algorithms for future applications. This paper outlines a design approach for implementing fuzzy-logic algorithms into reconfigurable computing devices. This paper is presented in an effort to connect with others who may be interested in collaboration as well as to establish a starting point for future research.
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. PMID:24620862
NASA Technical Reports Server (NTRS)
2005-01-01
A new all-electronic Particle Image Velocimetry technique that can efficiently map high speed gas flows has been developed in-house at the NASA Lewis Research Center. Particle Image Velocimetry is an optical technique for measuring the instantaneous two component velocity field across a planar region of a seeded flow field. A pulsed laser light sheet is used to illuminate the seed particles entrained in the flow field at two instances in time. One or more charged coupled device (CCD) cameras can be used to record the instantaneous positions of particles. Using the time between light sheet pulses and determining either the individual particle displacements or the average displacement of particles over a small subregion of the recorded image enables the calculation of the fluid velocity. Fuzzy logic minimizes the required operator intervention in identifying particles and computing velocity. Using two cameras that have the same view of the illumination plane yields two single exposure image frames. Two competing techniques that yield unambiguous velocity vector direction information have been widely used for reducing the single-exposure, multiple image frame data: (1) cross-correlation and (2) particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. For the correlation technique, the correlation peak corresponding to the average displacement of particles across the subregion must be identified. Noise on the images and particle dropout result in misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work, fuzzy logic techniques are used to determine the true
Simulation and Verification of Synchronous Set Relations in Rewriting Logic
NASA Technical Reports Server (NTRS)
Rocha, Camilo; Munoz, Cesar A.
2011-01-01
This paper presents a mathematical foundation and a rewriting logic infrastructure for the execution and property veri cation of synchronous set relations. The mathematical foundation is given in the language of abstract set relations. The infrastructure consists of an ordersorted rewrite theory in Maude, a rewriting logic system, that enables the synchronous execution of a set relation provided by the user. By using the infrastructure, existing algorithm veri cation techniques already available in Maude for traditional asynchronous rewriting, such as reachability analysis and model checking, are automatically available to synchronous set rewriting. The use of the infrastructure is illustrated with an executable operational semantics of a simple synchronous language and the veri cation of temporal properties of a synchronous system.
Reversible logic gates on Physarum Polycephalum
Schumann, Andrew
2015-03-10
In this paper, we consider possibilities how to implement asynchronous sequential logic gates and quantum-style reversible logic gates on Physarum polycephalum motions. We show that in asynchronous sequential logic gates we can erase information because of uncertainty in the direction of plasmodium propagation. Therefore quantum-style reversible logic gates are more preferable for designing logic circuits on Physarum polycephalum.
NASA Technical Reports Server (NTRS)
Cleaveland, Rance; Luettgen, Gerald; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
This paper presents the Logical Process Calculus (LPC), a formalism that supports heterogeneous system specifications containing both operational and declarative subspecifications. Syntactically, LPC extends Milner's Calculus of Communicating Systems with operators from the alternation-free linear-time mu-calculus (LT(mu)). Semantically, LPC is equipped with a behavioral preorder that generalizes Hennessy's and DeNicola's must-testing preorder as well as LT(mu's) satisfaction relation, while being compositional for all LPC operators. From a technical point of view, the new calculus is distinguished by the inclusion of: (1) both minimal and maximal fixed-point operators and (2) an unimple-mentability predicate on process terms, which tags inconsistent specifications. The utility of LPC is demonstrated by means of an example highlighting the benefits of heterogeneous system specification.
Kenny, A.
1985-01-01
In The Logic of Deterrence, Kenny presents a guide to the theory and ethics of the complicated subject of deterrence. Kenny begins by examining the necessary conditions for any war to be just and then applies these principles to the cases of limited and total nuclear war. He then critiques current deterrence policies of both East and West, concluding that they are based on a willingness to kill millions of innocent people and are morally wrong. In the final section of the book, Kenny offers proposals for nuclear disarmament. Charting a course ''between the illusory hopes of the multilateralists who seek disarmament by negotiating and the impractical idealism of those who call for immediate and total unilateral disarmament by the West,'' Kenny proposes a series of phased and partial unilateral steps by the West, coupled with pressure on the East to reciprocate.
Borresen, Jon; Lynch, Stephen
2012-01-01
In the 1940s, the first generation of modern computers used vacuum tube oscillators as their principle components, however, with the development of the transistor, such oscillator based computers quickly became obsolete. As the demand for faster and lower power computers continues, transistors are themselves approaching their theoretical limit and emerging technologies must eventually supersede them. With the development of optical oscillators and Josephson junction technology, we are again presented with the possibility of using oscillators as the basic components of computers, and it is possible that the next generation of computers will be composed almost entirely of oscillatory devices. Here, we demonstrate how coupled threshold oscillators may be used to perform binary logic in a manner entirely consistent with modern computer architectures. We describe a variety of computational circuitry and demonstrate working oscillator models of both computation and memory. PMID:23173034
Partial quantum logics revisited
NASA Astrophysics Data System (ADS)
Vetterlein, Thomas
2011-01-01
Partial Boolean algebras (PBAs) were introduced by Kochen and Specker as an algebraic model reflecting the mutual relationships among quantum-physical yes-no tests. The fact that not all pairs of tests are compatible was taken into special account. In this paper, we review PBAs from two sides. First, we generalise the concept, taking into account also those yes-no tests which are based on unsharp measurements. Namely, we introduce partial MV-algebras, and we define a corresponding logic. Second, we turn to the representation theory of PBAs. In analogy to the case of orthomodular lattices, we give conditions for a PBA to be isomorphic to the PBA of closed subspaces of a complex Hilbert space. Hereby, we do not restrict ourselves to purely algebraic statements; we rather give preference to conditions involving automorphisms of a PBA. We conclude by outlining a critical view on the logico-algebraic approach to the foundational problem of quantum physics.
Quantificational logic of context
Buvac, Sasa
1996-12-31
In this paper we extend the Propositional Logic of Context, to the quantificational (predicate calculus) case. This extension is important in the declarative representation of knowledge for two reasons. Firstly, since contexts are objects in the semantics which can be denoted by terms in the language and which can be quantified over, the extension enables us to express arbitrary first-order properties of contexts. Secondly, since the extended language is no longer only propositional, we can express that an arbitrary predicate calculus formula is true in a context. The paper describes the syntax and the semantics of a quantificational language of context, gives a Hilbert style formal system, and outlines a proof of the system`s completeness.
NASA Astrophysics Data System (ADS)
Whitfield, James; Faccin, Mauro; Biamonte, Jacob
2013-03-01
Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground-state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground-state subspace encoding the truth tables of Boolean formulas. The ground-state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground-state embeddings found in both classical optimization as well as adiabatic quantum optimization.
NASA Technical Reports Server (NTRS)
2003-01-01
The same software controlling autonomous and crew-assisted operations for the International Space Station (ISS) is enabling commercial enterprises to integrate and automate manual operations, also known as decision logic, in real time across complex and disparate networked applications, databases, servers, and other devices, all with quantifiable business benefits. Auspice Corporation, of Framingham, Massachusetts, developed the Auspice TLX (The Logical Extension) software platform to effectively mimic the human decision-making process. Auspice TLX automates operations across extended enterprise systems, where any given infrastructure can include thousands of computers, servers, switches, and modems that are connected, and therefore, dependent upon each other. The concept behind the Auspice software spawned from a computer program originally developed in 1981 by Cambridge, Massachusetts-based Draper Laboratory for simulating tasks performed by astronauts aboard the Space Shuttle. At the time, the Space Shuttle Program was dependent upon paper-based procedures for its manned space missions, which typically averaged 2 weeks in duration. As the Shuttle Program progressed, NASA began increasing the length of manned missions in preparation for a more permanent space habitat. Acknowledging the need to relinquish paper-based procedures in favor of an electronic processing format to properly monitor and manage the complexities of these longer missions, NASA realized that Draper's task simulation software could be applied to its vision of year-round space occupancy. In 1992, Draper was awarded a NASA contract to build User Interface Language software to enable autonomous operations of a multitude of functions on Space Station Freedom (the station was redesigned in 1993 and converted into the international venture known today as the ISS)
Simulated Laboratory in Digital Logic.
ERIC Educational Resources Information Center
Cleaver, Thomas G.
Design of computer circuits used to be a pencil and paper task followed by laboratory tests, but logic circuit design can now be done in half the time as the engineer accesses a program which simulates the behavior of real digital circuits, and does all the wiring and testing on his computer screen. A simulated laboratory in digital logic has been…
Japanese Logic Puzzles and Proof
ERIC Educational Resources Information Center
Wanko, Jeffrey J.
2009-01-01
An understanding of proof does not start in a high school geometry course. Rather, attention to logical reasoning throughout a student's school experience can help the development of proof readiness. In the spirit of problem solving, the author has begun to use some Japanese logic puzzles other than sudoku to help students develop additional…
Programmable Logic Controllers. Teacher Edition.
ERIC Educational Resources Information Center
Rauh, Bob; Kaltwasser, Stan
These materials were developed for a seven-unit secondary or postsecondary education course on programmable logic controllers (PLCs) that treats most of the skills needed to work effectively with PLCs as programming skills. The seven units of the course cover the following topics: fundamentals of programmable logic controllers; contracts, timers,…
[Brunschvicg, bachelard and the internal logic of scientific discourse].
Gauthier, Yvon
2013-01-01
Bachelard is seen as sharing with Brunschvicg an "internalist" epistemology of mathematics and exact sciences. Brunschvicg's notion of constructive idealism concurs with Bachelard's surrationalism. Both philosophers defended the idea of an internal logic of scientific discourse which discloses the dialectics inherent in the dynamics of reason. The aim of philosophy is then to emphasize the genesis and progress of rationality in the historical development of science. PMID:24091652
Power optimization in logic isomers
NASA Technical Reports Server (NTRS)
Panwar, Ramesh; Rennels, David; Alkalaj, Leon
1993-01-01
Logic isomers are labeled, 2-isomorphic graphs that implement the same logic function. Logic isomers may have significantly different power requirements even though they have the same number of transistors in the implementation. The power requirements of the isomers depend on the transition activity of the input signals. The power requirements of isomorphic graph isomers of n-input NAND and NOR gates are shown. Choosing the less power-consuming isomer instead of the others can yield significant power savings. Experimental results on a ripple-carry adder are presented to show that the implementation using the least power-consuming isomers requires approximately 10 percent less power than the implementation using the most power-consuming isomers. Simulations of other random logic designs also confirm that designs using less power-consuming isomers can reduce the logic power demand by approximately 10 percent as compared to designs using more power-consuming isomers.
Investigating Student Use of Electronic Support Tools and Mathematical Reasoning
ERIC Educational Resources Information Center
Higgins, Kristina N.; Crawford, Lindy; Huscroft-D'Angelo, Jacqueline; Horney, Mark
2016-01-01
Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are…
A Mathematics Educator's Introduction to Rural Policy Issues
ERIC Educational Resources Information Center
Waters, Michael S., Ed.
2005-01-01
Most of the scholarship and commentary on mathematics education deals with issues of curriculum and instruction; this is understandable in a field logically belonging to the domain of curriculum and instruction. Moreover, issues of teaching and learning are compelling to people who love to learn and teach mathematics. Policy receives shorter…
Teaching Mathematics from a Chemist's Viewpoint.
ERIC Educational Resources Information Center
DeLorenzo, Ronald A.
This paper describes a chemistry professor's approach to teaching mathematics in the college classroom. Based on the assumption that the four main goals of the educational process in general are to teach students to communicate clearly, study regularly, master basic math skills, and think logically, a description is provided of the manner in which…
A Teacher's Notebook: Mathematics, K-9.
ERIC Educational Resources Information Center
National Association of Independent Schools, Boston, MA.
This guide is divided into seven sections according to specific topics rather than by grade levels and/or grade level expectations. The topics encompass a K-9 program and include: numeration; measurement; operations and computational skills; algebra; informal geometry; sets, logic, and proof; and mathematical patterns. Each section lists concepts…
Killeen's (2005) p rep coefficient: logical and mathematical problems.
Maraun, Michael; Gabriel, Stephanie
2010-06-01
In his article, "An alternative to null-hypothesis significance tests," Killeen (2005) urged the discipline to abandon the practice of p obs-based null hypothesis testing and to quantify the signal-to-noise characteristics of experimental outcomes with replication probabilities. He described the coefficient that he invented, prep, as the probability of obtaining "an effect of the same sign as that found in an original experiment" (Killeen, 2005, p. 346). The journal Psychological Science quickly came to encourage researchers to employ prep, rather than p obs, in the reporting of their experimental findings. In the current article, we (a) establish that Killeen's derivation of prep contains an error, the result of which is that prep is not, in fact, the probability that Killeen set out to derive; (b) establish that prep is not a replication probability of any kind but, rather, is a quasi-power coefficient; and (c) suggest that Killeen has mischaracterized both the relationship between replication probabilities and statistical inference, and the kinds of claims that are licensed by knowledge of the value assumed by the replication probability that he attempted to derive. PMID:20515239
Motivating Computer Engineering Freshmen through Mathematical and Logical Puzzles
ERIC Educational Resources Information Center
Parhami, B.
2009-01-01
As in many other fields of science and technology, college students in computer engineering do not come into full contact with the key ideas and challenges of their chosen discipline until the third year of their studies. This situation poses a problem in terms of keeping the students motivated as they labor through their foundational, basic…
Cognitive Rationality and Its Logic-Mathematical Language
ERIC Educational Resources Information Center
Masalova, Svetlana
2012-01-01
The article deals with the cognitive (flexible) rationality, combining rational and irrational moments of the scientific search of the cognizing subject. Linguo-cognitive model of the concept as the flexible regulative rationality reveals the activity of the cognitive processes and the mentality of the epistemological-ontic subject, its leading…
Developing Learning Materials Using an Ontology of Mathematical Logic
ERIC Educational Resources Information Center
Boyatt, Russell; Joy, Mike
2012-01-01
Ontologies describe a body of knowledge and give formal structure to a domain by describing concepts and their relationships. The construction of an ontology provides an opportunity to develop a shared understanding and a consistent vocabulary to be used for a given activity. This paper describes the construction of an ontology for an area of…
Computerized logic design of digital circuits
NASA Technical Reports Server (NTRS)
Gussow, S.; Oglesby, R.
1974-01-01
Procedure performs all work required for logic design of digital counters or sequential circuits and simplification of Boolean expressions. Program provides simple, accurate, and comprehensive logic design capability to users both experienced and totally inexperienced in logic design
MLS, a magnetic logic simulator for magnetic bubble logic design
NASA Astrophysics Data System (ADS)
Kinsman, Thomas B.; Cendes, Zoltan J.
1987-04-01
A computer program that simulates the logic functions of magnetic bubble devices has been developed. The program uses a color graphics screen to display the locations of bubbles on a chip during operation. It complements the simulator previously developed for modeling bubble devices on the gate level [Smith et al., IEEE Trans. Magn. MAG-19, 1835 (1983); Smith and Kryder, ibid. MAG-21, 1779 (1985)]. This new tool simplifies the design and testing of bubble logic devices, and facilitates the development of complicated LSI bubble circuits. The program operation is demonstrated with the design of an in-stream faulty loop compensator using bubble logic.
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
Mathematical opportunities in nonlinear optics
NASA Astrophysics Data System (ADS)
The Board on Mathematical Sciences takes as one of its functions that of identifying areas of important or emerging research activity and focusing attention on them. The Board seeks to stimulate cross-disciplinary research between mathematical sciences and disciplines. This survey notes that on the technological side nonlinear optics is likely to revolutionize future telecommunications and computer technologies, while on the mathematical side it is an ideal subject for the applied mathematician, who is particularly well positioned to make major contributions. Topics covered include wave propagation and the nonlinear Schrodinger equation; soliton propagation in the optical fibers; nonlinear waveguides; four-wave mixing, phase conjunction, and beam cleanup; lasers; optical bistability, logic elements, and information storing patterns; and spatiotemporal complexity and turbulence in nonlinear optics.
A hierarchical cellular logic for pyramid computers
Tanimoto, S.L.
1984-11-01
Hierarchical structure occurs in biological vision systems and there is good reason to incorporate it into a model of computation for processing binary images. A mathematical formalism is presented which can describe a wide variety of operations useful in image processing and graphics. The formalism allows for two kinds of simple transformations on the values (called pyramids) of a set of cells called a hierarchical domain: the first are binary operations on boolean values, and the second are neighborhood-matching operations. The implied model of computation is more structured than previously discussed pyramidal models, and is more readily realized in parallel hardware, while it remains sufficiently rich to provide efficient solutions to a wide variety of problems. The model has a simplicity which is due to the restricted nature of the operations and the implied synchronization across the hierarchical domain. A corresponding algebraic simplicity in the logic makes possible the concise representation of many cellular-data operations.
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
ERIC Educational Resources Information Center
Siskiyou County Superintendent of Schools, Yreka, CA.
The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
Cognitive dynamic logic algorithms for situational awareness
NASA Astrophysics Data System (ADS)
Perlovsky, L. I.; Ilin, R.
2010-04-01
Autonomous situational awareness (SA) requires an ability to learn situations. It is mathematically difficult because in every situation there are many objects nonessential for this situation. Moreover, most objects around are random, unrelated to understanding contexts and situations. We learn in early childhood to ignore these irrelevant objects effortlessly, usually we do not even notice their existence. Here we consider an agent that can recognize a large number of objects in the world; in each situation it observes many objects, while only few of them are relevant to the situation. Most of situations are collections of random objects containing no relevant objects, only few situations "make sense," they contain few objects, which are always present in these situations. The training data contains sufficient information to identify these situations. However, to discover this information all objects in all situations should be sorted out to find regularities. This "sorting out" is computationally complex; its combinatorial complexity exceeds by far all events in the Universe. The talk relates this combinatorial complexity to Gödelian limitations of logic. We describe dynamic logic (DL) that quickly learns essential regularities-relevant, repeatable objects and situations. DL is related to mechanisms of the brain-mind and we describe brain-imaging experiments that have demonstrated these relations.
Contradicting logics in everyday practice.
Kristiansen, Margrethe; Obstfelder, Aud; Lotherington, Ann Therese
2016-03-21
Purpose - Performance management is criticised as a direct challenge to the dominant logic of professionalism in health care organisations. The purpose of this paper is to report an ethnographic study that investigates how performance management and professionalism as contradicting logics are interpreted and implemented by managers and nurses in everyday practice within Norwegian nursing homes. Design/methodology/approach - The paper presents an analysis of 18 semistructured interviews and 100 hours of observation of managers and nurses from three nursing homes. The study draws on the institutional logic perspective as a theoretical framework. In the analysis, the authors searched for patterns of activities and interactions that reflected managers and nurses' coping strategies for handling contradicting logics. Qualitative content analysis was used to systematically code the data, supported by NVIVO software. Findings - The authors identified three forms of coping strategies: the adjustment of professionalism to standards, the reinforcement of professional flexibility and problem solving, and the strategic adoption of documentation. These patterns of activities and interactions reflect new organisational structures that allowed contradicting logics to co-exist. The study demonstrates that a new complex dimension of governing processes within nursing homes is the way in which managers and nurses handle the tension between contradicting logics in their daily work and clinicians' everyday practice. Originality/value - The study provides new insight into how managers and nurses reshape internal organisational structures to cope with contradicting logics in nursing homes. PMID:26964849
Fuzzy logic in control systems: Fuzzy logic controller. I, II
NASA Technical Reports Server (NTRS)
Lee, Chuen Chien
1990-01-01
Recent advances in the theory and applications of fuzzy-logic controllers (FLCs) are examined in an analytical review. The fundamental principles of fuzzy sets and fuzzy logic are recalled; the basic FLC components (fuzzification and defuzzification interfaces, knowledge base, and decision-making logic) are described; and the advantages of FLCs for incorporating expert knowledge into a control system are indicated. Particular attention is given to fuzzy implication functions, the interpretation of sentence connectives (and, also), compositional operators, and inference mechanisms. Applications discussed include the FLC-guided automobile developed by Sugeno and Nishida (1985), FLC hardware systems, FLCs for subway trains and ship-loading cranes, fuzzy-logic chips, and fuzzy computers.
Kral, M J
1994-01-01
Although suicide is not viewed as a mental disorder per se, it is viewed by many if not most clinicians, researchers, and lay people as a real or natural symptom of depression. It is at least most typically seen as the unfortunate, severe, yet logical end result of a chain of negative self-appraisals, negative events, and hopelessness. Extending an approach articulated by the early French sociologist Gabriel Tarde, in this paper I argue that suicide is merely an idea, albeit a very bad one, having more in common with societal beliefs and norms regarding such things as divorce, abortion, sex, politics, consumer behavior, and fashion. I make a sharp contrast between perturbation and lethality, concepts central to Edwin S. Shneidman's theory of suicide. Evidence supportive of suicide as an idea is discussed based on what we are learning from the study of history and culture, and about contagion/cluster phenomena, media/communication, and choice of method. It is suggested that certain individuals are more vulnerable to incorporate the idea and act of suicide into their concepts of self, based on the same principles by which ideas are spread throughout society. Just as suicide impacts on society, so does society impact on suicide. PMID:7825197
NASA Technical Reports Server (NTRS)
Smith, David E.; Jonsson, Ari K.; Clancy, Daniel (Technical Monitor)
2001-01-01
In recent years, Graphplan style reachability analysis and mutual exclusion reasoning have been used in many high performance planning systems. While numerous refinements and extensions have been developed, the basic plan graph structure and reasoning mechanisms used in these systems are tied to the very simple STRIPS model of action. In 1999, Smith and Weld generalized the Graphplan methods for reachability and mutex reasoning to allow actions to have differing durations. However, the representation of actions still has some severe limitations that prevent the use of these techniques for many real-world planning systems. In this paper, we 1) separate the logic of reachability from the particular representation and inference methods used in Graphplan, and 2) extend the notions of reachability and mutual exclusion to more general notions of time and action. As it turns out, the general rules for mutual exclusion reasoning take on a remarkably clean and simple form. However, practical instantiations of them turn out to be messy, and require that we make representation and reasoning choices.
Logic synthesis of cascade circuits
NASA Astrophysics Data System (ADS)
Zakrevskii, A. D.
The work reviews aspects of the logic design of cascade circuits, particularly programmable logic matrices. Effective methods for solving various problems of the analysis and synthesis of these devices are examined; these methods are based on a matrix representation of the structure of these devices, and a vector-matrix interpretation of certain aspects of Boolean algebra. Particular consideration is given to the theory of elementary matrix circuits, methods for the minimization of Boolean functions, the synthesis of programmable logic matrices, multilevel combinational networks, and the development of automata with memory.
Comparing Knowledge Bases and Reasoning Structures in Discussions of Mathematics and Pedagogy
ERIC Educational Resources Information Center
Steele, Michael D.
2005-01-01
While teaching, teachers need to access both their knowledge of mathematics and knowledge of pedagogy. Practice-based materials afford teachers opportunities to reason about both mathematics and pedagogy within the context of teaching. Accepted systems exist for explaining and reasoning in the domain of mathematics; logic, procedures, and…
ERIC Educational Resources Information Center
Weber, Keith
2009-01-01
This paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
Knowledge representation in fuzzy logic
NASA Technical Reports Server (NTRS)
Zadeh, Lotfi A.
1989-01-01
The author presents a summary of the basic concepts and techniques underlying the application of fuzzy logic to knowledge representation. He then describes a number of examples relating to its use as a computational system for dealing with uncertainty and imprecision in the context of knowledge, meaning, and inference. It is noted that one of the basic aims of fuzzy logic is to provide a computational framework for knowledge representation and inference in an environment of uncertainty and imprecision. In such environments, fuzzy logic is effective when the solutions need not be precise and/or it is acceptable for a conclusion to have a dispositional rather than categorical validity. The importance of fuzzy logic derives from the fact that there are many real-world applications which fit these conditions, especially in the realm of knowledge-based systems for decision-making and control.
Fuzzy logic and neural networks
Loos, J.R.
1994-11-01
Combine fuzzy logic`s fuzzy sets, fuzzy operators, fuzzy inference, and fuzzy rules - like defuzzification - with neural networks and you can arrive at very unfuzzy real-time control. Fuzzy logic, cursed with a very whimsical title, simply means multivalued logic, which includes not only the conventional two-valued (true/false) crisp logic, but also the logic of three or more values. This means one can assign logic values of true, false, and somewhere in between. This is where fuzziness comes in. Multi-valued logic avoids the black-and-white, all-or-nothing assignment of true or false to an assertion. Instead, it permits the assignment of shades of gray. When assigning a value of true or false to an assertion, the numbers typically used are {open_quotes}1{close_quotes} or {open_quotes}0{close_quotes}. This is the case for programmed systems. If {open_quotes}0{close_quotes} means {open_quotes}false{close_quotes} and {open_quotes}1{close_quotes} means {open_quotes}true,{close_quotes} then {open_quotes}shades of gray{close_quotes} are any numbers between 0 and 1. Therefore, {open_quotes}nearly true{close_quotes} may be represented by 0.8 or 0.9, {open_quotes}nearly false{close_quotes} may be represented by 0.1 or 0.2, and {close_quotes}your guess is as good as mine{close_quotes} may be represented by 0.5. The flexibility available to one is limitless. One can associate any meaning, such as {open_quotes}nearly true{close_quotes}, to any value of any granularity, such as 0.9999. 2 figs.
Heat exchanger expert system logic
NASA Technical Reports Server (NTRS)
Cormier, R.
1988-01-01
The reduction is described of the operation and fault diagnostics of a Deep Space Network heat exchanger to a rule base by the application of propositional calculus to a set of logic statements. The value of this approach lies in the ease of converting the logic and subsequently implementing it on a computer as an expert system. The rule base was written in Process Intelligent Control software.
Optically controllable molecular logic circuits
NASA Astrophysics Data System (ADS)
Nishimura, Takahiro; Fujii, Ryo; Ogura, Yusuke; Tanida, Jun
2015-07-01
Molecular logic circuits represent a promising technology for observation and manipulation of biological systems at the molecular level. However, the implementation of molecular logic circuits for temporal and programmable operation remains challenging. In this paper, we demonstrate an optically controllable logic circuit that uses fluorescence resonance energy transfer (FRET) for signaling. The FRET-based signaling process is modulated by both molecular and optical inputs. Based on the distance dependence of FRET, the FRET pathways required to execute molecular logic operations are formed on a DNA nanostructure as a circuit based on its molecular inputs. In addition, the FRET pathways on the DNA nanostructure are controlled optically, using photoswitching fluorescent molecules to instruct the execution of the desired operation and the related timings. The behavior of the circuit can thus be controlled using external optical signals. As an example, a molecular logic circuit capable of executing two different logic operations was studied. The circuit contains functional DNAs and a DNA scaffold to construct two FRET routes for executing Input 1 AND Input 2 and Input 1 AND NOT Input 3 operations on molecular inputs. The circuit produced the correct outputs with all possible combinations of the inputs by following the light signals. Moreover, the operation execution timings were controlled based on light irradiation and the circuit responded to time-dependent inputs. The experimental results demonstrate that the circuit changes the output for the required operations following the input of temporal light signals.
Optically controllable molecular logic circuits
Nishimura, Takahiro Fujii, Ryo; Ogura, Yusuke; Tanida, Jun
2015-07-06
Molecular logic circuits represent a promising technology for observation and manipulation of biological systems at the molecular level. However, the implementation of molecular logic circuits for temporal and programmable operation remains challenging. In this paper, we demonstrate an optically controllable logic circuit that uses fluorescence resonance energy transfer (FRET) for signaling. The FRET-based signaling process is modulated by both molecular and optical inputs. Based on the distance dependence of FRET, the FRET pathways required to execute molecular logic operations are formed on a DNA nanostructure as a circuit based on its molecular inputs. In addition, the FRET pathways on the DNA nanostructure are controlled optically, using photoswitching fluorescent molecules to instruct the execution of the desired operation and the related timings. The behavior of the circuit can thus be controlled using external optical signals. As an example, a molecular logic circuit capable of executing two different logic operations was studied. The circuit contains functional DNAs and a DNA scaffold to construct two FRET routes for executing Input 1 AND Input 2 and Input 1 AND NOT Input 3 operations on molecular inputs. The circuit produced the correct outputs with all possible combinations of the inputs by following the light signals. Moreover, the operation execution timings were controlled based on light irradiation and the circuit responded to time-dependent inputs. The experimental results demonstrate that the circuit changes the output for the required operations following the input of temporal light signals.
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
Theorem Proving In Higher Order Logics
NASA Technical Reports Server (NTRS)
Carreno, Victor A. (Editor); Munoz, Cesar A.; Tahar, Sofiene
2002-01-01
The TPHOLs International Conference serves as a venue for the presentation of work in theorem proving in higher-order logics and related areas in deduction, formal specification, software and hardware verification, and other applications. Fourteen papers were submitted to Track B (Work in Progress), which are included in this volume. Authors of Track B papers gave short introductory talks that were followed by an open poster session. The FCM 2002 Workshop aimed to bring together researchers working on the formalisation of continuous mathematics in theorem proving systems with those needing such libraries for their applications. Many of the major higher order theorem proving systems now have a formalisation of the real numbers and various levels of real analysis support. This work is of interest in a number of application areas, such as formal methods development for hardware and software application and computer supported mathematics. The FCM 2002 consisted of three papers, presented by their authors at the workshop venue, and one invited talk.
Neural logic molecular, counter-intuitive.
Egorov, Igor K
2007-09-01
A hypothesis is proposed that multiple "LOGIC" genes control Boolean logic in a neuron. Each hypothetical LOGIC gene encodes a transcription factor that regulates another LOGIC gene(s). Through transcription regulation, LOGIC genes connect into a complex circuit, such as a XOR logic gate or a two-input flip-flop logic circuit capable of retaining information. LOGIC gene duplication, mutation and recombination may result in the diversification of Boolean logic gates. Creative thinking may sometimes require counter-intuitive reasoning, rather than common sense. Such reasoning is likely to engage novel logic circuits produced by LOGIC somatic mutations. An individual's logic maturates by a mechanism of somatic hypermutation, gene conversion and recombination of LOGIC genes in precursor cells followed by selection of neurons in the brain for functional competence. In this model, a single neuron among billions in the brain may contain a unique logic circuit being the key to a hard intellectual problem. The output of a logic neuron is likely to be a neurotransmitter. This neuron is connected to other neurons in the spiking neural network. The LOGIC gene hypothesis is testable by molecular techniques. Understanding mechanisms of authentic human ingenuity may help to invent digital systems capable of creative thinking. PMID:17509937
Application of linear logic to simulation
NASA Astrophysics Data System (ADS)
Clarke, Thomas L.
1998-08-01
Linear logic, since its introduction by Girard in 1987 has proven expressive and powerful. Linear logic has provided natural encodings of Turing machines, Petri nets and other computational models. Linear logic is also capable of naturally modeling resource dependent aspects of reasoning. The distinguishing characteristic of linear logic is that it accounts for resources; two instances of the same variable are considered differently from a single instance. Linear logic thus must obey a form of the linear superposition principle. A proportion can be reasoned with only once, unless a special operator is applied. Informally, linear logic distinguishes two kinds of conjunction, two kinds of disjunction, and also introduces a modal storage operator that explicitly indicates propositions that can be reused. This paper discuses the application of linear logic to simulation. A wide variety of logics have been developed; in addition to classical logic, there are fuzzy logics, affine logics, quantum logics, etc. All of these have found application in simulations of one sort or another. The special characteristics of linear logic and its benefits for simulation will be discussed. Of particular interest is a connection that can be made between linear logic and simulated dynamics by using the concept of Lie algebras and Lie groups. Lie groups provide the connection between the exponential modal storage operators of linear logic and the eigen functions of dynamic differential operators. Particularly suggestive are possible relations between complexity result for linear logic and non-computability results for dynamical systems.
Pass transistor implementations of multivalued logic
NASA Technical Reports Server (NTRS)
Maki, G.; Whitaker, S.
1990-01-01
A simple straight-forward Karnaugh map logic design procedure for realization of multiple-valued logic circuits is presented in this paper. Pass transistor logic gates are used to realize multiple-valued networks. This work is an extension of pass transistor implementations for binary-valued logic.
The reasonable effectiveness of mathematics in the natural sciences
NASA Astrophysics Data System (ADS)
Harvey, Alex
2011-12-01
Mathematics and its relation to the physical universe have been the topic of speculation since the days of Pythagoras. Several different views of the nature of mathematics have been considered: Realism—mathematics exists and is discovered; Logicism—all mathematics may be deduced through pure logic; Formalism—mathematics is just the manipulation of formulas and rules invented for the purpose; Intuitionism—mathematics comprises mental constructs governed by self evident rules. The debate among the several schools has major importance in understanding what Eugene Wigner called, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. In return, this `Unreasonable Effectiveness' suggests a possible resolution of the debate in favor of Realism. The crucial element is the extraordinary predictive capacity of mathematical structures descriptive of physical theories.
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Mathematical algorithms for approximate reasoning
NASA Technical Reports Server (NTRS)
Murphy, John H.; Chay, Seung C.; Downs, Mary M.
1988-01-01
Most state of the art expert system environments contain a single and often ad hoc strategy for approximate reasoning. Some environments provide facilities to program the approximate reasoning algorithms. However, the next generation of expert systems should have an environment which contain a choice of several mathematical algorithms for approximate reasoning. To meet the need for validatable and verifiable coding, the expert system environment must no longer depend upon ad hoc reasoning techniques but instead must include mathematically rigorous techniques for approximate reasoning. Popular approximate reasoning techniques are reviewed, including: certainty factors, belief measures, Bayesian probabilities, fuzzy logic, and Shafer-Dempster techniques for reasoning. A group of mathematically rigorous algorithms for approximate reasoning are focused on that could form the basis of a next generation expert system environment. These algorithms are based upon the axioms of set theory and probability theory. To separate these algorithms for approximate reasoning various conditions of mutual exclusivity and independence are imposed upon the assertions. Approximate reasoning algorithms presented include: reasoning with statistically independent assertions, reasoning with mutually exclusive assertions, reasoning with assertions that exhibit minimum overlay within the state space, reasoning with assertions that exhibit maximum overlay within the state space (i.e. fuzzy logic), pessimistic reasoning (i.e. worst case analysis), optimistic reasoning (i.e. best case analysis), and reasoning with assertions with absolutely no knowledge of the possible dependency among the assertions. A robust environment for expert system construction should include the two modes of inference: modus ponens and modus tollens. Modus ponens inference is based upon reasoning towards the conclusion in a statement of logical implication, whereas modus tollens inference is based upon reasoning away
Fuzzy logic of Aristotelian forms
Perlovsky, L.I.
1996-12-31
Model-based approaches to pattern recognition and machine vision have been proposed to overcome the exorbitant training requirements of earlier computational paradigms. However, uncertainties in data were found to lead to a combinatorial explosion of the computational complexity. This issue is related here to the roles of a priori knowledge vs. adaptive learning. What is the a-priori knowledge representation that supports learning? I introduce Modeling Field Theory (MFT), a model-based neural network whose adaptive learning is based on a priori models. These models combine deterministic, fuzzy, and statistical aspects to account for a priori knowledge, its fuzzy nature, and data uncertainties. In the process of learning, a priori fuzzy concepts converge to crisp or probabilistic concepts. The MFT is a convergent dynamical system of only linear computational complexity. Fuzzy logic turns out to be essential for reducing the combinatorial complexity to linear one. I will discuss the relationship of the new computational paradigm to two theories due to Aristotle: theory of Forms and logic. While theory of Forms argued that the mind cannot be based on ready-made a priori concepts, Aristotelian logic operated with just such concepts. I discuss an interpretation of MFT suggesting that its fuzzy logic, combining a-priority and adaptivity, implements Aristotelian theory of Forms (theory of mind). Thus, 2300 years after Aristotle, a logic is developed suitable for his theory of mind.
Fuzzy logic control of the building structure with CLEMR dampers
NASA Astrophysics Data System (ADS)
Zhang, Xiang-Cheng; Xu, Zhao-Dong; Huang, Xing-Huai; Zhu, Jun-Tao
2013-04-01
The semi-active control technology has been paid more attention in the field of structural vibration control due to its high controllability, excellent control effect and low power requirement. When semi-active control device are used for vibration control, some challenges must be taken into account, such as the reliability and the control strategy of the device. This study presents a new large tonnage compound lead extrusion magnetorheological (CLEMR) damper, whose mathematical model is introduced to describe the variation of damping force with current and velocity. Then a current controller based on the fuzzy logic control strategy is designed to determine control currents of the CLEMR dampers rapidly. A ten-floor frame structure with CLEMR dampers using the fuzzy logic control strategy is built and calculated by using MATLAB. Calculation results show that CLEMR dampers can reduce the seismic responses of structures effectively. Calculation results of the fuzzy logic control strategy are compared with those of the semi-active limit Hrovat control structure, the passive-off control structure, and the uncontrolled structure. Comparison results show that the fuzzy logic control strategy can determine control currents of CLEMR dampers quickly and can reduce seismic responses of the structures more effectively than the passive-off control strategy and the uncontrolled structure.
Fuzzy logic particle tracking velocimetry
NASA Technical Reports Server (NTRS)
Wernet, Mark P.
1993-01-01
Fuzzy logic has proven to be a simple and robust method for process control. Instead of requiring a complex model of the system, a user defined rule base is used to control the process. In this paper the principles of fuzzy logic control are applied to Particle Tracking Velocimetry (PTV). Two frames of digitally recorded, single exposure particle imagery are used as input. The fuzzy processor uses the local particle displacement information to determine the correct particle tracks. Fuzzy PTV is an improvement over traditional PTV techniques which typically require a sequence (greater than 2) of image frames for accurately tracking particles. The fuzzy processor executes in software on a PC without the use of specialized array or fuzzy logic processors. A pair of sample input images with roughly 300 particle images each, results in more than 200 velocity vectors in under 8 seconds of processing time.
Intersecting Adjectives in Syllogistic Logic
NASA Astrophysics Data System (ADS)
Moss, Lawrence S.
The goal of natural logic is to present and study logical systems for reasoning with sentences of (or which are reasonably close to) ordinary language. This paper explores simple systems of natural logic which make use of intersecting adjectives; these are adjectives whose interpretation does not vary with the noun they modify. Our project in this paper is to take one of the simplest syllogistic fragments, that of all and some, and to add intersecting adjectives. There are two ways to do this, depending on whether one allows iteration or prefers a "flat" structure of at most one adjective. We present rules of inference for both types of syntax, and these differ. The main results are four completeness theorems: for each of the two types of syntax we have completeness for the all fragment and for the full language of this paper.
Reversible logic gate using adiabatic superconducting devices
Takeuchi, N.; Yamanashi, Y.; Yoshikawa, N.
2014-01-01
Reversible computing has been studied since Rolf Landauer advanced the argument that has come to be known as Landauer's principle. This principle states that there is no minimum energy dissipation for logic operations in reversible computing, because it is not accompanied by reductions in information entropy. However, until now, no practical reversible logic gates have been demonstrated. One of the problems is that reversible logic gates must be built by using extremely energy-efficient logic devices. Another difficulty is that reversible logic gates must be both logically and physically reversible. Here we propose the first practical reversible logic gate using adiabatic superconducting devices and experimentally demonstrate the logical and physical reversibility of the gate. Additionally, we estimate the energy dissipation of the gate, and discuss the minimum energy dissipation required for reversible logic operations. It is expected that the results of this study will enable reversible computing to move from the theoretical stage into practical usage. PMID:25220698
MD-Logic Artificial Pancreas System
Atlas, Eran; Nimri, Revital; Miller, Shahar; Grunberg, Eli A.; Phillip, Moshe
2010-01-01
OBJECTIVE Current state-of-the-art artificial pancreas systems are either based on traditional linear control theory or rely on mathematical models of glucose-insulin dynamics. Blood glucose control using these methods is limited due to the complexity of the biological system. The aim of this study was to describe the principles and clinical performance of the novel MD-Logic Artificial Pancreas (MDLAP) System. RESEARCH DESIGN AND METHODS The MDLAP applies fuzzy logic theory to imitate lines of reasoning of diabetes caregivers. It uses a combination of control-to-range and control-to-target strategies to automatically regulate individual glucose levels. Feasibility clinical studies were conducted in seven adults with type 1 diabetes (aged 19–30 years, mean diabetes duration 10 ± 4 years, mean A1C 6.6 ± 0.7%). All underwent 14 full, closed-loop control sessions of 8 h (fasting and meal challenge conditions) and 24 h. RESULTS The mean peak postprandial (overall sessions) glucose level was 224 ± 22 mg/dl. Postprandial glucose levels returned to <180 mg/dl within 2.6 ± 0.6 h and remained stable in the normal range for at least 1 h. During 24-h closed-loop control, 73% of the sensor values ranged between 70 and 180 mg/dl, 27% were >180 mg/dl, and none were <70 mg/dl. There were no events of symptomatic hypoglycemia during any of the trials. CONCLUSIONS The MDLAP system is a promising tool for individualized glucose control in patients with type 1 diabetes. It is designed to minimize high glucose peaks while preventing hypoglycemia. Further studies are planned in the broad population under daily-life conditions. PMID:20150292
High-speed, cascaded optical logic operations using programmable optical logic gate arrays
Lu, B.; Lu, Y.C.; Cheng, J.; Hafich, M.J.; Klem, J.; Zolper, J.C.
1996-01-01
Programmable optical logic operations are demonstrated using arrays of nonlatching binary optical switches consisting of vertical-cavity surface-emitting lasers, p-i-n photodetectors and heterojunction bipolar transistors. Individual arrays can perform Boolean optical logic functions at 100 Mb/s using both optical and electrical logic inputs, while the routing and fan-out of the optical logic outputs can be controlled at the gate level. Cascaded optical logic operation is demonstrated using two programmable logic gate arrays.
NASA Technical Reports Server (NTRS)
Ruspini, Enrique H.
1991-01-01
Summarized here are the results of recent research on the conceptual foundations of fuzzy logic. The focus is primarily on the principle characteristics of a model that quantifies resemblance between possible worlds by means of a similarity function that assigns a number between 0 and 1 to every pair of possible worlds. Introduction of such a function permits one to interpret the major constructs and methods of fuzzy logic: conditional and unconditional possibility and necessity distributions and the generalized modus ponens of Zadeh on the basis of related metric relationships between subsets of possible worlds.
A Logical Approach to Entanglement
NASA Astrophysics Data System (ADS)
Das, Abhishek
2016-05-01
In this paper we innovate a logical approach to develop an intuition regarding the phenomenon of quantum entanglement. In the vein of the logic introduced we substantiate that particles that were entangled in the past will be entangled in perpetuity and thereby abide a rule that restricts them to act otherwise. We also introduce a game and by virtue of the concept of Nash equilibrium we have been able to show that entangled particles will mutually correspond to an experiment that is performed on any one of the particle.
Logic programming and metadata specifications
NASA Technical Reports Server (NTRS)
Lopez, Antonio M., Jr.; Saacks, Marguerite E.
1992-01-01
Artificial intelligence (AI) ideas and techniques are critical to the development of intelligent information systems that will be used to collect, manipulate, and retrieve the vast amounts of space data produced by 'Missions to Planet Earth.' Natural language processing, inference, and expert systems are at the core of this space application of AI. This paper presents logic programming as an AI tool that can support inference (the ability to draw conclusions from a set of complicated and interrelated facts). It reports on the use of logic programming in the study of metadata specifications for a small problem domain of airborne sensors, and the dataset characteristics and pointers that are needed for data access.
Quantum Decoherence: A Logical Perspective
NASA Astrophysics Data System (ADS)
Fortin, Sebastian; Vanni, Leonardo
2014-12-01
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have presented the possibility of studying the classical limit in terms of the decoherence of relevant observables of the system. On the basis of this approach, in this paper we introduce the classical limit from a logical perspective, by studying the way in which the logical structure of quantum properties corresponding to relevant observables acquires Boolean characteristics.
An Objectivist Critique of Relativism in Mathematics Education
NASA Astrophysics Data System (ADS)
Rowlands, Stuart; Graham, Ted; Berry, John
Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
Lapointe, Archie E.; And Others
In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
Proof and Proving: Logic, Impasses, and the Relationship to Problem Solving
ERIC Educational Resources Information Center
Savic, Milos
2012-01-01
Becoming a skillful prover is critical for success in advanced undergraduate and graduate mathematics courses. In this dissertation, I report my investigations of proof and the proving process in three separate studies. In the first study, I examined the amount of logic used in student-constructed proofs to help in the design of…
Test Equating Procedures: A Primer on the Logic and Applications of Test Equating.
ERIC Educational Resources Information Center
Buras, Avery
The logic and uses of test equating are discussed, including three methods of test equating. The focus is on the conceptual underpinnings of each test equating method, rather than on the mathematics of the procedures. Additional consideration is given to the assumptions of each method and its respective strengths and weaknesses. A commonly…
Computer-Assisted Instruction in Elementary Logic at the University Level. Technical Report No. 239.
ERIC Educational Resources Information Center
Goldberg, Adele; Suppes, Patrick
Earlier research by the authors in the design and use of computer-assisted instructional systems and curricula for teaching mathematical logic to gifted elementary school students has been extended to the teaching of university-level courses. This report is a description of the curriculum and problem types of a computer-based course offered at…
Fuzzy logic controller for the electric motor driving the astronomical telescope
NASA Astrophysics Data System (ADS)
Soliman, Hussein F.; Attia, Abdel-Fattah A.; Badr, Mohammed A.; Osman, Anas M.; Gamaleldin, Abdul A.
1998-05-01
The paper presents an application of fuzzy logic controller to regulate the DC motor driver system of astronomical telescope. The mathematical model of such a telescope is highly nonlinear coupled equations. However, the accuracy requirement in telescope system exceed those of other industrial plants. Fuzzy logic controller provides means to deal with nonlinear functions. A fuzzy logic controller (FLC) was designed to enhance the performance of a two-link model of astronomical telescope. The proposed FLC utilizes the position deviation for the desired value, and its rate of change to regulate the armature voltage of the DC motor drive of each link. The final action of FLC is equivalent to PD controller with a variable gain by using an expert look- up table. This work presents the derivation of the mathematical model of 14 inch Celestron telescope and computer simulation of its motion. The FLC contains two groups of fuzzy sets.
Miniaturization of magnetic logic circuitry
NASA Technical Reports Server (NTRS)
Baba, P. D.
1969-01-01
Magnetic logic circuit design features two ferrite materials, with different formulation and magnetic characteristics, which are bonded into a continuous structure by preparing the materials as a slurry and using the doctor blade method to form flexible ferrite sheets. After firing, the sintering process was continuous across the bond.
Energy Science and Technology Software Center (ESTSC)
2011-05-07
Current mode logic is used in high speed timing systems for particle accelerators due to the fast rise time of the electrical signal. This software provides the necessary documentation to produce multiple copies of a single input for distribution to multiple devices. This software supports the DOE mission by providing a method for producing high speed signals in accelerator timing systems.
Logical Empiricism, Politics, and Professionalism
ERIC Educational Resources Information Center
Edgar, Scott
2009-01-01
This paper considers George A. Reisch's account of the role of Cold War political forces in shaping the apolitical stance that came to dominate philosophy of science in the late 1940s and 1950s. It argues that at least as early as the 1930s, Logical Empiricists such as Rudolf Carnap already held that philosophy of science could not properly have…
Boggle Logic Puzzles: Minimal Solutions
ERIC Educational Resources Information Center
Needleman, Jonathan
2013-01-01
Boggle logic puzzles are based on the popular word game Boggle played backwards. Given a list of words, the problem is to recreate the board. We explore these puzzles on a 3 x 3 board and find the minimum number of three-letter words needed to create a puzzle with a unique solution. We conclude with a series of open questions.
Program Theory Evaluation: Logic Analysis
ERIC Educational Resources Information Center
Brousselle, Astrid; Champagne, Francois
2011-01-01
Program theory evaluation, which has grown in use over the past 10 years, assesses whether a program is designed in such a way that it can achieve its intended outcomes. This article describes a particular type of program theory evaluation--logic analysis--that allows us to test the plausibility of a program's theory using scientific knowledge.…
Gateways to Writing Logical Arguments
ERIC Educational Resources Information Center
McCann, Thomas M.
2010-01-01
Middle school and high school students have a conception of what the basic demands of logic are, and they draw on this understanding in anticipating certain demands of parents and teachers when the adolescents have to defend positions. At the same time, many adolescents struggle to "write" highly elaborated arguments. Teaching students lessons in…
The Temporal Logic Model Concept.
ERIC Educational Resources Information Center
den Heyer, Molly
2002-01-01
Proposes an alternative program logic model based on the concepts of learning organizations and systems theory. By redefining time as an evolutionary process, the model provides a space for stakeholders to record changes in program context, interim assessments, and program modifications. (SLD)
Generic physical protection logic trees
Paulus, W.K.
1981-10-01
Generic physical protection logic trees, designed for application to nuclear facilities and materials, are presented together with a method of qualitative evaluation of the trees for design and analysis of physical protection systems. One or more defense zones are defined where adversaries interact with the physical protection system. Logic trees that are needed to describe the possible scenarios within a defense zone are selected. Elements of a postulated or existing physical protection system are tagged to the primary events of the logic tree. The likelihood of adversary success in overcoming these elements is evaluated on a binary, yes/no basis. The effect of these evaluations is propagated through the logic of each tree to determine whether the adversary is likely to accomplish the end event of the tree. The physical protection system must be highly likely to overcome the adversary before he accomplishes his objective. The evaluation must be conducted for all significant states of the site. Deficiencies uncovered become inputs to redesign and further analysis, closing the loop on the design/analysis cycle.
Implementing Exclusive-OR Logic
NASA Technical Reports Server (NTRS)
Hough, M. E.
1983-01-01
Two integrated circuits, BCD-to-decimal decoder and four-input NAND gate, form basic four, input XOR circuit. Multiple-input exclusive-OR logic is implemented by combining several basic elements. 16-input XOR gate is assembled from five NAND gates and five decoders. Same principle extended to handle more inputs.
Coreflections in Algebraic Quantum Logic
NASA Astrophysics Data System (ADS)
Jacobs, Bart; Mandemaker, Jorik
2012-07-01
Various generalizations of Boolean algebras are being studied in algebraic quantum logic, including orthomodular lattices, orthomodular po-sets, orthoalgebras and effect algebras. This paper contains a systematic study of the structure in and between categories of such algebras. It does so via a combination of totalization (of partially defined operations) and transfer of structure via coreflections.
The Logic of Research Evaluation
ERIC Educational Resources Information Center
Scriven, Michael; Coryn, Chris L. S.
2008-01-01
The authors offer suggestions about logical distinctions often overlooked in the evaluation of research, beginning with a strong plea not to treat technology as applied science, and especially not to treat research in technology as important only if it makes a contribution to scientific knowledge. They argue that the frameworks illustrated in this…
Soft computing and fuzzy logic
Zadeh, L.A.
1994-12-31
Soft computing is a collection of methodologies that aim to exploit the tolerance for imprecision and uncertainty to achieve tractability, robustness, and low solution cost. Its principal constituents are fuzzy logic, neuro-computing, and probabilistic reasoning. Soft computing is likely to play an increasingly important role in many application areas, including software engineering. The role model for soft computing is the human mind.
Cooperative development of logical modelling standards and tools with CoLoMoTo.
Naldi, Aurélien; Monteiro, Pedro T; Müssel, Christoph; Kestler, Hans A; Thieffry, Denis; Xenarios, Ioannis; Saez-Rodriguez, Julio; Helikar, Tomas; Chaouiya, Claudine
2015-04-01
The identification of large regulatory and signalling networks involved in the control of crucial cellular processes calls for proper modelling approaches. Indeed, models can help elucidate properties of these networks, understand their behaviour and provide (testable) predictions by performing in silico experiments. In this context, qualitative, logical frameworks have emerged as relevant approaches, as demonstrated by a growing number of published models, along with new methodologies and software tools. This productive activity now requires a concerted effort to ensure model reusability and interoperability between tools. Following an outline of the logical modelling framework, we present the most important achievements of the Consortium for Logical Models and Tools, along with future objectives. Our aim is to advertise this open community, which welcomes contributions from all researchers interested in logical modelling or in related mathematical and computational developments. PMID:25619997
Learning fuzzy logic control system
NASA Technical Reports Server (NTRS)
Lung, Leung Kam
1994-01-01
The performance of the Learning Fuzzy Logic Control System (LFLCS), developed in this thesis, has been evaluated. The Learning Fuzzy Logic Controller (LFLC) learns to control the motor by learning the set of teaching values that are generated by a classical PI controller. It is assumed that the classical PI controller is tuned to minimize the error of a position control system of the D.C. motor. The Learning Fuzzy Logic Controller developed in this thesis is a multi-input single-output network. Training of the Learning Fuzzy Logic Controller is implemented off-line. Upon completion of the training process (using Supervised Learning, and Unsupervised Learning), the LFLC replaces the classical PI controller. In this thesis, a closed loop position control system of a D.C. motor using the LFLC is implemented. The primary focus is on the learning capabilities of the Learning Fuzzy Logic Controller. The learning includes symbolic representation of the Input Linguistic Nodes set and Output Linguistic Notes set. In addition, we investigate the knowledge-based representation for the network. As part of the design process, we implement a digital computer simulation of the LFLCS. The computer simulation program is written in 'C' computer language, and it is implemented in DOS platform. The LFLCS, designed in this thesis, has been developed on a IBM compatible 486-DX2 66 computer. First, the performance of the Learning Fuzzy Logic Controller is evaluated by comparing the angular shaft position of the D.C. motor controlled by a conventional PI controller and that controlled by the LFLC. Second, the symbolic representation of the LFLC and the knowledge-based representation for the network are investigated by observing the parameters of the Fuzzy Logic membership functions and the links at each layer of the LFLC. While there are some limitations of application with this approach, the result of the simulation shows that the LFLC is able to control the angular shaft position of the
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
Quantitative and logic modelling of gene and molecular networks
Le Novère, Nicolas
2015-01-01
Behaviours of complex biomolecular systems are often irreducible to the elementary properties of their individual components. Explanatory and predictive mathematical models are therefore useful for fully understanding and precisely engineering cellular functions. The development and analyses of these models require their adaptation to the problems that need to be solved and the type and amount of available genetic or molecular data. Quantitative and logic modelling are among the main methods currently used to model molecular and gene networks. Each approach comes with inherent advantages and weaknesses. Recent developments show that hybrid approaches will become essential for further progress in synthetic biology and in the development of virtual organisms. PMID:25645874
SASIL. Sandia ATM SONET Interface Logic
Kitta, J.P.
1994-07-01
SASIL is used to program the EPLD`s (Erasable Programmable Logic Devices) and PAL`s (Programmable Array Logic) that make up a large percentage of the Sandia ATM SONET Interface (OC3 version) for the INTEL Paragon.
Quantum Logics of Idempotents of Unital Rings
NASA Astrophysics Data System (ADS)
Bikchentaev, Airat; Navara, Mirko; Yakushev, Rinat
2015-06-01
We introduce some new examples of quantum logics of idempotents in a ring. We continue the study of symmetric logics, i.e., collections of subsets generalizing Boolean algebras and closed under the symmetric difference.
Computerized logic design of digital circuits
NASA Technical Reports Server (NTRS)
Sussow, S.; Oglesby, R.
1973-01-01
This manual presents a computer program that performs all the work required for the logic design of digital counters or sequential circuits and the simplification of Boolean logic expressions. The program provides both the experienced and inexperienced logic designer with a comprehensive logic design capability. The manual contains Boolean simplification and sequential design theory, detailed instructions for use of the program, a large number of illustrative design examples, and complete program documentation.
Circulating Packet Threshold Logic To Implement Msd Logic Modules
NASA Astrophysics Data System (ADS)
Flannery, David L.; Vail, L. Maugh; Gustafson, Steven C.
1986-03-01
Threshold logic element designs in circulating packet form are presented for the implementation of addition and subtraction using modified sign digit (MSD) arithmetic. This arithmetic is attractive for digital optical computing due to its inherent parallelism and pipelining characteristics, which capitalize on natural strengths of optics. To illustrate application of these concepts, a design for CORDIC rotation modules to accomplish the complex Givens rotations required for systolic array QU matrix factorization is presented. This design accomplishes QU factorization using only threshold logic elements and bit-shift operations in a systolic configuration. Although implementable in principle by either electronic or optical means, the design is amenable to optical implementation because it involves high levels of parallelism and interconnections.
Piaget's Logic of Meanings: Still Relevant Today
ERIC Educational Resources Information Center
Wavering, Michael James
2011-01-01
In his last book, "Toward a Logic of Meanings" (Piaget & Garcia, 1991), Jean Piaget describes how thought can be categorized into a form of propositional logic, a logic of meanings. The intent of this article is to offer this analysis by Piaget as a means to understand the language and teaching of science. Using binary propositions, conjunctions,…
Applications of Logic Coverage Criteria and Logic Mutation to Software Testing
ERIC Educational Resources Information Center
Kaminski, Garrett K.
2011-01-01
Logic is an important component of software. Thus, software logic testing has enjoyed significant research over a period of decades, with renewed interest in the last several years. One approach to detecting logic faults is to create and execute tests that satisfy logic coverage criteria. Another approach to detecting faults is to perform mutation…
Noisy signaling through promoter logic gates
NASA Astrophysics Data System (ADS)
Gerstung, Moritz; Timmer, Jens; Fleck, Christian
2009-01-01
We study the influence of noisy transcription factor signals on cis-regulatory promoter elements. These elements process the probability of binary binding events analogous to computer logic gates. At equilibrium, this probability is given by the so-called input function. We show that transcription factor noise causes deviations from the equilibrium value due to the nonlinearity of the input function. For a single binding site, the correction is always negative resulting in an occupancy below the mean-field level. Yet for more complex promoters it depends on the correlation of the transcription factor signals and the geometry of the input function. We present explicit solutions for the basic types of AND and OR gates. The correction size varies among these different types of gates and signal types, mainly being larger in AND gates and for correlated fluctuations. In all cases we find excellent agreement between the analytical results and numerical simulations. We also study the E. coli Lac operon as an example of an AND NOR gate. We present a consistent mathematical method that allows one to separate different sources of noise and quantifies their effect on promoter occupation. A surprising result of our analysis is that Poissonian molecular fluctuations, in contrast to external fluctuations, do no contribute to the correction.
Optimized parameter extraction using fuzzy logic
NASA Astrophysics Data System (ADS)
Picos, Rodrigo; Calvo, Oscar; Iñiguez, Benjamín; García-Moreno, Eugeni; García, Rodolfo; Estrada, Magali
2007-05-01
Precise extraction of transistor model parameters is of much importance for modeling and at the same time a difficult and time consuming task. Methods for parameter extraction can rely on purely mathematical basis, calling for intensive use of computational resources, or in human expertise to interpret results. In this work, we propose a method for parameter extraction based on fuzzy logic that includes a precise knowledge about the function of each parameter in the model to create a set of simple fitting rules that are easy to describe in human language. To simplify the computational effort, the parameter fitting rules work using only data at specific points (e.g. the distance between the calculated curve and the measured one at VDS corresponding to 50% of the maximum current). If necessary, a more accurate implementation can be used without altering the basic underlying philosophy of the method. In this work, the method is applied to extract model parameters required by Level 3 bulk MOS model and by a compact model for TFTs used in the Unified Model and Extraction Method (UMEM), which is based on an integral function. Results obtained show that the method is quite insensitive to the initial conditions and that it is also quite fast. Extension of this method for more complex models requires only the creation of the corresponding rule base, using the appropriate measurements. The method is especially useful for production testing or design.
Fuzzy Versions of Epistemic and Deontic Logic
NASA Technical Reports Server (NTRS)
Gounder, Ramasamy S.; Esterline, Albert C.
1998-01-01
Epistemic and deontic logics are modal logics, respectively, of knowledge and of the normative concepts of obligation, permission, and prohibition. Epistemic logic is useful in formalizing systems of communicating processes and knowledge and belief in AI (Artificial Intelligence). Deontic logic is useful in computer science wherever we must distinguish between actual and ideal behavior, as in fault tolerance and database integrity constraints. We here discuss fuzzy versions of these logics. In the crisp versions, various axioms correspond to various properties of the structures used in defining the semantics of the logics. Thus, any axiomatic theory will be characterized not only by its axioms but also by the set of properties holding of the corresponding semantic structures. Fuzzy logic does not proceed with axiomatic systems, but fuzzy versions of the semantic properties exist and can be shown to correspond to some of the axioms for the crisp systems in special ways that support dependency networks among assertions in a modal domain. This in turn allows one to implement truth maintenance systems. For the technical development of epistemic logic, and for that of deontic logic. To our knowledge, we are the first to address fuzzy epistemic and fuzzy deontic logic explicitly and to consider the different systems and semantic properties available. We give the syntax and semantics of epistemic logic and discuss the correspondence between axioms of epistemic logic and properties of semantic structures. The same topics are covered for deontic logic. Fuzzy epistemic and fuzzy deontic logic discusses the relationship between axioms and semantic properties for these logics. Our results can be exploited in truth maintenance systems.
An Embedded Reconfigurable Logic Module
NASA Technical Reports Server (NTRS)
Tucker, Jerry H.; Klenke, Robert H.; Shams, Qamar A. (Technical Monitor)
2002-01-01
A Miniature Embedded Reconfigurable Computer and Logic (MERCAL) module has been developed and verified. MERCAL was designed to be a general-purpose, universal module that that can provide significant hardware and software resources to meet the requirements of many of today's complex embedded applications. This is accomplished in the MERCAL module by combining a sub credit card size PC in a DIMM form factor with a XILINX Spartan I1 FPGA. The PC has the ability to download program files to the FPGA to configure it for different hardware functions and to transfer data to and from the FPGA via the PC's ISA bus during run time. The MERCAL module combines, in a compact package, the computational power of a 133 MHz PC with up to 150,000 gate equivalents of digital logic that can be reconfigured by software. The general architecture and functionality of the MERCAL hardware and system software are described.
Nanowire NMOS Logic Inverter Characterization.
Hashim, Yasir
2016-06-01
This study is the first to demonstrate characteristics optimization of nanowire N-Channel Metal Oxide Semiconductor (NW-MOS) logic inverter. Noise margins and inflection voltage of transfer characteristics are used as limiting factors in this optimization. A computer-based model used to produce static characteristics of NW-NMOS logic inverter. In this research two circuit configuration of NW-NMOS inverter was studied, in first NW-NMOS circuit, the noise margin for (low input-high output) condition was very low. For second NMOS circuit gives excellent noise margins, and results indicate that optimization depends on applied voltage to the inverter. Increasing gate to source voltage with (2/1) nanowires ratio results better noise margins. Increasing of applied DC load transistor voltage tends to increasing in decreasing noise margins; decreasing this voltage will improve noise margins significantly. PMID:27427653
The Logic Behind Feynman's Paths
NASA Astrophysics Data System (ADS)
García Álvarez, Edgardo T.
The classical notions of continuity and mechanical causality are left in order to reformulate the Quantum Theory starting from two principles: (I) the intrinsic randomness of quantum process at microphysical level, (II) the projective representations of symmetries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random and discontinuous events. So the theory is reduced to determining the probability distribution for such histories accordingly with the symmetries of the system. The representation of the logic in terms of amplitudes leads to Feynman rules and, alternatively, its representation in terms of projectors results in the Schwinger trace formula.
All-optical symmetric ternary logic gate
NASA Astrophysics Data System (ADS)
Chattopadhyay, Tanay
2010-09-01
Symmetric ternary number (radix=3) has three logical states (1¯, 0, 1). It is very much useful in carry free arithmetical operation. Beside this, the logical operation using this type of number system is also effective in high speed computation and communication in multi-valued logic. In this literature all-optical circuits for three basic symmetrical ternary logical operations (inversion, MIN and MAX) are proposed and described. Numerical simulation verifies the theoretical model. In this present scheme the different ternary logical states are represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch has been used categorically in this manuscript.
Logic and structured design for computer programmers
Rood, H.J.
1985-01-01
This text provides a language- and system-independent introduction to logical structures, and teaches logic plus the programming and data processing applications in which logic is used. The author has eliminated the need to cover basic program design at the beginning of every language course, and has used logic of sets, Boolean algebra, conditional statements, and truth tables to establish logic of structure flowchart, pseudocode, Warnier/Orr diagrams, and so on. After chapter three, the chapters are independent so that instructors can select the coverage of programming tools and techniques most relevant to their students.
Cosmic logic: a computational model
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-02-01
We initiate a formal study of logical inferences in context of the measure problem in cosmology or what we call cosmic logic. We describe a simple computational model of cosmic logic suitable for analysis of, for example, discretized cosmological systems. The construction is based on a particular model of computation, developed by Alan Turing, with cosmic observers (CO), cosmic measures (CM) and cosmic symmetries (CS) described by Turing machines. CO machines always start with a blank tape and CM machines take CO's Turing number (also known as description number or Gödel number) as input and output the corresponding probability. Similarly, CS machines take CO's Turing number as input, but output either one if the CO machines are in the same equivalence class or zero otherwise. We argue that CS machines are more fundamental than CM machines and, thus, should be used as building blocks in constructing CM machines. We prove the non-computability of a CS machine which discriminates between two classes of CO machines: mortal that halts in finite time and immortal that runs forever. In context of eternal inflation this result implies that it is impossible to construct CM machines to compute probabilities on the set of all CO machines using cut-off prescriptions. The cut-off measures can still be used if the set is reduced to include only machines which halt after a finite and predetermined number of steps.
Teaching Mathematical Modeling in Mathematics Education
ERIC Educational Resources Information Center
Saxena, Ritu; Shrivastava, Keerty; Bhardwaj, Ramakant
2016-01-01
Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…
Edwards, A W F
2011-03-01
Ernst Mayr called the first part of the evolutionary synthesis the 'Fisherian synthesis' on account of the dominant role played by R.A. Fisher in forging a mathematical theory of natural selection together with J.B.S. Haldane and Sewall Wright in the decade 1922-1932. It is here argued that Fisher's contribution relied on a close reading of Darwin's work to a much greater extent than did the contributions of Haldane and Wright, that it was synthetic in contrast to their analytic approach and that it was greatly influenced by his friendship with the Darwin family, particularly with Charles's son Leonard. PMID:21423339
Qualitative information modeling: The role of fuzzy logic in project economic evaluations
Warnken, P.G.
1995-12-31
Conventional models rely on a precise mathematical formalism to express the quantitative essentials of the system being modeled. In contrast, decisionmakers in the real world employ cognitive skills to process information and arrive at decisions based on judgement and experience. Bridging the gap between the two analytic approaches -- that is, formulating intelligent models -- has met with very limited success using traditional computational methods. The difficulty stems from two problems. First, imprecision, which is the distinguishing feature of qualitative factors, is an information attribute that is not easily computable using the rules of traditional set theory and Boolean (bivalent) logic. Second, cognitive information processing is cumbersome using the numerical rule-based approaches common in today`s expert systems. Fuzzy models overcome these problems by employing new mathematical rules for expressing and processing knowledge. These rules are based on fuzzy logic. Fuzzy logic is the formal symbolic language used to represent linguistic terms and verbal rules for computational and modeling purposes. This language provides model builders with the means to incorporate subjective judgements, imprecise information, and human reasoning capabilities as part of a model`s framework. This paper outlines the concepts needed to understand fuzzy modeling systems. The key concepts discussed include fuzzy sets, fuzzy logical operators, linguistic variables, and verbal rules. A simple fuzzy economic rating model for project investments is presented to demonstrate the fuzzy modeling technique. Finally, the paper discusses the role of fuzzy logic in the economic modeling process.
The principle of least action as the logical empiricist's Shibboleth
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
The present paper investigates why logical empiricists remained silent about one of the most philosophy-laden matters of theoretical physics of their day, the principle of least action (PLA). In the two decades around 1900, the PLA enjoyed a remarkable renaissance as a formal unification of mechanics, electrodynamics, thermodynamics, and relativity theory. Taking Ernst Mach's historico-critical stance, it could be liberated from much of its physico-theological dross. Variational calculus, the mathematical discipline on which the PLA was based, obtained a new rigorous basis. These three developments prompted Max Planck to consider the PLA as formal embodiment of his convergent realist methodology. Typically rejecting ontological reductionism, David Hilbert took the PLA as the key concept in his axiomatizations of physical theories. It served one of the main goals of the axiomatic method: "deepening the foundations." Although Moritz Schlick was a student of Planck's, and Hans Hahn and Philipp Frank enjoyed close ties to Göttingen, the PLA became a veritable Shibboleth to them. Rather than being worried by its historical connections with teleology and determinism, they erroneously identified Hilbert's axiomatic method tout court with Planck's metaphysical realism. Logical empiricists' strict containment policy against metaphysics required so strict a separation between physics and mathematics to exclude even those features of the PLA and the axiomatic method not tainted with metaphysics.
NASA Astrophysics Data System (ADS)
Kalanov, Temur Z.
2015-04-01
Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.
Explaining Definitions in Secondary School Mathematics: A[superscript 0], A[superscript n], 0!
ERIC Educational Resources Information Center
Guan, Tay Eng; Hoong, Leong Yew
2012-01-01
Educators look for "teaching opportunities" within the curriculum to "bring the practice of knowing mathematics in school closer to what it means to know within the discipline". The need to emphasise disciplinarity--and the concomitant canons of logic, consistency, and connections--in the teaching of mathematics is in line with the proficiency…
Mixed Methods Study Using Constructive Learning Team Model for Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Ritter, Kristy L.
2010-01-01
The constructive learning team model for secondary mathematics teachers (CLTM) was created to provide students with learning opportunities and experiences that address deficiencies in oral and written communication, logical processes and analysis, mathematical operations, independent learning, teamwork, and technology utilization. This study…
Sequential Mathematics Course III. Volume One. Staff Development Program 1986-1987.
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
The Sequential Mathematics Sequence provides students with an integrated course of study, including lessons which interweave algebra, geometry, logic, probability, and mathematical systems. This handbook is designed to meet the needs of teachers who will be teaching Course III in the sequence. The handbook, for use with staff development programs,…
ERIC Educational Resources Information Center
Healey, Muriel
This study assesses the abilities of kindergarten children who attended the Mt. Druitt Early Childhood Project (MDECP) in Australia to apply logical processes to mathematic problems not generally found in the classroom. The mathematical abilities of 56 children enrolled in one of the MDECP's five programs (competency, cognitive, behaviorist,…
ERIC Educational Resources Information Center
Syzmanowicz, Agata; Furnham, Adrian
2011-01-01
Four meta-analyses were conducted to examine the magnitude of sex differences in self-estimates of general, mathematical/logical, spatial and verbal abilities. For all but verbal ability males gave significantly higher self-estimates than did females. The weighted mean effect size d for general intelligence was 0.37, for mathematical 0.44, for…
The Beauty of "and" and "or": Connections within Mathematics for Students with Learning Differences.
ERIC Educational Resources Information Center
Bosse, Michael J.
2003-01-01
Investigates a way to assist students with learning differences. Considers mathematical connections appropriate in middle grades through college mathematics centered around the words "and" and "or" within the fields of logic, set theory, algebra, number theory, and probability. Teachers and students should be encouraged to investigate mathematical…
The universal magnetic tunnel junction logic gates representing 16 binary Boolean logic operations
NASA Astrophysics Data System (ADS)
Lee, Junwoo; Suh, Dong Ik; Park, Wanjun
2015-05-01
The novel devices are expected to shift the paradigm of a logic operation by their own nature, replacing the conventional devices. In this study, the nature of our fabricated magnetic tunnel junction (MTJ) that responds to the two external inputs, magnetic field and voltage bias, demonstrated seven basic logic operations. The seven operations were obtained by the electric-field-assisted switching characteristics, where the surface magnetoelectric effect occurs due to a sufficiently thin free layer. The MTJ was transformed as a universal logic gate combined with three supplementary circuits: A multiplexer (MUX), a Wheatstone bridge, and a comparator. With these circuits, the universal logic gates demonstrated 16 binary Boolean logic operations in one logic stage. A possible further approach is parallel computations through a complimentary of MUX and comparator, capable of driving multiple logic gates. A reconfigurable property can also be realized when different logic operations are produced from different level of voltages applying to the same configuration of the logic gate.
Leveling Students' Creative Thinking in Solving and Posing Mathematical Problem
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2010-01-01
Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…
Communication Theory Offers Insight into Mathematics Teachers' Talk
ERIC Educational Resources Information Center
Forrest, Denise B.
2008-01-01
This article discusses how communication theory is used to understand the thoughts mathematics teachers employ when creating messages intended for students. According to communication theory, individuals have different premises about the act of communicating, and these thoughts, called message design logics, guide the process of reasoning from…
Actualizacion Matematica, AM-2 (Modernizing Mathematics, AM-2).
ERIC Educational Resources Information Center
[Parot, Jean Jacques
This document presents a series of exercises designed to help elementary school children develop skills in mathematics and logic. By means of stories, games, questions, and illustrations, the first set of exercises presents the idea of number systems with bases other than 10. Similar means are used to explain the concept of exponents and to teach…
Level of Student's Creative Thinking in Classroom Mathematics
ERIC Educational Resources Information Center
Siswono, Tatag Yuli Eko
2011-01-01
It is reasonable to assume that people are creative, but the degree of creativity is different. The Idea of the level of student's creative thinking has been expressed by experts, such as Gotoh (2004), and Krulik and Rudnick (1999). The perspective of the mathematics creative thinking refers to a combination of logical and divergent thinking which…
A Formalized Design Process for Bacterial Consortia That Perform Logic Computing
Sun, Rui; Xi, Jingyi; Wen, Dingqiao; Feng, Jingchen; Chen, Yiwei; Qin, Xiao; Ma, Yanrong; Luo, Wenhan; Deng, Linna; Lin, Hanchi; Yu, Ruofan; Ouyang, Qi
2013-01-01
The concept of microbial consortia is of great attractiveness in synthetic biology. Despite of all its benefits, however, there are still problems remaining for large-scaled multicellular gene circuits, for example, how to reliably design and distribute the circuits in microbial consortia with limited number of well-behaved genetic modules and wiring quorum-sensing molecules. To manage such problem, here we propose a formalized design process: (i) determine the basic logic units (AND, OR and NOT gates) based on mathematical and biological considerations; (ii) establish rules to search and distribute simplest logic design; (iii) assemble assigned basic logic units in each logic operating cell; and (iv) fine-tune the circuiting interface between logic operators. We in silico analyzed gene circuits with inputs ranging from two to four, comparing our method with the pre-existing ones. Results showed that this formalized design process is more feasible concerning numbers of cells required. Furthermore, as a proof of principle, an Escherichia coli consortium that performs XOR function, a typical complex computing operation, was designed. The construction and characterization of logic operators is independent of “wiring” and provides predictive information for fine-tuning. This formalized design process provides guidance for the design of microbial consortia that perform distributed biological computation. PMID:23468999
[Gaston Bachelard in front of mathematics].
Alunni, Charles
2015-01-01
The issue regarding the bond between Bachelard's thought and contemporaneous mathematics has for a long time been concealed, aiming at the restricted benefit of an entirely misrepresented interpretation. The interpretation that indeed prevails, and in particular following the colloquium of Cerisy in 1974, is that of a man nurtured in the domain of both, physics and chemistry, and that has never drawn significant attention to mathematics. That is precisely the standpoint of the logician Roger Martin who sustains that the matters concerning the foundational problems (set theory, axiomatization and logicism) are in fact buried in a guilty silence. Departing from a meticulous assessment of the philosopher's texts, the present study thus aims at restoring a more appropriate image of a Bachelard, for whom mathematics is no less than the "superego" of science. PMID:25894420
Pan, Deng; Wei, Hong; Xu, Hongxing
2013-04-22
Optical interferometric logic gates in metal slot waveguide network are designed and investigated by electromagnetic simulations. The designed logic gates can realize all fundamental logic operations. A single Y-shaped junction can work as logic gate for four logic functions: AND, NOT, OR and XOR. By cascading two Y-shaped junctions, NAND, NOR and XNOR can be realized. The working principle is analyzed in detail. In the simulations, these gates show large intensity contrast for the Boolean logic states of the output. These results can be useful for future integrated optical computing. PMID:23609666
Logical elements in living cells.
Kremen, A
1984-11-01
Recognition processes with enhanced accuracy (as performed by structures like enzymes or ribosomes) are investigated using elementary ideas of statistical mechanics and related concepts of thermodynamics. The analysis starts from a formal definition of recognition and provides a correspondence with appropriate physical properties of the macromolecular logical elements. Transitions of the recognizing system between different modifications are a necessary feature of a more exacting recognition process. Rearrangement steps provide the process with higher accuracy by performing two physical operations: (1) rearranging the phase space of the system so that the "correct" states be better separated from the "wrong" states and the probability of occupation of the "correct" states be enhanced, (2) directing the process toward the more favourable modifications thus formed. Both operations are related to changes in the physical properties of the recognizing system. These changes can be expressed as differences of macromolecular Gibbs energy levels; if ligand binding or release participate in a step, directivity of the step depends also on the actual chemical potentials of the ligands in solution. The two operations just mentioned resemble two basic operations known to be necessary in electronic digital networks: directivity of control and signal standardization. An analysis of the entire reaction catalysed by a macromolecular logical element takes into account the requirements imposed by the logical functions as well as the need that the chemical potential of the product be not restricted to very low values. To satisfy these conditions, the reaction must be supported by a so-called non-specific reaction, usually implemented by the cleavage reaction of a nucleoside triphosphate. PMID:6513567
Examining Classroom Interactions & Mathematical Discourses
ERIC Educational Resources Information Center
Grant, Melva R.
2009-01-01
This investigation examined interactions in three classrooms to determine how they influenced Discourses related to mathematics learning and teaching. Mathematics education literature suggests that effective mathematics instruction includes mathematical Discourses. However, effective mathematical Discourses within mathematics classrooms vary…
Authenticity of Mathematical Modeling
ERIC Educational Resources Information Center
Tran, Dung; Dougherty, Barbara J.
2014-01-01
Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…
Synthesizing Biomolecule-based Boolean Logic Gates
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
Electronic logic for enhanced switch reliability
Cooper, J.A.
1984-01-20
A logic circuit is used to enhance redundant switch reliability. Two or more switches are monitored for logical high or low output. The output for the logic circuit produces a redundant and fail-safe representation of the switch outputs. When both switch outputs are high, the output is high. Similarly, when both switch outputs are low, the logic circuit's output is low. When the output states of the two switches do not agree, the circuit resolves the conflict by memorizing the last output state which both switches were simultaneously in and produces the logical complement of this output state. Thus, the logic circuit of the present invention allows the redundant switches to be treated as if they were in parallel when the switches are open and as if they were in series when the switches are closed. A failsafe system having maximum reliability is thereby produced.
HDL to verification logic translator
NASA Astrophysics Data System (ADS)
Gambles, J. W.; Windley, P. J.
The increasingly higher number of transistors possible in VLSI circuits compounds the difficulty in insuring correct designs. As the number of possible test cases required to exhaustively simulate a circuit design explodes, a better method is required to confirm the absence of design faults. Formal verification methods provide a way to prove, using logic, that a circuit structure correctly implements its specification. Before verification is accepted by VLSI design engineers, the stand alone verification tools that are in use in the research community must be integrated with the CAD tools used by the designers. One problem facing the acceptance of formal verification into circuit design methodology is that the structural circuit descriptions used by the designers are not appropriate for verification work and those required for verification lack some of the features needed for design. We offer a solution to this dilemma: an automatic translation from the designers' HDL models into definitions for the higher-ordered logic (HOL) verification system. The translated definitions become the low level basis of circuit verification which in turn increases the designer's confidence in the correctness of higher level behavioral models.
HDL to verification logic translator
NASA Technical Reports Server (NTRS)
Gambles, J. W.; Windley, P. J.
1992-01-01
The increasingly higher number of transistors possible in VLSI circuits compounds the difficulty in insuring correct designs. As the number of possible test cases required to exhaustively simulate a circuit design explodes, a better method is required to confirm the absence of design faults. Formal verification methods provide a way to prove, using logic, that a circuit structure correctly implements its specification. Before verification is accepted by VLSI design engineers, the stand alone verification tools that are in use in the research community must be integrated with the CAD tools used by the designers. One problem facing the acceptance of formal verification into circuit design methodology is that the structural circuit descriptions used by the designers are not appropriate for verification work and those required for verification lack some of the features needed for design. We offer a solution to this dilemma: an automatic translation from the designers' HDL models into definitions for the higher-ordered logic (HOL) verification system. The translated definitions become the low level basis of circuit verification which in turn increases the designer's confidence in the correctness of higher level behavioral models.
NASA Astrophysics Data System (ADS)
Kasturirangan, Rajesh
2014-07-01
Mathematics is a human pursuit. Whether the truths of mathematics lie outside the human mind or emerge out of it, the actual practice of mathematics is conducted by human beings. In other words, human mathematics is the only kind of mathematics that we can pursue and human mathematics has to be built on top of cognitive capacities that are possessed by all human beings. Another way of stating the same claim is that mathematics is experienced by human beings using their cognitive capacities. This paper argues that exploring the experience of mathematics is a useful way to make headway on the foundations of mathematics. Focusing on the experience of mathematics is an empirical approach to the study of mathematics that sidesteps some of the thorniest debates from an earlier era about Platonism and Formalism in the foundations of mathematics.
Discrete Mathematics and the Secondary Mathematics Curriculum.
ERIC Educational Resources Information Center
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Mathematical Language and Advanced Mathematics Learning
ERIC Educational Resources Information Center
Ferrari, Pier Luigi
2004-01-01
This paper is concerned with the role of language in mathematics learning at college level. Its main aim is to provide a perspective on mathematical language appropriate to effectively interpret students' linguistic behaviors in mathematics and to suggest new teaching ideas. Examples are given to show that the explanation of students' behaviors…
Mathematical Modelling Approach in Mathematics Education
ERIC Educational Resources Information Center
Arseven, Ayla
2015-01-01
The topic of models and modeling has come to be important for science and mathematics education in recent years. The topic of "Modeling" topic is especially important for examinations such as PISA which is conducted at an international level and measures a student's success in mathematics. Mathematical modeling can be defined as using…
Mathematics for Life: Sustainable Mathematics Education
ERIC Educational Resources Information Center
Renert, Moshe
2011-01-01
Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…
Mathematical Story: A Metaphor for Mathematics Curriculum
ERIC Educational Resources Information Center
Dietiker, Leslie
2015-01-01
This paper proposes a theoretical framework for interpreting the content found in mathematics curriculum in order to offer teachers and other mathematics educators comprehensive conceptual tools with which to make curricular decisions. More specifically, it describes a metaphor of "mathematics curriculum as story" and defines and…
ERIC Educational Resources Information Center
Dundar, Sefa
2015-01-01
The pattern, which is a key concept in understanding the mathematical information and concepts, is the basis in comprehending mathematical relations and in understanding mathematical order and logic. The fact that students discover the relationships contained within the patterns and generalize them helps them develop their skills to better…
ERIC Educational Resources Information Center
Santi, Terri
This book contains a classroom-tested approach to the teaching of problem solving to all students in Grades 6-8, regardless of ability. Information on problem solving in general is provided, then mathematical problems on logic, exponents, fractions, pre-algebra, algebra, geometry, number theory, set theory, ratio, proportion, percent, probability,…
Double patterning compliant logic design
NASA Astrophysics Data System (ADS)
Ma, Yuangsheng; Sweis, Jason; Bencher, Chris; Deng, Yunfei; Dai, Huixiong; Yoshida, Hidekazu; Gisuthan, Bimal; Kye, Jongwook; Levinson, Harry J.
2011-04-01
Double patterning technology (DPT) is the only solution to enable the scaling for advanced technology nodes before EUV or any other advanced patterning techniques become available. In general, there are two major double patterning techniques: one is Litho-Etch-Litho-Etch (LELE), and the other is sidewall spacer technology, a Self-Aligned Double Patterning technique (SADP). While numerous papers have previously demonstrated these techniques on wafer process capabilities and processing costs, more study needs to be done in the context of standard cell design flow to enable their applications in mass production. In this paper, we will present the impact of DPT on logic designs, and give a thorough discussion on how to make DPT-compliant constructs, placement and routing using examples with Cadence's Encounter Digital Implementation System (EDI System).
A Logic for Qualified Syllogisms
NASA Astrophysics Data System (ADS)
Schwartz, Daniel G.
In various works, L.A. Zadeh has introduced fuzzy quantifiers, fuzzy usuality modifiers, and fuzzy likelihood modifiers. This paper provides these notions with a unified semantics and uses this to define a formal logic capable of expressing and validating arguments such as 'Most birds can fly; Tweety is a bird; therefore, it is likely that Tweety can fly'. In effect, these are classical Aristotelean syllogisms that have been "qualified" through the use of fuzzy quantifiers. It is briefly outlined how these, together with some likelihood combination rules, can be used to address some well-known problems in the theory of nonmonotonic reasoning. The work is aimed at future applications in expert systems and robotics, including both hardware and software agents.
Quantum logics and chemical kinetics
NASA Astrophysics Data System (ADS)
Ivanov, C. I.
1981-06-01
A statistical theory of chemical kinetics is presented based on the quantum logical concept of chemical observables. The apparatus of Boolean algebra B is applied for the construction of appropriate composition polynomials referring to any stipulated arrangement of the atomic constituents. A physically motivated probability measure μ( F) is introduced on the field B of chemical observables, which considers the occurrence of the yes response of a given F ɛ B. The equations for the time evolution of the species density operators and the master equations for the corresponding number densities are derived. The general treatment is applied to a superposition of elementary substitution reactions (AB) α + C ⇄ (AC) β + B. The expressions for the reaction rate coefficients are established.
Logical Empiricism, Politics, and Professionalism
NASA Astrophysics Data System (ADS)
Edgar, Scott
2009-02-01
This paper considers George A. Reisch’s account of the role of Cold War political forces in shaping the apolitical stance that came to dominate philosophy of science in the late 1940s and 1950s. It argues that at least as early as the 1930s, Logical Empiricists such as Rudolf Carnap already held that philosophy of science could not properly have political aims, and further suggests that political forces alone cannot explain this view’s rise to dominance during the Cold War, since political forces cannot explain why a philosophy of science with liberal democratic, anti-communist aims did not flourish. The paper then argues that if professionalization is understood in the right way, it might point toward an explanation of the apolitical stance of Cold War philosophy of science.
Moral Particularism and Deontic Logic
NASA Astrophysics Data System (ADS)
Parent, Xavier
The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty's point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides with Horty's one, this is not true in more complicated or "realistic" settings in which more than two norms collide. My chosen formalism is so-called input/output logic.
NASA Astrophysics Data System (ADS)
Whitfield, J. D.; Faccin, M.; Biamonte, J. D.
2012-09-01
Designing and optimizing cost functions and energy landscapes is a problem encountered in many fields of science and engineering. These landscapes and cost functions can be embedded and annealed in experimentally controllable spin Hamiltonians. Using an approach based on group theory and symmetries, we examine the embedding of Boolean logic gates into the ground-state subspace of such spin systems. We describe parameterized families of diagonal Hamiltonians and symmetry operations which preserve the ground-state subspace encoding the truth tables of Boolean formulas. The ground-state embeddings of adder circuits are used to illustrate how gates are combined and simplified using symmetry. Our work is relevant for experimental demonstrations of ground-state embeddings found in both classical optimization as well as adiabatic quantum optimization.
Rationality and the Logic of Good Reasons.
ERIC Educational Resources Information Center
Fisher, Walter R.
This paper contends that the rationality of the logic of good reasons is constituted in its use. To support this claim, the paper presents an analysis of the relationship between being reasonable and being rational. It then considers how following the logic of good reasons leads to rationality in the behavior of individuals and groups; the latter…
Toward a Logic of Good Reasons.
ERIC Educational Resources Information Center
Fisher, Walter R.
1978-01-01
Explores the assumptions underlying the role of values in rhetorical interactions, the meaning of "logic" in relation to "good reasons," a reconceptualization of "good reasons," implementation of a "logic of 'good reasons'," and the uses of hierarchies of values in assessing rhetorical reasoning. (JMF)
Fuzzy Logic in Medicine and Bioinformatics
Torres, Angela; Nieto, Juan J.
2006-01-01
The purpose of this paper is to present a general view of the current applications of fuzzy logic in medicine and bioinformatics. We particularly review the medical literature using fuzzy logic. We then recall the geometrical interpretation of fuzzy sets as points in a fuzzy hypercube and present two concrete illustrations in medicine (drug addictions) and in bioinformatics (comparison of genomes). PMID:16883057
Logic Design Pathology and Space Flight Electronics
NASA Technical Reports Server (NTRS)
Katz, Richard B.; Barto, Rod L.; Erickson, Ken
1999-01-01
This paper presents a look at logic design from early in the US Space Program and examines faults in recent logic designs. Most examples are based on flight hardware failures and analysis of new tools and techniques. The paper is presented in viewgraph form.
Strategy: The logic of war and peace
Luttwak, E.N.
1987-01-01
This book expounds a new way of thinking about the conduct of war and the diplomacy of peace, a theory Luttwak calls ''paradoxical logic,'' and illustrates, through abundant historical examples, the failure of commonsense logic in matters of military strategy and international politics. Topics considered include nuclear weapons, military strategy, decision making, historical aspects, political aspects, global aspects, and warfare.
Hardware verification at Computational Logic, Inc.
NASA Technical Reports Server (NTRS)
Brock, Bishop C.; Hunt, Warren A., Jr.
1990-01-01
The following topics are covered in viewgraph form: (1) hardware verification; (2) Boyer-Moore logic; (3) core RISC; (4) the FM8502 fabrication, implementation specification, and pinout; (5) hardware description language; (6) arithmetic logic generator; (7) near term expected results; (8) present trends; (9) future directions; (10) collaborations and technology transfer; and (11) technology enablers.
Zhang, Lina; Zhang, Hui; Liu, Mei; Dong, Bin
2016-06-22
In this paper, we report a polymer-based raspberry-like micromotor. Interestingly, the resulting micromotor exhibits multistimuli-responsive motion behavior. Its on-off-on motion can be regulated by the application of stimuli such as H2O2, near-infrared light, NH3, or their combinations. Because of the versatility in motion control, the current micromotor has great potential in the application field of logic gate and logic circuit. With use of different stimuli as the inputs and the micromotor motion as the output, reprogrammable OR and INHIBIT logic gates or logic circuit consisting of OR, NOT, and AND logic gates can be achieved. PMID:27237969
Magnetic tunnel junction based spintronic logic devices
NASA Astrophysics Data System (ADS)
Lyle, Andrew Paul
The International Technology Roadmap for Semiconductors (ITRS) predicts that complimentary metal oxide semiconductor (CMOS) based technologies will hit their last generation on or near the 16 nm node, which we expect to reach by the year 2025. Thus future advances in computational power will not be realized from ever-shrinking device sizes, but rather by 'outside the box' designs and new physics, including molecular or DNA based computation, organics, magnonics, or spintronic. This dissertation investigates magnetic logic devices for post-CMOS computation. Three different architectures were studied, each relying on a different magnetic mechanism to compute logic functions. Each design has it benefits and challenges that must be overcome. This dissertation focuses on pushing each design from the drawing board to a realistic logic technology. The first logic architecture is based on electrically connected magnetic tunnel junctions (MTJs) that allow direct communication between elements without intermediate sensing amplifiers. Two and three input logic gates, which consist of two and three MTJs connected in parallel, respectively were fabricated and are compared. The direct communication is realized by electrically connecting the output in series with the input and applying voltage across the series connections. The logic gates rely on the fact that a change in resistance at the input modulates the voltage that is needed to supply the critical current for spin transfer torque switching the output. The change in resistance at the input resulted in a voltage margin of 50--200 mV and 250--300 mV for the closest input states for the three and two input designs, respectively. The two input logic gate realizes the AND, NAND, NOR, and OR logic functions. The three input logic function realizes the Majority, AND, NAND, NOR, and OR logic operations. The second logic architecture utilizes magnetostatically coupled nanomagnets to compute logic functions, which is the basis of
Processing device with self-scrubbing logic
Wojahn, Christopher K.
2016-03-01
An apparatus includes a processing unit including a configuration memory and self-scrubber logic coupled to read the configuration memory to detect compromised data stored in the configuration memory. The apparatus also includes a watchdog unit external to the processing unit and coupled to the self-scrubber logic to detect a failure in the self-scrubber logic. The watchdog unit is coupled to the processing unit to selectively reset the processing unit in response to detecting the failure in the self-scrubber logic. The apparatus also includes an external memory external to the processing unit and coupled to send configuration data to the configuration memory in response to a data feed signal outputted by the self-scrubber logic.
Wu, Cuichen; Wan, Shuo; Hou, Weijia; Zhang, Liqin; Xu, Jiehua; Cui, Cheng; Wang, Yanyue; Hu, Jun
2015-01-01
Nucleic acid-based logic devices were first introduced in 1994. Since then, science has seen the emergence of new logic systems for mimicking mathematical functions, diagnosing disease and even imitating biological systems. The unique features of nucleic acids, such as facile and high-throughput synthesis, Watson-Crick complementary base pairing, and predictable structures, together with the aid of programming design, have led to the widespread applications of nucleic acids (NA) for logic gating and computing in biotechnology and biomedicine. In this feature article, the development of in vitro NA logic systems will be discussed, as well as the expansion of such systems using various input molecules for potential cellular, or even in vivo, applications. PMID:25597946
ERIC Educational Resources Information Center
Levin-Rozalis, Miri
2010-01-01
Background: Two kinds of research logic prevail in scientific research: deductive research logic and inductive research logic. However, both fail in the field of evaluation, especially evaluation conducted in unfamiliar environments. Purpose: In this article I wish to suggest the application of a research logic--"abduction"--"the logic of…
Transforming Primary Mathematics
ERIC Educational Resources Information Center
Askew, Mike
2011-01-01
What is good mathematics teaching? What is mathematics teaching good for? Who is mathematics teaching for? These are just some of the questions addressed in "Transforming Primary Mathematics", a highly timely new resource for teachers which accessibly sets out the key theories and latest research in primary maths today. Under-pinned by findings…
Mathematical Epistemologies at Work.
ERIC Educational Resources Information Center
Noss, Richard
2002-01-01
Investigates young people's expression of mathematical ideas with a computer, the nature of mathematical practices, and the problem of mathematical meaning from cognitive and socio-cultural perspectives. Describes a mathematical activity system designed for learning and the role of digital technologies in helping to understand and reshape the…
NASA Astrophysics Data System (ADS)
Tegmark, Max
2014-02-01
The world can be described using mathematical equations and numbers, but why does maths do it so well? In his new book Our Mathematical Universe, a section of which is abridged and edited here, Max Tegmark makes the radical proposal that our reality isn't just described by mathematics - it is mathematics.
Students as Mathematics Consultants
ERIC Educational Resources Information Center
Jensen, Jennifer L.
2013-01-01
If students are going to develop reasoning and thinking skills, use their mathematical knowledge, and recognize the relevance of mathematics in their lives, they need to experience mathematics in meaningful ways. Only then will their mathematical skills be transferrable to all other parts of their lives. To promote such flexible mathematical…
ERIC Educational Resources Information Center
Cain, David
2007-01-01
This article presents the first part of the closing address given by the author to the 2007 Association of Teachers of Mathematics (ATM) Easter conference at Loughborough. In his closing address, the author focuses on functioning mathematically as opposed to functional mathematics. His view of functional mathematics is that the focus is on someone…
Mathematics Lessons without ...
ERIC Educational Resources Information Center
Cross, Kath; Hibbs, John
2006-01-01
In the Association of Teachers of Mathematics (ATM) Easter conference, 2006, the authors presented a list of important aspects of mathematics lessons, recommended for students to have a positive attitude to mathematics and for teachers to acquire effective teaching. The following are discussed in detail: (1) Mathematics lessons without good…
Project W-058 monitor and control system logic
ROBERTS, J.B.
1999-05-12
This supporting document contains the printout of the control logic for the Project W-058 Monitor and Control System, as developed by Programmable Control Services, Inc. The logic is arranged in five appendices, one for each programmable logic controller console.
Probabilistic logic modeling of network reliability for hybrid network architectures
Wyss, G.D.; Schriner, H.K.; Gaylor, T.R.
1996-10-01
Sandia National Laboratories has found that the reliability and failure modes of current-generation network technologies can be effectively modeled using fault tree-based probabilistic logic modeling (PLM) techniques. We have developed fault tree models that include various hierarchical networking technologies and classes of components interconnected in a wide variety of typical and atypical configurations. In this paper we discuss the types of results that can be obtained from PLMs and why these results are of great practical value to network designers and analysts. After providing some mathematical background, we describe the `plug-and-play` fault tree analysis methodology that we have developed for modeling connectivity and the provision of network services in several current- generation network architectures. Finally, we demonstrate the flexibility of the method by modeling the reliability of a hybrid example network that contains several interconnected ethernet, FDDI, and token ring segments. 11 refs., 3 figs., 1 tab.
Fuzzy logic sliding mode control for command guidance law design.
Elhalwagy, Y Z; Tarbouchi, M
2004-04-01
Recently, the combination of sliding mode and fuzzy logic techniques has emerged as a promising methodology for dealing with nonlinear, uncertain, dynamical systems. In this paper, a sliding mode control algorithm combined with a fuzzy control scheme is developed for the trajectory control of a command guidance system. The acceleration command input is mathematically derived. The proposed controller is used to compensate for the influence of unmodeled dynamics and to alleviate chattering. Simulation results show that the proposed controller gives good system performance in the face of system parameters variation and external disturbances. In addition, they show the effectiveness of the proposed missile guidance law against different engagement scenarios where the results demonstrate better performance over the conventional sliding mode control. PMID:15098583
DAIDALUS: Detect and Avoid Alerting Logic for Unmanned Systems
NASA Technical Reports Server (NTRS)
Munoz, Cesar; Narkawicz, Anthony; Hagen, George; Upchurch, Jason; Dutle, Aaron; Consiglio, Maria; Chamberlain, James
2015-01-01
This paper presents DAIDALUS (Detect and Avoid Alerting Logic for Unmanned Systems), a reference implementation of a detect and avoid concept intended to support the integration of Unmanned Aircraft Systems into civil airspace. DAIDALUS consists of self-separation and alerting algorithms that provide situational awareness to UAS remote pilots. These algorithms have been formally specified in a mathematical notation and verified for correctness in an interactive theorem prover. The software implementation has been verified against the formal models and validated against multiple stressing cases jointly developed by the US Air Force Research Laboratory, MIT Lincoln Laboratory, and NASA. The DAIDALUS reference implementation is currently under consideration for inclusion in the appendices to the Minimum Operational Performance Standards for Unmanned Aircraft Systems presently being developed by RTCA Special Committee 228.
Stock and option portfolio using fuzzy logic approach
NASA Astrophysics Data System (ADS)
Sumarti, Novriana; Wahyudi, Nanang
2014-03-01
Fuzzy Logic in decision-making process has been widely implemented in various problems in industries. It is the theory of imprecision and uncertainty that was not based on probability theory. Fuzzy Logic adds values of degree between absolute true and absolute false. It starts with and builds on a set of human language rules supplied by the user. The fuzzy systems convert these rules to their mathematical equivalents. This could simplify the job of the system designer and the computer, and results in much more accurate representations of the way systems behave in the real world. In this paper we examine the decision making process of stock and option trading by the usage of MACD (Moving Average Convergence Divergence) technical analysis and Option Pricing with Fuzzy Logic approach. MACD technical analysis is for the prediction of the trends of underlying stock prices, such as bearish (going downward), bullish (going upward), and sideways. By using Fuzzy C-Means technique and Mamdani Fuzzy Inference System, we define the decision output where the value of MACD is high then decision is "Strong Sell", and the value of MACD is Low then the decision is "Strong Buy". We also implement the fuzzification of the Black-Scholes option-pricing formula. The stock and options methods are implemented on a portfolio of one stock and its options. Even though the values of input data, such as interest rates, stock price and its volatility, cannot be obtain accurately, these fuzzy methods can give a belief degree of the calculated the Black-Scholes formula so we can make the decision on option trading. The results show the good capability of the methods in the prediction of stock price trends. The performance of the simulated portfolio for a particular period of time also shows good return.
Use of LOGIC to support lidar operations
NASA Astrophysics Data System (ADS)
Davis-Lunde, Kimberley; Jugan, Laurie A.; Shoemaker, J. Todd
1999-10-01
The Naval Oceanographic Office (NAVOCEANO) and Planning Systems INcorporated are developing the Littoral Optics Geospatial Integrated Capability (LOGIC). LOGIC supports NAVOCEANO's directive to assess the impact of the environment on Fleet systems in areas of operational interest. LOGIC is based in the Geographic Information System (GIS) ARC/INFO and offers a method to view and manipulate optics and ancillary data to support emerging Fleet lidar systems. LOGIC serves as a processing (as required) and quality-checking mechanism for data entering NAVOCEANO's Data Warehouse and handles both remotely sensed and in-water data. LOGIC provides a link between these data and the GIS-based Graphical User Interface, allowing the user to select data manipulation routines and/or system support products. The results of individual modules are displayed via the GIS to provide such products as lidar system performance, laser penetration depth, and asset vulnerability from a lidar threat. LOGIC is being developed for integration into other NAVOCEANO programs, most notably for Comprehensive Environmental Assessment System, an established tool supporting sonar-based systems. The prototype for LOGIC was developed for the Yellow Sea, focusing on a diver visibility support product.
ERIC Educational Resources Information Center
Cupani, Marcos; de Minzi, Maria Cristina Richaud; Perez, Edgardo Raul; Pautassi, Ricardo Marcos
2010-01-01
This study tested a set of hypotheses derived from the model of academic achievement in mathematics of the Social Cognitive Career Theory in a sample of Argentinean middle school students. To this aim, 277 students (male and female; age: 13-15 years) were assessed using the following instruments: logical-mathematical self-efficacy scale,…
Closed terminologies in description logics
Weida, R.A. |
1996-12-31
We introduce a predictive concept recognition methodology for description logics based on a new closed terminology assumption. During knowledge engineering, our system adopts the standard open terminology assumption as it automatically classifies concept descriptions into a taxonomy via subsumption inferences. However, for applications like configuration, the terminology becomes fixed during problem solving. Then, closed terminology reasoning is more appropriate. In our interactive configuration application, a user incrementally specifies an individual computer system in collaboration with a configuration engine. Choices can be made in any order and at any level of abstraction. We distinguish between abstract and concrete concepts to formally define when an individual`s description may be considered finished. We also take advantage of the closed terminology assumption, together with the terminology`s subsumption-based organization, to efficiently track the types of systems and components consistent with current choices, infer additional constraints on current choices, and appropriately guide future choices. Thus, we can help focus the efforts of both user and configuration engine.
Earthquake Archaeology: a logical approach?
NASA Astrophysics Data System (ADS)
Stewart, I. S.; Buck, V. A.
2001-12-01
Ancient earthquakes can leave their mark in the mythical and literary accounts of ancient peoples, the stratigraphy of their site histories, and the structural integrity of their constructions. Within this broad cross-disciplinary tramping ground, earthquake geologists have tended to focus on those aspects of the cultural record that are most familiar to them; the physical effects of seismic deformation on ancient constructions. One of the core difficulties with this 'earthquake archaeology' approach is that recent attempts to isolate structural criteria that are diagnostic or strongly suggestive of a seismic origin are undermined by the recognition that signs of ancient seismicity are generally indistinguishable from non-seismic mechanisms (poor construction, adverse geotechnical conditions). We illustrate the difficulties and inconsistencies in current proposed 'earthquake diagnostic' schemes by reference to two case studies of archaeoseismic damage in central Greece. The first concerns fallen columns at various Classical temple localities in mainland Greece (Nemea, Sounio, Olympia, Bassai) which, on the basis of observed structural criteria, are earthquake-induced but which are alternatively explained by archaeologists as the action of human disturbance. The second re-examines the almost type example of the Kyparissi site in the Atalanti region as a Classical stoa offset across a seismic surface fault, arguing instead for its deformation by ground instability. Finally, in highlighting the inherent ambiguity of archaeoseismic data, we consider the value of a logic-tree approach for quantifying and quantifying our uncertainities for seismic-hazard analysis.
Logical composition of Lyapunov functions
NASA Astrophysics Data System (ADS)
Balestrino, A.; Caiti, A.; Crisostomi, E.
2011-03-01
This article introduces the use of R-functions to compose single Lyapunov functions (LFs) via classic Boolean operators, with the aim to obtain a rich family of non-conventional, generally non-convex functions. The main benefit of the proposed composition is the nice geometric interpretation, since it corresponds to intersection and union operations in the phase space region. The composition of LFs is parameterised through a variable γ and classic compositions of LFs through min and max operations are recovered as a special case for a particular value of γ. The proposed logical composition is applied to region of asymptotic stability (RAS) estimation problems, where the union of several LFs corresponds to the union of the RAS estimates obtained from the separate use of each LF. Likewise, the intersection of several LFs defined on independent subsets of the state space variables provides a single LF for the overall dynamical system. Sufficient conditions for the composition function to be an LF are provided and results are described through several examples of classic nonlinear dynamical systems.
NASA Astrophysics Data System (ADS)
Kapit, Eliot
Superconducting qubits are among the most promising platforms for building a quantum computer. However, individual qubit coherence times are not far past the scalability threshold for quantum error correction, meaning that millions of physical devices would be required to construct a useful quantum computer. Consequently, further increases in coherence time are very desirable. In this letter, we blueprint a simple circuit consisting of two transmon qubits and two additional lossy qubits or resonators, which is passively protected against all single qubit quantum error channels through a combination of continuous driving and engineered dissipation. Photon losses are rapidly corrected through two-photon drive fields implemented with driven SQUID couplings, and dephasing from random potential fluctuations is heavily suppressed by the drive fields used to implement the multi-qubit Hamiltonian. Comparing our theoretical model to published noise estimates from recent experiments on flux and transmon qubits, we find that logical state coherence could be improved by a factor of forty or more compared to the individual qubit T1 and T2 using this technique.
Intelligent medical diagnostics via molecular logic
Konry, Tania; Walt, David R.
2009-01-01
In this communication, we describe the integration of microarray sensor technology with logic capability for screening combinations of proteins and DNA in a biological sample. In this system, we have demonstrated the use of a single platform amenable to both protein detection and protein-DNA detection using molecular logic gates. The pattern of protein and DNA inputs results in fluorescence outputs according to a truth table for AND and INHIBIT gates, thereby demonstrating the feasibility of performing medical diagnostics using a logic gate design. One possible application of this technique would be for the direct screening of various medical conditions that are dependent on combinations of diagnostic markers. PMID:19715272
Coordination Logic for Repulsive Resolution Maneuvers
NASA Technical Reports Server (NTRS)
Narkawicz, Anthony J.; Munoz, Cesar A.; Dutle, Aaron M.
2016-01-01
This paper presents an algorithm for determining the direction an aircraft should maneuver in the event of a potential conflict with another aircraft. The algorithm is implicitly coordinated, meaning that with perfectly reliable computations and information, it will in- dependently provide directional information that is guaranteed to be coordinated without any additional information exchange or direct communication. The logic is inspired by the logic of TCAS II, the airborne system designed to reduce the risk of mid-air collisions between aircraft. TCAS II provides pilots with only vertical resolution advice, while the proposed algorithm, using a similar logic, provides implicitly coordinated vertical and horizontal directional advice.
Bilayer avalanche spin-diode logic
Friedman, Joseph S. Querlioz, Damien; Fadel, Eric R.; Wessels, Bruce W.; Sahakian, Alan V.
2015-11-15
A novel spintronic computing paradigm is proposed and analyzed in which InSb p-n bilayer avalanche spin-diodes are cascaded to efficiently perform complex logic operations. This spin-diode logic family uses control wires to generate magnetic fields that modulate the resistance of the spin-diodes, and currents through these devices control the resistance of cascaded devices. Electromagnetic simulations are performed to demonstrate the cascading mechanism, and guidelines are provided for the development of this innovative computing technology. This cascading scheme permits compact logic circuits with switching speeds determined by electromagnetic wave propagation rather than electron motion, enabling high-performance spintronic computing.
Bilayer avalanche spin-diode logic
NASA Astrophysics Data System (ADS)
Friedman, Joseph S.; Fadel, Eric R.; Wessels, Bruce W.; Querlioz, Damien; Sahakian, Alan V.
2015-11-01
A novel spintronic computing paradigm is proposed and analyzed in which InSb p-n bilayer avalanche spin-diodes are cascaded to efficiently perform complex logic operations. This spin-diode logic family uses control wires to generate magnetic fields that modulate the resistance of the spin-diodes, and currents through these devices control the resistance of cascaded devices. Electromagnetic simulations are performed to demonstrate the cascading mechanism, and guidelines are provided for the development of this innovative computing technology. This cascading scheme permits compact logic circuits with switching speeds determined by electromagnetic wave propagation rather than electron motion, enabling high-performance spintronic computing.
Ternary logic and mass quantum numbers
Sheppeard, M. D.
2010-06-15
Koide's prediction of the tau mass may be formulated as a condition on the three eigenvalues of a quantum Fourier series, using simple parameters, and similar triplets have been found for neutrino and hadron masses [2]. Assuming these parameters arise from quantum gravity, one would like to understand them from the more abstract context of category theory. In particular, whereas the logic of lepton spin is a linear analogue of the ordinary Boolean logic of the category of sets, mass triplets suggest an analogous ternary logic, requiring higher dimensional categorical structures.
Inference engine using optical array logic
NASA Astrophysics Data System (ADS)
Iwata, Masaya; Tanida, Jun; Ichioka, Yoshiki
1990-07-01
An implementation method for an inference engine using optical array logic is presented. Optical array logic is a technique for parallel neighborhood operation using spatial coding and 2-D correlation. For efficient execution of inference in artificial intelligence problems, a large number of data must be searched effectively. To achieve this demand, a template matching technique is applied to the inference operation. By introducing a new function of data conversion, the inference operation can be implemented with optical array logic, which utilizes parallelism in optical techniques.
Software Safety Assurance of Programmable Logic
NASA Technical Reports Server (NTRS)
Berens, Kalynnda
2002-01-01
Programmable Logic (PLC, FPGA, ASIC) devices are hybrids - hardware devices that are designed and programmed like software. As such, they fall in an assurance gray area. Programmable Logic is usually tested and verified as hardware, and the software aspects are ignored, potentially leading to safety or mission success concerns. The objective of this proposal is to first determine where and how Programmable Logic (PL) is used within NASA and document the current methods of assurance. Once that is known, raise awareness of the PL software aspects within the NASA engineering community and provide guidance for the use and assurance of PL form a software perspective.
Inference System Integration Via Logic Morphisms
NASA Technical Reports Server (NTRS)
Bjorner, Nikolaj S.; Espinosa, David
2000-01-01
This is a final report on the accomplishments during the period of the NASA grant. The work on inference servers accomplished the integration of the SLANG logic (Specware's default specification logic) with a number of inference servers in order to make their complementary strengths available. These inverence servers are (1) SNARK. (2) Gandalf, Setheo, and Spass, (3) the Prototype Verification System (PVS) from SRI. (4) HOL98. We designed and implemented MetaSlang, an ML-like language, which we are using to specify and implement all our logic morphisms.
The Logic of Reflection: Samuel Taylor Coleridge's "treatise on Logic"
NASA Astrophysics Data System (ADS)
Land, Janet Sanders
Though others discuss Coleridge's interest in science, light imagery, the phenomenon of reflection, and his references to Newton and Opticks,^1 this is the first study to examine Coleridge's art in terms of optics, its developing theories, and the nature-of-light debate. This study examines Coleridge's early predilection for visions, illusions, and the supernatural and demonstrates that he gradually shifts from the supernatural to the scientific aspects of "visions" and "illusions," concentrating on causes of illusions and the effects of their deceptive qualities rather than their mystical features. By the 1820's, his preoccupation with illusions had become an interest in optics, fueled, no doubt, by the increasing controversy of the nature-of-light debate and the number of advances in optics resulting from the efforts of its opponents to prove their theories. Tracing the development of the debate, its escalation in the early nineteenth century, and the formation of Coleridge's opinion concerning key issues of the debate, I outline the evolution of Coleridge's theory of reflection and examine the exposition of that theory in his treatise, Logic (1981). Finally, I analyze the relationship between the advances in optics and Coleridge's concepts of thought and knowledge and his notion of the mind as an instrument of knowledge. These ideas in turn, altered his opinions concerning the validity of knowledge resulting from philosophic debate, scientific experiment, and poetic exploration. ftn^1John Beer, "Coleridge and Wordsworth on Reflection," The Wordsworth Circle 20 (1989): 20-29; Coleridge the Visionary. London: Chatto and Windus, 1959; and Coleridge's Poetic Intelligence. London: Macmillan, 1977 and M. H. Abrams Natural Supernaturalism: Tradition and Revolution in Romantic Literature. New York: Norton, 1971; and "Coleridge's 'A Light in Sound': Science, Metascience, and Poetic Imagination." The Correspondent Breeze: Essays on English Romanticism. Eds. M. H. Abrams
Mathematical Modelling: A New Approach to Teaching Applied Mathematics.
ERIC Educational Resources Information Center
Burghes, D. N.; Borrie, M. S.
1979-01-01
Describes the advantages of mathematical modeling approach in teaching applied mathematics and gives many suggestions for suitable material which illustrates the links between real problems and mathematics. (GA)
Preface of the "Symposium on Logic Synthesis for Programmable Logic Devices"
NASA Astrophysics Data System (ADS)
Kania, Dariusz
2015-12-01
Logic synthesis is an indirect link between design description and technology mapping. In the result of synthesis process an implementation in terms of an interconnection of logic gates, flip-flops, LUTs, etc. is generated. Typically, synthesis is performed for an objective function, such as minimizing the number of logic blocks (area), delay of interconnection, minimizing the power consumed, or making the implementation more testable. Logic synthesis is typically separated into two stages: technology-independent optimization, followed by a technology mapping. Technology mapping is the process of expressing a boolean network in terms of elements characteristic for a given technology (or device family). The aim of the symposium is to show all aspects of logic synthesis dedicated for Programmable Logic Devices.
Spectral Automorphisms in Quantum Logics
NASA Astrophysics Data System (ADS)
Ivanov, Alexandru; Caragheorgheopol, Dan
2010-12-01
In quantum mechanics, the Hilbert space formalism might be physically justified in terms of some axioms based on the orthomodular lattice (OML) mathematical structure (Piron in Foundations of Quantum Physics, Benjamin, Reading, 1976). We intend to investigate the extent to which some fundamental physical facts can be described in the more general framework of OMLs, without the support of Hilbert space-specific tools. We consider the study of lattice automorphisms properties as a “substitute” for Hilbert space techniques in investigating the spectral properties of observables. This is why we introduce the notion of spectral automorphism of an OML. Properties of spectral automorphisms and of their spectra are studied. We prove that the presence of nontrivial spectral automorphisms allow us to distinguish between classical and nonclassical theories. We also prove, for finite dimensional OMLs, that for every spectral automorphism there is a basis of invariant atoms. This is an analogue of the spectral theorem for unitary operators having purely point spectrum.
An Argumentation Framework based on Paraconsistent Logic
NASA Astrophysics Data System (ADS)
Umeda, Yuichi; Takahashi, Takehisa; Sawamura, Hajime
Argumentation is the most representative of intelligent activities of humans. Therefore, it is natural to think that it could have many implications for artificial intelligence and computer science as well. Specifically, argumentation may be considered a most primitive capability for interaction among computational agents. In this paper we present an argumentation framework based on the four-valued paraconsistent logic. Tolerance and acceptance of inconsistency that this logic has as its logical feature allow for arguments on inconsistent knowledge bases with which we are often confronted. We introduce various concepts for argumentation, such as arguments, attack relations, argument justification, preferential criteria of arguments based on social norms, and so on, in a way proper to the four-valued paraconsistent logic. Then, we provide the fixpoint semantics and dialectical proof theory for our argumentation framework. We also give the proofs of the soundness and completeness.
Procedural and Logic Programming: A Comparison.
ERIC Educational Resources Information Center
Watkins, Will; And Others
1988-01-01
Examines the similarities and fundamental differences between procedural programing and logic programing by comparing LogoWriter and PROLOG. Suggests that PROLOG may be a good first programing language for students to learn. (MVL)
Logical operator tradeoff for local quantum codes
NASA Astrophysics Data System (ADS)
Haah, Jeongwan; Preskill, John
2011-03-01
We study the structure of logical operators in local D -dimensional quantum codes, considering both subsystem codes with geometrically local gauge generators and codes defined by geometrically local commuting projectors. We show that if the code distance is d , then any logical operator can be supported on a set of specified geometry containing d~ qubits, where d~d 1 / (D - 1) = O (n) and n is the code length. Our results place limitations on partially self-correcting quantum memories, in which at least some logical operators are protected by energy barriers that grow with system size. We also show that two-dimensional codes defined by local commuting projectors admit logical ``string'' operators and are not self correcting. NSF PHY-0803371, DOE DE-FG03-92-ER40701, NSA/ARO W911NF-09-1-0442, and KFAS.
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.
Purification of Logic-Qubit Entanglement
NASA Astrophysics Data System (ADS)
Zhou, Lan; Sheng, Yu-Bo
2016-07-01
Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network.
Purification of Logic-Qubit Entanglement.
Zhou, Lan; Sheng, Yu-Bo
2016-01-01
Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network. PMID:27377165
Electro-optical graphene plasmonic logic gates.
Ooi, Kelvin J A; Chu, Hong Son; Bai, Ping; Ang, Lay Kee
2014-03-15
The versatile control of graphene's plasmonic modes via an external gate-voltage inspires us to design efficient electro-optical graphene plasmonic logic gates at the midinfrared wavelengths. We show that these devices are superior to the conventional optical logic gates because the former possess cut-off states and interferometric effects. Moreover, the designed six basic logic gates (i.e., NOR/AND, NAND/OR, XNOR/XOR) achieved not only ultracompact size lengths of less than λ/28 with respect to the operating wavelength of 10 μm, but also a minimum extinction ratio as high as 15 dB. These graphene plasmonic logic gates are potential building blocks for future nanoscale midinfrared photonic integrated circuits. PMID:24690855
On Ho's "Modern Logic and Schizophrenic Thinking"
ERIC Educational Resources Information Center
Marini, James L.
1976-01-01
Points out that conclusions drawn in the title paper about the role of logic in the schizophrenic thought process are not reliable since they are based on patients medicated with antipsychotic drugs. (MS)
Hierarchical structure of the logical Internet graph
NASA Astrophysics Data System (ADS)
Ge, Zihui; Figueiredo, Daniel R.; Jaiswal, Sharad; Gao, Lixin
2001-07-01
The study of the Internet topology has recently received much attention from the research community. In particular, the observation that the network graph has interesting properties, such as power laws, that might be explored in a myriad of ways. Most of the work in characterizing the Internet graph is based on the physical network graph, i.e., the connectivity graph. In this paper we investigate how logical relationships between nodes of the AS graph can be used to gain insight to its structure. We characterize the logical graph using various metrics and identify the presence of power laws in the number of customers that a provider has. Using these logical relationships we define a structural model of the AS graph. The model highlights the hierarchical nature of logical relationships and the preferential connection to larger providers. We also investigate the consistency of this model over time and observe interesting properties of the hierarchical structure.
Purification of Logic-Qubit Entanglement
Zhou, Lan; Sheng, Yu-Bo
2016-01-01
Recently, the logic-qubit entanglement shows its potential application in future quantum communication and quantum network. However, the entanglement will suffer from the noise and decoherence. In this paper, we will investigate the first entanglement purification protocol for logic-qubit entanglement. We show that both the bit-flip error and phase-flip error in logic-qubit entanglement can be well purified. Moreover, the bit-flip error in physical-qubit entanglement can be completely corrected. The phase-flip in physical-qubit entanglement error equals to the bit-flip error in logic-qubit entanglement, which can also be purified. This entanglement purification protocol may provide some potential applications in future quantum communication and quantum network. PMID:27377165
A Logical Framework to Deal with Variability
NASA Astrophysics Data System (ADS)
Asirelli, Patrizia; Ter Beek, Maurice H.; Fantechi, Alessandro; Gnesi, Stefania
We present a logical framework that is able to deal with variability in product family descriptions. The temporal logic MHML is based on the classical Hennessy-Milner logic with Until and we interpret it over Modal Transition Systems (MTSs). MTSs extend the classical notion of Labelled Transition Systems by distinguishing possible (may) and required (must) transitions: these two types of transitions are useful to describe variability in behavioural descriptions of product families. This leads to a novel deontic interpretation of the classical modal and temporal operators, which allows the expression of both constraints over the products of a family and constraints over their behaviour in a single logical framework. Finally, we sketch model-checking algorithms to verify MHML formulae as well as a way to derive correct products from a product family description.
Queuing register uses fluid logic elements
NASA Technical Reports Server (NTRS)
1966-01-01
Queuing register /a multistage bit-shifting device/ uses a series of pure fluid elements to perform the required logic operations. The register has several stages of three-state pure fluid elements combined with two-input NOR gates.
Mathematics Coursework Regulates Growth in Mathematics Achievement
ERIC Educational Resources Information Center
Ma, Xin; Wilkins, Jesse L. M.
2007-01-01
Using data from the Longitudinal Study of American Youth (LSAY), we examined the extent to which students' mathematics coursework regulates (influences) the rate of growth in mathematics achievement during middle and high school. Graphical analysis showed that students who started middle school with higher achievement took individual mathematics…
Preparatory Mathematics Programs in Departments of Mathematics.
ERIC Educational Resources Information Center
Lindberg, Karl
This paper reports on a survey of remedial mathematics programs offered at the college level. The paper is divided into five sections. Section I describes the sampling procedures used in the study. In Section II, the occurrence of remedial mathematics programs in the various types of institutions and some general characteristics of these programs…
Negotiation of Mathematical Meaning and Learning Mathematics.
ERIC Educational Resources Information Center
Voigt, Jorg
1994-01-01
Presents a case study of a first-grade class and their teacher who were observed as they ascribed mathematical meanings of numbers and of numerical operations to empirical phenomena. Differences in ascriptions led to negotiation of meanings. Discusses some indirect relations between social interaction and mathematics learning. (Contains 60…
Convection automated logic oven control
Boyer, M.A.; Eke, K.I.
1998-03-01
For the past few years, there has been a greater push to bring more automation to the cooling process. There have been attempts at automated cooking using a wide range of sensors and procedures, but with limited success. The authors have the answer to the automated cooking process; this patented technology is called Convection AutoLogic (CAL). The beauty of the technology is that it requires no extra hardware for the existing oven system. They use the existing temperature probe, whether it is an RTD, thermocouple, or thermistor. This means that the manufacturer does not have to be burdened with extra costs associated with automated cooking in comparison to standard ovens. The only change to the oven is the program in the central processing unit (CPU) on the board. As for its operation, when the user places the food into the oven, he or she is required to select a category (e.g., beef, poultry, or casseroles) and then simply press the start button. The CAL program then begins its cooking program. It first looks at the ambient oven temperature to see if it is a cold, warm, or hot start. CAL stores this data and then begins to look at the food`s thermal footprint. After CAL has properly detected this thermal footprint, it can calculate the time and temperature at which the food needs to be cooked. CAL then sets up these factors for the cooking stage of the program and, when the food has finished cooking, the oven is turned off automatically. The total time for this entire process is the same as the standard cooking time the user would normally set. The CAL program can also compensate for varying line voltages and detect when the oven door is opened. With all of these varying factors being monitored, CAL can produce a perfectly cooked item with minimal user input.
Quantum integrals and anhomomorphic logics
NASA Astrophysics Data System (ADS)
Gudder, Stan
2010-11-01
The basic arena for a probabilistic structure is a set A of events. Corresponding to A is a dual structure A^* of coevents. We call A^* an anhomomorphic logic and the coevents are given by "truth functions" from A to the two-element Boolean algebra {Z}_2=lbrace 0,1rbrace. One of the main goals of a physical theory is to describe physical reality and a coevent φ:ArArr {Z}_2 provides such a description in the sense that an event Ain A "actually occurs" if and only if ϕ(A) = 1. The quantum integral over an event A with respect to a coevent ϕ is defined and its properties are treated. Integrals with respect to various coevents are computed. Quantum systems are frequently described by a quantum measure μ which gives the propensity μ(A) that an event A occurs. For φ in A^*, if ϕ(A) = 0 whenever μ(A) = 0 we say that ϕ is preclusive. Preclusivity is a reality filter because it eliminates coevents that do not describe a possible reality for the system. A quantum measure that can be represented as a quantum integral with respect to a coevent ϕ is said to 1-generate ϕ. This gives a stronger reality filter than preclusivity. What we believe to be a more general filter is defined in terms of a double quantum integral and is called 2-generation. We show that there are quantum measures that 2-generate coevents, but do not 1-generate coevents. Examples also show that there are coevents that are 2-generated but not 1-generated. For simplicity only finite systems are considered.
The development of a digital logic concept inventory
NASA Astrophysics Data System (ADS)
Herman, Geoffrey Lindsay
Instructors in electrical and computer engineering and in computer science have developed innovative methods to teach digital logic circuits. These methods attempt to increase student learning, satisfaction, and retention. Although there are readily accessible and accepted means for measuring satisfaction and retention, there are no widely accepted means for assessing student learning. Rigorous assessment of learning is elusive because differences in topic coverage, curriculum and course goals, and exam content prevent direct comparison of two teaching methods when using tools such as final exam scores or course grades. Because of these difficulties, computing educators have issued a general call for the adoption of assessment tools to critically evaluate and compare the various teaching methods. Science, Technology, Engineering, and Mathematics (STEM) education researchers commonly measure students' conceptual learning to compare how much different pedagogies improve learning. Conceptual knowledge is often preferred because all engineering courses should teach a fundamental set of concepts even if they emphasize design or analysis to different degrees. Increasing conceptual learning is also important, because students who can organize facts and ideas within a consistent conceptual framework are able to learn new information quickly and can apply what they know in new situations. If instructors can accurately assess their students' conceptual knowledge, they can target instructional interventions to remedy common problems. To properly assess conceptual learning, several researchers have developed concept inventories (CIs) for core subjects in engineering sciences. CIs are multiple-choice assessment tools that evaluate how well a student's conceptual framework matches the accepted conceptual framework of a discipline or common faulty conceptual frameworks. We present how we created and evaluated the digital logic concept inventory (DLCI).We used a Delphi process to
Application of Fuzzy Logic to Matrix FMECA
NASA Astrophysics Data System (ADS)
Shankar, N. Ravi; Prabhu, B. S.
2001-04-01
A methodology combining the benefits of Fuzzy Logic and Matrix FMEA is presented in this paper. The presented methodology extends the risk prioritization beyond the conventional Risk Priority Number (RPN) method. Fuzzy logic is used to calculate the criticality rank. Also the matrix approach is improved further to develop a pictorial representation retaining all relevant qualitative and quantitative information of several FMEA elements relationships. The methodology presented is demonstrated by application to an illustrative example.
Pattern recognition using linguistic fuzzy logic predictors
NASA Astrophysics Data System (ADS)
Habiballa, Hashim
2016-06-01
The problem of pattern recognition has been solved with numerous methods in the Artificial Intelligence field. We present an unconventional method based on Lingustic Fuzzy Logic Forecaster which is primarily used for the task of time series analysis and prediction through logical deduction wtih linguistic variables. This method should be used not only to the time series prediction itself, but also for recognition of patterns in a signal with seasonal component.
Synchronous universal droplet logic and control
NASA Astrophysics Data System (ADS)
Katsikis, Georgios; Cybulski, James S.; Prakash, Manu
2015-07-01
Droplets are versatile digital materials; they can be produced at high throughput, perform chemical reactions as miniature beakers and carry biological entities. Droplets have been manipulated with electric, optical, acoustic and magnetic forces, but all these methods use serial controls to address individual droplets. An alternative is algorithmic manipulation based on logic operations that automatically compute where droplets are stored or directed, thereby enabling parallel control. However, logic previously implemented in low-Reynolds-number droplet hydrodynamics is asynchronous and thus prone to errors that prevent scaling up the complexity of logic operations. Here we present a platform for error-free physical computation via synchronous universal logic. Our platform uses a rotating magnetic field that enables parallel manipulation of arbitrary numbers of ferrofluid droplets on permalloy tracks. Through the coupling of magnetic and hydrodynamic interaction forces between droplets, we developed AND, OR, XOR, NOT and NAND logic gates, fanouts, a full adder, a flip-flop and a finite-state machine. Our platform enables large-scale integration of droplet logic, analogous to the scaling seen in digital electronics, and opens new avenues in mesoscale material processing.
Recognition and processing of logic diagrams
NASA Astrophysics Data System (ADS)
Darwish, Ahmed M.; Bashandy, Ahmed R.
1996-03-01
In this paper we present a vision system that is capable of interpreting schematic logic diagrams, i.e. determine the output as a logic function of the inputs. The system is composed of a number of modules each designed to perform a specific subtask. Each module bears a minor contribution in the form of a new mixture of known algorithms or extensions to handle actual real life image imperfections which researchers tend to ignore when they develop their theoretical foundations. The main contribution, thus, is not in any individual module, it is rather in their integration to achieve the target job. The system is organized more or less in a classical fashion. Aside from the image acquisition and preprocessing modules, interesting modules include: the segmenter, the identifier, the connector and the grapher. A good segmentation output is one reason for the success of the presented system. Several novelties exist in the presented approach. Following segmentation the type of each logic gate is determined and its topological connectivity. The logic diagram is then transformed to a directed acyclic graph in which the final node is the output logic gate. The logic function is then determined by backtracking techniques. The system is not only aimed at recognition applications. In fact its main usage may be to target other processing applications such as storage compression and graphics modification and manipulation of the diagram as is explained.
Interpreting Abstract Interpretations in Membership Equational Logic
NASA Technical Reports Server (NTRS)
Fischer, Bernd; Rosu, Grigore
2001-01-01
We present a logical framework in which abstract interpretations can be naturally specified and then verified. Our approach is based on membership equational logic which extends equational logics by membership axioms, asserting that a term has a certain sort. We represent an abstract interpretation as a membership equational logic specification, usually as an overloaded order-sorted signature with membership axioms. It turns out that, for any term, its least sort over this specification corresponds to its most concrete abstract value. Maude implements membership equational logic and provides mechanisms to calculate the least sort of a term efficiently. We first show how Maude can be used to get prototyping of abstract interpretations "for free." Building on the meta-logic facilities of Maude, we further develop a tool that automatically checks and abstract interpretation against a set of user-defined properties. This can be used to select an appropriate abstract interpretation, to characterize the specified loss of information during abstraction, and to compare different abstractions with each other.
Jauch-Piron logics with finiteness conditions
Rogalewicz, V. )
1991-04-01
An event structure (so-called quantum logic) of a quantum mechanical system is commonly assumed to be an orthomodular poset L. A state of such a system is then interpreted as a probability measure on L. It turns out that the orthomodular posets which may potentially serve as logics must have reasonably rich spaces of states. Moreover, the following condition on the state space appears among the axioms of a quantum system: if {Phi} is a state on a logic L, and {Phi}(a) = {Phi}(b) = 1 for some a, b {element of} L, then there is a c {element of} L such that c {le} a, c {le} b, and {Phi}(c) = 1. Such a state is said to be a Jauch-Piron state. If all states on L fulfill this condition, then L is called a Jauch-Piron logic. The condition was originally introduced by Jauch (1968) and Piron (1976). The author investigates unital Jauch-Piron logics with finitely many blocks (maximal Boolean subalgebras). He shows that such a logic is always Boolean, i.e., it represents a purely classical system. In other words, and orthomodular poset must have infinitely many blocks in order to describe a (nonclassical) quantum system.
Mathematical and statistical analysis
NASA Technical Reports Server (NTRS)
Houston, A. Glen
1988-01-01
The goal of the mathematical and statistical analysis component of RICIS is to research, develop, and evaluate mathematical and statistical techniques for aerospace technology applications. Specific research areas of interest include modeling, simulation, experiment design, reliability assessment, and numerical analysis.
John von Neumann's mathematical "Utopia" in quantum theory
NASA Astrophysics Data System (ADS)
Valente, Giovanni
This paper surveys John von Neumann's work on the mathematical foundations of quantum theories in the light of Hilbert's Sixth Problem concerning the geometrical axiomatization of physics. We argue that in von Neumann's view geometry was so tied to logic that he ultimately developed a logical interpretation of quantum probabilities. That motivated his abandonment of Hilbert space in favor of von Neumann algebras, specifically the type II1 factors, as the proper limit of quantum mechanics in infinite dimensions. Finally, we present the reasons why his axiomatic program remained an "unsolved problem" in mathematical physics. A recent unpublished result by Huzimiro Araki, proving that no algebra with a tracial state defined on it, such as the type II1 factors, can support any (regular) representation of the canonical commutation relations, is also reviewed and its consequences for von Neumann's projects are discussed.
The Temporal Logic of the Tower Chief System
NASA Technical Reports Server (NTRS)
Hazelton, Lyman R., Jr.
1990-01-01
The purpose is to describe the logic used in the reasoning scheme employed in the Tower Chief system, a runway configuration management system. First, a review of classical logic is given. Defensible logics, truth maintenance, default logic, temporally dependent propositions, and resource allocation and planning are discussed.
On symbolic models for Single-Conclusion Logic of Proofs
Krupski, Vladimir N
2011-05-31
In this paper we define symbolic models for Single-Conclusion Logics of Proofs. We prove the soundness and completeness of these logics with respect to the corresponding classes of symbolic models. We apply the semantic methods developed in this paper to justify the use of terms of single-conclusion logic of proofs as notation for derivations in this logic. Bibliography: 17 titles.
Nonmonotonic Logic for Use in Information Retrieval: An Exploratory Paper.
ERIC Educational Resources Information Center
Hurt, C. D.
1998-01-01
Monotonic logic requires reexamination of the entire logic string when there is a contradiction. Nonmonotonic logic allows the user to withdraw conclusions in the face of contradiction without harm to the logic string, which has considerable application to the field of information searching. Artificial intelligence models and neural networks based…
Rural Mathematics Educator, 2002.
ERIC Educational Resources Information Center
Rural Mathematics Educator, 2002
2002-01-01
This document contains the two issues of "Rural Mathematics Educator" published in 2002. This newsletter of the Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics (ACCLAIM) includes articles on rural mathematics education, as well as information and descriptions of professional development opportunities for…
Mathematics. [SITE 2001 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2001 conference: "Secondary Mathematics Methods Course with Technology Units: Encouraging Pre-Service Teachers To Use Technology" (Rajee Amarasinghe); "Competency Exams in College Mathematics" (Kathy R. Autrey and Leigh…
Making Mathematics Culturally Relevant.
ERIC Educational Resources Information Center
Moyer, Patricia
2001-01-01
Examines three strands of elementary mathematics--numerals and counting, recording and calculating, and mathematics exploration and play--and provides ways to integrate culture and mathematics experiences in each area. Specific topics include Egyptian methods for multiplication, the abacus, and the words for the numbers 1-10 in seven different…
ERIC Educational Resources Information Center
Galligan, Linda
2016-01-01
A "National Numeracy Report" and the Australian Curriculum (2014) have recognised the importance of language in mathematics. The general capabilities contained within the "Australian Curriculum: Mathematics" (2014) highlight literacy as an important tool in the teaching and learning of mathematics, from the interpretation of…
ERIC Educational Resources Information Center
Clary, Joseph R.; Nery, Karen P.
This set of 20 modules was designed for use primarily to help teach and reinforce the basic mathematics skills in electronics classes. The modules are based on electronics competencies that require mathematics skills, as determined by a panel of high school electronics and mathematics teachers. Each module consists of one or two pages of basic…
ERIC Educational Resources Information Center
Martin, Tami S.; Speer, William R.
2009-01-01
This article describes features, consistent messages, and new components of "Mathematics Teaching Today: Improving Practice, Improving Student Learning" (NCTM 2007), an updated edition of "Professional Standards for Teaching Mathematics" (NCTM 1991). The new book describes aspects of high-quality mathematics teaching; offers a model for observing,…
Abraham, Ralph
2015-12-01
Is there a world of mathematics above and beyond ordinary reality, as Plato proposed? Or is mathematics a cultural construct? In this short article we speculate on the place of mathematical reality from the perspective of the mystical cosmologies of the ancient traditions of meditation, psychedelics, and divination. PMID:26278644
ERIC Educational Resources Information Center
Pratt, Dave
2012-01-01
Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…
Applying Mathematical Processes (AMP)
ERIC Educational Resources Information Center
Kathotia, Vinay
2011-01-01
This article provides insights into the "Applying Mathematical Processes" resources, developed by the Nuffield Foundation. It features Nuffield AMP activities--and related ones from Bowland Maths--that were designed to support the teaching and assessment of key processes in mathematics--representing a situation mathematically, analysing,…
Mathematical Epistemologies at Work.
ERIC Educational Resources Information Center
Noss, Richard
In this paper, I draw together a corpus of findings derived from two sources: studies of students using computers to learn mathematics, and research into the use of mathematics in professional practice. Using this as a basis, I map some elements of a theoretical framework for understanding the nature of mathematical knowledge in use, and how it is…
Revisiting Mathematics Manipulative Materials
ERIC Educational Resources Information Center
Swan, Paul; Marshall, Linda
2010-01-01
It is over 12 years since "APMC" published Bob Perry and Peter Howard's research on the use of mathematics manipulative materials in primary mathematics classrooms. Since then the availability of virtual manipulatives and associated access to computers and interactive whiteboards have caused educators to rethink the use of mathematics manipulative…
Mathematics in Masons' Workplace
ERIC Educational Resources Information Center
Moreira, Darlinda; Pardal, Eugénia
2012-01-01
This paper presents masons' professional practices, which are related to mathematics. It aims to contribute to the area of adult mathematics education and to enlarge knowledge about how mathematics is used at the workplace. Methodologically it was followed an ethnographic approach. The key informants of the study were four masons aged between 40…
ERIC Educational Resources Information Center
Ortiz-Franco, Luis
An historical perspective reveals that sophisticated mathematical activity has been going on in the Latino culture for thousands of years. This paper provides a general definition of the area of mathematics education that deals with issues of culture and mathematics (ethnomathematics) and defines what is meant by the term Latino in this essay.…
Mathenger Hunt: Mathematics Matters.
ERIC Educational Resources Information Center
Falba, Christy J.; Weiss, Maria J.
1991-01-01
Presented is an activity which shows how mathematics is used in real life and helps to establish a need for mathematics in students' futures. Adapted from a scavenger-hunt idea, this activity helps students to discover that almost every career makes use of mathematics. (KR)
Mathematics and Global Survival.
ERIC Educational Resources Information Center
Schwartz, Richard H.
This resource was written to provide students with an awareness of critical issues facing the world today. In courses for college students, it can motivate their study of mathematics, teach them how to solve mathematical problems related to current global issues, provide coherence to mathematical studies through a focus on issues of human…
ERIC Educational Resources Information Center
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
ERIC Educational Resources Information Center
Darlington, Ellie
2014-01-01
This article describes part of a study which investigated the role of questions in students' approaches to learning mathematics at the secondary-tertiary interface, focussing on the enculturation of students at the University of Oxford. Use of the Mathematical Assessment Task Hierarchy taxonomy revealed A-level Mathematics and Further Mathematics…
Applied Vocational Mathematics.
ERIC Educational Resources Information Center
South Carolina State Dept. of Education, Columbia. Office of Vocational Education.
Developed for use in teaching a two-semester, one-unit course, this course guide is intended to aid the high school instructor in teaching mathematical problem-solving and computational skills to vocational education students. The state-adopted textbook for general mathematics III, "Applied General Mathematics" serves as the major resource…
A "Mathematics Background Check"
ERIC Educational Resources Information Center
Hubisz, John
2009-01-01
Early in my career someone else reported that the best indicator of success in calculus-based physics (CBP) at our school was whether students had taken mathematics in a certain region of New Brunswick. I sat down with a very longtime mathematics teacher and asked him what he thought students should know in mathematics after high school to succeed…
ERIC Educational Resources Information Center
Nisbet, Steven
1991-01-01
The relationship between mathematics and music has been investigated for thousands of years. Presented are the mathematical features of music through a study of melody, harmony, and rhythm, and the musical features of mathematics through a study of pattern, ratio, modular arithmetic, Pythagorean triples, and number sequences. (MDH)
The Creative Mathematics Teacher.
ERIC Educational Resources Information Center
Ediger, Marlow
The creative mathematics teacher who has love and enthusiasm for mathematics as a curriculum area should be in great demand in all schools. This paper discusses the characteristics of creative mathematics teachers, including those who guide students to engage in divergent thinking; have learners do much creative writing; and integrate creative…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
ERIC Educational Resources Information Center
Posey, Johnsie Jo, Ed.; And Others
This manual is a collection of materials and teaching strategies to motivate the development of mathematical ideas in secondary school mathematics programs or in beginning college mathematics programs. The unit is written for the instructor with step-by-step procedures including lists of needed materials. The exercises in this unit also appear in…
ERIC Educational Resources Information Center
Gallian, Joseph A., Ed.
2010-01-01
"Mathematics and Sports", edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play. Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an…
Mathematical Friends and Relations
ERIC Educational Resources Information Center
Tomalin, Jo
2012-01-01
The Institute of Mathematical pedagogy meets annually--the theme for 2010 was: "Mathematical Friends & Relations: Recognising Structural Relationships". Here one participant documents her reflections on the experience of working with a group of mathematics educators at the Institute. The challenges, the responses--both the predictable and the…
Mathematical description of human body constitution and fatness.
Sheikh-Zade, Yu R; Galenko-Yaroshevskii, P A; Cherednik, I L
2014-02-01
Using mathematical modeling of human body, we demonstrated logical drawbacks of body mass index (BMI1 = M/H(2); A. Quetelet, 1832) and proposed more precise body mass index (BMI2 = M/H(3)) as well as body constitution index (BCI = (M/H(3))(1/2)) and fatness index (FI = M/HC(2)), where M, H, and C are body weight, height, and wrist circumference of the individual. PMID:24771443
NASA Astrophysics Data System (ADS)
Riezler, Stefan
2000-08-01
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint logic programming, is conceptualized in a clear logical framework, and presents a sound and complete system of quantitative inference for definite clauses annotated with subjective weights. This approach combines a rigorous formal semantics for quantitative inference based on subjective weights with efficient weight-based pruning for constraint-based systems. The second approach, called probabilistic constraint logic programming, introduces a log-linear probability distribution on the proof trees of a constraint logic program and an algorithm for statistical inference of the parameters and properties of such probability models from incomplete, i.e., unparsed data. The possibility of defining arbitrary properties of proof trees as properties of the log-linear probability model and efficiently estimating appropriate parameter values for them permits the probabilistic modeling of arbitrary context-dependencies in constraint logic programs. The usefulness of these ideas is evaluated empirically in a small-scale experiment on finding the correct parses of a constraint-based grammar. In addition, we address the problem of computational intractability of the calculation of expectations in the inference task and present various techniques to approximately solve this task. Moreover, we present an approximate heuristic technique for searching for the most probable analysis in probabilistic constraint logic programs.
Acerbi, Alberto; Ghirlanda, Stefano; Enquist, Magnus
2012-01-01
Many cultural traits exhibit volatile dynamics, commonly dubbed fashions or fads. Here we show that realistic fashion-like dynamics emerge spontaneously if individuals can copy others' preferences for cultural traits as well as traits themselves. We demonstrate this dynamics in simple mathematical models of the diffusion, and subsequent abandonment, of a single cultural trait which individuals may or may not prefer. We then simulate the coevolution between many cultural traits and the associated preferences, reproducing power-law frequency distributions of cultural traits (most traits are adopted by few individuals for a short time, and very few by many for a long time), as well as correlations between the rate of increase and the rate of decrease of traits (traits that increase rapidly in popularity are also abandoned quickly and vice versa). We also establish that alternative theories, that fashions result from individuals signaling their social status, or from individuals randomly copying each other, do not satisfactorily reproduce these empirical observations. PMID:22412887
Does Logic Feel Good? Testing for Intuitive Detection of Logicality in Syllogistic Reasoning
ERIC Educational Resources Information Center
Klauer, Karl Christoph; Singmann, Henrik
2013-01-01
Recent research on syllogistic reasoning suggests that the logical status (valid vs. invalid) of even difficult syllogisms can be intuitively detected via small changes in affective state (Morsanyi & Handley, 2012). In a series of 6 experiments, we replicated effects of logical status on liking ratings of difficult syllogisms (although their…
Complementary transistor-transistor logic /CTTL/ - An approach to high-speed micropower logic.
NASA Technical Reports Server (NTRS)
Stehlin, R. A.; Niemann, G. W.
1972-01-01
Description of a new approach to micropower integrated circuits that is called complementary transistor-transistor logic (CTTL). This logic combines the inherent low standby power of a complementary inverter with the high speed of the TTL-type input. Results of monolithic fabricated circuits are presented. These circuits are shown to be equally adaptable to hybrid and discrete circuitry.
NASA Technical Reports Server (NTRS)
Burgin, G. H.; Owens, A. J.
1975-01-01
A detailed description is presented of the computer programs in order to provide an understanding of the mathematical and geometrical relationships as implemented in the programs. The individual sbbroutines and their underlying mathematical relationships are described, and the required input data and the output provided by the program are explained. The relationship of the adaptive maneuvering logic program with the program to drive the differential maneuvering simulator is discussed.
Logical reformulation of quantum mechanics. I. Foundations
Omnes, R.
1988-11-01
The basic rules of quantum mechanics are reformulated. They deal primarily with individual systems and do not assume that every ket may represent a physical state. The customary kinematic and dynamic rules then allow to construct consistent Boolean logics describing the history of a system, following essentially Griffiths' proposal. Logical implication is defined within these logics, the multiplicity of which reflects the complementary principle. Only one interpretive rule of quantum mechanics is necessary in such a framework. It states that these logics provide bona fide foundations for the description of a quantum system and for reasoning about it. One attempts to build up classical physics, including classical logic, on these quantum foundations. The resulting theory of measurement needs not to state a priori that the eigenvalues of an observable have to be the results of individual measurements nor to assume wave packet reduction. Both these properties can be obtained as consequences of the basic rules. One also needs not to postulate that every observable is measurable, even in principle. A proposition calculus is obtained, allowing in principle the replacement of the discussion of problems concerned with the practical interpretation of experiments by due calculations.
A computational paradigm for dynamic logic-gates in neuronal activity.
Goldental, Amir; Guberman, Shoshana; Vardi, Roni; Kanter, Ido
2014-01-01
In 1943 McCulloch and Pitts suggested that the brain is composed of reliable logic-gates similar to the logic at the core of today's computers. This framework had a limited impact on neuroscience, since neurons exhibit far richer dynamics. Here we propose a new experimentally corroborated paradigm in which the truth tables of the brain's logic-gates are time dependent, i.e., dynamic logic-gates (DLGs). The truth tables of the DLGs depend on the history of their activity and the stimulation frequencies of their input neurons. Our experimental results are based on a procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro. We demonstrate that the underlying biological mechanism is the unavoidable increase of neuronal response latencies to ongoing stimulations, which imposes a non-uniform gradual stretching of network delays. The limited experimental results are confirmed and extended by simulations and theoretical arguments based on identical neurons with a fixed increase of the neuronal response latency per evoked spike. We anticipate our results to lead to better understanding of the suitability of this computational paradigm to account for the brain's functionalities and will require the development of new systematic mathematical methods beyond the methods developed for traditional Boolean algebra. PMID:24808856
A computational paradigm for dynamic logic-gates in neuronal activity
Goldental, Amir; Guberman, Shoshana; Vardi, Roni; Kanter, Ido
2014-01-01
In 1943 McCulloch and Pitts suggested that the brain is composed of reliable logic-gates similar to the logic at the core of today's computers. This framework had a limited impact on neuroscience, since neurons exhibit far richer dynamics. Here we propose a new experimentally corroborated paradigm in which the truth tables of the brain's logic-gates are time dependent, i.e., dynamic logic-gates (DLGs). The truth tables of the DLGs depend on the history of their activity and the stimulation frequencies of their input neurons. Our experimental results are based on a procedure where conditioned stimulations were enforced on circuits of neurons embedded within a large-scale network of cortical cells in-vitro. We demonstrate that the underlying biological mechanism is the unavoidable increase of neuronal response latencies to ongoing stimulations, which imposes a non-uniform gradual stretching of network delays. The limited experimental results are confirmed and extended by simulations and theoretical arguments based on identical neurons with a fixed increase of the neuronal response latency per evoked spike. We anticipate our results to lead to better understanding of the suitability of this computational paradigm to account for the brain's functionalities and will require the development of new systematic mathematical methods beyond the methods developed for traditional Boolean algebra. PMID:24808856
Fuzzy logic control of water level in advanced boiling water reactor
Lin, Chaung; Lee, Chi-Szu; Raghavan, R.; Fahrner, D.M.
1995-12-31
The feedwater control system in the Advanced Boiling Water Reactor (ABWR) is more challenging to design compared to other control systems in the plant, due to the possible change in level from void collapses and swells during transient events. A basic fuzzy logic controller is developed using a simplified ABWR mathematical model to demonstrate and compare the performance of this controller with a simplified conventional controller. To reduce the design effort, methods are developed to automatically tune the scaling factors and control rules. As a first step in developing the fuzzy controller, a fuzzy controller with a limited number of rules is developed to respond to normal plant transients such as setpoint changes of plant parameters and load demand changes. Various simulations for setpoint and load demand changes of plant performances were conducted to evaluate the modeled fuzzy logic design against the simplified ABWR model control system. The simulation results show that the performance of the fuzzy logic controller is comparable to that of the Proportional-Integral (PI) controller, However, the fuzzy logic controller produced shorter settling time for step setpoint changes compared to the simplified conventional controller.
NASA Technical Reports Server (NTRS)
Richardson, Albert O.
1997-01-01
This research has investigated the use of fuzzy logic, via the Matlab Fuzzy Logic Tool Box, to design optimized controller systems. The engineering system for which the controller was designed and simulate was the container crane. The fuzzy logic algorithm that was investigated was the 'predictive control' algorithm. The plant dynamics of the container crane is representative of many important systems including robotic arm movements. The container crane that was investigated had a trolley motor and hoist motor. Total distance to be traveled by the trolley was 15 meters. The obstruction height was 5 meters. Crane height was 17.8 meters. Trolley mass was 7500 kilograms. Load mass was 6450 kilograms. Maximum trolley and rope velocities were 1.25 meters per sec. and 0.3 meters per sec., respectively. The fuzzy logic approach allowed the inclusion, in the controller model, of performance indices that are more effectively defined in linguistic terms. These include 'safety' and 'cargo swaying'. Two fuzzy inference systems were implemented using the Matlab simulation package, namely the Mamdani system (which relates fuzzy input variables to fuzzy output variables), and the Sugeno system (which relates fuzzy input variables to crisp output variable). It is found that the Sugeno FIS is better suited to including aspects of those plant dynamics whose mathematical relationships can be determined.
NASA Astrophysics Data System (ADS)
Bogdanov, Alexander; Khramushin, Vasily
2016-02-01
The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.
Molecular implementation of simple logic programs.
Ran, Tom; Kaplan, Shai; Shapiro, Ehud
2009-10-01
Autonomous programmable computing devices made of biomolecules could interact with a biological environment and be used in future biological and medical applications. Biomolecular implementations of finite automata and logic gates have already been developed. Here, we report an autonomous programmable molecular system based on the manipulation of DNA strands that is capable of performing simple logical deductions. Using molecular representations of facts such as Man(Socrates) and rules such as Mortal(X) <-- Man(X) (Every Man is Mortal), the system can answer molecular queries such as Mortal(Socrates)? (Is Socrates Mortal?) and Mortal(X)? (Who is Mortal?). This biomolecular computing system compares favourably with previous approaches in terms of expressive power, performance and precision. A compiler translates facts, rules and queries into their molecular representations and subsequently operates a robotic system that assembles the logical deductions and delivers the result. This prototype is the first simple programming language with a molecular-scale implementation. PMID:19809454
On Logic and Standards for Structuring Documents
NASA Astrophysics Data System (ADS)
Eyers, David M.; Jones, Andrew J. I.; Kimbrough, Steven O.
The advent of XML has been widely seized upon as an opportunity to develop document representation standards that lend themselves to automated processing. This is a welcome development and much good has come of it. That said, present standardization efforts may be criticized on a number of counts. We explore two issues associated with document XML standardization efforts. We label them (i) the dynamic point and (ii) the logical point. Our dynamic point is that in many cases experience has shown that the search for a final, or even reasonably permanent, document representation standard is futile. The case is especially strong for electronic data interchange (EDI). Our logical point is that formalization into symbolic logic is materially helpful for understanding and designing dynamic document standards.
Fuzzy logic and neural network technologies
NASA Technical Reports Server (NTRS)
Villarreal, James A.; Lea, Robert N.; Savely, Robert T.
1992-01-01
Applications of fuzzy logic technologies in NASA projects are reviewed to examine their advantages in the development of neural networks for aerospace and commercial expert systems and control. Examples of fuzzy-logic applications include a 6-DOF spacecraft controller, collision-avoidance systems, and reinforcement-learning techniques. The commercial applications examined include a fuzzy autofocusing system, an air conditioning system, and an automobile transmission application. The practical use of fuzzy logic is set in the theoretical context of artificial neural systems (ANSs) to give the background for an overview of ANS research programs at NASA. The research and application programs include the Network Execution and Training Simulator and faster training algorithms such as the Difference Optimized Training Scheme. The networks are well suited for pattern-recognition applications such as predicting sunspots, controlling posture maintenance, and conducting adaptive diagnoses.
Fuzzy logic in autonomous orbital operations
NASA Technical Reports Server (NTRS)
Lea, Robert N.; Jani, Yashvant
1991-01-01
Fuzzy logic can be used advantageously in autonomous orbital operations that require the capability of handling imprecise measurements from sensors. Several applications are underway to investigate fuzzy logic approaches and develop guidance and control algorithms for autonomous orbital operations. Translational as well as rotational control of a spacecraft have been demonstrated using space shuttle simulations. An approach to a camera tracking system has been developed to support proximity operations and traffic management around the Space Station Freedom. Pattern recognition and object identification algorithms currently under development will become part of this camera system at an appropriate level in the future. A concept to control environment and life support systems for large Lunar based crew quarters is also under development. Investigations in the area of reinforcement learning, utilizing neural networks, combined with a fuzzy logic controller, are planned as a joint project with the Ames Research Center.
Anatomy Ontology Matching Using Markov Logic Networks
Li, Chunhua; Zhao, Pengpeng; Wu, Jian; Cui, Zhiming
2016-01-01
The anatomy of model species is described in ontologies, which are used to standardize the annotations of experimental data, such as gene expression patterns. To compare such data between species, we need to establish relationships between ontologies describing different species. Ontology matching is a kind of solutions to find semantic correspondences between entities of different ontologies. Markov logic networks which unify probabilistic graphical model and first-order logic provide an excellent framework for ontology matching. We combine several different matching strategies through first-order logic formulas according to the structure of anatomy ontologies. Experiments on the adult mouse anatomy and the human anatomy have demonstrated the effectiveness of proposed approach in terms of the quality of result alignment. PMID:27382498
Logic Design Pathology and Space Flight Electronics
NASA Technical Reports Server (NTRS)
Katz, Richard; Barto, Rod L.; Erickson, K.
1997-01-01
Logic design errors have been observed in space flight missions and the final stages of ground test. The technologies used by designers and their design/analysis methodologies will be analyzed. This will give insight to the root causes of the failures. These technologies include discrete integrated circuit based systems, systems based on field and mask programmable logic, and the use computer aided engineering (CAE) systems. State-of-the-art (SOTA) design tools and methodologies will be analyzed with respect to high-reliability spacecraft design and potential pitfalls are discussed. Case studies of faults from large expensive programs to "smaller, faster, cheaper" missions will be used to explore the fundamental reasons for logic design problems.
Molecular implementation of simple logic programs
NASA Astrophysics Data System (ADS)
Ran, Tom; Kaplan, Shai; Shapiro, Ehud
2009-11-01
Autonomous programmable computing devices made of biomolecules could interact with a biological environment and be used in future biological and medical applications. Biomolecular implementations of finite automata and logic gates have already been developed. Here, we report an autonomous programmable molecular system based on the manipulation of DNA strands that is capable of performing simple logical deductions. Using molecular representations of facts such as Man(Socrates) and rules such as Mortal(X) <-- Man(X) (Every Man is Mortal), the system can answer molecular queries such as Mortal(Socrates)? (Is Socrates Mortal?) and Mortal(X)? (Who is Mortal?). This biomolecular computing system compares favourably with previous approaches in terms of expressive power, performance and precision. A compiler translates facts, rules and queries into their molecular representations and subsequently operates a robotic system that assembles the logical deductions and delivers the result. This prototype is the first simple programming language with a molecular-scale implementation.
Quantum Computational Logics and Possible Applications
NASA Astrophysics Data System (ADS)
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Leporini, Roberto; di Francia, Giuliano Toraldo
2008-01-01
In quantum computational logics meanings of formulas are identified with quantum information quantities: systems of qubits or, more generally, mixtures of systems of qubits. We consider two kinds of quantum computational semantics: (1) a compositional semantics, where the meaning of a compound formula is determined by the meanings of its parts; (2) a holistic semantics, which makes essential use of the characteristic “holistic” features of the quantum-theoretic formalism. The compositional and the holistic semantics turn out to characterize the same logic. In this framework, one can introduce the notion of quantum-classical truth table, which corresponds to the most natural way for a quantum computer to calculate classical tautologies. Quantum computational logics can be applied to investigate different kinds of semantic phenomena where holistic, contextual and gestaltic patterns play an essential role (from natural languages to musical compositions).
Spin gated transistors for reprogrammable logic
NASA Astrophysics Data System (ADS)
Ciccarelli, Chiara; Gonzalez-Zalba, Fernando; Irvine, Andrew; Campion, Richard; Zarbo, Liviu; Gallagher, Brian; Ferguson, Andrew; Jungwirth, Tomas; Wunderlich, Joerg; Institute of Physics ASCR Collaboration; University of Nottingham Collaboration; Hitachi Cambridge Laboratory Team; Institute of Physics ASCR Collaboration; University of Nottingham Collaboration; University of Cambridge Team
2014-03-01
In spin-orbit coupled magnetic materials the chemical potential depends on the orientation of the magnetisation. By making the gate of a field effect transistor magnetic, it is possible to tune the channel conductance not only electrically but also magnetically. We show that these magnetic transistor can be used to realise non-volatile reprogrammable Boolean logic. The non-volatile reconfigurable capability resides in the magnetization-dependent band structure of the magnetic stack. A change in magnetization orientation produces a change in the electrochemical potential, which induces a charge accumulation in the correspondent gate electrode. This is readily sensed by a field-effect device such as standard field-effect transistors or more exotic single-electron transistors. We propose circuits for low power consumption applications that can be magnetically switched between NAND and OR logic functions and between NOR and AND logic functions.
Development of ferrite logic devices for an arithmetic processor
NASA Technical Reports Server (NTRS)
Heckler, C. H., Jr.
1972-01-01
A number of fundamentally ultra-reliable, all-magnetic logic circuits are developed using as a basis a single element ferrite structure wired as a logic delay element. By making minor additions or changes to the basic wiring pattern of the delay element other logic functions such as OR, AND, NEGATION, MAJORITY, EXCLUSIVE-OR, and FAN-OUT are developed. These logic functions are then used in the design of a full-adder, a set/reset flip-flop, and an edge detector. As a demonstration of the utility of all the developed devices, an 8-bit, all-magnetic, logic arithmetic unit capable of controlled addition, subtraction, and multiplication is designed. A new basic ferrite logic element and associated complementary logic scheme with the potential of improved performance is also described. Finally, an improved batch process for fabricating joint-free power drive and logic interconnect conductors for this basic class of all-magnetic logic is presented.
Multiple neural representations of elementary logical connectives.
Baggio, Giosuè; Cherubini, Paolo; Pischedda, Doris; Blumenthal, Anna; Haynes, John-Dylan; Reverberi, Carlo
2016-07-15
A defining trait of human cognition is the capacity to form compounds out of simple thoughts. This ability relies on the logical connectives AND, OR and IF. Simple propositions, e.g., 'There is a fork' and 'There is a knife', can be combined in alternative ways using logical connectives: e.g., 'There is a fork AND there is a knife', 'There is a fork OR there is a knife', 'IF there is a fork, there is a knife'. How does the brain represent compounds based on different logical connectives, and how are compounds evaluated in relation to new facts? In the present study, participants had to maintain and evaluate conjunctive (AND), disjunctive (OR) or conditional (IF) compounds while undergoing functional MRI. Our results suggest that, during maintenance, the left posterior inferior frontal gyrus (pIFG, BA44, or Broca's area) represents the surface form of compounds. During evaluation, the left pIFG switches to processing the full logical meaning of compounds, and two additional areas are recruited: the left anterior inferior frontal gyrus (aIFG, BA47) and the left intraparietal sulcus (IPS, BA40). The aIFG shows a pattern of activation similar to pIFG, and compatible with processing the full logical meaning of compounds, whereas activations in IPS differ with alternative interpretations of conditionals: logical vs conjunctive. These results uncover the functions of a basic cortical network underlying human compositional thought, and provide a shared neural foundation for the cognitive science of language and reasoning. PMID:27138210
Unlimited multistability and Boolean logic in microbial signalling
Kothamachu, Varun B.; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S.
2015-01-01
The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology. PMID:26040599
Unlimited multistability and Boolean logic in microbial signalling.
Kothamachu, Varun B; Feliu, Elisenda; Cardelli, Luca; Soyer, Orkun S
2015-07-01
The ability to map environmental signals onto distinct internal physiological states or programmes is critical for single-celled microbes. A crucial systems dynamics feature underpinning such ability is multistability. While unlimited multistability is known to arise from multi-site phosphorylation seen in the signalling networks of eukaryotic cells, a similarly universal mechanism has not been identified in microbial signalling systems. These systems are generally known as two-component systems comprising histidine kinase (HK) receptors and response regulator proteins engaging in phosphotransfer reactions. We develop a mathematical framework for analysing microbial systems with multi-domain HK receptors known as hybrid and unorthodox HKs. We show that these systems embed a simple core network that exhibits multistability, thereby unveiling a novel biochemical mechanism for multistability. We further prove that sharing of downstream components allows a system with n multi-domain hybrid HKs to attain 3n steady states. We find that such systems, when sensing distinct signals, can readily implement Boolean logic functions on these signals. Using two experimentally studied examples of two-component systems implementing hybrid HKs, we show that bistability and implementation of logic functions are possible under biologically feasible reaction rates. Furthermore, we show that all sequenced microbial genomes contain significant numbers of hybrid and unorthodox HKs, and some genomes have a larger fraction of these proteins compared with regular HKs. Microbial cells are thus theoretically unbounded in mapping distinct environmental signals onto distinct physiological states and perform complex computations on them. These findings facilitate the understanding of natural two-component systems and allow their engineering through synthetic biology. PMID:26040599
Logical computation using algorithmic self-assembly of DNA triple-crossover molecules
NASA Astrophysics Data System (ADS)
Mao, Chengde; LaBean, Thomas H.; Reif, John H.; Seeman, Nadrian C.
2000-09-01
Recent work has demonstrated the self-assembly of designed periodic two-dimensional arrays composed of DNA tiles, in which the intermolecular contacts are directed by `sticky' ends. In a mathematical context, aperiodic mosaics may be formed by the self-assembly of `Wang' tiles, a process that emulates the operation of a Turing machine. Macroscopic self-assembly has been used to perform computations; there is also a logical equivalence between DNA sticky ends and Wang tile edges. This suggests that the self-assembly of DNA-based tiles could be used to perform DNA-based computation. Algorithmic aperiodic self-assembly requires greater fidelity than periodic self-assembly, because correct tiles must compete with partially correct tiles. Here we report a one-dimensional algorithmic self-assembly of DNA triple-crossover molecules that can be used to execute four steps of a logical (cumulative XOR) operation on a string of binary bits.
Digital Poetry: A Narrow Relation between Poetics and the Codes of the Computational Logic
NASA Astrophysics Data System (ADS)
Laurentiz, Silvia
The project "Percorrendo Escrituras" (Walking Through Writings Project) has been developed at ECA-USP Fine Arts Department. Summarizing, it intends to study different structures of digital information that share the same universe and are generators of a new aesthetics condition. The aim is to search which are the expressive possibilities of the computer among the algorithm functions and other of its specific properties. It is a practical, theoretical and interdisciplinary project where the study of programming evolutionary language, logic and mathematics take us to poetic experimentations. The focus of this research is the digital poetry, and it comes from poetics of permutation combinations and culminates with dynamic and complex systems, autonomous, multi-user and interactive, through agents generation derivations, filtration and emergent standards. This lecture will present artworks that use some mechanisms introduced by cybernetics and the notion of system in digital poetry that demonstrate the narrow relationship between poetics and the codes of computational logic.
Nonlinear interferometry approach to photonic sequential logic
NASA Astrophysics Data System (ADS)
Mabuchi, Hideo
2011-10-01
Motivated by rapidly advancing capabilities for extensive nanoscale patterning of optical materials, I propose an approach to implementing photonic sequential logic that exploits circuit-scale phase coherence for efficient realizations of fundamental components such as a NAND-gate-with-fanout and a bistable latch. Kerr-nonlinear optical resonators are utilized in combination with interference effects to drive the binary logic. Quantum-optical input-output models are characterized numerically using design parameters that yield attojoule-scale energy separation between the latch states.
Universal programmable logic gate and routing method
NASA Technical Reports Server (NTRS)
Fijany, Amir (Inventor); Vatan, Farrokh (Inventor); Akarvardar, Kerem (Inventor); Blalock, Benjamin (Inventor); Chen, Suheng (Inventor); Cristoloveanu, Sorin (Inventor); Kolawa, Elzbieta (Inventor); Mojarradi, Mohammad M. (Inventor); Toomarian, Nikzad (Inventor)
2009-01-01
An universal and programmable logic gate based on G.sup.4-FET technology is disclosed, leading to the design of more efficient logic circuits. A new full adder design based on the G.sup.4-FET is also presented. The G.sup.4-FET can also function as a unique router device offering coplanar crossing of signal paths that are isolated and perpendicular to one another. This has the potential of overcoming major limitations in VLSI design where complex interconnection schemes have become increasingly problematic.
Nonlinear dynamics based digital logic and circuits
Kia, Behnam; Lindner, John. F.; Ditto, William L.
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two. PMID:26029096
Valve system incorporating single failure protection logic
Ryan, Rodger; Timmerman, Walter J. H.
1980-01-01
A valve system incorporating single failure protective logic. The system consists of a valve combination or composite valve which allows actuation or de-actuation of a device such as a hydraulic cylinder or other mechanism, integral with or separate from the valve assembly, by means of three independent input signals combined in a function commonly known as two-out-of-three logic. Using the input signals as independent and redundant actuation/de-actuation signals, a single signal failure, or failure of the corresponding valve or valve set, will neither prevent the desired action, nor cause the undesired action of the mechanism.
Refining fuzzy logic controllers with machine learning
NASA Technical Reports Server (NTRS)
Berenji, Hamid R.
1994-01-01
In this paper, we describe the GARIC (Generalized Approximate Reasoning-Based Intelligent Control) architecture, which learns from its past performance and modifies the labels in the fuzzy rules to improve performance. It uses fuzzy reinforcement learning which is a hybrid method of fuzzy logic and reinforcement learning. This technology can simplify and automate the application of fuzzy logic control to a variety of systems. GARIC has been applied in simulation studies of the Space Shuttle rendezvous and docking experiments. It has the potential of being applied in other aerospace systems as well as in consumer products such as appliances, cameras, and cars.
Runtime Analysis of Linear Temporal Logic Specifications
NASA Technical Reports Server (NTRS)
Giannakopoulou, Dimitra; Havelund, Klaus
2001-01-01
This report presents an approach to checking a running program against its Linear Temporal Logic (LTL) specifications. LTL is a widely used logic for expressing properties of programs viewed as sets of executions. Our approach consists of translating LTL formulae to finite-state automata, which are used as observers of the program behavior. The translation algorithm we propose modifies standard LTL to B chi automata conversion techniques to generate automata that check finite program traces. The algorithm has been implemented in a tool, which has been integrated with the generic JPaX framework for runtime analysis of Java programs.
Nonlinear dynamics based digital logic and circuits.
Kia, Behnam; Lindner, John F; Ditto, William L
2015-01-01
We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two. PMID:26029096
NASA Astrophysics Data System (ADS)
Sommer, Hanns; Schreiber, Lothar
2012-05-01
Dreyfus' call ‘to make artificial intelligence (AI) more Heideggerian‘ echoes Heidegger's affirmation that pure calculations produce no ‘intelligence’ (Dreyfus, 2007). But what exactly is it that AI needs more than mathematics? The question in the title gives rise to a reexamination of the basic principles of cognition in Husserl's Phenomenology. Using Husserl's Phenomenological Method, a formalization of these principles is presented that provides the principal idea of cognition, and as a consequence, a ‘natural logic’. Only in a second step, mathematics is obtained from this natural logic by abstraction. The limitations of pure reasoning are demonstrated for fundamental considerations (Hilbert's ‘finite Einstellung’) as well as for the task of solving practical problems. Principles will be presented for the design of general intelligent systems, which make use of a natural logic.
Specifying real-time systems with interval logic
NASA Technical Reports Server (NTRS)
Rushby, John
1988-01-01
Pure temporal logic makes no reference to time. An interval temporal logic and an extension to that logic which includes real time constraints are described. The application of this logic by giving a specification for the well-known lift (elevator) example is demonstrated. It is shown how interval logic can be extended to include a notion of process. How the specification language and verification environment of EHDM could be enhanced to support this logic is described. A specification of the alternating bit protocol in this extended version of the specification language of EHDM is given.
The Tower of Hanoi and Inductive Logic
ERIC Educational Resources Information Center
Merrotsy, Peter
2015-01-01
In the "Australian Curriculum," the concept of mathematical induction is first met in the senior secondary subject Specialist Mathematics. This article details an example, the Tower of Hanoi problem, which provides an enactive introduction to the inductive process before moving to more abstract and cognitively demanding representations.…
ERIC Educational Resources Information Center
House, Peggy A.
1994-01-01
Describes some mathematical investigations of the necktie which includes applications of geometry, statistics, data analysis, sampling, probability, symmetry, proportion, problem solving, and business. (MKR)
Teaching the Blue-Eyed Islanders Puzzle in a Liberal Arts Mathematics Course
ERIC Educational Resources Information Center
Shea, Stephen
2012-01-01
The blue-eyed islanders puzzle is an old and challenging logic puzzle. This is a narrative of an experience introducing a variation of this puzzle on the first day of classes in a liberal arts mathematics course for non-majors. I describe an exercise that was used to facilitate the class's understanding of the puzzle.
Geometry Students' Hedged Statements and Their Self-Regulation of Mathematics
ERIC Educational Resources Information Center
Kosko, Karl W.
2012-01-01
Statements conveying a degree of certainty or doubt, in the form of hedging, have been linked with logical inference in students' talk (Rowland, 2000). Considering the current emphasis on increasing student autonomy for effective mathematical discourse, I posit a relationship between hedging and student autonomy. In the current study, high school…
NASA Technical Reports Server (NTRS)
Lennington, R. K.; Rassbach, M. E.
1979-01-01
Discussed in this report is the clustering algorithm CLASSY, including detailed descriptions of its general structure and mathematical background and of the various major subroutines. The report provides a development of the logic and equations used with specific reference to program variables. Some comments on timing and proposed optimization techniques are included.
The Role of Automata and Machine Theory in School and College Mathematics Syllabuses.
ERIC Educational Resources Information Center
Holcombe, M.
1981-01-01
The introduction of certain topics in the theory of machines and languages into school and college mathematics courses in place of the more usual discussion of groups and formal logic is proposed. Examples of machines and languages and their interconnections suitable for such courses are outlined. (MP)
Mathematics Curriculum Outline and Sample Activities for Gifted Students Grades 2 through 8.
ERIC Educational Resources Information Center
Barson, Alan; And Others
This document includes a statement of 11 basic considerations for a mathematics curriculum for the gifted in grades two through eight and a series of activities appropriate for such a curriculum. The activities are grouped under five strands: (1) logic; (2) combinations (combinatorics), probability, introduction to statistics; (3) geometry,…
Inequalities, Absolute Value, and Logical Connectives.
ERIC Educational Resources Information Center
Parish, Charles R.
1992-01-01
Presents an approach to the concept of absolute value that alleviates students' problems with the traditional definition and the use of logical connectives in solving related problems. Uses a model that maps numbers from a horizontal number line to a vertical ray originating from the origin. Provides examples solving absolute value equations and…
Giving Programming Students a Logical Step Up.
ERIC Educational Resources Information Center
Brown, David W.
1990-01-01
Presents a method to enhance the teaching of computer programing to secondary students that establishes a connection between logic, truth tables, switching circuits, gating symbols, flow charts, and pseudocode. The author asserts that the method prepares students for thinking processes related to programing. (MDH)
Faster Evolution of More Multifunctional Logic Circuits
NASA Technical Reports Server (NTRS)
Stoica, Adrian; Zebulum, Ricardo
2005-01-01
A modification in a method of automated evolutionary synthesis of voltage-controlled multifunctional logic circuits makes it possible to synthesize more circuits in less time. Prior to the modification, the computations for synthesizing a four-function logic circuit by this method took about 10 hours. Using the method as modified, it is possible to synthesize a six-function circuit in less than half an hour. The concepts of automated evolutionary synthesis and voltage-controlled multifunctional logic circuits were described in a number of prior NASA Tech Briefs articles. To recapitulate: A circuit is designed to perform one of several different logic functions, depending on the value of an applied control voltage. The circuit design is synthesized following an automated evolutionary approach that is so named because it is modeled partly after the repetitive trial-and-error process of biological evolution. In this process, random populations of integer strings that encode electronic circuits play a role analogous to that of chromosomes. An evolved circuit is tested by computational simulation (prior to testing in real hardware to verify a final design). Then, in a fitness-evaluation step, responses of the circuit are compared with specifications of target responses and circuits are ranked according to how close they come to satisfying specifications. The results of the evaluation provide guidance for refining designs through further iteration.
FUZZY LOGIC CONTROL OF AC INDUCTION MOTORS
The paper discusses the fuzzy logic control (FLC) of electric motors, being investigated under the sponsorship of the U.S. EPA to reduce energy consumption when motors are operated at less than rated speeds and loads. lectric motors use 60% of the electrical energy generated in t...
Multiplexed logic controls solar-heating system
NASA Technical Reports Server (NTRS)
Currie, J. R.
1981-01-01
Four inexpensive thermocouples monitor temperatures at key points. On command from logic circuitry, dampers open and close to direct airflow, and fan and auxiliary heater shut on or off. Controlling complex arranges heating system in any one of four operating configurations.
Fuzzy logic mode switching in helicopters
NASA Technical Reports Server (NTRS)
Sherman, Porter D.; Warburton, Frank W.
1993-01-01
The application of fuzzy logic to a wide range of control problems has been gaining momentum internationally, fueled by a concentrated Japanese effort. Advanced Research & Development within the Engineering Department at Sikorsky Aircraft undertook a fuzzy logic research effort designed to evaluate how effective fuzzy logic control might be in relation to helicopter operations. The mode switching module in the advanced flight control portion of Sikorsky's motion based simulator was identified as a good candidate problem because it was simple to understand and contained imprecise (fuzzy) decision criteria. The purpose of the switching module is to aid a helicopter pilot in entering and leaving coordinated turns while in flight. The criteria that determine the transitions between modes are imprecise and depend on the varied ranges of three flight conditions (i.e., simulated parameters): Commanded Rate, Duration, and Roll Attitude. The parameters were given fuzzy ranges and used as input variables to a fuzzy rulebase containing the knowledge of mode switching. The fuzzy control program was integrated into a real time interactive helicopter simulation tool. Optimization of the heading hold and turn coordination was accomplished by interactive pilot simulation testing of the handling quality performance of the helicopter dynamic model. The fuzzy logic code satisfied all the requirements of this candidate control problem.
Logical Access Control Mechanisms in Computer Systems.
ERIC Educational Resources Information Center
Hsiao, David K.
The subject of access control mechanisms in computer systems is concerned with effective means to protect the anonymity of private information on the one hand, and to regulate the access to shareable information on the other hand. Effective means for access control may be considered on three levels: memory, process and logical. This report is a…
New Logic Circuit with DC Parametric Excitation
NASA Astrophysics Data System (ADS)
Sugahara, Masanori; Kaneda, Hisayoshi
1982-12-01
It is shown that dc parametric excitation is possible in a circuit named JUDO, which is composed of two resistively-connected Josephson junctions. Simulation study proves that the circuit has large gain and properties suitable for the construction of small, high-speed logic circuits.
Quantum logic gates for superconducting resonator qudits
Strauch, Frederick W.
2011-11-15
We study quantum information processing using superpositions of Fock states in superconducting resonators as quantum d-level systems (qudits). A universal set of single and coupled logic gates is theoretically proposed for resonators coupled by superconducting circuits of Josephson junctions. These gates use experimentally demonstrated interactions and provide an attractive route to quantum information processing using harmonic oscillator modes.
Mapping individual logical processes in information searching
NASA Technical Reports Server (NTRS)
Smetana, F. O.
1974-01-01
An interactive dialog with a computerized information collection was recorded and plotted in the form of a flow chart. The process permits one to identify the logical processes employed in considerable detail and is therefore suggested as a tool for measuring individual thought processes in a variety of situations. A sample of an actual test case is given.
Teleology as Logical Phenomenology: Some Therapeutic Implications.
ERIC Educational Resources Information Center
Rychlak, Joseph F.
Phenomenology is an important force in the development of psychological theory, rather than a variant type of counseling method. A distinction must be drawn between the sensory phenomenology in which gestaltists focus on sensory receptors, and logical pheomenology in which the grounding of belief or self-identity is viewed as a prediction or…
Demonstrating Boolean Logic Using Simple Electrical Circuits
ERIC Educational Resources Information Center
McElhaney, Kevin W.
2004-01-01
While exploring the subject of geometric proofs, boolean logic operators AND and OR can be used to allow students to visualize their true-or-false patterns. An activity in the form of constructing electrical circuits is illustrated to explain the concept.
Young Children's Comprehension of Logical Connectives.
ERIC Educational Resources Information Center
Suppes, Patrick; Feldman, Shirley
To determine to what extent children of preschool age comprehend the meaning of logical connectives, 64 5- and 6-year-olds were told to hand differently colored and shaped wooden blocks to an experimenter. The commands involved various English idioms used for conjunction (e.g. both black and round), disjunction (either black or round), and…
Interacting institutional logics in general dental practice☆
Harris, Rebecca; Holt, Robin
2013-01-01
We investigate the organisational field of general dental practice and how agents change or maintain the institution of values associated with the everyday work of health care provision. Our dataset comprise archival literature and policy documents, interview data from field level actors, as well as service delivery level interview data and secondary data gathered (2011–12) from 16 English dental practices. Our analysis provides a typology of institutional logics (prevailing systems of value) experienced in the field of dental practice. Confirming current literature, we find two logics dominate how care is assessed: business-like health care and medical professionalism. We advance the literature by finding the business-like health care logic further distinguished by values of commercialism on the one hand and those of accountability and procedural diligence on the other. The logic of professionalism we also find is further distinguished into a commitment to clinical expertise and independence in delivering patient care on the one hand, and concerns for the autonomy and sustainability of a business enterprise on the other. PMID:23931946
Using Mathematics Literature with Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Jett, Christopher C.
2014-01-01
Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…
A Capstone Mathematics Course for Prospective Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Artzt, Alice F.; Sultan, Alan; Curcio, Frances R.; Gurl, Theresa
2012-01-01
This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered…
Mathematics for Teaching: A Form of Applied Mathematics
ERIC Educational Resources Information Center
Stylianides, Gabriel J.; Stylianides, Andreas J.
2010-01-01
In this article we elaborate a conceptualisation of "mathematics for teaching" as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design…
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics
ERIC Educational Resources Information Center
Wang, Youjun
2009-01-01
In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…
Fuzzy Logic Based Controller for a Grid-Connected Solid Oxide Fuel Cell Power Plant.
Chatterjee, Kalyan; Shankar, Ravi; Kumar, Amit
2014-10-01
This paper describes a mathematical model of a solid oxide fuel cell (SOFC) power plant integrated in a multimachine power system. The utilization factor of a fuel stack maintains steady state by tuning the fuel valve in the fuel processor at a rate proportional to a current drawn from the fuel stack. A suitable fuzzy logic control is used for the overall system, its objective being controlling the current drawn by the power conditioning unit and meet a desirable output power demand. The proposed control scheme is verified through computer simulations. PMID:25053926
The music of morality and logic.
Mesz, Bruno; Rodriguez Zivic, Pablo H; Cecchi, Guillermo A; Sigman, Mariano; Trevisan, Marcos A
2015-01-01
Musical theory has built on the premise that musical structures can refer to something different from themselves (Nattiez and Abbate, 1990). The aim of this work is to statistically corroborate the intuitions of musical thinkers and practitioners starting at least with Plato, that music can express complex human concepts beyond merely "happy" and "sad" (Mattheson and Lenneberg, 1958). To do so, we ask whether musical improvisations can be used to classify the semantic category of the word that triggers them. We investigated two specific domains of semantics: morality and logic. While morality has been historically associated with music, logic concepts, which involve more abstract forms of thought, are more rarely associated with music. We examined musical improvisations inspired by positive and negative morality (e.g., good and evil) and logic concepts (true and false), analyzing the associations between these words and their musical representations in terms of acoustic and perceptual features. We found that music conveys information about valence (good and true vs. evil and false) with remarkable consistency across individuals. This information is carried by several musical dimensions which act in synergy to achieve very high classification accuracy. Positive concepts are represented by music with more ordered pitch structure and lower harmonic and sensorial dissonance than negative concepts. Music also conveys information indicating whether the word which triggered it belongs to the domains of logic or morality (true vs. good), principally through musical articulation. In summary, improvisations consistently map logic and morality information to specific musical dimensions, testifying the capacity of music to accurately convey semantic information in domains related to abstract forms of thought. PMID:26191020
The music of morality and logic
Mesz, Bruno; Rodriguez Zivic, Pablo H.; Cecchi, Guillermo A.; Sigman, Mariano; Trevisan, Marcos A.
2015-01-01
Musical theory has built on the premise that musical structures can refer to something different from themselves (Nattiez and Abbate, 1990). The aim of this work is to statistically corroborate the intuitions of musical thinkers and practitioners starting at least with Plato, that music can express complex human concepts beyond merely “happy” and “sad” (Mattheson and Lenneberg, 1958). To do so, we ask whether musical improvisations can be used to classify the semantic category of the word that triggers them. We investigated two specific domains of semantics: morality and logic. While morality has been historically associated with music, logic concepts, which involve more abstract forms of thought, are more rarely associated with music. We examined musical improvisations inspired by positive and negative morality (e.g., good and evil) and logic concepts (true and false), analyzing the associations between these words and their musical representations in terms of acoustic and perceptual features. We found that music conveys information about valence (good and true vs. evil and false) with remarkable consistency across individuals. This information is carried by several musical dimensions which act in synergy to achieve very high classification accuracy. Positive concepts are represented by music with more ordered pitch structure and lower harmonic and sensorial dissonance than negative concepts. Music also conveys information indicating whether the word which triggered it belongs to the domains of logic or morality (true vs. good), principally through musical articulation. In summary, improvisations consistently map logic and morality information to specific musical dimensions, testifying the capacity of music to accurately convey semantic information in domains related to abstract forms of thought. PMID:26191020
Troiani, Vanessa; Peelle, Jonathan E.; Clark, Robin; Grossman, Murray
2009-01-01
The present study examined the neural substrate of two classes of quantifiers: Numerical quantifiers like “at least three” which require magnitude processing, and logical quantifiers like “some” which can be satisfied using a simple form of perceptual logic. We assessed these distinct classes of quantifiers with converging observations from two sources: functional imaging data from healthy adults, and behavioral and structural data from patients with corticobasal degeneration, who have acalculia. Our findings are consistent with the claim that numerical quantifier comprehension depends on a parietal-dorsolateral prefrontal network, but logical quantifier comprehension depends instead on a rostral medial prefrontal-posterior cingulate network. These observations emphasize the important contribution of abstract number knowledge to the meaning of numerical quantifiers in semantic memory and the potential role of a logic-based evaluation in the service of non-numerical quantifiers. PMID:18789346
Cognitive and brain systems underlying early mathematical development.
Geary, D C; Moore, A M
2016-01-01
We review current debate regarding the core competencies that support early mathematics learning, focusing on the contributions of the inherent system for representing approximate magnitudes, and domain-general systems that facilitate learning across academic domains. The latter include the executive control system that enables explicit processing of quantitative symbols, such as Arabic numerals, and the logical problem-solving abilities (intelligence) that facilitate learning the relations among numerals. The neural systems that underlie these abilities, as related to mathematical learning, are also discussed, albeit briefly. We place the contributions of inherent quantitative abilities and domain-general mechanisms in an evolutionary context and provide some discussion as to how they interact during the learning of evolutionarily novel mathematics. PMID:27339009
The Three Rs of Teaching Logic: Revelation, Relevance, and Reinforcement
ERIC Educational Resources Information Center
Covel, Robert C.
2010-01-01
Covel offers a primer on logic and describes how students react when they realize what a useful resource it can be in their real lives. His article includes useful definitions of critical concepts and logical fallacies. (Contains 2 figures.)
Remedial Mathematics for Quantum Chemistry
ERIC Educational Resources Information Center
Koopman, Lodewijk; Brouwer, Natasa; Heck, Andre; Buma, Wybren Jan
2008-01-01
Proper mathematical skills are important for every science course and mathematics-intensive chemistry courses rely on a sound mathematical pre-knowledge. In the first-year quantum chemistry course at this university, it was noticed that many students lack basic mathematical knowledge. To tackle the mathematics problem, a remedial mathematics…
Experimenting with Mathematical Biology
ERIC Educational Resources Information Center
Sanft, Rebecca; Walter, Anne
2016-01-01
St. Olaf College recently added a Mathematical Biology concentration to its curriculum. The core course, Mathematics of Biology, was redesigned to include a wet laboratory. The lab classes required students to collect data and implement the essential modeling techniques of formulation, implementation, validation, and analysis. The four labs…
The Relativity of Mathematics.
ERIC Educational Resources Information Center
Kleiner, Israel; Avital, Shmuel
1984-01-01
The development of the idea that "The essence of mathematics lies in its freedom," a quotation from Cantor, is discussed. Several examples are given of relative truth, and the problem of consistency is discussed. Mathematics and its relationship to the physical world is also explored. (MNS)
The Applied Mathematics Laboratory.
ERIC Educational Resources Information Center
Siegel, Martha J.
This report describes the Applied Mathematics Laboratory (AML) operated by the Department of Mathematics at Towson State University, Maryland. AML is actually a course offered to selected undergraduates who are given the opportunity to apply their skills in investigating industrial and governmental problems. By agreement with sponsoring…
ERIC Educational Resources Information Center
Heck, Andre; Van Gastel, Leendert
2006-01-01
Lowering the dropout rate of incoming mathematics and science students, and enhancing the provision of mathematics support for freshmen are two important aims of the University of Amsterdam. The approach recently adopted to support first year students is to set up a diagnostic pretest and posttest and use these tests to identify students being at…
ERIC Educational Resources Information Center
Hallenberg, Harvey
1995-01-01
Presents ideas for creating mathematical classroom activities associated with the history of mathematics: calculating sums and products the way ancient Greeks did it, using an abacus or moving stones on a sanded floor, and engaging elementary students through role playing specific mathematicians. Suggests that through such techniques, mathematics…
Designing Assessment for Mathematics
ERIC Educational Resources Information Center
Depka, Eileen
2007-01-01
Teaching mathematics in today's world requires practices and procedures integrated with performance tasks that actively involve students. In this second edition of Designing Rubrics for Mathematics, Eileen Depka clarifies the purpose of rubrics in math instruction and illustrates the relationship between assessment, rubrics, and the National…
Modularizing Remedial Mathematics
ERIC Educational Resources Information Center
Wong, Aaron
2013-01-01
As remedial mathematics education has become an increasingly important topic of conversation in higher education. Mathematics departments have been put under increased pressure to change their programs to increase the student success rate. A number of models have been introduced over the last decade that represent a wide range of new ideas and…
Quality Teaching in Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2012-01-01
The best teaching possible needs to accrue in the mathematics curriculum. Pupils also need to become proficient in using mathematics in every day situations in life. Individuals buy goods and services. They pay for these in different ways, including cash. Here, persons need to be able to compute the total cost of items purchased and then pay for…
Mathematics. [SITE 2002 Section].
ERIC Educational Resources Information Center
Connell, Michael L., Ed.; Lowery, Norene Vail, Ed.; Harnisch, Delwyn L., Ed.
This document contains the following papers on mathematics from the SITE (Society for Information Technology & Teacher Education) 2002 conference: (1) "Teachers' Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship" (Mara Alagic); (2) "A Fractal Is a Pattern in Your Neighborhood" (Craig N. Bach); (3)…
ERIC Educational Resources Information Center
Dodd, Jennifer
2010-01-01
In this article, the author reports on the findings of her research on what her Year 10 students consider to be "mathematical." The class contains thirteen students who will all sit the higher tier IGCSE next year. The author found out that the students considered things she told them to have a higher mathematical status than work they did…
Mathematics: The Universal Language?
ERIC Educational Resources Information Center
Hoffert, Sharon B.
2009-01-01
Mathematics is considered the universal language, but students who speak languages other than English have difficulty doing mathematics in English. For instance, because of a lack of familiarity with the problem's context, many have trouble understanding exactly what operations to perform. In the United States, approximately one in seven students…
Elementary Mathematics Leaders
ERIC Educational Resources Information Center
Fennell, Francis; Kobett, Beth McCord; Wray, Jonathan A.
2013-01-01
Elementary school mathematics leaders often come to the realization that their position, however titled and determined, although dedicated to addressing needs in math teaching and learning, also entails and directly involves leadership. Elementary school math specialists/instructional leaders (referenced here as elementary mathematics leaders, or…
ERIC Educational Resources Information Center
Corle, Clyde G.
This guide is to assist teachers with motivational ideas for teaching elementary school mathematics. The items included are a wide variety of games (paper and pencil, verbal, and physical), jingles, contests, teaching devices, and thought provoking exercises. Suggestions for selection of mathematical games are offered. The devices are used to…
Solving Common Mathematical Problems
NASA Technical Reports Server (NTRS)
Luz, Paul L.
2005-01-01
Mathematical Solutions Toolset is a collection of five software programs that rapidly solve some common mathematical problems. The programs consist of a set of Microsoft Excel worksheets. The programs provide for entry of input data and display of output data in a user-friendly, menu-driven format, and for automatic execution once the input data has been entered.
Mathematical Graphic Organizers
ERIC Educational Resources Information Center
Zollman, Alan
2009-01-01
As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…
Learning Mathematics while Black
ERIC Educational Resources Information Center
Martin, Danny Bernard
2012-01-01
While research by scholars has contributed greatly to an emerging knowledge base on Black children and mathematics, there continues to be a dire need for insightful research that de-centers longstanding accounts that have contributed to the construction of Black children as mathematically illiterate and as less than ideal learners relative to…
ERIC Educational Resources Information Center
Goldsmith, Lynn T.
2000-01-01
Parents can help ensure that their children are well-equipped with the necessary mathematical skills and understanding for the future by: having high expectations for their children's learning; helping their children see mathematical connections and applications in the world; being curious about their children's thinking; and being enthusiastic…
ERIC Educational Resources Information Center
Stallings, L. Lynn
2007-01-01
This article proposes four strategies for posing mathematics problems that raise the cognitive demands of the tasks given to students. Each strategy is illustrated with three common middle school mathematics examples: finding the greatest common factor, finding area or perimeter, and finding the equation of a line. Posing these types of problems…
[Collected Papers on Mathematics.
ERIC Educational Resources Information Center
Connell, Michael L., Ed.
This document contains the following papers on issues related to mathematics in technology and teacher education: "A Case for Strong Conceptualization in Technology Enhanced Mathematics Instruction" (Michael L. Connell and Delwyn L. Harnisch); "Faculty/Student Collaboration in Education and Math--Using the Web To Improve Student Learning and…
Astronomy and Mathematics Education
NASA Astrophysics Data System (ADS)
Ros, Rosa M.
There are many European countries where Astronomy does not appear as a specific course on the secondary school. In these cases Astronomy content can be introduced by means of other subjects. There are some astronomical topics within the subject of Physics but this talk concerns introducing Astronomy in Mathematics classes. Teaching Astronomy through Mathematics would result in more exposure than through Physics as Mathematics is more prevalent in the curriculum. Generally it is not easy to motivate students in Mathematics but they are motivated to find out more about the universe and Astronomy current events than appears in the media. This situation can be an excellent introduction to several mathematics topics. The teachers in secondary and high school can use this idea in order to present more attractive mathematics courses. In particular some different examples will be offered regarding * Angles and spherical coordinates considering star traces * Logarithms and visual magnitudes * Plane trigonometry related orbital movements * Spherical trigonometry in connection with ecliptic obliquity * Conic curves related to sundial at several latitudes Some students do not enjoy studying Mathematics but they can be attracted by practical situations using Applied Mathematics: Astronomy is always very attractive to teenagers.
ERIC Educational Resources Information Center
Fennema, Elizabeth, Ed.; Leder, Gilah C., Ed.
This book reports on various studies that have increased our understanding of why females and males learn different kinds and amounts of mathematics. In particular, this book explicates the Autonomous Learning Behavior model, proposed by Fennema and Peterson, which is a possible explanation of the development of gender differences in mathematics.…
Business Mathematics Curriculum.
ERIC Educational Resources Information Center
EASTCONN Regional Educational Services Center, North Windham, CT.
This curriculum guide for teaching business mathematics in the Connecticut Vocational-Technical School System is based on the latest thinking of instructors in the field, suggestions from mathematics authorities, and current instructional approaches in education. The curriculum guide consists of six sections: (1) career relationships and…
Strengthen Your Mathematical Muscles
ERIC Educational Resources Information Center
Wohlhuter, Kay A.; Breyfogle, M. Lynn; McDuffie, Amy Roth
2010-01-01
Developing deep knowledge and understanding of mathematics is a lifelong process, and building the foundation for teachers' development must begin in preservice preparation and continue throughout one's professional life. While teaching mathematics content courses and methods courses, the authors have found that preservice elementary school…
ERIC Educational Resources Information Center
Sharp, John
2012-01-01
This relationship is omnipresent to those who appreciate the shared attributes of these two areas of creativity. The dynamic nature of media, and further study, enable mathematicians and artists to present new and exciting manifestations of the "mathematics in art", and the "art in mathematics". The illustrative images of the relationship--that…
Genders, Mathematics, and Feminisms.
ERIC Educational Resources Information Center
Damarin, Suzanne
Historical studies reveal that mathematics has been claimed as a private domain by men, while studies of the popular press document that women and girls are considered incompetent in that field. The study of gender and mathematics as viewed through feminism can create a new reading which exposes hidden assumptions, unwarranted conclusions, and…
Mathematics Projects Handbook.
ERIC Educational Resources Information Center
Hess, Adrien L.
This handbook is designed as a guide for teachers and students in choosing and developing mathematics projects, from simple demonstrations of mathematical problems or principles that the teacher has assigned as classroom learning experiences to complex, sophisticated exhibits, intended for entrance in fairs and competitions. The use of projects to…
Developing Mathematical Proficiency
ERIC Educational Resources Information Center
Groves, Susie
2012-01-01
It has long been recognised that successful mathematical learning comprises much more than just knowledge of skills and procedures. For example, Skemp (1976) identified the advantages of teaching mathematics for what he referred to as "relational" rather than "instrumental" understanding. More recently, Kilpatrick, Swafford and Findell (2001)…
ERIC Educational Resources Information Center
Bureau of Naval Personnel, Washington, DC.
The first of three volumes of a mathematics training course for Navy personnel, this document covers a wide range of basic mathematics. The text begins with number systems, signed numbers, fractions, decimals, and percentages and continues into algebra with exponents, polynomials, and linear equations. Early chapters were designed to give insight…
Issues in Teaching Mathematics
ERIC Educational Resources Information Center
Ediger, Marlow
2013-01-01
In this article, the author states that there are selected issues in mathematics instruction that educators should be well aware of when planning lessons and units of study. These issues provide a basis for thought and discussion when assisting pupils to attain more optimally. Purposeful studying of issues guides mathematics teachers in…
Teaching Mathematics Using Steplets
ERIC Educational Resources Information Center
Bringslid, Odd; Norstein, Anne
2008-01-01
This article evaluates online mathematical content used for teaching mathematics in engineering classes and in distance education for teacher training students. In the EU projects Xmath and dMath online computer algebra modules (Steplets) for undergraduate students assembled in the Xmath eBook have been designed. Two questionnaires, a compulsory…
Dyslexia, Dyspraxia and Mathematics.
ERIC Educational Resources Information Center
Yeo, Dorian
This book explores how primary school children with dyslexia or dyspraxia and difficulty in math can learn math and provides practical support and detailed teaching suggestions. It considers cognitive features that underlie difficulty with mathematics generally or with specific aspects of mathematics. It outlines the ways in which children usually…
Mathematical thinking and origami
NASA Astrophysics Data System (ADS)
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
Mathematics Education in Argentina
ERIC Educational Resources Information Center
Varsavsky, Cristina; Anaya, Marta
2009-01-01
This article gives an overview of the state of mathematics education in Argentina across all levels, in the regional and world contexts. Statistics are drawn from Mercosur and UNESCO data bases, World Education Indicators and various national time-series government reports. Mathematics results in national testing programmes, Programme for…
ERIC Educational Resources Information Center
Oldfield, Christine
1996-01-01
Describes aspects of learning the language of mathematics including vocabulary and grammar, the origins of the vocabulary, the pronunciation problem, and translation of English phrases and sentences into mathematical language accompanied by conceptual understanding of the process being described. Gives suggestions for teachers in class and…
Developing Mathematically Promising Students.
ERIC Educational Resources Information Center
Sheffield, Linda Jensen, Ed.
This book, written on the recommendation of the Task Force on Mathematically Promising Students, investigates issues involving the development of promising mathematics students. Recommendations are made concerning topics such as the definition of promising students; the identification of such students; appropriate curriculum, instruction, and…
Student Nurses and Mathematics.
ERIC Educational Resources Information Center
Hutton, B. Meriel
For the safety of the public, it is essential that nurses are competent at least in the mathematics that enables them to calculate medications accurately. From a survey by G. Hek (1994), it is apparent that mathematics is not universally included in the nursing curricula, nor asked for as a pre-requisite to entry. Changes in the profile of the…
Mathematical techniques: A compilation
NASA Technical Reports Server (NTRS)
1975-01-01
Articles on theoretical and applied mathematics are introduced. The articles cover information that might be of interest to workers in statistics and information theory, computational aids that could be used by scientists and engineers, and mathematical techniques for design and control.
Encouraging Good Mathematical Writing
ERIC Educational Resources Information Center
O'Shea, J.
2006-01-01
This paper is a report on an attempt to teach students in their first and second year of university how to write mathematics. The problems faced by these students are outlined and the system devised to emphasize the importance of communicating mathematics is explained.
ERIC Educational Resources Information Center
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
A biochemical logic gate using an enzyme and its inhibitor. Part II: The logic gate.
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. PMID:12753934
Technical Mathematics: Restructure of Technical Mathematics.
ERIC Educational Resources Information Center
Flannery, Carol A.
Designed to accompany a series of videotapes, this textbook provides information, examples, problems, and solutions relating to mathematics and its applications in technical fields. Chapter I deals with basic arithmetic, providing information on fractions, decimals, ratios, proportions, percentages, and order of operations. Chapter II focuses on…
Logical Connectives as Catalysts for Interactive L2 Reading.
ERIC Educational Resources Information Center
Ozono, Shuichi; Ito, Harumi
2003-01-01
Focuses on logical connectives as catalysts for interactive reading. Clarifies how text comprehension can be affected by the types of logical relations and by the levels of proficiency in English as a Second Language, using Japanese university students as the subjects for experimentation and focusing on three logical connectives: "for…
Critical Thinking: Teaching Students To Seek the Logic of Things.
ERIC Educational Resources Information Center
Paul, Richard; Elder, Linda
1999-01-01
Asserts that becoming adept at understanding the logic of subjects, issues, and questions is a competency that, once learned, becomes a foundation for highly skilled and practical teaching and learning. Promotes the model of teaching students to seek the logic of things through the logic of science. (VWC)