Analysis of DIRAC's behavior using model checking with process algebra
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-12-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Analysis of DIRAC's behavior using model checking with process algebra
International Nuclear Information System (INIS)
Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof; Diaz, Ricardo Graciani
2012-01-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.
Analysis of DIRAC's behavior using model checking with process algebra
Remenska, Daniela; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Diaz, Ricardo Graciani; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof
2012-01-01
DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple, the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike con...
LHCb: Analysing DIRAC's Behavior using Model Checking with Process Algebra
Remenska, Daniela
2012-01-01
DIRAC is the Grid solution designed to support LHCb production activities as well as user data analysis. Based on a service-oriented architecture, DIRAC consists of many cooperating distributed services and agents delivering the workload to the Grid resources. Services accept requests from agents and running jobs, while agents run as light-weight components, fulfilling specific goals. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check for changes in the service states, and react to these accordingly. A characteristic of DIRAC's architecture is the relatively low complexity in the logic of each agent; the main source of complexity lies in their cooperation. These agents run concurrently, and communicate using the services' databases as a shared memory for synchronizing the state transitions. Although much effort is invested in making DIRAC reliable, entities occasionally get into inconsistent states, leadi...
Performance evaluation:= (process algebra + model checking) x Markov chains
Hermanns, H.; Larsen, K.G.; Nielsen, Mogens; Katoen, Joost P.
2001-01-01
Markov chains are widely used in practice to determine system performance and reliability characteristics. The vast majority of applications considers continuous-time Markov chains (CTMCs). This tutorial paper shows how successful model specification and analysis techniques from concurrency theory
Model Checking Process Algebra of Communicating Resources for Real-time Systems
DEFF Research Database (Denmark)
Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand
2014-01-01
This paper presents a new process algebra, called PACOR, for real-time systems which deals with resource constrained timed behavior as an improved version of the ACSR algebra. We define PACOR as a Process Algebra of Communicating Resources which allows to express preemptiveness, urgent ness...... and resource usage over a dense-time model. The semantic interpretation of PACOR is defined in the form of a timed transition system expressing the timed behavior and dynamic creation of processes. We define a translation of PACOR systems to Parameterized Stopwatch Automata (PSA). The translation preserves...
Model checking process algebra of communicating resources for real-time systems
DEFF Research Database (Denmark)
Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand
2014-01-01
This paper presents a new process algebra, called PACoR, for real-time systems which deals with resource- constrained timed behavior as an improved version of the ACSR algebra. We define PACoR as a Process Algebra of Communicating Resources which allows to explicitly express preemptiveness......, urgentness and resource usage over a dense-time model. The semantic interpretation of PACoR is defined in the form of a timed transition system expressing the timed behavior and dynamic creation of processes. We define a translation of PACoR systems to Parameterized Stopwatch Automata (PSA). The translation...
Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras
Andrade, Jefferson O.; Kameyama, Yukiyoshi
2012-01-01
Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In thi...
Efficient Multi-Valued Bounded Model Checking for LTL over Quasi-Boolean Algebras
Andrade, Jefferson O.; Kameyama, Yukiyoshi
Multi-valued Model Checking extends classical, two-valued model checking to multi-valued logic such as Quasi-Boolean logic. The added expressivity is useful in dealing with such concepts as incompleteness and uncertainty in target systems, while it comes with the cost of time and space. Chechik and others proposed an efficient reduction from multi-valued model checking problems to two-valued ones, but to the authors' knowledge, no study was done for multi-valued bounded model checking. In this paper, we propose a novel, efficient algorithm for multi-valued bounded model checking. A notable feature of our algorithm is that it is not based on reduction of multi-values into two-values; instead, it generates a single formula which represents multi-valuedness by a suitable encoding, and asks a standard SAT solver to check its satisfiability. Our experimental results show a significant improvement in the number of variables and clauses and also in execution time compared with the reduction-based one.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 14; Issue 7. Model Checking - Automated Verification of Computational Systems. Madhavan Mukund. General Article Volume 14 Issue 7 July 2009 pp 667-681. Fulltext. Click here to view fulltext PDF. Permanent link:
Model Checking Feature Interactions
DEFF Research Database (Denmark)
Le Guilly, Thibaut; Olsen, Petur; Pedersen, Thomas
2015-01-01
This paper presents an offline approach to analyzing feature interactions in embedded systems. The approach consists of a systematic process to gather the necessary information about system components and their models. The model is first specified in terms of predicates, before being refined to t...... to timed automata. The consistency of the model is verified at different development stages, and the correct linkage between the predicates and their semantic model is checked. The approach is illustrated on a use case from home automation....
"Lost chains" in algebraic models
Fortunato, L.; de Graaf, W. A.
2011-03-01
The algebraic structure of some of the simplest algebraic models u(2), u(3) and u(4), widely used in several branches of physics either as toy models or as working instruments, are reanalyzed under a new perspective that releases the requirement that chains should terminate or pass through the angular momentum algebra. Unitary algebras are non-semisimple, therefore we first apply the Levi-Malcev decomposition. Then we use the theory of weighted Dynkin diagrams to identify conjugacy classes of A1 ~ su(2) ~ so(3) subalgebras: a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries follows that we substantiate with examples.
Parallel Algorithms for Model Checking
van de Pol, Jaco; Mousavi, Mohammad Reza; Sgall, Jiri
2017-01-01
Model checking is an automated verification procedure, which checks that a model of a system satisfies certain properties. These properties are typically expressed in some temporal logic, like LTL and CTL. Algorithms for LTL model checking (linear time logic) are based on automata theory and graph
Linear Algebra and Linear Models
Indian Academy of Sciences (India)
Linear Algebra and Linear. Models. Kalyan Das. Linear Algebra and linear Models. (2nd Edn) by R P Bapat. Hindustan Book Agency, 1999 pp.xiii+180, Price: Rs.135/-. This monograph provides an introduction to the basic aspects of the theory oflinear estima- tion and that of testing linear hypotheses. The primary objective ...
Compositional and Quantitative Model Checking
DEFF Research Database (Denmark)
Larsen, Kim Guldstrand
2010-01-01
This paper gives a survey of a composition model checking methodology and its succesfull instantiation to the model checking of networks of finite-state, timed, hybrid and probabilistic systems with respect; to suitable quantitative versions of the modal mu-calculus [Koz82]. The method is based...
Model Checking Algorithms for CTMDPs
DEFF Research Database (Denmark)
Buchholz, Peter; Hahn, Ernst Moritz; Hermanns, Holger
2011-01-01
Continuous Stochastic Logic (CSL) can be interpreted over continuoustime Markov decision processes (CTMDPs) to specify quantitative properties of stochastic systems that allow some external control. Model checking CSL formulae over CTMDPs requires then the computation of optimal control strategie...
Model Checking Algorithms for Markov Reward Models
Cloth, Lucia; Cloth, L.
2006-01-01
Model checking Markov reward models unites two different approaches of model-based system validation. On the one hand, Markov reward models have a long tradition in model-based performance and dependability evaluation. On the other hand, a formal method like model checking allows for the precise
The Probabilistic Model Checking Landscape
Katoen, Joost P.
Randomization is a key element in sequential and distributed computing. Reasoning about randomized algorithms is highly nontrivial. In the 1980s, this initiated first proof methods, logics, and model-checking algorithms. The field of probabilistic verification has developed considerably since then.
Model checking embedded system designs
Brinksma, Hendrik; Mader, Angelika H.
2002-01-01
Model checking has established itself as a successful tool supported technique for the verification and debugging of various hardware and software systems [16]. Not only in academia, but also by industry this technique is increasingly being regarded as a promising and practical proposition,
Advances in Probabilistic Model Checking
Katoen, Joost P.; Barthe, G.; Hermenegildo, M.
Random phenomena occur in many applications: security, communication protocols, distributed algorithms, and performance and dependability analysis, to mention a few. In the last two decades, efficient model-checking algorithms and tools have been developed to support the automated verification of
Matrix algebra for linear models
Gruber, Marvin H J
2013-01-01
Matrix methods have evolved from a tool for expressing statistical problems to an indispensable part of the development, understanding, and use of various types of complex statistical analyses. This evolution has made matrix methods a vital part of statistical education. Traditionally, matrix methods are taught in courses on everything from regression analysis to stochastic processes, thus creating a fractured view of the topic. Matrix Algebra for Linear Models offers readers a unique, unified view of matrix analysis theory (where and when necessary), methods, and their applications. Written f
Compositional and Quantitative Model Checking
DEFF Research Database (Denmark)
Larsen, Kim Guldstrand
2010-01-01
on the existence of a quotient construction, allowing a property phi of a parallel system phi/A to be transformed into a sufficient and necessary quotient-property yolA to be satisfied by the component 13. Given a model checking problem involving a network Pi I and a property yo, the method gradually move (by...... quotienting) components Pi from the network into the formula co. Crucial to the success of the method is the ability to manage the size of the intermediate quotient-properties by a suitable collection of efficient minimization heuristics....
Model Checking as Static Analysis
DEFF Research Database (Denmark)
Zhang, Fuyuan
fairness problems can be encoded into ALFP as well. To deal with multi-valued model checking problems, we have proposed multivalued ALFP. A Moore Family result for multi-valued ALFP is also established, which ensures the existence and uniqueness of the least model. When the truth values in multi-valued...... of states satisfying a CTL formula can be characterized as the least model of ALFP clauses specifying this CTL formula. The existence of the least model of ALFP clauses is ensured by the Moore Family property of ALFP. Then, we take fairness assumptions in CTL into consideration and have shown that CTL...... ALFP constitute a nite distributive complete lattice, multi-valued ALFP can be reduced to two-valued ALFP. This result enables to implement a solver for multi-valued ALFP by reusing existing solvers for twovalued ALFP. Our ALFP-based technique developed for the two-valued CTL naturally generalizes...
Model Checking Structured Infinite Markov Chains
Remke, Anne Katharina Ingrid
2008-01-01
In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special
Critical analysis of algebraic collective models
International Nuclear Information System (INIS)
Moshinsky, M.
1986-01-01
The author shall understand by algebraic collective models all those based on specific Lie algebras, whether the latter are suggested through simple shell model considerations like in the case of the Interacting Boson Approximation (IBA), or have a detailed microscopic foundation like the symplectic model. To analyze these models critically, it is convenient to take a simple conceptual example of them in which all steps can be implemented analytically or through elementary numerical analysis. In this note he takes as an example the symplectic model in a two dimensional space i.e. based on a sp(4,R) Lie algebra, and show how through its complete discussion we can get a clearer understanding of the structure of algebraic collective models of nuclei. In particular he discusses the association of Hamiltonians, related to maximal subalgebras of our basic Lie algebra, with specific types of spectra, and the connections between spectra and shapes
Program Analysis as Model Checking
DEFF Research Database (Denmark)
Olesen, Mads Chr.
and abstract interpretation. Model checking views the program as a finite automaton and tries to prove logical properties over the automaton model, or present a counter-example if not possible — with a focus on precision. Abstract interpretation translates the program semantics into abstract semantics...... are considered, among others numerical analysis of c programs, and worst-case execution time analysis of ARM programs. It is shown how lattice automata allow automatic and manual tuning of the precision and efficiency of the verification procedure. In the case of worst-case execution time analysis a sound......Software programs are proliferating throughout modern life, to a point where even the simplest appliances such as lightbulbs contain software, in addition to the software embedded in cars and airplanes. The correct functioning of these programs is therefore of the utmost importance, for the quality...
Modeling digital switching circuits with linear algebra
Thornton, Mitchell A
2014-01-01
Modeling Digital Switching Circuits with Linear Algebra describes an approach for modeling digital information and circuitry that is an alternative to Boolean algebra. While the Boolean algebraic model has been wildly successful and is responsible for many advances in modern information technology, the approach described in this book offers new insight and different ways of solving problems. Modeling the bit as a vector instead of a scalar value in the set {0, 1} allows digital circuits to be characterized with transfer functions in the form of a linear transformation matrix. The use of transf
Representations of the Virasoro algebra from lattice models
International Nuclear Information System (INIS)
Koo, W.M.; Saleur, H.
1994-01-01
We investigate in detail how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic relations are obeyed in the scaling limit. The latter is under reasonable control thanks to the Bethe-ansatz solution. The results, which are mostly numerical for technical reasons, are remarkably precise. They are also corroborated by exact pieces of information from various sources, in particular Temperley-Lieb algebra representation theory. Most features of the Virasoro algebra (like central term, null vectors, metric properties, etc.) can thus be observed using the lattice models. This seems of general interest for lattice field theory, and also more specifically for finding relations between conformal invariance and lattice integrability, since a basis for the irreducible representations of the Virasoro algebra should now follow (at least in principle) from Bethe-ansatz computations. ((orig.))
Model checking mobile ad hoc networks
Ghassemi, Fatemeh; Fokkink, Wan
2016-01-01
Modeling arbitrary connectivity changes within mobile ad hoc networks (MANETs) makes application of automated formal verification challenging. We use constrained labeled transition systems as a semantic model to represent mobility. To model check MANET protocols with respect to the underlying
W algebra in the SU(3) parafermion model
International Nuclear Information System (INIS)
Ding, X.; Fan, H.; Shi, K.; Wang, P.; Zhu, C.
1993-01-01
A construction of W 3 algebra for the SU(3) parafermion model is proposed, in which a Z algebra technique is used instead of the popular free-field realization. The central charge of the underlying algebra is different from known W algebras
Compositional model checking of concurrent systems, with Petri nets
Directory of Open Access Journals (Sweden)
Paweł Sobociński
2016-03-01
Full Text Available Compositionality and process equivalence are both standard concepts of process algebra. Compositionality means that the behaviour of a compound system relies only on the behaviour of its components, i.e. there is no emergent behaviour. Process equivalence means that the explicit statespace of a system takes a back seat to its interaction patterns: the information that an environment can obtain though interaction. Petri nets are a classical, yet widely used and understood, model of concurrency. Nevertheless, they have often been described as a non-compositional model, and tools tend to deal with monolithic, globally-specified models. This tutorial paper concentrates on Petri Nets with Boundaries (PNB: a compositional, graphical algebra of 1-safe nets, and its applications to reachability checking within the tool Penrose. The algorithms feature the use of compositionality and process equivalence, a powerful combination that can be harnessed to improve the performance of checking reachability and coverability in several common examples where Petri nets model realistic concurrent systems.
Chiral algebras in Landau-Ginzburg models
Dedushenko, Mykola
2018-03-01
Chiral algebras in the cohomology of the {\\overline{Q}}+ supercharge of two-dimensional N=(0,2) theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group invariant for theories with an R-symmetry. For N=(0,2) Landau-Ginzburg models, the chiral algebra is determined by the operator equations of motion, which preserve their classical form, and quantum renormalization of composite operators. We study these theories and then specialize to the N=(2,2) models and consider some examples.
Solving scheduling problems by untimed model checking. The clinical chemical analyser case study
Margaria, T.; Wijs, Anton J.; Massink, M.; van de Pol, Jan Cornelis; Bortnik, Elena M.
2009-01-01
In this article, we show how scheduling problems can be modelled in untimed process algebra, by using special tick actions. A minimal-cost trace leading to a particular action, is one that minimises the number of tick steps. As a result, we can use any (timed or untimed) model checking tool to find
Logical Specification and Analysis of Fault Tolerant Systems through Partial Model Checking
Gnesi, S.; Etalle, Sandro; Mukhopadhyay, S.; Lenzini, Gabriele; Lenzini, G.; Martinelli, F.; Roychoudhury, A.
2003-01-01
This paper presents a framework for a logical characterisation of fault tolerance and its formal analysis based on partial model checking techniques. The framework requires a fault tolerant system to be modelled using a formal calculus, here the CCS process algebra. To this aim we propose a uniform
A process algebra model of QED
International Nuclear Information System (INIS)
Sulis, William
2016-01-01
The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics. (paper)
Model checking sum and product
van Ditmarsch, H; Ruan, H; Verbrugge, L.C.; Zhang, S.; Jarvis, R.
2005-01-01
We model the well-known Sum-and-Product problem in a modal logic, and verify its solution in a model checker. The modal logic is public announcement logic. The riddle is then implemented and its solution verified in the epistemic model checker DEMO.
Current algebra, statistical mechanics and quantum models
Vilela Mendes, R.
2017-11-01
Results obtained in the past for free boson systems at zero and nonzero temperatures are revisited to clarify the physical meaning of current algebra reducible functionals which are associated to systems with density fluctuations, leading to observable effects on phase transitions. To use current algebra as a tool for the formulation of quantum statistical mechanics amounts to the construction of unitary representations of diffeomorphism groups. Two mathematical equivalent procedures exist for this purpose. One searches for quasi-invariant measures on configuration spaces, the other for a cyclic vector in Hilbert space. Here, one argues that the second approach is closer to the physical intuition when modelling complex systems. An example of application of the current algebra methodology to the pairing phenomenon in two-dimensional fermion systems is discussed.
Model Checking Discounted Temporal Properties
de Alfaro, Luca; Faella, Marco; Henzinger, Thomas A.; Majumdar, Rupak; Stoelinga, Mariëlle Ida Antoinette; Jensen, K; Podelski, A.
2004-01-01
Temporal logic is two-valued: a property is either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a
Model Checking Discounted Temporal Properties
de Alfaro, Luca; Faella, Marco; Henzinger, Thomas A.; Majumdar, Rupak; Stoelinga, Mariëlle Ida Antoinette
2005-01-01
Temporal logic is two-valued: a property is either true or false. When applied to the analysis of stochastic systems, or systems with imprecise formal models, temporal logic is therefore fragile: even small changes in the model can lead to opposite truth values for a specification. We present a
ERBE bidirectional model consistency check
Baldwin, D. G.; Coakley, J. A., Jr.
1986-01-01
A short analysis is presented of Earth Radiation Budget Experiment (ERBE) errors inherent in the directional models used for data interpretation. The models were all developed on the basis of experience with the Nimbus-7 ERB experiment, which had a spatial resolution one-third that of ERBE instrumentation. A pseudo-directional model is defined to simulate the ERBE scanner data, using the assumptions that the average radiant exitance for any particular scene is independent of the viewing geometry, geographic location and time the data is collected. The directionality of the view angle and solar zenith angle is accounted for by a method of bins.
Model Checking Discounted Temporal Properties
National Research Council Canada - National Science Library
de Alfaro, Luca; Faella, Marco; Henzinger, Thomas A; Majumdar, Rupak; Stoelinga, Marieelle
2005-01-01
...) which achieves robustness with respect to model perturbations by giving a quantitative interpretation to predicates and logical operators, and by discounting the importance of events according to how late they occur...
Posterior Predictive Model Checking in Bayesian Networks
Crawford, Aaron
2014-01-01
This simulation study compared the utility of various discrepancy measures within a posterior predictive model checking (PPMC) framework for detecting different types of data-model misfit in multidimensional Bayesian network (BN) models. The investigated conditions were motivated by an applied research program utilizing an operational complex…
Improved Nonequilibrium Algebraic Model Of Turbulence
Johnson, D. A.; Coakley, T. J.
1993-01-01
Blend of previous models predicts pressure distributions more accurately. Improved algebraic model represents some of time-averaged effects of turbulence in transonic flow of air over airfoil. Based partly on comparisons among various eddy-viscosity formulations for turbulence and partly on premise that law of wall more universally valid in immediate region of surface in presence of adverse gradient of pressure than mixing-length theory and original Johnson and King model.
Map algebra and model algebra for integrated model building
Schmitz, O.; Karssenberg, D.J.; Jong, K. de; Kok, J.-L. de; Jong, S.M. de
2013-01-01
Computer models are important tools for the assessment of environmental systems. A seamless workflow of construction and coupling of model components is essential for environmental scientists. However, currently available software packages are often tailored either to the construction of model
Tabak, John
2004-01-01
Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.
Model checking exact cost for attack scenarios
DEFF Research Database (Denmark)
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
. However, current model checking does not encompass the exact cost analysis of an attack, which is standard for attack trees. Our first contribution is the logic erPCTL with cost-related operators. The extended logic allows to analyse the probability of an event satisfying given cost bounds and to compute......Attack trees constitute a powerful tool for modelling security threats. Many security analyses of attack trees can be seamlessly expressed as model checking of Markov Decision Processes obtained from the attack trees, thus reaping the benefits of a coherent framework and a mature tool support...... the exact cost of an event. Our second contribution is the model checking algorithm for erPCTL. Finally, we apply our framework to the analysis of attack trees....
Engineering Abstractions in Model Checking and Testing
DEFF Research Database (Denmark)
Achenbach, Michael; Ostermann, Klaus
2009-01-01
Abstractions are used in model checking to tackle problems like state space explosion or modeling of IO. The application of these abstractions in real software development processes, however, lacks engineering support. This is one reason why model checking is not widely used in practice yet...... and testing is still state of the art in falsification. We show how user-defined abstractions can be integrated into a Java PathFinder setting with tools like AspectJ or Javassist and discuss implications of remaining weaknesses of these tools. We believe that a principled engineering approach to designing...
A Method for Model Checking Feature Interactions
DEFF Research Database (Denmark)
Pedersen, Thomas; Le Guilly, Thibaut; Ravn, Anders Peter
2015-01-01
This paper presents a method to check for feature interactions in a system assembled from independently developed concurrent processes as found in many reactive systems. The method combines and refines existing definitions and adds a set of activities. The activities describe how to populate the ...... the definitions with models to ensure that all interactions are captured. The method is illustrated on a home automation example with model checking as analysis tool. In particular, the modelling formalism is timed automata and the analysis uses UPPAAL to find interactions....
A Simple and Practical Linear Algebra Library Interface with Static Size Checking
Directory of Open Access Journals (Sweden)
Akinori Abe
2015-12-01
Full Text Available Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime errors. While advanced type systems—specifically, dependent types on natural numbers—can ensure consistency among the sizes of collections such as lists and arrays, such type systems generally require non-trivial changes to existing languages and application programs, or tricky type-level programming. We have developed a linear algebra library interface that verifies the consistency (with respect to dimensions of matrix operations by means of generative phantom types, implemented via fairly standard ML types and module system. To evaluate its usability, we ported to it a practical machine learning library from a traditional linear algebra library. We found that most of the changes required for the porting could be made mechanically, and changes that needed human thought are minor.
Stoutemyer, D. R.
1977-01-01
The computer algebra language MACSYMA enables the programmer to include symbolic physical units in computer calculations, and features automatic detection of dimensionally-inhomogeneous formulas and conversion of inconsistent units in a dimensionally homogeneous formula. Some examples illustrate these features.
Model Checking Dynamic States in GROOVE
Kastenberg, H.; Rensink, Arend; Valmari, A.
2006-01-01
Much research has been done in the field of model-checking complex systems (either hardware or software). Approaches that use explicit state modelling mostly use bit vectors to represent the states of such systems. Unfortunately, that kind of representation does not extend smoothly to systems in
Discrete-time rewards model-checked
Larsen, K.G.; Andova, S.; Niebert, Peter; Hermanns, H.; Katoen, Joost P.
2003-01-01
This paper presents a model-checking approach for analyzing discrete-time Markov reward models. For this purpose, the temporal logic probabilistic CTL is extended with reward constraints. This allows to formulate complex measures – involving expected as well as accumulated rewards – in a precise and
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand
2012-01-01
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique ap...
Algebra of charges in the supersymmetric nonlinear sigma model
Energy Technology Data Exchange (ETDEWEB)
Barcelos-Neto, J.; Das, A.; Maharana, J.
1986-03-01
We examine the algebra of the nonlocal charges in the supersymmetric nonlinear sigma model and show that they satisfy a nonlinear algebra at the tree-level. We also discuss other interesting questions like the transformation of these charges under a supersymmetry transformation and speculate that this algebra possibly continues to hold in the full quantum theory. (orig.).
Flanders, Harley
1975-01-01
Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a
Model checking the HAVi leader election protocol
J.M.T. Romijn (Judi)
1999-01-01
textabstractThe HAVi specification proposes an architecture for audio/video interoperability in home networks. Part of the HAVi specification is a distributed leader election protocol. We have modelled this leader election protocol in Promela and Lotos and have checked several properties with the
Model Checking - Automated Verification of Computational Systems
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 14; Issue 7. Model Checking - Automated Verification of Computational Systems. Madhavan Mukund. General Article Volume 14 Issue 7 July 2009 pp 667-681. Fulltext. Click here to view fulltext PDF. Permanent link:
Automata-Based CSL Model Checking
DEFF Research Database (Denmark)
Zhang, Lijun; Jansen, David N.; Nielson, Flemming
2011-01-01
For continuous-time Markov chains, the model-checking problem with respect to continuous-time stochastic logic (CSL) has been introduced and shown to be decidable by Aziz, Sanwal, Singhal and Brayton in 1996. The presented decision procedure, however, has exponential complexity. In this paper, we...
Posterior predictive checking of multiple imputation models.
Nguyen, Cattram D; Lee, Katherine J; Carlin, John B
2015-07-01
Multiple imputation is gaining popularity as a strategy for handling missing data, but there is a scarcity of tools for checking imputation models, a critical step in model fitting. Posterior predictive checking (PPC) has been recommended as an imputation diagnostic. PPC involves simulating "replicated" data from the posterior predictive distribution of the model under scrutiny. Model fit is assessed by examining whether the analysis from the observed data appears typical of results obtained from the replicates produced by the model. A proposed diagnostic measure is the posterior predictive "p-value", an extreme value of which (i.e., a value close to 0 or 1) suggests a misfit between the model and the data. The aim of this study was to evaluate the performance of the posterior predictive p-value as an imputation diagnostic. Using simulation methods, we deliberately misspecified imputation models to determine whether posterior predictive p-values were effective in identifying these problems. When estimating the regression parameter of interest, we found that more extreme p-values were associated with poorer imputation model performance, although the results highlighted that traditional thresholds for classical p-values do not apply in this context. A shortcoming of the PPC method was its reduced ability to detect misspecified models with increasing amounts of missing data. Despite the limitations of posterior predictive p-values, they appear to have a valuable place in the imputer's toolkit. In addition to automated checking using p-values, we recommend imputers perform graphical checks and examine other summaries of the test quantity distribution. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Algebraic model of baryon resonances
International Nuclear Information System (INIS)
Bijker, R.; Leviatan, A.
1997-01-01
We discuss recent calculations of electromagnetic form factors and strong decay widths of nucleon and delta resonances. The calculations are done in a collective constituent model of the nucleon, in which the baryons are interpreted as rotations and vibrations of an oblate top
Model Checking as Static Analysis: Revisited
DEFF Research Database (Denmark)
Zhang, Fuyuan; Nielson, Flemming; Nielson, Hanne Riis
2012-01-01
We show that the model checking problem of the μ-calculus can be viewed as an instance of static analysis. We propose Succinct Fixed Point Logic (SFP) within our logical approach to static analysis as an extension of Alternation-free Least Fixed Logic (ALFP). We generalize the notion of stratific......We show that the model checking problem of the μ-calculus can be viewed as an instance of static analysis. We propose Succinct Fixed Point Logic (SFP) within our logical approach to static analysis as an extension of Alternation-free Least Fixed Logic (ALFP). We generalize the notion...... of stratification to weak stratification and establish a Moore Family result for the new logic as well. The semantics of the μ-calculus is encoded as the intended model of weakly stratified clause sequences in SFP....
Sepanski, Mark R
2010-01-01
Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems
Current algebra of WZNW models at and away from criticality
International Nuclear Information System (INIS)
Abdalla, E.; Forger, M.
1992-01-01
In this paper, the authors derive the current algebra of principal chiral models with a Wess-Zumino term. At the critical coupling where the model becomes conformally invariant (Wess-Zumino-Novikov-Witten theory), this algebra reduces to two commuting Kac-Moody algebras, while in the limit where the coupling constant is taken to zero (ordinary chiral model), we recover the current algebra of that model. In this way, the latter is explicitly realized as a deformation of the former, with the coupling constant as the deformation parameter
Vibrational spectrum of CF4 isotopes in an algebraic model
Indian Academy of Sciences (India)
This new model appears to describe the molecular spectra successfully even in complex situations. The use of Lie algebra did not develop fully until 1970s when it was introduced in a systematic fashion by Iachello and Arima to study the spectra of atomic nuclei (interacting boson model) [3]. The algebraic model which was ...
Isovectorial pairing in solvable and algebraic models
International Nuclear Information System (INIS)
Lerma, Sergio; Vargas, Carlos E; Hirsch, Jorge G
2011-01-01
Schematic interactions are useful to gain some insight in the behavior of very complicated systems such as the atomic nuclei. Prototypical examples are, in this context, the pairing interaction and the quadrupole interaction of the Elliot model. In this contribution the interplay between isovectorial pairing, spin-orbit, and quadrupole terms in a harmonic oscillator shell (the so-called pairing-plus-quadrupole model) is studied by algebraic methods. The ability of this model to provide a realistic description of N = Z even-even nuclei in the fp-shell is illustrated with 44 Ti. Our calculations which derive from schematic and simple terms confirm earlier conclusions obtained by using realistic interactions: the SU(3) symmetry of the quadrupole term is broken mainly by the spin-orbit term, but the energies depends strongly on pairing.
'Lost chains' in algebraic models
Energy Technology Data Exchange (ETDEWEB)
Fortunato, L [European Centre for Theoretical Studies in Nuclear Physics and Related Areas, Strada delle Tabarelle 286, I-38123 Villazzano (Italy); Graaf, W A de, E-mail: fortunat@pd.infn.it [Dip. Matematica, Universita di Trento, via Sommarive 24, I-38123 Povo, Trento (Italy)
2011-03-01
The algebraic structure of some of the simplest algebraic models u(2), u(3) and u(4), widely used in several branches of physics either as toy models or as working instruments, are reanalyzed under a new perspective that releases the requirement that chains should terminate or pass through the angular momentum algebra. Unitary algebras are non-semisimple, therefore we first apply the Levi-Malcev decomposition. Then we use the theory of weighted Dynkin diagrams to identify conjugacy classes of A{sub 1} {approx} su(2) {approx} so(3) subalgebras: a complete classification of new angular momentum non conserving (AMNC) dynamical symmetries follows that we substantiate with examples.
Statistical Model Checking for Biological Systems
DEFF Research Database (Denmark)
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel
2014-01-01
Statistical Model Checking (SMC) is a highly scalable simulation-based verification approach for testing and estimating the probability that a stochastic system satisfies a given linear temporal property. The technique has been applied to (discrete and continuous time) Markov chains, stochastic...... timed automata and most recently hybrid systems using the tool Uppaal SMC. In this paper we enable the application of SMC to complex biological systems, by combining Uppaal SMC with ANIMO, a plugin of the tool Cytoscape used by biologists, as well as with SimBiology®, a plugin of Matlab to simulate...
Statistical Model Checking for Product Lines
DEFF Research Database (Denmark)
ter Beek, Maurice H.; Legay, Axel; Lluch Lafuente, Alberto
2016-01-01
We report on the suitability of statistical model checking for the analysis of quantitative properties of product line models by an extended treatment of earlier work by the authors. The type of analysis that can be performed includes the likelihood of specific product behaviour, the expected...... average cost of products (in terms of the attributes of the products’ features) and the probability of features to be (un)installed at runtime. The product lines must be modelled in QFLan, which extends the probabilistic feature-oriented language PFLan with novel quantitative constraints among features...... behaviour converge in a discrete-time Markov chain semantics, enabling the analysis of quantitative properties. Technically, a Maude implementation of QFLan, integrated with Microsoft’s SMT constraint solver Z3, is combined with the distributed statistical model checker MultiVeStA, developed by one...
N=2 current algebra and coset models
International Nuclear Information System (INIS)
Hull, C.M.; Spence, B.
1990-01-01
The N=2 supersymmetric extension of the Kac-Moody algebra and the corresponding Sugawara construction of the N=2 superconformal algebra are discussed both in components and in N=1 superspace. A formulation of the Kac-Moody algebra and Sugawara construction is given in N=2 superspace in terms of supercurrents satisfying a non-linear chiral constraint. The operator product of two supercurrents includes terms that are non-linear in the supercurrents. The N=2 generalization of the GKO coset construction is then given and the conditions found by Kazama and Suzuki are seen to arise from the non-linearity of the algebra. (orig.)
Model Checking JAVA Programs Using Java Pathfinder
Havelund, Klaus; Pressburger, Thomas
2000-01-01
This paper describes a translator called JAVA PATHFINDER from JAVA to PROMELA, the "programming language" of the SPIN model checker. The purpose is to establish a framework for verification and debugging of JAVA programs based on model checking. This work should be seen in a broader attempt to make formal methods applicable "in the loop" of programming within NASA's areas such as space, aviation, and robotics. Our main goal is to create automated formal methods such that programmers themselves can apply these in their daily work (in the loop) without the need for specialists to manually reformulate a program into a different notation in order to analyze the program. This work is a continuation of an effort to formally verify, using SPIN, a multi-threaded operating system programmed in Lisp for the Deep-Space 1 spacecraft, and of previous work in applying existing model checkers and theorem provers to real applications.
Experimental Tests of the Algebraic Cluster Model
Gai, Moshe
2018-02-01
The Algebraic Cluster Model (ACM) of Bijker and Iachello that was proposed already in 2000 has been recently applied to 12C and 16O with much success. We review the current status in 12C with the outstanding observation of the ground state rotational band composed of the spin-parity states of: 0+, 2+, 3-, 4± and 5-. The observation of the 4± parity doublet is a characteristic of (tri-atomic) molecular configuration where the three alpha- particles are arranged in an equilateral triangular configuration of a symmetric spinning top. We discuss future measurement with electron scattering, 12C(e,e’) to test the predicted B(Eλ) of the ACM.
Galois Connections for Flow Algebras
DEFF Research Database (Denmark)
Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis
2011-01-01
to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Current algebra of classical non-linear sigma models
International Nuclear Information System (INIS)
Forger, M.; Laartz, J.; Schaeper, U.
1992-01-01
The current algebra of classical non-linear sigma models on arbitrary Riemannian manifolds is analyzed. It is found that introducing, in addition to the Noether current j μ associated with the global symmetry of the theory, a composite scalar field j, the algebra closes under Poisson brackets. (orig.)
Software engineering with process algebra: Modelling client / server architecures
Diertens, B.
2009-01-01
In previous work we described how the process algebra based language PSF can be used in software engineering, using the ToolBus, a coordination architecture also based on process algebra, as implementation model. We also described this software development process more formally by presenting the
Action Algebras and Model Algebras in Denotational Semantics
Guedes, Luiz Carlos Castro; Haeusler, Edward Hermann
This article describes some results concerning the conceptual separation of model dependent and language inherent aspects in a denotational semantics of a programming language. Before going into the technical explanation, the authors wish to relate a story that illustrates how correctly and precisely posed questions can influence the direction of research. By means of his questions, Professor Mosses aided the PhD research of one of the authors of this article and taught the other, who at the time was a novice supervisor, the real meaning of careful PhD supervision. The student’s research had been partially developed towards the implementation of programming languages through denotational semantics specification, and the student had developed a prototype [12] that compared relatively well to some industrial compilers of the PASCAL language. During a visit to the BRICS lab in Aarhus, the student’s supervisor gave Professor Mosses a draft of an article describing the prototype and its implementation experiments. The next day, Professor Mosses asked the supervisor, “Why is the generated code so efficient when compared to that generated by an industrial compiler?” and “You claim that the efficiency is simply a consequence of the Object- Orientation mechanisms used by the prototype programming language (C++); this should be better investigated. Pay more attention to the class of programs that might have this good comparison profile.” As a result of these aptly chosen questions and comments, the student and supervisor made great strides in the subsequent research; the advice provided by Professor Mosses made them perceive that the code generated for certain semantic domains was efficient because it mapped to the “right aspect” of the language semantics. (Certain functional types, used to represent mappings such as Stores and Environments, were pushed to the level of the object language (as in gcc). This had the side-effect of generating code for arrays in
Algebraic Modeling of Topological and Computational Structures and Applications
Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis
2017-01-01
This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w...
Classification and checking model of pedestrian crossing
Directory of Open Access Journals (Sweden)
Luis Delgado Méndez
2012-11-01
After realizing this investigation it can be confirmed that the functionality of a pedestrian crossing depends on almost a hundred parameters which must be checked or measured, in turn proving that this design and construction process is indeed complex.
Statistical Model Checking of Rich Models and Properties
DEFF Research Database (Denmark)
Poulsen, Danny Bøgsted
Software is in increasing fashion embedded within safety- and business critical processes of society. Errors in these embedded systems can lead to human casualties or severe monetary loss. Model checking technology has proven formal methods capable of finding and correcting errors in software...... motivates why existing model checking technology should be supplemented by new techniques. It also contains a brief introduction to probability theory and concepts covered by the six papers making up the second part. The first two papers are concerned with developing online monitoring techniques...... systems. The fifth paper shows how stochastic hybrid automata are useful for modelling biological systems and the final paper is concerned with showing how statistical model checking is efficiently distributed. In parallel with developing the theory contained in the papers, a substantial part of this work...
Posterior Predictive Model Checking for Multidimensionality in Item Response Theory
Levy, Roy; Mislevy, Robert J.; Sinharay, Sandip
2009-01-01
If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold. The current work pursues posterior predictive model checking, a flexible family of model-checking procedures, as a tool for criticizing models due to unaccounted for dimensions in the context of item response theory. Factors…
Hyper-lattice algebraic model for data warehousing
Sen, Soumya; Chaki, Nabendu
2016-01-01
This book presents Hyper-lattice, a new algebraic model for partially ordered sets, and an alternative to lattice. The authors analyze some of the shortcomings of conventional lattice structure and propose a novel algebraic structure in the form of Hyper-lattice to overcome problems with lattice. They establish how Hyper-lattice supports dynamic insertion of elements in a partial order set with a partial hierarchy between the set members. The authors present the characteristics and the different properties, showing how propositions and lemmas formalize Hyper-lattice as a new algebraic structure.
Model checking in multiple imputation: an overview and case study
Directory of Open Access Journals (Sweden)
Cattram D. Nguyen
2017-08-01
Full Text Available Abstract Background Multiple imputation has become very popular as a general-purpose method for handling missing data. The validity of multiple-imputation-based analyses relies on the use of an appropriate model to impute the missing values. Despite the widespread use of multiple imputation, there are few guidelines available for checking imputation models. Analysis In this paper, we provide an overview of currently available methods for checking imputation models. These include graphical checks and numerical summaries, as well as simulation-based methods such as posterior predictive checking. These model checking techniques are illustrated using an analysis affected by missing data from the Longitudinal Study of Australian Children. Conclusions As multiple imputation becomes further established as a standard approach for handling missing data, it will become increasingly important that researchers employ appropriate model checking approaches to ensure that reliable results are obtained when using this method.
Model checking in multiple imputation: an overview and case study.
Nguyen, Cattram D; Carlin, John B; Lee, Katherine J
2017-01-01
Multiple imputation has become very popular as a general-purpose method for handling missing data. The validity of multiple-imputation-based analyses relies on the use of an appropriate model to impute the missing values. Despite the widespread use of multiple imputation, there are few guidelines available for checking imputation models. In this paper, we provide an overview of currently available methods for checking imputation models. These include graphical checks and numerical summaries, as well as simulation-based methods such as posterior predictive checking. These model checking techniques are illustrated using an analysis affected by missing data from the Longitudinal Study of Australian Children. As multiple imputation becomes further established as a standard approach for handling missing data, it will become increasingly important that researchers employ appropriate model checking approaches to ensure that reliable results are obtained when using this method.
Observable algebras for the rational and trigonometric Euler-Calogero-Moser Models
International Nuclear Information System (INIS)
Avan, J.; Billey, E.
1995-01-01
We construct polynomial Poisson algebras of observables for the classical Euler-Calogero-Moser (ECM) models. Their structure connects them to flavour-indexed non-linear W ∞ algebras, albeit with qualitative differences. The conserved Hamiltonians and symmetry algebras derived in a previous work are subsets of these algebra. We define their linear, N →∞ limits, realizing W ∞ type algebras coupled to current algebras. ((orig.))
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, S.; van den Broek, P.M.; Avgeriou, P.; Zdun, U.; Borne, I.
We show how evolution requests can be formalized using algebraic graph rewriting. In particular, we present a way to convert the UML class diagrams to colored graphs. Since changes in software may effect the relation between the methods of classes, our colored graph representation also employs the
A Method for Model Checking Feature Interactions
DEFF Research Database (Denmark)
Pedersen, Thomas; Le Guilly, Thibaut; Ravn, Anders Peter
2015-01-01
This paper presents a method to check for feature interactions in a system assembled from independently developed concurrent processes as found in many reactive systems. The method combines and refines existing definitions and adds a set of activities. The activities describe how to populate the ...
Optimisation of BPMN Business Models via Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2013-01-01
We present a framework for the optimisation of business processes modelled in the business process modelling language BPMN, which builds upon earlier work, where we developed a model checking based method for the analysis of BPMN models. We define a structure for expressing optimisation goals...... for synthesized BPMN components, based on probabilistic computation tree logic and real-valued reward structures of the BPMN model, allowing for the specification of complex quantitative goals. We here present a simple algorithm, inspired by concepts from evolutionary algorithms, which iteratively generates...... candidate improved processes based on the fittest of the previous generation. The evaluation of the fitness of each candidate in a generation is performed via model checking, detailed in previous work. At each iteration, this allows the determination of the precise numerical evaluation of the performance...
Partial-Order Reduction for GPU Model Checking
Neele, T.; Wijs, A.; Bosnacki, D.; van de Pol, Jan Cornelis; Artho, C; Legay, A.; Peled, D.
2016-01-01
Model checking using GPUs has seen increased popularity over the last years. Because GPUs have a limited amount of memory, only small to medium-sized systems can be verified. For on-the-fly explicit-state model checking, we improve memory efficiency by applying partial-order reduction. We propose
Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation
Trujillo Arredondo, Mariana
2014-06-01
We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.
Tensor models, Kronecker coefficients and permutation centralizer algebras
Geloun, Joseph Ben; Ramgoolam, Sanjaye
2017-11-01
We show that the counting of observables and correlators for a 3-index tensor model are organized by the structure of a family of permutation centralizer algebras. These algebras are shown to be semi-simple and their Wedderburn-Artin decompositions into matrix blocks are given in terms of Clebsch-Gordan coefficients of symmetric groups. The matrix basis for the algebras also gives an orthogonal basis for the tensor observables which diagonalizes the Gaussian two-point functions. The centres of the algebras are associated with correlators which are expressible in terms of Kronecker coefficients (Clebsch-Gordan multiplicities of symmetric groups). The color-exchange symmetry present in the Gaussian model, as well as a large class of interacting models, is used to refine the description of the permutation centralizer algebras. This discussion is extended to a general number of colors d: it is used to prove the integrality of an infinite family of number sequences related to color-symmetrizations of colored graphs, and expressible in terms of symmetric group representation theory data. Generalizing a connection between matrix models and Belyi maps, correlators in Gaussian tensor models are interpreted in terms of covers of singular 2-complexes. There is an intriguing difference, between matrix and higher rank tensor models, in the computational complexity of superficially comparable correlators of observables parametrized by Young diagrams.
Schedulability of Herschel revisited using statistical model checking
DEFF Research Database (Denmark)
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel
2015-01-01
to obtain some guarantee on the (un)schedulability of the model even in the presence of undecidability. Two methods are considered: symbolic model checking and statistical model checking. Since the model uses stop-watches, the reachability problem becomes undecidable so we are using an over......-approximation technique. We can safely conclude that the system is schedulable for varying values of BCET. For the cases where deadlines are violated, we use polyhedra to try to confirm the witnesses. Our alternative method to confirm non-schedulability uses statistical model-checking (SMC) to generate counter...
Implementing Model-Check for Employee and Management Satisfaction
Jones, Corey; LaPha, Steven
2013-01-01
This presentation will discuss methods to which ModelCheck can be implemented to not only improve model quality, but also satisfy both employees and management through different sets of quality checks. This approach allows a standard set of modeling practices to be upheld throughout a company, with minimal interaction required by the end user. The presenter will demonstrate how to create multiple ModelCheck standards, preventing users from evading the system, and how it can improve the quality of drawings and models.
Lessons Learned Model Checking an Industrial Communications Library
National Research Council Canada - National Science Library
Ivers, James
2005-01-01
Model checking is a fully automated formal verification technology that can be used to determine whether models of software satisfy behavioral requirements in such areas as safety, reliability, and security...
Multi-Valued Modal Fixed Point Logics for Model Checking
Nishizawa, Koki
In this paper, I will show how multi-valued logics are used for model checking. Model checking is an automatic technique to analyze correctness of hardware and software systems. A model checker is based on a temporal logic or a modal fixed point logic. That is to say, a system to be checked is formalized as a Kripke model, a property to be satisfied by the system is formalized as a temporal formula or a modal formula, and the model checker checks that the Kripke model satisfies the formula. Although most existing model checkers are based on 2-valued logics, recently new attempts have been made to extend the underlying logics of model checkers to multi-valued logics. I will summarize these new results.
Inverse Modelling Problems in Linear Algebra Undergraduate Courses
Martinez-Luaces, Victor E.
2013-01-01
This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…
Optical linear algebra processors - Noise and error-source modeling
Casasent, D.; Ghosh, A.
1985-01-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Optical linear algebra processors: noise and error-source modeling.
Casasent, D; Ghosh, A
1985-06-01
The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.
Algebraic models of hadron structure. I. Nonstrange baryons
International Nuclear Information System (INIS)
Bijker, R.; Iachello, F.; Leviatan, A.
1994-01-01
The authors introduce an algebraic framework for the description of baryons. Within this framework they study a collective string-like model and show that this model gives a good overall description of the presently available data. They discuss in particular masses and electromagnetic couplings, including the transition form factors that can be measured at new electron facilities. 44 refs., 15 figs., 11 tabs
Algebraic models of hadron structure. I. Nonstrange baryons
Energy Technology Data Exchange (ETDEWEB)
Bijker, R. [Univ. of Utrecht (Netherlands); Iachello, F. [Yale Univ., New Haven, CT (United States); Leviatan, A. [Hebrew Univ., Jerusalem (Israel)
1994-11-15
The authors introduce an algebraic framework for the description of baryons. Within this framework they study a collective string-like model and show that this model gives a good overall description of the presently available data. They discuss in particular masses and electromagnetic couplings, including the transition form factors that can be measured at new electron facilities. 44 refs., 15 figs., 11 tabs.
Firm Deadline Checking of Safety-Critical Java Applications with Statistical Model Checking
DEFF Research Database (Denmark)
Ravn, Anders P.; Thomsen, Bent; Søe Luckow, Kasper
2017-01-01
In cyber-physical applications many programs have hard real-time constraints that have to be stringently validated. In some applications, there are programs that have hard deadlines, which must not be violated. Other programs have soft deadlines where the value of the response decreases when...... hard deadline constraints to the case of firm deadlines for application programs written in Safety-Critical Java (SCJ). The existing approach uses models and model checking with the Uppaal toolset; the extension uses the statistical model checking features of Uppaal-smc to provide a hold on firm...... deadlines and performance in the case of soft deadlines. The extended approach is illustrated with examples from applications....
An algebraic approach to modeling in software engineering
International Nuclear Information System (INIS)
Loegel, C.J.; Ravishankar, C.V.
1993-09-01
Our work couples the formalism of universal algebras with the engineering techniques of mathematical modeling to develop a new approach to the software engineering process. Our purpose in using this combination is twofold. First, abstract data types and their specification using universal algebras can be considered a common point between the practical requirements of software engineering and the formal specification of software systems. Second, mathematical modeling principles provide us with a means for effectively analyzing real-world systems. We first use modeling techniques to analyze a system and then represent the analysis using universal algebras. The rest of the software engineering process exploits properties of universal algebras that preserve the structure of our original model. This paper describes our software engineering process and our experience using it on both research and commercial systems. We need a new approach because current software engineering practices often deliver software that is difficult to develop and maintain. Formal software engineering approaches use universal algebras to describe ''computer science'' objects like abstract data types, but in practice software errors are often caused because ''real-world'' objects are improperly modeled. There is a large semantic gap between the customer's objects and abstract data types. In contrast, mathematical modeling uses engineering techniques to construct valid models for real-world systems, but these models are often implemented in an ad hoc manner. A combination of the best features of both approaches would enable software engineering to formally specify and develop software systems that better model real systems. Software engineering, like mathematical modeling, should concern itself first and foremost with understanding a real system and its behavior under given circumstances, and then with expressing this knowledge in an executable form
A Succinct Approach to Static Analysis and Model Checking
DEFF Research Database (Denmark)
Filipiuk, Piotr
In a number of areas software correctness is crucial, therefore it is often desirable to formally verify the presence of various properties or the absence of errors. This thesis presents a framework for concisely expressing static analysis and model checking problems. The framework facilitates...... in the classical formulation of ALFP logic. Finally, we show that the logics and the associated solvers can be used for rapid prototyping. We illustrate that by a variety of case studies from static analysis and model checking....
Dynamic State Space Partitioning for External Memory Model Checking
DEFF Research Database (Denmark)
Evangelista, Sami; Kristensen, Lars Michael
2009-01-01
We describe a dynamic partitioning scheme usable by model checking techniques that divide the state space into partitions, such as most external memory and distributed model checking algorithms. The goal of the scheme is to reduce the number of transitions that link states belonging to different...... partitions, and thereby limit the amount of disk access and network communication. We report on several experiments made with our verification platform ASAP that implements the dynamic partitioning scheme proposed in this paper....
Model Checking Timed Automata with Priorities using DBM Subtraction
DEFF Research Database (Denmark)
David, Alexandre; Larsen, Kim Guldstrand; Pettersson, Paul
2006-01-01
In this paper we describe an extension of timed automata with priorities, and efficient algorithms to compute subtraction on DBMs (difference bounded matrices), needed in symbolic model-checking of timed automata with priorities. The subtraction is one of the few operations on DBMs that result in...... this number affects the performance of symbolic model-checking. The uses of the DBM subtraction operation extend beyond timed automata with priorities. It is also useful for allowing guards on transitions with urgent actions, deadlock checking, and timed games.......In this paper we describe an extension of timed automata with priorities, and efficient algorithms to compute subtraction on DBMs (difference bounded matrices), needed in symbolic model-checking of timed automata with priorities. The subtraction is one of the few operations on DBMs that result...
Learning Markov Decision Processes for Model Checking
DEFF Research Database (Denmark)
Mao, Hua; Chen, Yingke; Jaeger, Manfred
2012-01-01
Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm...... is performed by analyzing the probabilistic linear temporal logic properties of the system as well as by analyzing the schedulers, in particular the optimal schedulers, induced by the learned models....
Extensions of Scott's Graph Model and Kleene's Second Algebra
van Oosten, J.; Voorneveld, Niels
We use a way to extend partial combinatory algebras (pcas) by forcing them to represent certain functions. In the case of Scott’s Graph Model, equality is computable relative to the complement function. However, the converse is not true. This creates a hierarchy of pcas which relates to similar
Algebraic models of hadron structure II. Strange baryons
International Nuclear Information System (INIS)
Bijker, R.; Iachello, F.; Leviatan, A.
2000-01-01
The algebraic treatment of baryons is extended to strange resonances. Within this framework we study a collective string-like model in which the radial excitations are interpreted as rotations and vibrations of the strings. We derive a mass formula and closed expressions for strong and electromagnetic decay widths and use these to analyze the available experimental data
Extending Model Checking To Object Process Validation
van Rein, H.
2002-01-01
Object-oriented techniques allow the gathering and modelling of system requirements in terms of an application area. The expression of data and process models at that level is a great asset in communication with non-technical people in that area, but it does not necessarily lead to consistent
Workflow Fault Tree Generation Through Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2014-01-01
We present a framework for the automated generation of fault trees from models of realworld process workflows, expressed in a formalised subset of the popular Business Process Modelling and Notation (BPMN) language. To capture uncertainty and unreliability in workflows, we extend this formalism...... to calculate the probabilities of reaching each non-error system state. Each generated error state is assigned a variable indicating its individual probability of occurrence. Our method can determine the probability of combined faults occurring, while accounting for the basic probabilistic structure...... of the system being modelled. From these calculations, a comprehensive fault tree is generated. Further, we show that annotating the model with rewards (data) allows the expected mean values of reward structures to be calculated at points of failure....
2D sigma models and differential Poisson algebras
Energy Technology Data Exchange (ETDEWEB)
Arias, Cesar [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Boulanger, Nicolas [Service de Mécanique et Gravitation, Université de Mons - UMONS,20 Place du Parc, 7000 Mons (Belgium); Laboratoire de Mathématiques et Physique Théorique,Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson,Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-18
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
Memoised Garbage Collection for Software Model Checking
Nguyen, V.Y.; Ruys, T.C.; Kowalewski, S.; Philippou, A.
Virtual machine based software model checkers like JPF and MoonWalker spend up to half of their veri��?cation time on garbage collection. This is no surprise as after nearly each transition the heap has to be cleaned from garbage. To improve this, this paper presents the Memoised Garbage Collection
Timed Model Checking of Security Protocols
Corin, R.J.; Etalle, Sandro; Hartel, Pieter H.; Mader, Angelika H.
We propose a method for engineering security protocols that are aware of timing aspects. We study a simplified version of the well-known Needham Schroeder protocol and the complete Yahalom protocol. Timing information allows the study of different attack scenarios. We illustrate the attacks by model
Linear Parametric Model Checking of Timed Automata
DEFF Research Database (Denmark)
Hune, Tohmas Seidelin; Romijn, Judi; Stoelinga, Mariëlle
2001-01-01
We present an extension of the model checker Uppaal capable of synthesize linear parameter constraints for the correctness of parametric timed automata. The symbolic representation of the (parametric) state-space is shown to be correct. A second contribution of this paper is the identication...... of a subclass of parametric timed automata (L/U automata), for which the emptiness problem is decidable, contrary to the full class where it is know to be undecidable. Also we present a number of lemmas enabling the verication eort to be reduced for L/U automata in some cases. We illustrate our approach...
Model Checking Temporal Logic Formulas Using Sticker Automata
Directory of Open Access Journals (Sweden)
Weijun Zhu
2017-01-01
Full Text Available As an important complex problem, the temporal logic model checking problem is still far from being fully resolved under the circumstance of DNA computing, especially Computation Tree Logic (CTL, Interval Temporal Logic (ITL, and Projection Temporal Logic (PTL, because there is still a lack of approaches for DNA model checking. To address this challenge, a model checking method is proposed for checking the basic formulas in the above three temporal logic types with DNA molecules. First, one-type single-stranded DNA molecules are employed to encode the Finite State Automaton (FSA model of the given basic formula so that a sticker automaton is obtained. On the other hand, other single-stranded DNA molecules are employed to encode the given system model so that the input strings of the sticker automaton are obtained. Next, a series of biochemical reactions are conducted between the above two types of single-stranded DNA molecules. It can then be decided whether the system satisfies the formula or not. As a result, we have developed a DNA-based approach for checking all the basic formulas of CTL, ITL, and PTL. The simulated results demonstrate the effectiveness of the new method.
CheckMATE 2: From the model to the limit
Dercks, Daniel; Desai, Nishita; Kim, Jong Soo; Rolbiecki, Krzysztof; Tattersall, Jamie; Weber, Torsten
2017-12-01
We present the latest developments to the CheckMATE program that allows models of new physics to be easily tested against the recent LHC data. To achieve this goal, the core of CheckMATE now contains over 60 LHC analyses of which 12 are from the 13 TeV run. The main new feature is that CheckMATE 2 now integrates the Monte Carlo event generation via MadGraph5_aMC@NLO and Pythia 8. This allows users to go directly from a SLHA file or UFO model to the result of whether a model is allowed or not. In addition, the integration of the event generation leads to a significant increase in the speed of the program. Many other improvements have also been made, including the possibility to now combine signal regions to give a total likelihood for a model.
Soliton surfaces associated with sigma models: differential and algebraic aspects
International Nuclear Information System (INIS)
Goldstein, P P; Grundland, A M; Post, S
2012-01-01
In this paper, we consider both differential and algebraic properties of surfaces associated with sigma models. It is shown that surfaces defined by the generalized Weierstrass formula for immersion for solutions of the CP N-1 sigma model with finite action, defined in the Riemann sphere, are themselves solutions of the Euler–Lagrange equations for sigma models. On the other hand, we show that the Euler–Lagrange equations for surfaces immersed in the Lie algebra su(N), with conformal coordinates, that are extremals of the area functional, subject to a fixed polynomial identity, are exactly the Euler–Lagrange equations for sigma models. In addition to these differential constraints, the algebraic constraints, in the form of eigenvalues of the immersion functions, are systematically treated. The spectrum of the immersion functions, for different dimensions of the model, as well as its symmetry properties and its transformation under the action of the ladder operators are discussed. Another approach to the dynamics is given, i.e. description in terms of the unitary matrix which diagonalizes both the immersion functions and the projectors constituting the model. (paper)
Applied Bounded Model Checking for Interlocking System Designs
DEFF Research Database (Denmark)
Haxthausen, Anne Elisabeth; Peleska, Jan; Pinger, Ralf
2013-01-01
In this article the verification and validation of interlocking systems is investigated. Reviewing both geographical and route-related interlocking, the verification objectives can be structured from a perspective of computer science into (1) verification of static semantics, and (2) verification...... of behavioural (operational) semantics. The former checks that the plant model – that is, the software components reflecting the physical components of the interlocking system – has been set up in an adequate way. The latter investigates trains moving through the network, with the objective to uncover potential...... safety violations. From a formal methods perspective, these verification objectives can be approached by theorem proving, global, or bounded model checking. This article explains the techniques for application of bounded model checking techniques, and discusses their advantages in comparison...
The humble Bayesian : Model checking from a fully Bayesian perspective
Morey, Richard D.; Romeijn, Jan-Willem; Rouder, Jeffrey N.
Gelman and Shalizi (2012) criticize what they call the usual story in Bayesian statistics: that the distribution over hypotheses or models is the sole means of statistical inference, thus excluding model checking and revision, and that inference is inductivist rather than deductivist. They present
Recent advances in importance sampling for statistical model checking
Reijsbergen, D.P.; de Boer, Pieter-Tjerk; Scheinhardt, Willem R.W.; Haverkort, Boudewijn R.H.M.
2013-01-01
In the following work we present an overview of recent advances in rare event simulation for model checking made at the University of Twente. The overview is divided into the several model classes for which we propose algorithms, namely multicomponent systems, Markov chains and stochastic Petri
Model checking: one can do much more than you think!
Katoen, Joost P.
2012-01-01
Model checking is an automated verification technique that actively is applied to find bugs in hardware and software designs. Companies like IBM and Cadence developed their in-house model checkers, and acted as driving forces behind the design of the IEEE-standardized temporal logic PSL. On the
Kac-Moody algebra is not hidden symmetry of chiral models
International Nuclear Information System (INIS)
Devchand, C.; Schiff, J.
1997-01-01
A detailed examination of the infinite dimensional loop algebra of hidden symmetry transformations of the Principal Chiral Model reveals it to have a structure differing from a standard centreless Kac-Moody algebra. A new infinite dimensional Abelian symmetry algebra is shown to preserve a symplectic form on the space of solutions. (author). 15 refs
Model Checking Coalition Nash Equilibria in MAD Distributed Systems
Mari, Federico; Melatti, Igor; Salvo, Ivano; Tronci, Enrico; Alvisi, Lorenzo; Clement, Allen; Li, Harry
We present two OBDD based model checking algorithms for the verification of Nash equilibria in finite state mechanisms modeling Multiple Administrative Domains (MAD) distributed systems with possibly colluding agents (coalitions) and with possibly faulty or malicious nodes (Byzantine agents). Given a finite state mechanism, a proposed protocol for each agent and the maximum sizes f for Byzantine agents and q for agents collusions, our model checkers return PASS if the proposed protocol is an ɛ-f-q-Nash equilibrium, i.e. no coalition of size up to q may have an interest greater than ɛ in deviating from the proposed protocol when up to f Byzantine agents are present, FAIL otherwise. We implemented our model checking algorithms within the NuSMV model checker: the first one explicitly checks equilibria for each coalition, while the second represents symbolically all coalitions. We present experimental results showing their effectiveness for moderate size mechanisms. For example, we can verify coalition Nash equilibria for mechanisms which corresponding normal form games would have more than 5 ×1021 entries. Moreover, we compare the two approaches, and the explicit algorithm turns out to outperform the symbolic one. To the best of our knowledge, no model checking algorithm for verification of Nash equilibria of mechanisms with coalitions has been previously published.
The algebra of non-local charges in non-linear sigma models
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.
1994-01-01
It is derived the complete Dirac algebra satisfied by non-local charges conserved in non-linear sigma models. Some examples of calculation are given for the O(N) symmetry group. The resulting algebra corresponds to a saturated cubic deformation (with only maximum order terms) of the Kac-Moody algebra. The results are generalized for when a Wess-Zumino term be present. In that case the algebra contains a minor order correction (sub-saturation). (author). 1 ref
Improvements to a nonequilibrium algebraic turbulence model
Johnson, D. A.; Coakley, T. J.
1990-01-01
It has been noted that while the nonequilibrium turbulence model of Johnson and King (1985, 1987) performed significantly better than alternative methods, differences between predicted and observed shock locations for certain weak interactions are produced due to a defficiency in the model's inner eddy viscosity formulation. A novel formulation for the model is presented which removes this deficiency, while satisfying the law of the wall for adverse pressure-gradient conditions better than either the original formulation or mixing-length theory.
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
Formalism based on GA is an alternative to distributed representation models developed so far: Smolensky's tensor product, Holographic Reduced Representations (HRR), and Binary Spatter Code (BSC). Convolutions are replaced by geometric products interpretable in terms of geometry, which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipped version of matrix representation. The influence of accidental blade equality on recognition is also studied. Finally, the efficiency of the GA model is compared to that of previously developed models.
Consistency checks in beam emission modeling for neutral beam injectors
International Nuclear Information System (INIS)
Punyapu, Bharathi; Vattipalle, Prahlad; Sharma, Sanjeev Kumar; Baruah, Ujjwal Kumar; Crowley, Brendan
2015-01-01
In positive neutral beam systems, the beam parameters such as ion species fractions, power fractions and beam divergence are routinely measured using Doppler shifted beam emission spectrum. The accuracy with which these parameters are estimated depend on the accuracy of the atomic modeling involved in these estimations. In this work, an effective procedure to check the consistency of the beam emission modeling in neutral beam injectors is proposed. As a first consistency check, at a constant beam voltage and current, the intensity of the beam emission spectrum is measured by varying the pressure in the neutralizer. Then, the scaling of measured intensity of un-shifted (target) and Doppler shifted intensities (projectile) of the beam emission spectrum at these pressure values are studied. If the un-shifted component scales with pressure, then the intensity of this component will be used as a second consistency check on the beam emission modeling. As a further check, the modeled beam fractions and emission cross sections of projectile and target are used to predict the intensity of the un-shifted component and then compared with the value of measured target intensity. An agreement between the predicted and measured target intensities provide the degree of discrepancy in the beam emission modeling. In order to test this methodology, a systematic analysis of Doppler shift spectroscopy data obtained on the JET neutral beam test stand data was carried out
Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
Directory of Open Access Journals (Sweden)
Sh. Khachatryan
2015-10-01
Full Text Available We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang–Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.
Algebraic properties and spectral collapse in nonlinear quantum Rabi models
Penna, V.; Raffa, F. A.; Franzosi, R.
2018-01-01
We investigate the origin of spectral collapse occurring in nonlinear Rabi Hamiltonians with an su(1,1) coupling scheme, showing how the collapse can be triggered by the competition between the Rabi parameter g and the field frequency W. The collapse already appears in the model Hamiltonian where the atomic-energy term is absent. After showing that su(1,1) is the dynamical algebra of the Hamiltonian, we demonstrate how the occurrence of spectral collapse can be directly related to the three types of equivalence classes characterizing the structure of this algebra. We highlight how the dramatic change of the spectrum significantly affects the structure of eigenstates represented in a suitable momentum–coordinate picture.
Model-Checking CTL* over Flat Presburger Counter Systems
DEFF Research Database (Denmark)
Demri, Stéphane; Finkel, Alain; Goranko, Valentin
2010-01-01
This paper studies model-checking of fragments and extensions of CTL* on infinite- state counter systems, where the states are vectors of integers and the transitions are determined by means of relations definable within Presburger arithmetic. In general, reachability properties of counter system...
Interactive comparison of hypothesis tests for statistical model checking
de Boer, Pieter-Tjerk; Reijsbergen, D.P.; Scheinhardt, Willem R.W.
2015-01-01
We present a web-based interactive comparison of hypothesis tests as are used in statistical model checking, providing users and tool developers with more insight into their characteristics. Parameters can be modified easily and their influence is visualized in real time; an integrated simulation
Application of Model-Checking Technology to Controller Synthesis
DEFF Research Database (Denmark)
David, Alexandre; Grunnet, Jacob Deleuran; Jessen, Jan Jacob
2011-01-01
In this paper we present two frameworks that have been implemented to link traditional model-checking techniques to the domain of control. The techniques are based on solving a timed game and using the resulting solution (a strategy) as a controller. The obtained discrete controller must fit with...
Model checking conditional CSL for continuous-time Markov chains
DEFF Research Database (Denmark)
Gao, Yang; Xu, Ming; Zhan, Naijun
2013-01-01
In this paper, we consider the model-checking problem of continuous-time Markov chains (CTMCs) with respect to conditional logic. To the end, we extend Continuous Stochastic Logic introduced in Aziz et al. (2000) [1] to Conditional Continuous Stochastic Logic (CCSL) by introducing a conditional p...
Geometric Algebra Model of Distributed Representations
Patyk, Agnieszka
2010-01-01
Formalism based on GA is an alternative to distributed representation models developed so far --- Smolensky's tensor product, Holographic Reduced Representations (HRR) and Binary Spatter Code (BSC). Convolutions are replaced by geometric products, interpretable in terms of geometry which seems to be the most natural language for visualization of higher concepts. This paper recalls the main ideas behind the GA model and investigates recognition test results using both inner product and a clipp...
Mixed Portmanteau Test for Diagnostic Checking of Time Series Models
Directory of Open Access Journals (Sweden)
Sohail Chand
2014-01-01
Full Text Available Model criticism is an important stage of model building and thus goodness of fit tests provides a set of tools for diagnostic checking of the fitted model. Several tests are suggested in literature for diagnostic checking. These tests use autocorrelation or partial autocorrelation in the residuals to criticize the adequacy of fitted model. The main idea underlying these portmanteau tests is to identify if there is any dependence structure which is yet unexplained by the fitted model. In this paper, we suggest mixed portmanteau tests based on autocorrelation and partial autocorrelation functions of the residuals. We derived the asymptotic distribution of the mixture test and studied its size and power using Monte Carlo simulations.
Kolman, Bernard
1985-01-01
College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c
An algebraic model of baryon spectroscopy
International Nuclear Information System (INIS)
Bijker, R.; Leviatan, A.
2000-01-01
We discuss recent calculations of the mass spectrum, electromagnetic and strong couplings of baryon resonances. The calculations are done in a collective constituent model for the nucleon, in which the resonances are interpreted as rotations and vibrations of a symmetric top with a prescribed distribution of the charge and magnetization. We analyze recent data on eta-photo- and eta- electroproduction, and the tensor analyzing power in deuteron scattering. (author)
Faugeras, Olivier; Papadopoulo, Théodore
1997-01-01
We show how to use the Grassmann-Cayley algebra to model systems of one, two and three cameras. We start with a brief introduction of the Grassmann-Cayley or double algebra and proceed to demonstrate its use for modeling systems of cameras. In the case of three cameras, we give a new interpretation of the trifocal tensors and study in detail some of the constraints that they satisfy. In particular we prove that simple subsets of those constraints characterize the trifocal tensors, in other wo...
Independence-Based Optimization of Epistemic Model Checking
2017-02-22
imperfect information of their environment. It has been applied to settings that include diagnosis [8], and reasoning in game - like settings [15, 16, 32...represents the model as a concurrent pro- gram, in which each of the agents executes a protocol in the context of an environment. We provide a symbolic ...handled by the symbolic model checking algorithms. The paper presents experimental results that demonstrate that the condi- tional independence
Model Checking for Energy Efficient Scheduling in Wireless Sensor Networks
Schmitt, Peter H.; Werner, Frank
2006-01-01
Networking and power management of wireless energy - conscious sensor networks is an important area of current research. We investigate a network of MicaZ sensor motes using the ZigBee protocol for communication, and provide a model using Timed Safety Automata. Our analysis focuses on estimating energy consumption by model checking in different scenarios using the Uppaal tool. Special interest is devoted to the energy use in margi...
Bayesian inference with information content model check for Langevin equations
DEFF Research Database (Denmark)
Krog, Jens F. C.; Lomholt, Michael Andersen
2017-01-01
The Bayesian data analysis framework has been proven to be a systematic and effective method of parameter inference and model selection for stochastic processes. In this work we introduce an information content model check which may serve as a goodness-of-fit, like the chi-square procedure......, to complement conventional Bayesian analysis. We demonstrate this extended Bayesian framework on a system of Langevin equations, where coordinate dependent mobilities and measurement noise hinder the normal mean squared displacement approach....
Logic Model Checking of Unintended Acceleration Claims in Toyota Vehicles
Gamble, Ed
2012-01-01
Part of the US Department of Transportation investigation of Toyota sudden unintended acceleration (SUA) involved analysis of the throttle control software, JPL Laboratory for Reliable Software applied several techniques including static analysis and logic model checking, to the software; A handful of logic models were build, Some weaknesses were identified; however, no cause for SUA was found; The full NASA report includes numerous other analyses
The algebra of non-local charges in non-linear sigma models
Abdalla, Elcio; Brunelli, J C; Zadra, Ayrton
1994-01-01
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower.
Methods of mathematical modeling using polynomials of algebra of sets
Kazanskiy, Alexandr; Kochetkov, Ivan
2018-03-01
The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.
2010-01-01
... OF FUNDS AND COLLECTION OF CHECKS (REGULATION CC) Pt. 229, App. C Appendix C to Part 229—Model... Checks and Your Rights— Substitute Checks and Your Rights What Is a Substitute Check? To make check... rights under other law with respect to those transactions. What Are My Rights Regarding Substitute Checks...
Efficient family-based model checking via variability abstractions
DEFF Research Database (Denmark)
Dimovski, Aleksandar; Al-Sibahi, Ahmad Salim; Brabrand, Claus
2016-01-01
Many software systems are variational: they can be configured to meet diverse sets of requirements. They can produce a (potentially huge) number of related systems, known as products or variants, by systematically reusing common parts. For variational models (variational systems or families...... with the abstract model checking of the concrete high-level variational model. This allows the use of Spin with all its accumulated optimizations for efficient verification of variational models without any knowledge about variability. We have implemented the transformations in a prototype tool, and we illustrate...
Probabilistic Model Checking of Biological Systems with Uncertain Kinetic Rates
Barbuti, Roberto; Levi, Francesca; Milazzo, Paolo; Scatena, Guido
We present an abstraction of the probabilistic semantics of Multiset Rewriting to formally express systems of reactions with uncertain kinetic rates. This allows biological systems modelling when the exact rates are not known, but are supposed to lie in some intervals. On these (abstract) models we perform probabilistic model checking obtaining lower and upper bounds for the probabilities of reaching states satisfying given properties. These bounds are under- and over-approximations, respectively, of the probabilities one would obtain by verifying the models with exact kinetic rates belonging to the intervals.
Model Checking for Licensing Support in the Finnish Nuclear Industry
Energy Technology Data Exchange (ETDEWEB)
Antti, Pakonen; Janne, Valkonen [VTT Technical Research, VTT (Finland); Sami, Matinaho; Markus, Hartikainen [Protum Power and Heat, Fortum (Finland)
2014-08-15
This paper examines how model checking can be used to support the qualification of digital I and C software in nuclear power plants, in a way that is consistent with regulatory demands specifically, the common position of seven European nuclear regulators and authorised technical support organisations. As a practical example, we discuss the third-party review service provided by VTT for the power company Fortum in the I and C renewal project of the Loviisa plant in southern Finland.
Approximating Attractors of Boolean Networks by Iterative CTL Model Checking.
Klarner, Hannes; Siebert, Heike
2015-01-01
This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: "faithfulness" which requires that the oscillating variables of all attractors in a trap space correspond to their dimensions, "univocality" which requires that there is a unique attractor in each trap space, and "completeness" which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal, and complete, which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Approximating attractors of Boolean networks by iterative CTL model checking
Directory of Open Access Journals (Sweden)
Hannes eKlarner
2015-09-01
Full Text Available This paper introduces the notion of approximating asynchronous attractors of Boolean networks by minimal trap spaces. We define three criteria for determining the quality of an approximation: faithfulness which requires that the oscillating variables of all attractors in a trapspace correspond to their dimensions, univocality which requires that there is a unique attractor in each trap space and completeness which requires that there are no attractors outside of a given set of trap spaces. Each is a reachability property for which we give equivalent model checking queries. Whereas faithfulness and univocality can be decided by model checking the corresponding subnetworks, the naive query for completeness must be evaluated on the full state space. Our main result is an alternative approach which is based on the iterative refinement of an initially poor approximation. The algorithm detects so-called autonomous sets in the interaction graph, variables that contain all their regulators, and considers their intersection and extension in order to perform model checking on the smallest possible state spaces. A benchmark, in which we apply the algorithm to 18 published Boolean networks, is given. In each case, the minimal trap spaces are faithful, univocal and complete which suggests that they are in general good approximations for the asymptotics of Boolean networks.
Introduction of Virtualization Technology to Multi-Process Model Checking
Leungwattanakit, Watcharin; Artho, Cyrille; Hagiya, Masami; Tanabe, Yoshinori; Yamamoto, Mitsuharu
2009-01-01
Model checkers find failures in software by exploring every possible execution schedule. Java PathFinder (JPF), a Java model checker, has been extended recently to cover networked applications by caching data transferred in a communication channel. A target process is executed by JPF, whereas its peer process runs on a regular virtual machine outside. However, non-deterministic target programs may produce different output data in each schedule, causing the cache to restart the peer process to handle the different set of data. Virtualization tools could help us restore previous states of peers, eliminating peer restart. This paper proposes the application of virtualization technology to networked model checking, concentrating on JPF.
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
A new (in)finite-dimensional algebra for quantum integrable models
International Nuclear Information System (INIS)
Baseilhac, Pascal; Koizumi, Kozo
2005-01-01
A new (in)finite-dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details. Finite-dimensional representations are constructed and mutually commuting quantities-which ensure the integrability of the system-are written in terms of the fundamental generators of the new algebra. Relation with the deformed Dolan-Grady integrable structure recently discovered by one of the authors and Terwilliger's tridiagonal algebras is described. Remarkably, this (in)finite-dimensional algebra is a 'q-deformed' analogue of the original Onsager's algebra arising in the planar Ising model. Consequently, it provides a new and alternative algebraic framework for studying massive, as well as conformal, quantum integrable models
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
International Nuclear Information System (INIS)
Gurau, Razvan
2012-01-01
Random tensor models for a generic complex tensor generalize matrix models in arbitrary dimensions and yield a theory of random geometries. They support a 1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson equations, generalizing the loop equations of matrix models, translate into constraints satisfied by the partition function. The constraints have been shown, in the large N limit, to close a Lie algebra indexed by colored rooted D-ary trees yielding a first generalization of the Virasoro algebra in arbitrary dimensions. In this paper we complete the Schwinger Dyson equations and the associated algebra at all orders in 1/N. The full algebra of constraints is indexed by D-colored graphs, and the leading order D-ary tree algebra is a Lie subalgebra of the full constraints algebra.
Model-checking techniques based on cumulative residuals.
Lin, D Y; Wei, L J; Ying, Z
2002-03-01
Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.
Optimizing ZigBee Security using Stochastic Model Checking
DEFF Research Database (Denmark)
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
ZigBee is a fairly new but promising wireless sensor network standard that offers the advantages of simple and low resource communication. Nevertheless, security is of great concern to ZigBee, and enhancements are prescribed in the latest ZigBee specication: ZigBee-2007. In this technical report......, we identify an important gap in the specification on key updates, and present a methodology for determining optimal key update policies and security parameters. We exploit the stochastic model checking approach using the probabilistic model checker PRISM, and assess the security needs for realistic...
Defect Detection: Combining Bounded Model Checking and Code Contracts
Directory of Open Access Journals (Sweden)
Marat Akhin
2013-01-01
Full Text Available Bounded model checking (BMC of C/C++ programs is a matter of scientific enquiry that attracts great attention in the last few years. In this paper, we present our approach to this problem. It is based on combining several recent results in BMC, namely, the use of LLVM as a baseline for model generation, employment of high-performance Z3 SMT solver to do the formula heavy-lifting, and the use of various function summaries to improve analysis efficiency and expressive power. We have implemented a basic prototype; experiment results on a set of simple test BMC problems are satisfactory.
Model Checking Geographically Distributed Interlocking Systems Using UMC
DEFF Research Database (Denmark)
Fantechi, Alessandro; Haxthausen, Anne Elisabeth; Nielsen, Michel Bøje Randahl
2017-01-01
The current trend of distributing computations over a network is here, as a novelty, applied to a safety critical system, namely a railway interlocking system. We show how the challenge of guaranteeing safety of the distributed application has been attacked by formally specifying and model checking...... the relevant distributed protocols. By doing that we obey the safety guidelines of the railway signalling domain, that require formal methods to support the certification of such products. We also show how formal modelling can help designing alternative distributed solutions, while maintaining adherence...
UPPAAL-SMC: Statistical Model Checking for Priced Timed Automata
DEFF Research Database (Denmark)
Bulychev, Petr; David, Alexandre; Larsen, Kim Guldstrand
2012-01-01
in the form of probability distributions and compare probabilities to analyze performance aspects of systems. The focus of the survey is on the evolution of the tool – including modeling and specification formalisms as well as techniques applied – together with applications of the tool to case studies....... on a series of extensions of the statistical model checking approach generalized to handle real-time systems and estimate undecidable problems. U PPAAL - SMC comes together with a friendly user interface that allows a user to specify complex problems in an efficient manner as well as to get feedback...
Applying Model Checking to Industrial-Sized PLC Programs
AUTHOR|(CDS)2079190; Darvas, Daniel; Blanco Vinuela, Enrique; Tournier, Jean-Charles; Bliudze, Simon; Blech, Jan Olaf; Gonzalez Suarez, Victor M
2015-01-01
Programmable logic controllers (PLCs) are embedded computers widely used in industrial control systems. Ensuring that a PLC software complies with its specification is a challenging task. Formal verification has become a recommended practice to ensure the correctness of safety-critical software but is still underused in industry due to the complexity of building and managing formal models of real applications. In this paper, we propose a general methodology to perform automated model checking of complex properties expressed in temporal logics (\\eg CTL, LTL) on PLC programs. This methodology is based on an intermediate model (IM), meant to transform PLC programs written in various standard languages (ST, SFC, etc.) to different modeling languages of verification tools. We present the syntax and semantics of the IM and the transformation rules of the ST and SFC languages to the nuXmv model checker passing through the intermediate model. Finally, two real cases studies of \\CERN PLC programs, written mainly in th...
Algebraic Traveling Wave Solutions of a Non-local Hydrodynamic-type Model
International Nuclear Information System (INIS)
Chen, Aiyong; Zhu, Wenjing; Qiao, Zhijun; Huang, Wentao
2014-01-01
In this paper we consider the algebraic traveling wave solutions of a non-local hydrodynamic-type model. It is shown that algebraic traveling wave solutions exist if and only if an associated first order ordinary differential system has invariant algebraic curve. The dynamical behavior of the associated ordinary differential system is analyzed. Phase portraits of the associated ordinary differential system is provided under various parameter conditions. Moreover, we classify algebraic traveling wave solutions of the model. Some explicit formulas of smooth solitary wave and cuspon solutions are obtained
SoS contract verification using statistical model checking
Directory of Open Access Journals (Sweden)
Alessandro Mignogna
2013-11-01
Full Text Available Exhaustive formal verification for systems of systems (SoS is impractical and cannot be applied on a large scale. In this paper we propose to use statistical model checking for efficient verification of SoS. We address three relevant aspects for systems of systems: 1 the model of the SoS, which includes stochastic aspects; 2 the formalization of the SoS requirements in the form of contracts; 3 the tool-chain to support statistical model checking for SoS. We adapt the SMC technique for application to heterogeneous SoS. We extend the UPDM/SysML specification language to express the SoS requirements that the implemented strategies over the SoS must satisfy. The requirements are specified with a new contract language specifically designed for SoS, targeting a high-level English- pattern language, but relying on an accurate semantics given by the standard temporal logics. The contracts are verified against the UPDM/SysML specification using the Statistical Model Checker (SMC PLASMA combined with the simulation engine DESYRE, which integrates heterogeneous behavioral models through the functional mock-up interface (FMI standard. The tool-chain allows computing an estimation of the satisfiability of the contracts by the SoS. The results help the system architect to trade-off different solutions to guide the evolution of the SoS.
Approximate Model Checking of PCTL Involving Unbounded Path Properties
Basu, Samik; Ghosh, Arka P.; He, Ru
We study the problem of applying statistical methods for approximate model checking of probabilistic systems against properties encoded as PCTL formulas. Such approximate methods have been proposed primarily to deal with state-space explosion that makes the exact model checking by numerical methods practically infeasible for large systems. However, the existing statistical methods either consider a restricted subset of PCTL, specifically, the subset that can only express bounded until properties; or rely on user-specified finite bound on the sample path length. We propose a new method that does not have such restrictions and can be effectively used to reason about unbounded until properties. We approximate probabilistic characteristics of an unbounded until property by that of a bounded until property for a suitably chosen value of the bound. In essence, our method is a two-phase process: (a) the first phase is concerned with identifying the bound k 0; (b) the second phase computes the probability of satisfying the k 0-bounded until property as an estimate for the probability of satisfying the corresponding unbounded until property. In both phases, it is sufficient to verify bounded until properties which can be effectively done using existing statistical techniques. We prove the correctness of our technique and present its prototype implementations. We empirically show the practical applicability of our method by considering different case studies including a simple infinite-state model, and large finite-state models such as IPv4 zeroconf protocol and dining philosopher protocol modeled as Discrete Time Markov chains.
Efficient Parallel Statistical Model Checking of Biochemical Networks
Directory of Open Access Journals (Sweden)
Paolo Ballarini
2009-12-01
Full Text Available We consider the problem of verifying stochastic models of biochemical networks against behavioral properties expressed in temporal logic terms. Exact probabilistic verification approaches such as, for example, CSL/PCTL model checking, are undermined by a huge computational demand which rule them out for most real case studies. Less demanding approaches, such as statistical model checking, estimate the likelihood that a property is satisfied by sampling executions out of the stochastic model. We propose a methodology for efficiently estimating the likelihood that a LTL property P holds of a stochastic model of a biochemical network. As with other statistical verification techniques, the methodology we propose uses a stochastic simulation algorithm for generating execution samples, however there are three key aspects that improve the efficiency: first, the sample generation is driven by on-the-fly verification of P which results in optimal overall simulation time. Second, the confidence interval estimation for the probability of P to hold is based on an efficient variant of the Wilson method which ensures a faster convergence. Third, the whole methodology is designed according to a parallel fashion and a prototype software tool has been implemented that performs the sampling/verification process in parallel over an HPC architecture.
su(1,2) Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame
International Nuclear Information System (INIS)
Jin Shuo; Xie Binghao; Yu Zhaoxian; Hou Jingmin
2008-01-01
The XYZ antiferromagnetic model in linear spin-wave frame is shown explicitly to have an su(1,2) algebraic structure: the Hamiltonian can be written as a linear function of the su(1,2) algebra generators. Based on it, the energy eigenvalues are obtained by making use of the similar transformations, and the algebraic diagonalization method is investigated. Some numerical solutions are given, and the results indicate that only one group solution could be accepted in physics
An algebraic approach to solving evolution problems in some nonlinear quantum models
International Nuclear Information System (INIS)
Karassiov, Valery P.; Klimov, Andrei B.
1994-01-01
A new general Lie-algebraic approach is proposed to solve evolution problems in some nonlinear models of quantum physics with polynomially deformed Lie algebras su pd (2) as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the su pd (2) shift operators and a (recursive) reduction of finding coefficient functions to solve auxiliary exactly solvable su(2) problems with quadratic Hamiltonians. ((orig.))
Using Stochastic Model Checking to Provision Complex Business Services
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2012-01-01
We present a framework for modelling and analysis of real-world business workflows. Business processes regularly form the basis for the design of software services, and frequently display complex stochastic behaviour. The accurate evaluation of their qualitative aspects can allow for determining...... bounds on resources consumed during execution of business processes. Accurate resource provisioning is often central to ensuring the safe execution of a process. We first introduce a formalised core subset of the Business Process Modelling and Notation (BPMN), which we extend with probabilistic and non......-deterministic branching and reward annotations. We then develop an algorithm for the efficient translation of these models into the guarded command language used by the model checker PRISM, in turn enabling model checking of BPMN processes and allowing for the calculation of a wide range of quantitative properties...
Model checking coalitional games in shortage resource scenarios
Directory of Open Access Journals (Sweden)
Dario Della Monica
2013-07-01
Full Text Available Verification of multi-agents systems (MAS has been recently studied taking into account the need of expressing resource bounds. Several logics for specifying properties of MAS have been presented in quite a variety of scenarios with bounded resources. In this paper, we study a different formalism, called Priced Resource-Bounded Alternating-time Temporal Logic (PRBATL, whose main novelty consists in moving the notion of resources from a syntactic level (part of the formula to a semantic one (part of the model. This allows us to track the evolution of the resource availability along the computations and provides us with a formalisms capable to model a number of real-world scenarios. Two relevant aspects are the notion of global availability of the resources on the market, that are shared by the agents, and the notion of price of resources, depending on their availability. In a previous work of ours, an initial step towards this new formalism was introduced, along with an EXPTIME algorithm for the model checking problem. In this paper we better analyze the features of the proposed formalism, also in comparison with previous approaches. The main technical contribution is the proof of the EXPTIME-hardness of the the model checking problem for PRBATL, based on a reduction from the acceptance problem for Linearly-Bounded Alternating Turing Machines. In particular, since the problem has multiple parameters, we show two fixed-parameter reductions.
Optlang: An algebraic modeling language for mathematical optimization
DEFF Research Database (Denmark)
Jensen, Kristian; Cardoso, Joao; Sonnenschein, Nikolaus
2016-01-01
Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e., maximizing or minimizing an objective function over a set of variables subject to a number of constraints. It provides a common native Python interface to a series of optimization...... tools, so different solver backends can be used and changed in a transparent way. Optlang’s object-oriented API takes advantage of the symbolic math library SymPy (Team 2016) to allow objective functions and constraints to be easily formulated algebraically from symbolic expressions of variables....... Optlang targets scientists who can thus focus on formulating optimization problems based on mathematical equations derived from domain knowledge. Solver interfaces can be added by subclassing the four main classes of the optlang API (Variable, Constraint, Objective, and Model) and implementing...
Symbolic Game Semantics for Model Checking Program Families
DEFF Research Database (Denmark)
Dimovski, Aleksandar
2016-01-01
. In this paper, we propose an efficient game semantics based approach for verifying open program families, i.e. program families with free (undefined) identifiers. We use symbolic representation of algorithmic game semantics, where concrete values are replaced with symbolic ones. In this way, we can compactly...... represent program families with infinite integers as so-called (finite-state) featured symbolic automata. Specifically designed model checking algorithms are then employed to verify safety of all programs from a family at once and pinpoint those programs that are unsafe (respectively, safe). We present...
Model Checking Degrees of Belief in a System of Agents
Raimondi, Franco; Primero, Giuseppe; Rungta, Neha
2014-01-01
Reasoning about degrees of belief has been investigated in the past by a number of authors and has a number of practical applications in real life. In this paper we present a unified framework to model and verify degrees of belief in a system of agents. In particular, we describe an extension of the temporal-epistemic logic CTLK and we introduce a semantics based on interpreted systems for this extension. In this way, degrees of beliefs do not need to be provided externally, but can be derived automatically from the possible executions of the system, thereby providing a computationally grounded formalism. We leverage the semantics to (a) construct a model checking algorithm, (b) investigate its complexity, (c) provide a Java implementation of the model checking algorithm, and (d) evaluate our approach using the standard benchmark of the dining cryptographers. Finally, we provide a detailed case study: using our framework and our implementation, we assess and verify the situational awareness of the pilot of Air France 447 flying in off-nominal conditions.
Automatic generation of Fortran programs for algebraic simulation models
International Nuclear Information System (INIS)
Schopf, W.; Rexer, G.; Ruehle, R.
1978-04-01
This report documents a generator program by which econometric simulation models formulated in an application-orientated language can be transformed automatically in a Fortran program. Thus the model designer is able to build up, test and modify models without the need of a Fortran programmer. The development of a computer model is therefore simplified and shortened appreciably; in chapter 1-3 of this report all rules are presented for the application of the generator to the model design. Algebraic models including exogeneous and endogeneous time series variables, lead and lag function can be generated. In addition, to these language elements, Fortran sequences can be applied to the formulation of models in the case of complex model interrelations. Automatically the generated model is a module of the program system RSYST III and is therefore able to exchange input and output data with the central data bank of the system and in connection with the method library modules can be used to handle planning problems. (orig.) [de
Methods to model-check parallel systems software
International Nuclear Information System (INIS)
Matlin, O. S.; McCune, W.; Lusk, E.
2003-01-01
We report on an effort to develop methodologies for formal verification of parts of the Multi-Purpose Daemon (MPD) parallel process management system. MPD is a distributed collection of communicating processes. While the individual components of the collection execute simple algorithms, their interaction leads to unexpected errors that are difficult to uncover by conventional means. Two verification approaches are discussed here: the standard model checking approach using the software model checker SPIN and the nonstandard use of a general-purpose first-order resolution-style theorem prover OTTER to conduct the traditional state space exploration. We compare modeling methodology and analyze performance and scalability of the two methods with respect to verification of MPD
Using Model Checking for Analyzing Distributed Power Control Problems
DEFF Research Database (Denmark)
Brihaye, Thomas; Jungers, Marc; Lasaulce, Samson
2010-01-01
Model checking (MC) is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control ( PC) problem can be modeled by a timed game between a given transmitter and its environment, the authors...... wanted to know whether this approach can be applied to distributed PC. It turns out that it can be applied successfully and allows one to analyze realistic scenarios including the case of discrete transmit powers and games with incomplete information. The proposed methodology is as follows. We state some...... objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired...
Using Model Checking for Analyzing Distributed Power Control Problems
Directory of Open Access Journals (Sweden)
Thomas Brihaye
2010-01-01
Full Text Available Model checking (MC is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control (PC problem can be modeled by a timed game between a given transmitter and its environment, the authors wanted to know whether this approach can be applied to distributed PC. It turns out that it can be applied successfully and allows one to analyze realistic scenarios including the case of discrete transmit powers and games with incomplete information. The proposed methodology is as follows. We state some objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired properties are verified and determine a winning strategy.
Model-checking dense-time Duration Calculus
DEFF Research Database (Denmark)
Fränzle, Martin
2004-01-01
Since the seminal work of Zhou Chaochen, M. R. Hansen, and P. Sestoft on decidability of dense-time Duration Calculus [Zhou, Hansen, Sestoft, 1993] it is well-known that decidable fragments of Duration Calculus can only be obtained through withdrawal of much of the interesting vocabulary...... of this logic. While this was formerly taken as an indication that key-press verification of implementations with respect to elaborate Duration Calculus specifications were also impossible, we show that the model property is well decidable for realistic designs which feature natural constraints...... suitably sparser model classes we obtain model-checking procedures for rich subsets of Duration Calculus. Together with undecidability results also obtained, this sheds light upon the exact borderline between decidability and undecidability of Duration Calculi and related logics....
Model checking as an aid to procedure design
International Nuclear Information System (INIS)
Zhang, Wenhu
2001-01-01
The OECD Halden Reactor Project has been actively working on computer assisted operating procedures for many years. The objective of the research has been to provide computerised assistance for procedure design, verification and validation, implementation and maintenance. For the verification purpose, the application of formal methods has been considered in several reports. The recent formal verification activity conducted at the Halden Project is based on using model checking to the verification of procedures. This report presents verification approaches based on different model checking techniques and tools for the formalization and verification of operating procedures. Possible problems and relative merits of the different approaches are discussed. A case study of one of the approaches is presented to show the practical application of formal verification. Application of formal verification in the traditional procedure design process can reduce the human resources involved in reviews and simulations, and hence reduce the cost of verification and validation. A discussion of the integration of the formal verification with the traditional procedure design process is given at the end of this report. (Author)
Phases and phase transitions in the algebraic microscopic shell model
Directory of Open Access Journals (Sweden)
Georgieva A. I.
2016-01-01
Full Text Available We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott’s SU(3 basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3 basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.
Transformation of UML Behavioral Diagrams to Support Software Model Checking
Directory of Open Access Journals (Sweden)
Luciana Brasil Rebelo dos Santos
2014-04-01
Full Text Available Unified Modeling Language (UML is currently accepted as the standard for modeling (object-oriented software, and its use is increasing in the aerospace industry. Verification and Validation of complex software developed according to UML is not trivial due to complexity of the software itself, and the several different UML models/diagrams that can be used to model behavior and structure of the software. This paper presents an approach to transform up to three different UML behavioral diagrams (sequence, behavioral state machines, and activity into a single Transition System to support Model Checking of software developed in accordance with UML. In our approach, properties are formalized based on use case descriptions. The transformation is done for the NuSMV model checker, but we see the possibility in using other model checkers, such as SPIN. The main contribution of our work is the transformation of a non-formal language (UML to a formal language (language of the NuSMV model checker towards a greater adoption in practice of formal methods in software development.
Take the Reins on Model Quality with ModelCHECK and Gatekeeper
Jones, Corey
2012-01-01
Model quality and consistency has been an issue for us due to the diverse experience level and imaginative modeling techniques of our users. Fortunately, setting up ModelCHECK and Gatekeeper to enforce our best practices has helped greatly, but it wasn't easy. There were many challenges associated with setting up ModelCHECK and Gatekeeper including: limited documentation, restrictions within ModelCHECK, and resistance from end users. However, we consider ours a success story. In this presentation we will describe how we overcame these obstacles and present some of the details of how we configured them to work for us.
Combining Decision Diagrams and SAT Procedures for Efficient Symbolic Model Checking
DEFF Research Database (Denmark)
Williams, Poul Frederick; Biere, Armin; Clarke, Edmund M.
2000-01-01
, combined with BDDs and SAT-solvers to perform satisfiability checking. As a result we are able to model check systems for which standard BDD-based methods fail. For example, we model check a liveness property of a 256 bit shift-and-add multiplier and we are able to find a previously undetected bug...
Spectroscopic factors within an algebraic model and an application to 12C+12C
International Nuclear Information System (INIS)
Hess, P. O.; Aguilera, E. F.; Martinez-Quiroz, E.; Algora, A.; Cseh, J.; Draayer, J. P.; Belyaeva, T. L.
2007-01-01
A parameterization of the spectroscopic factor is presented which almost matches the ones obtained via the microscopic SU(3) model of the nucleus. A short introduction of the algebraic model (the Semimicroscopic Algebraic Cluster Model, SACM) is given. The parameterization of the spectroscopic factor is explained, justified and compared, for light nuclei, to the microscopic SU(3) model. The applications concern the calculation of the total fusion cross section of 12C+12C
The algebra of non-local charges in non-linear sigma models
International Nuclear Information System (INIS)
Abdalla, E.; Abdalla, M.C.B.; Brunelli, J.C.; Zadra, A.
1993-07-01
We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group O(N). As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower. (author). 22 refs, 5 figs
An algebraic formulation of level one Wess-Zumino-Witten models
International Nuclear Information System (INIS)
Boeckenhauer, J.
1995-07-01
The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras. It is shown that the representation theory of the underlying even CAR algebras reproduces precisely the sectors of the chiral algebra. This fact allows to develop a theory of local von Neumann algebras on the punctured circle, fitting nicely in the Doplicher-Haag-Roberts framework. The relevant localized endomorphisms which generate the charged sectors are explicitly constructed by means of Bogoliubov transformations. Using CAR theory, the fusion rules in terms of sector equivalence classes are proven. (orig.)
Simple nonparametric checks for model data fit in CAT
Meijer, R.R.
2005-01-01
In this paper, the usefulness of several nonparametric checks is discussed in a computerized adaptive testing (CAT) context. Although there is no tradition of nonparametric scalability in CAT, it can be argued that scalability checks can be useful to investigate, for example, the quality of item
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Energy Technology Data Exchange (ETDEWEB)
Dobay, M. P. D., E-mail: maria.pamela.david@physik.uni-muenchen.de; Alberola, A. Piera; Mendoza, E. R.; Raedler, J. O., E-mail: joachim.raedler@physik.uni-muenchen.de [Ludwig-Maximilians University, Faculty of Physics, Center for NanoScience (Germany)
2012-03-15
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
International Nuclear Information System (INIS)
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-01-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
Dobay, M. P. D.; Alberola, A. Piera; Mendoza, E. R.; Rädler, J. O.
2012-03-01
Computational modeling is increasingly important to help understand the interaction and movement of nanoparticles (NPs) within living cells, and to come to terms with the wealth of data that microscopy imaging yields. A quantitative description of the spatio-temporal distribution of NPs inside cells; however, it is challenging due to the complexity of multiple compartments such as endosomes and nuclei, which themselves are dynamic and can undergo fusion and fission and exchange their content. Here, we show that stochastic pi calculus, a widely-used process algebra, is well suited for mapping surface and intracellular NP interactions and distributions. In stochastic pi calculus, each NP is represented as a process, which can adopt various states such as bound or aggregated, as well as be passed between processes representing location, as a function of predefined stochastic channels. We created a pi calculus model of gold NP uptake and intracellular movement and compared the evolution of surface-bound, cytosolic, endosomal, and nuclear NP densities with electron microscopy data. We demonstrate that the computational approach can be extended to include specific molecular binding and potential interaction with signaling cascades as characteristic for NP-cell interactions in a wide range of applications such as nanotoxicity, viral infection, and drug delivery.
Application of conditional moment tests to model checking for generalized linear models.
Pan, Wei
2002-06-01
Generalized linear models (GLMs) are increasingly being used in daily data analysis. However, model checking for GLMs with correlated discrete response data remains difficult. In this paper, through a case study on marginal logistic regression using a real data set, we illustrate the flexibility and effectiveness of using conditional moment tests (CMTs), along with other graphical methods, to do model checking for generalized estimation equation (GEE) analyses. Although CMTs provide an array of powerful diagnostic tests for model checking, they were originally proposed in the econometrics literature and, to our knowledge, have never been applied to GEE analyses. CMTs cover many existing tests, including the (generalized) score test for an omitted covariate, as special cases. In summary, we believe that CMTs provide a class of useful model checking tools.
Heuristics for Hierarchical Partitioning with Application to Model Checking
DEFF Research Database (Denmark)
Möller, Michael Oliver; Alur, Rajeev
2001-01-01
Given a collection of connected components, it is often desired to cluster together parts of strong correspondence, yielding a hierarchical structure. We address the automation of this process and apply heuristics to battle the combinatorial and computational complexity. We define a cost function...... studies. A longer version of this paper is available as technical report BRICS Research Series RS-00-21. Basic Research in Computer Science, Center of the Danish National Research Foundation....... function. We argue for a heuristic function based on four criteria: the number of enclosed connections, the number of components, the number of touched connections and the depth of the structure. We report on an application in the context of formal verification, where our algorithm serves as a preprocessor...... for a temporal scaling technique, called “Next” heuristic [2]. The latter is applicable in reachability analysis and is included in a recent version of the Mocha model checking tool. We demonstrate performance and benefits of our method and use an asynchronous parity computer and an opinion poll protocol as case...
Developing ontological model of computational linear algebra - preliminary considerations
Wasielewska, K.; Ganzha, M.; Paprzycki, M.; Lirkov, I.
2013-10-01
The aim of this paper is to propose a method for application of ontologically represented domain knowledge to support Grid users. The work is presented in the context provided by the Agents in Grid system, which aims at development of an agent-semantic infrastructure for efficient resource management in the Grid. Decision support within the system should provide functionality beyond the existing Grid middleware, specifically, help the user to choose optimal algorithm and/or resource to solve a problem from a given domain. The system assists the user in at least two situations. First, for users without in-depth knowledge about the domain, it should help them to select the method and the resource that (together) would best fit the problem to be solved (and match the available resources). Second, if the user explicitly indicates the method and the resource configuration, it should "verify" if her choice is consistent with the expert recommendations (encapsulated in the knowledge base). Furthermore, one of the goals is to simplify the use of the selected resource to execute the job; i.e., provide a user-friendly method of submitting jobs, without required technical knowledge about the Grid middleware. To achieve the mentioned goals, an adaptable method of expert knowledge representation for the decision support system has to be implemented. The selected approach is to utilize ontologies and semantic data processing, supported by multicriterial decision making. As a starting point, an area of computational linear algebra was selected to be modeled, however, the paper presents a general approach that shall be easily extendable to other domains.
Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving
Engerman, Jason; Rusek, Matthew; Clariana, Roy
2014-01-01
This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…
Gauging the nonlinear sigma-model through a non-Abelian algebra
Energy Technology Data Exchange (ETDEWEB)
Barcelos Neto, J. [Universidade Federal, Rio de Janeiro, RJ (Brazil); Oliveira, W. [Juiz de Fora Univ., MG (Brazil)
1997-12-31
We have used an extension of the BFFT formalism presented by Banerjee et al. in order to gauge the nonlinear sigma model by means of a non-Abelian algebra. we have considered the supersymmetric and the usual cases. We have shown that the supersymmetric case is only consistently transformed in a first-class theory by means of a non-Abelian algebra. The usual BFFT treatment leads to a nonlocal theory. (author) 6 refs.
Model Checking and Model-based Testing in the Railway Domain
DEFF Research Database (Denmark)
Haxthausen, Anne Elisabeth; Peleska, Jan
2015-01-01
This chapter describes some approaches and emerging trends for verification and model-based testing of railway control systems. We describe state-of-the-art methods and associated tools for verifying interlocking systems and their configuration data, using bounded model checking and k-induction. ......This chapter describes some approaches and emerging trends for verification and model-based testing of railway control systems. We describe state-of-the-art methods and associated tools for verifying interlocking systems and their configuration data, using bounded model checking and k...
Creating Büchi automata for multi-valued model checking
Vijzelaar, Stefan J.J.; Fokkink, Wan J.
2017-01-01
In explicit state model checking of linear temporal logic properties, a Büchi automaton encodes a temporal property. It interleaves with a Kripke model to form a state space, which is searched for counterexamples. Multi-valued model checking considers additional truth values beyond the Boolean true
WCET Analysis of ARM Processors using Real-Time Model Checking
DEFF Research Database (Denmark)
Toft, Martin; Olesen, Mads Christian; Dalsgaard, Andreas
2009-01-01
This paper presents a flexible method that utilises real-time model checking to determine safe and sharp WCETs for processes running on hardware platforms featuring pipelining and caching.......This paper presents a flexible method that utilises real-time model checking to determine safe and sharp WCETs for processes running on hardware platforms featuring pipelining and caching....
A computer code for calculations in the algebraic collective model of the atomic nucleus
Welsh, T. A.; Rowe, D. J.
2014-01-01
A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1,1) x SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functi...
PVeStA: A Parallel Statistical Model Checking and Quantitative Analysis Tool
AlTurki, Musab
2011-01-01
Statistical model checking is an attractive formal analysis method for probabilistic systems such as, for example, cyber-physical systems which are often probabilistic in nature. This paper is about drastically increasing the scalability of statistical model checking, and making such scalability of analysis available to tools like Maude, where probabilistic systems can be specified at a high level as probabilistic rewrite theories. It presents PVeStA, an extension and parallelization of the VeStA statistical model checking tool [10]. PVeStA supports statistical model checking of probabilistic real-time systems specified as either: (i) discrete or continuous Markov Chains; or (ii) probabilistic rewrite theories in Maude. Furthermore, the properties that it can model check can be expressed in either: (i) PCTL/CSL, or (ii) the QuaTEx quantitative temporal logic. As our experiments show, the performance gains obtained from parallelization can be very high. © 2011 Springer-Verlag.
Algebraic partial Boolean algebras
Smith, D
2003-01-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial...
Mathematical Modelling and the Learning Trajectory: Tools to Support the Teaching of Linear Algebra
Cárcamo Bahamonde, Andrea Dorila; Fortuny Aymemí, Josep Maria; Gómez i Urgellés, Joan Vicenç
2017-01-01
In this article we present a didactic proposal for teaching linear algebra based on two compatible theoretical models: emergent models and mathematical modelling. This proposal begins with a problematic situation related to the creation and use of secure passwords, which leads students toward the construction of the concepts of spanning set and…
AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S
Klumpp, A. R.
1994-01-01
This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.
Mathematical modelling in engineering: A proposal to introduce linear algebra concepts
Directory of Open Access Journals (Sweden)
Andrea Dorila Cárcamo
2016-03-01
Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
Using Canonical Forms for Isomorphism Reduction in Graph-based Model Checking
Kant, Gijs
Graph isomorphism checking can be used in graph-based model checking to achieve symmetry reduction. Instead of one-to-one comparing the graph representations of states, canonical forms of state graphs can be computed. These canonical forms can be used to store and compare states. However, computing
Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
2016-01-01
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings
International Nuclear Information System (INIS)
Arnaudon, D.
1997-01-01
Two quantum spin chains Hamiltonians with quantum sl(2/1) invariance are constructed. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings. A cubic algebra that admits the Birman-Wenzl-Murakami algebra as a quotient allows exact solvability of the periodic chain. The two Hamiltonians, respectively built using the distinguished and the fermionic bases of U q (sl(2/1)) differ only in the boundary terms. They are actually equivalent, but the equivalence is non local. Reflection equations are solved to get exact solvability on open chains with non trivial boundary conditions. Two families of diagonal solutions are found. The centre and the s-Casimir of the quantum enveloping algebra of sl(2/1) appear as tools for the construction of exactly solvable Hamiltonians. (author)
Algebraic partial Boolean algebras
Smith, Derek
2003-04-01
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space Script H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E8.
Algebraic partial Boolean algebras
Energy Technology Data Exchange (ETDEWEB)
Smith, Derek [Math Department, Lafayette College, Easton, PA 18042 (United States)
2003-04-04
Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A{sub 5} sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E{sub 8}.
Checking the new IRI model The bottomside B parameters
Mosert, M; Ezquer, R; Lazo, B; Miro, G
2002-01-01
Electron density profiles obtained at Pruhonice (50.0, 15.0), El Arenosillo (37.1, 353.2) and Havana (23, 278) were used to check the bottom-side B parameters BO (thickness parameter) and B1 (shape parameter) predicted by the new IRI - 2000 version. The electron density profiles were derived from ionograms using the ARP technique. The data base includes daytime and nighttime ionograms recorded under different seasonal and solar activity conditions. Comparisons with IRI predictions were also done. The analysis shows that: a) The parameter B1 given by IRI 2000 reproduces better the observed ARP values than the IRI-90 version and b) The observed BO values are in general well reproduced by both IRI versions: IRI-90 and IRI-2000.
A note on probabilistic models over strings: the linear algebra approach.
Bouchard-Côté, Alexandre
2013-12-01
Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems.
Gauging the nonlinear {sigma} model through a non-Abelian algebra
Energy Technology Data Exchange (ETDEWEB)
Barcelos-Neto, J.; Oliveira, W. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, RJ 21945-970, Caixa Postal 68528 (Brazil)
1997-08-01
We use an extension of the method due to Batalin, Fradkin, Fradkina, and Tyutin (BFFT) for transforming the nonlinear {sigma} model in a non-Abelian gauge theory. We deal with both supersymmetric and nonsupersymmetric cases. The bosonic case was already considered in the literature but just gauged with an Abelian algebra. We show that the supersymmetric version is only compatible with a non-Abelian gauge theory. The usual BFFT method for this case leads to a nonlocal algebra. {copyright} {ital 1997} {ital The American Physical Society}
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
Ashwinkumar, Meer; Cao, Jingnan; Luo, Yuan; Tan, Meng-Chwan; Zhao, Qin
2018-03-01
We study the ground states and left-excited states of the Ak-1 N = (2 , 0) little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU (k). The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
Directory of Open Access Journals (Sweden)
Meer Ashwinkumar
2018-03-01
Full Text Available We study the ground states and left-excited states of the Ak−1 N=(2,0 little string theory. Via a theorem by Atiyah [1], these sectors can be captured by a supersymmetric nonlinear sigma model on CP1 with target space the based loop group of SU(k. The ground states, described by L2-cohomology classes, form modules over an affine Lie algebra, while the left-excited states, described by chiral differential operators, form modules over a toroidal Lie algebra. We also apply our results to analyze the 1/2 and 1/4 BPS sectors of the M5-brane worldvolume theory.
Model-Checking of Component-Based Event-Driven Real-Time Embedded Software
National Research Council Canada - National Science Library
Gu, Zonghua; Shin, Kang G
2005-01-01
.... We discuss application of model-checking to verify system-level concurrency properties of component-based real-time embedded software based on CORBA Event Service, using Avionics Mission Computing...
Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking
Directory of Open Access Journals (Sweden)
Christian Appold
2010-06-01
Full Text Available One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking.
Deterministic Compilation of Temporal Safety Properties in Explicit State Model Checking
National Aeronautics and Space Administration — The translation of temporal logic specifications constitutes an essen- tial step in model checking and a major influence on the efficiency of formal verification via...
Algebraic Specifications, Higher-order Types and Set-theoretic Models
DEFF Research Database (Denmark)
Kirchner, Hélène; Mosses, Peter David
2001-01-01
, and power-sets. This paper presents a simple framework for algebraic specifications with higher-order types and set-theoretic models. It may be regarded as the basis for a Horn-clause approximation to the Z framework, and has the advantage of being amenable to prototyping and automated reasoning. Standard...
Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis
Czech Academy of Sciences Publication Activity Database
Bulíček, M.; Haslinger, J.; Málek, J.; Stebel, Jan
2009-01-01
Roč. 60, č. 2 (2009), s. 185-212 ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model * outflow boundary condition Subject RIV: BA - General Mathematics Impact factor: 0.757, year: 2009
Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra
Domínguez-García, S.; García-Planas, M. I.; Taberna, J.
2016-01-01
Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…
Schwinger-Dyson equations for the two-matrix model and W3 algebra
International Nuclear Information System (INIS)
Gava, E.; Narain, K.S.
1991-04-01
The continuum Schwinger-Dyson equations for the two-matrix model, around the Ising critical point, are derived for operators involving one of the two matrices. It is shown that, within the space of the corresponding couplings, the resulting constraints obey a W 3 algebra. (author). 11 refs
International Nuclear Information System (INIS)
Lahtinen, J.; Launiainen, T.; Heljanko, K.; Ropponen, J.
2012-01-01
Digital instrumentation and control (I and C) systems are challenging to verify. They enable complicated control functions, and the state spaces of the models easily become too large for comprehensive verification through traditional methods. Model checking is a formal method that can be used for system verification. A number of efficient model checking systems are available that provide analysis tools to determine automatically whether a given state machine model satisfies the desired safety properties. This report reviews the work performed in the Safety Evaluation and Reliability Analysis of Nuclear Automation (SARANA) project in 2011 regarding model checking. We have developed new, more exact modelling methods that are able to capture the behaviour of a system more realistically. In particular, we have developed more detailed fault models depicting the hardware configuration of a system, and methodology to model function-block-based systems asynchronously. In order to improve the usability of our model checking methods, we have developed an algorithm for model checking large modular systems. The algorithm can be used to verify properties of a model that could otherwise not be verified in a straightforward manner. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Lahtinen, J. [VTT Technical Research Centre of Finland, Espoo (Finland); Launiainen, T.; Heljanko, K.; Ropponen, J. [Aalto Univ., Espoo (Finland). Dept. of Information and Computer Science
2012-07-01
Digital instrumentation and control (I and C) systems are challenging to verify. They enable complicated control functions, and the state spaces of the models easily become too large for comprehensive verification through traditional methods. Model checking is a formal method that can be used for system verification. A number of efficient model checking systems are available that provide analysis tools to determine automatically whether a given state machine model satisfies the desired safety properties. This report reviews the work performed in the Safety Evaluation and Reliability Analysis of Nuclear Automation (SARANA) project in 2011 regarding model checking. We have developed new, more exact modelling methods that are able to capture the behaviour of a system more realistically. In particular, we have developed more detailed fault models depicting the hardware configuration of a system, and methodology to model function-block-based systems asynchronously. In order to improve the usability of our model checking methods, we have developed an algorithm for model checking large modular systems. The algorithm can be used to verify properties of a model that could otherwise not be verified in a straightforward manner. (orig.)
modelling of queuing process at airport check-in system
African Journals Online (AJOL)
HOD
models in queue studies. The study adopted travel demand data for Manchester and Leeds-Bradford airports from the United Kingdom. Civil Aviation Authority database. 1.2 Analytical Models for Queuing Studies. Previous researchers have examined queuing process extensively and developed analytical models used for.
On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations
Directory of Open Access Journals (Sweden)
Yongning Wang
2013-04-01
Full Text Available This paper focuses on the diagnostic checking of vector ARMA (VARMA models with multivariate GARCH errors. For a fitted VARMA-GARCH model with Gaussian or Student-t innovations, we derive the asymptotic distributions of autocorrelation matrices of the cross-product vector of standardized residuals. This is different from the traditional approach that employs only the squared series of standardized residuals. We then study two portmanteau statistics, called Q1(M and Q2(M, for model checking. A residual-based bootstrap method is provided and demonstrated as an effective way to approximate the diagnostic checking statistics. Simulations are used to compare the performance of the proposed statistics with other methods available in the literature. In addition, we also investigate the effect of GARCH shocks on checking a fitted VARMA model. Empirical sizes and powers of the proposed statistics are investigated and the results suggest a procedure of using jointly Q1(M and Q2(M in diagnostic checking. The bivariate time series of FTSE 100 and DAX index returns is used to illustrate the performance of the proposed portmanteau statistics. The results show that it is important to consider the cross-product series of standardized residuals and GARCH effects in model checking.
Global identifiability of linear compartmental models--a computer algebra algorithm.
Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C
1998-01-01
A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.
Simonn Zayas, David; Monceaux, Anne; Ait-Ameur, Yamine
2011-08-01
Nowadays, complexity of systems frequently implies different engineering teams handling various descriptive models. Each team having a variety of expertise backgrounds, domain knowledge and modeling practices, the heterogeneity of the models themselves is a logical consequence. Therefore, even individually models are well managed; their diversity becomes a problem when engineers need to share their models to perform some overall validations. One way of reducing this heterogeneity is to take into consideration the implicit knowledge which is not contained in the models but it is cardinal to understand them. In a first stage of our research, we have defined and implemented an approach recommending the formalization of implicit knowledge to enrich models in order to ease cross- model checks. Nevertheless, to fill the gap between the specification of the system and the validation of a cross- model constraint, in this paper we suggest giving values to some relevant characteristics to reinforce the approach.
Modelling and Analysis of Smart Grid: A Stochastic Model Checking Case Study
DEFF Research Database (Denmark)
Yuksel, Ender; Zhu, Huibiao; Nielson, Hanne Riis
2012-01-01
that require novel methods and applications. In this context, an important issue is the verification of certain quantitative properties of the system. In this paper, we consider a specific Chinese Smart Grid implementation as a case study and address the verification problem for performance and energy......Cyber-physical systems integrate information and communication technology functions to the physical elements of a system for monitoring and controlling purposes. The conversion of traditional power grid into a smart grid, a fundamental example of a cyber-physical system, raises a number of issues...... consumption. We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker....
Quantitative modelling and analysis of a Chinese smart grid: a stochastic model checking case study
DEFF Research Database (Denmark)
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
2014-01-01
that require novel methods and applications. One of the important issues in this context is the verification of certain quantitative properties of the system. In this paper, we consider a specific Chinese smart grid implementation as a case study and address the verification problem for performance and energy......Cyber-physical systems integrate information and communication technology with the physical elements of a system, mainly for monitoring and controlling purposes. The conversion of traditional power grid into a smart grid, a fundamental example of a cyber-physical system, raises a number of issues...... consumption.We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker....
Posterior Predictive Model Checking for Conjunctive Multidimensionality in Item Response Theory
Levy, Roy
2011-01-01
If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold. The current work pursues posterior predictive model checking (PPMC) as a tool for criticizing models due to unaccounted for dimensions in data structures that follow conjunctive multidimensional models. These pursuits are couched in…
Abstraction and Model Checking in the PEPA Plug-in for Eclipse
DEFF Research Database (Denmark)
Smith, Michael James Andrew
2010-01-01
lead to very large Markov chains. One way of analysing such models is to use abstraction - constructing a smaller model that bounds the properties of the original. We present an extension to the PEPA plug-in for Eclipse that enables abstracting and model checking of PEPA models. This implements two new...
The algebras of higher order currents of the fermionic Gross-Neveu model
Energy Technology Data Exchange (ETDEWEB)
Saltini, Luis Eduardo [Sao Paulo Univ., SP (Brazil). Inst. de Fisica. Dept. de Fisica Matematica
1996-07-01
Results are reported from our studies on the following 2-dimensional field theories: the supersymmetric non-linear sigma model and the fermionic Gross-Neveu model. About the supersymmetric non-linear sigma model, an attempt is made to solve the the algebraic problem of finding the non-local conserved charges and the corresponding algebra, extending the methods described in a previous article for the case of the purely bosonic non linear sigma model. For the fermionic Gross-Neveu model, we intend to construct the conserved currents and the respective charges, related to the abelian U(1) symmetry and non-abelian SU(n) symmetry, at the conformal point and calculate the correlation functions between them. From these results at the conformal point, we want to study the effects of perturbation to get a massive but integral theory.
The algebras of higher order currents of the fermionic Gross-Neveu model
International Nuclear Information System (INIS)
Saltini, Luis Eduardo
1996-01-01
Results are reported from our studies on the following 2-dimensional field theories: the supersymmetric non-linear sigma model and the fermionic Gross-Neveu model. About the supersymmetric non-linear sigma model, an attempt is made to solve the the algebraic problem of finding the non-local conserved charges and the corresponding algebra, extending the methods described in a previous article for the case of the purely bosonic non linear sigma model. For the fermionic Gross-Neveu model, we intend to construct the conserved currents and the respective charges, related to the abelian U(1) symmetry and non-abelian SU(n) symmetry, at the conformal point and calculate the correlation functions between them. From these results at the conformal point, we want to study the effects of perturbation to get a massive but integral theory
PKreport: report generation for checking population pharmacokinetic model assumptions
Directory of Open Access Journals (Sweden)
Li Jun
2011-05-01
Full Text Available Abstract Background Graphics play an important and unique role in population pharmacokinetic (PopPK model building by exploring hidden structure among data before modeling, evaluating model fit, and validating results after modeling. Results The work described in this paper is about a new R package called PKreport, which is able to generate a collection of plots and statistics for testing model assumptions, visualizing data and diagnosing models. The metric system is utilized as the currency for communicating between data sets and the package to generate special-purpose plots. It provides ways to match output from diverse software such as NONMEM, Monolix, R nlme package, etc. The package is implemented with S4 class hierarchy, and offers an efficient way to access the output from NONMEM 7. The final reports take advantage of the web browser as user interface to manage and visualize plots. Conclusions PKreport provides 1 a flexible and efficient R class to store and retrieve NONMEM 7 output, 2 automate plots for users to visualize data and models, 3 automatically generated R scripts that are used to create the plots; 4 an archive-oriented management tool for users to store, retrieve and modify figures, 5 high-quality graphs based on the R packages, lattice and ggplot2. The general architecture, running environment and statistical methods can be readily extended with R class hierarchy. PKreport is free to download at http://cran.r-project.org/web/packages/PKreport/index.html.
Model-Checking Real-Time Control Programs
DEFF Research Database (Denmark)
Iversen, T. K.; Kristoffersen, K. J.; Larsen, Kim Guldstrand
2000-01-01
In this paper, we present a method for automatic verification of real-time control programs running on LEGO(R) RCX(TM) bricks using the verification tool UPPALL. The control programs, consisting of a number of tasks running concurrently, are automatically translated into the mixed automata model...... of UPPAAL. The fixed scheduling algorithm used by the LEGO(R) RCX(TM) processor is modeled in UPPALL, and supply of similar (sufficient) timed automata models for the environment allows analysis of the overall real-time system using the tools of UPPALL. To illustrate our technique for sorting LEGO(R) bricks...
International Nuclear Information System (INIS)
Garcia, R.L.
1983-11-01
The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt
Lefschetz, Solomon
2005-01-01
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Hypersonic: Model Analysis and Checking in the Cloud
DEFF Research Database (Denmark)
Acretoaie, Vlad; Störrle, Harald
2014-01-01
”. Objective: In this paper we investigate the conceptual and technical feasibility of a new software architecture for modeling tools, where certain advanced features are factored out of the client and moved towards the Cloud. With this approach we plan to address the above mentioned drawbacks of existing...
Dynamic Delayed Duplicate Detection for External Memory Model Checking
DEFF Research Database (Denmark)
Evangelista, Sami
2008-01-01
Duplicate detection is an expensive operation of disk-based model checkers. It consists of comparing some potentially new states, the candidate states, to previous visited states. We propose a new approach to this technique called dynamic delayed duplicate detection. This one exploits some typical...
Efficient Proof Engines for Bounded Model Checking of Hybrid Systems
DEFF Research Database (Denmark)
Fränzle, Martin; Herde, Christian
2005-01-01
In this paper we present HySat, a new bounded model checker for linear hybrid systems, incorporating a tight integration of a DPLL-based pseudo-Boolean SAT solver and a linear programming routine as core engine. In contrast to related tools like MathSAT, ICS, or CVC, our tool exploits all...
Algebraic solution of the Stein-Stein model for stochastic volatility
Sophocleous, C.; O'Hara, J. G.; Leach, P. G. L.
2011-04-01
We provide an algebraic approach to the solution of the Stein-Stein model for stochastic volatility which arises in the determination of the Radon-Nikodym density of the minimal entropy of the martingale measure. We extend our investigation to the case in which the parameters of the model are time-dependent. Our algorithmic approach obviates the need for Ansätze for the structure of the solution.
UML Statechart Fault Tree Generation By Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Herbert-Hansen, Zaza Nadja Lee
Creating fault tolerant and efficient process work-flows poses a significant challenge. Individual faults, defined as an abnormal conditions or defects in a component, equipment, or sub-process, must be handled so that the system may continue to operate, and are typically addressed by implementing...... engineers imagine what undesirable events can occur under which conditions. Fault Tree Analysis (FTA) attempts to analyse the failure of systems by composing logic diagrams of separate individual faults to determine the probabil-ity of larger compound faults occurring. FTA is a commonly used method......-pleteness). To avoid these deficiencies, our approach derives the fault tree directly from the formal system model, under the assumption that any state can fail. We present a framework for the automated gener-ation of fault trees from models of real-world pro-cess workflows, expressed in a formalised subset...
Using Runtime Analysis to Guide Model Checking of Java Programs
Havelund, Klaus; Norvig, Peter (Technical Monitor)
2001-01-01
This paper describes how two runtime analysis algorithms, an existing data race detection algorithm and a new deadlock detection algorithm, have been implemented to analyze Java programs. Runtime analysis is based on the idea of executing the program once. and observing the generated run to extract various kinds of information. This information can then be used to predict whether other different runs may violate some properties of interest, in addition of course to demonstrate whether the generated run itself violates such properties. These runtime analyses can be performed stand-alone to generate a set of warnings. It is furthermore demonstrated how these warnings can be used to guide a model checker, thereby reducing the search space. The described techniques have been implemented in the b e grown Java model checker called PathFinder.
Modelling of queuing process at airport check-in system: a case ...
African Journals Online (AJOL)
This study built a Simulation Model (SM) using SimEvents toolbox in MATLAB for implementing Analytical Models (AM) of queuing process at airport check - in system. Air travel demand data for Manchester and Leeds - Bradford airports in 2014 were adopted for validation of the model. There was no statistical differenc e ...
Beilinson, Alexander
2004-01-01
Chiral algebras form the primary algebraic structure of modern conformal field theory. Each chiral algebra lives on an algebraic curve, and in the special case where this curve is the affine line, chiral algebras invariant under translations are the same as well-known and widely used vertex algebras. The exposition of this book covers the following topics: the "classical" counterpart of the theory, which is an algebraic theory of non-linear differential equations and their symmetries; the local aspects of the theory of chiral algebras, including the study of some basic examples, such as the ch
Iachello, Francesco
2015-01-01
This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...
Model-Checking Driven Design of QoS-Based Routing Protocol for Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
Zhi Chen
2015-01-01
Full Text Available Accurate and reliable routing protocols with Quality of Service (QoS support determine the mission-critical application efficiency in WSNs. This paper proposes a model-checking design driven framework for designing the QoS-based routing protocols of WSNs, which involves the light-weight design process, the timed automata model, and the alternative QoS verification properties. The accurate feedback of continually model checking in the iterative design process effectively stimulates the parameter tuning of the protocols. We demonstrate the straightforward and modular characteristics of the proposed framework in designing a prototype QoS-based routing protocol. The prototype study shows that the model-checking design framework may complement other design methods and ensure the QoS implementation of the QoS-based routing protocol design for WSNs.
Model-Checking Web Services Business Activity Protocols
DEFF Research Database (Denmark)
Marques, Abinoam P.; Ravn, Anders Peter; Srba, Jiri
2013-01-01
Web Services Business Activity specification defines two coordination protocols BAwCC (Business Agreement with Coordination Completion) and BAwPC (Business Agreement with Participant Completion)that ensure a consistent agreement on the outcome of long-running distributed applications. In order...... to verify fundamental properties of the protocols we provide formal analyses in the model checker UPPAAL.Our analyses are supported by a newly developed tool chain,where in the first step we translatetables with state-transition protocol descriptionsinto an intermediate XML format, and in the second step we...... whereas the original protocols do not.All verification results presented in this article were performedin a fully automatic way using our new tool csv2uppaal....
Prototype of Automated PLC Model Checking Using Continuous Integration Tools
Lettrich, Michael
2015-01-01
To deal with the complexity of operating and supervising large scale industrial installations at CERN, often Programmable Logic Controllers (PLCs) are used. A failure in these control systems can cause a disaster in terms of economic loses, environmental damages or human losses. Therefore the requirements to software quality are very high. To provide PLC developers with a way to verify proper functionality against requirements, a Java tool named PLCverif has been developed which encapsulates and thus simplifies the use of third party model checkers. One of our goals in this project is to integrate PLCverif in development process of PLC programs. When the developer changes the program, all the requirements should be verified again, as a change on the code can produce collateral effects and violate one or more requirements. For that reason, PLCverif has been extended to work with Jenkins CI in order to trigger automatically the verication cases when the developer changes the PLC program. This prototype has been...
An algebraic stress/flux model for two-phase turbulent flow
International Nuclear Information System (INIS)
Kumar, R.
1995-12-01
An algebraic stress model (ASM) for turbulent Reynolds stress and a flux model for turbulent heat flux are proposed for two-phase bubbly and slug flows. These mathematical models are derived from the two-phase transport equations for Reynolds stress and turbulent heat flux, and provide C μ , a turbulent constant which defines the level of eddy viscosity, as a function of the interfacial terms. These models also include the effect of heat transfer. When the interfacial drag terms and the interfacial momentum transfer terms are absent, the model reduces to a single-phase model used in the literature
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.
Exact boson mappings for nuclear neutron (proton) shell-model algebras having SU(3) subalgebras
International Nuclear Information System (INIS)
Bonatsos, D.; Klein, A.
1986-01-01
In this paper the commutation relations of the fermion pair operators of identical nucleons coupled to spin zero are given for the general nuclear major shell in LST coupling. The associated Lie algebras are the unitary symplectic algebras Sp(2M). The corresponding multipole subalgebras are the unitary algebras U(M), which possess SU(3) subalgebras. Number conserving exact boson mappings of both the Dyson and hermitian form are given for the nuclear neutron (proton) s--d, p--f, s--d--g, and p--f--h shells, and their group theoretical structure is emphasized. The results are directly applicable in the case of the s--d shell, while in higher shells the experimentally plausible pseudo-SU(3) symmetry makes them applicable. The final purpose of this work is to provide a link between the shell model and the Interacting Boson Model (IBM) in the deformed limit. As already implied in the work of Draayer and Hecht, it is difficult to associate the boson model developed here with the conventional IBM model. The differences between the two approaches (due mainly to the effects of the Pauli principle) as well as their physical implications are extensively discussed
Deformed su(1,1 Algebra as a Model for Quantum Oscillators
Directory of Open Access Journals (Sweden)
Elchin I. Jafarov
2012-05-01
Full Text Available The Lie algebra su(1,1 can be deformed by a reflection operator, in such a way that the positive discrete series representations of su}(1,1 can be extended to representations of this deformed algebra su(1,1_gamma. Just as the positive discrete series representations of su(1,1 can be used to model a quantum oscillator with Meixner-Pollaczek polynomials as wave functions, the corresponding representations of su(1,1_gamma can be utilized to constructmodels of a quantum oscillator. In this case, the wave functions are expressed in terms of continuous dual Hahn polynomials. We study some properties of these wave functions, and illustrate some features in plots. We also discuss some interesting limits and special cases of the obtained oscillator models.
Intrinsic and collective structure of an algebraic model of molecular rotation-vibration spectra
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A.; Kirson, M.W.
1988-11-15
A geometrical framework is provided for a recently proposed interacting boson model of molecular rotation-vibration spectra. An intrinsic state is defined by way of a boson condensate parametrized in terms of shape variables and is used to generate an energy surface. The global minimum of the energy surface determines an equilibrium condensate which serves as the basis for an exact separation of the Hamiltonian into intrinsic and collective parts. A Bogoliubov treatment of the intrinsic part produces, in leading order, the normal modes of vibration and their frequencies, the collective degrees of freedom being represented by zero-frequency Goldstone modes associated with spontaneous symmetry breaking in the condensate. The method is very useful in interpreting numerical results of the algebraic model, in identifying the capabilities and inadequacies of the Hamiltonian, and in constructing appropriate algebraic Hamiltonians for specific molecules. copyright 1988 Academic Press, Inc.
Intrinsic and collective structure of an algebraic model of molecular rotation-vibration spectra
International Nuclear Information System (INIS)
Leviatan, A.; Kirson, M.W.
1988-01-01
A geometrical framework is provided for a recently proposed interacting boson model of molecular rotation-vibration spectra. An intrinsic state is defined by way of a boson condensate parametrized in terms of shape variables and is used to generate an energy surface. The global minimum of the energy surface determines an equilibrium condensate which serves as the basis for an exact separation of the Hamiltonian into intrinsic and collective parts. A Bogoliubov treatment of the intrinsic part produces, in leading order, the normal modes of vibration and their frequencies, the collective degrees of freedom being represented by zero-frequency Goldstone modes associated with spontaneous symmetry breaking in the condensate. The method is very useful in interpreting numerical results of the algebraic model, in identifying the capabilities and inadequacies of the Hamiltonian, and in constructing appropriate algebraic Hamiltonians for specific molecules. copyright 1988 Academic Press, Inc
DEFF Research Database (Denmark)
ter Beek, Maurice H.; Legay, Axel; Lluch Lafuente, Alberto
2015-01-01
We investigate the suitability of statistical model checking techniques for analysing quantitative properties of software product line models with probabilistic aspects. For this purpose, we enrich the feature-oriented language FLAN with action rates, which specify the likelihood of exhibiting...... particular behaviour or of installing features at a specific moment or in a specific order. The enriched language (called PFLAN) allows us to specify models of software product lines with probabilistic configurations and behaviour, e.g. by considering a PFLAN semantics based on discrete-time Markov chains....... The Maude implementation of PFLAN is combined with the distributed statistical model checker MultiVeStA to perform quantitative analyses of a simple product line case study. The presented analyses include the likelihood of certain behaviour of interest (e.g. product malfunctioning) and the expected average...
Directory of Open Access Journals (Sweden)
Maurice H. ter Beek
2015-04-01
Full Text Available We investigate the suitability of statistical model checking techniques for analysing quantitative properties of software product line models with probabilistic aspects. For this purpose, we enrich the feature-oriented language FLan with action rates, which specify the likelihood of exhibiting particular behaviour or of installing features at a specific moment or in a specific order. The enriched language (called PFLan allows us to specify models of software product lines with probabilistic configurations and behaviour, e.g. by considering a PFLan semantics based on discrete-time Markov chains. The Maude implementation of PFLan is combined with the distributed statistical model checker MultiVeStA to perform quantitative analyses of a simple product line case study. The presented analyses include the likelihood of certain behaviour of interest (e.g. product malfunctioning and the expected average cost of products.
Sound statistical model checking for MDP using partial order and confluence reduction
Hartmanns, Arnd; Timmer, Mark
Statistical model checking (SMC) is an analysis method that circumvents the state space explosion problem in model-based verification by combining probabilistic simulation with statistical methods that provide clear error bounds. As a simulation-based technique, it can in general only provide sound
On-the-fly confluence detection for statistical model checking (extended version)
Hartmanns, Arnd; Timmer, Mark
Statistical model checking is an analysis method that circumvents the state space explosion problem in model-based verification by combining probabilistic simulation with statistical methods that provide clear error bounds. As a simulation-based technique, it can only provide sound results if the
Gamble, Ed; Holzmann, Gerard
2011-01-01
Part of the US DOT investigation of Toyota SUA involved analysis of the throttle control software. JPL LaRS applied several techniques, including static analysis and logic model checking, to the software. A handful of logic models were built. Some weaknesses were identified; however, no cause for SUA was found. The full NASA report includes numerous other analyses
Requirements-level semantics and model checking of object-oriented statecharts
Eshuis, H.; Jansen, D.N.; Wieringa, Roelf J.
2002-01-01
In this paper we define a requirements-level execution semantics for object-oriented statecharts and show how properties of a system specified by these statecharts can be model checked using tool support for model checkers. Our execution semantics is requirements-level because it uses the perfect
Directory of Open Access Journals (Sweden)
R. Lestari
2012-07-01
Full Text Available Tujuan penelitian tindakan kelas ini untuk mengetahui pengaruh proses pembelajaran dengan menggunakan model pembelajaran kooperatif tipe Pair Checks pemecahan masalah terhadap peningkatan social skill siswa. Pada proses penerapan model pembelajaran kooperatif tipe Pair Checks pemecahan masalah siswa dibagi dalam kelompok-kelompok dan satu kelompok terdiri dari dua orang. Setiap kelompok berdiskusi untuk menyelesaikan suatu masalah, kemudian hasil diskusi kelompok akan dicek oleh pasangan dari kelompok lain. Metode Penelitian yang digunakan adalah penelitian tindakan kelas yang dilaksanakan dua siklus. Metode pengumpulan data menggunakan tes dan angket skala sikap, sedangkan teknik analisis data menggunakan teknik analisis data kuantitatif. Social Skill siswa dari siklus I ke siklus II mengalami peningkatan. Hal ini didapatkan dari data angket skala sikap siklus I ke siklus II ketuntasan klasikalnya meningkat dan sebagian besar siswa sudah memiliki social skill yang baik. Hasil belajar kognitif siswa juga mengalami peningkatan. Model pembelajaran kooperatif tipe Pair Checks pemecahan masalah dapat meningkatkan social skill siswa.This two cycles-action research aimed to know learning process applying cooperative learning model-pair checks problem solving type and improvement of studentâ€™s social skills. The process of the model was as follows: deviding students into some groups consisting of two students, solving problem by each group and checking result of the discussion by other groups. Data collection method used was test and the use of attitude scale questionnaire, while technique of data analysis used was quantitative data analysis technique. The data analysis result showed that there was an increase of studentâ€™s social skill and studentsâ€™ achievement from cycle one to two. It is concluded that cooperative learning model-pair checks problem solving type can enhance studentâ€™s social skills
Czech Academy of Sciences Publication Activity Database
Haslinger, J.; Stebel, Jan
2011-01-01
Roč. 63, č. 2 (2011), s. 277-308 ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2011 http://link.springer.com/article/10.1007%2Fs00245-010-9121-x
Hopf Bifurcation of a Differential-Algebraic Bioeconomic Model with Time Delay
Directory of Open Access Journals (Sweden)
Xiaojian Zhou
2012-01-01
Full Text Available We investigate the dynamics of a differential-algebraic bioeconomic model with two time delays. Regarding time delay as a bifurcation parameter, we show that a sequence of Hopf bifurcations occur at the positive equilibrium as the delay increases. Using the theories of normal form and center manifold, we also give the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions. Numerical tests are provided to verify our theoretical analysis.
Algebraic statistics computational commutative algebra in statistics
Pistone, Giovanni; Wynn, Henry P
2000-01-01
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
DiVinE-CUDA - A Tool for GPU Accelerated LTL Model Checking
Directory of Open Access Journals (Sweden)
Jiří Barnat
2009-12-01
Full Text Available In this paper we present a tool that performs CUDA accelerated LTL Model Checking. The tool exploits parallel algorithm MAP adjusted to the NVIDIA CUDA architecture in order to efficiently detect the presence of accepting cycles in a directed graph. Accepting cycle detection is the core algorithmic procedure in automata-based LTL Model Checking. We demonstrate that the tool outperforms non-accelerated version of the algorithm and we discuss where the limits of the tool are and what we intend to do in the future to avoid them.
Vibrational spectrum of CF4 isotopes in an algebraic model
Indian Academy of Sciences (India)
n this paper the stretching vibrational modes of CF4 isotopes are calculated up to first overtone using the one-dimensional vibron model for the first time. The model Hamiltonian so constructed seems to describe the C–F stretching modes accurately using a relatively small set of well-defined parameters.
Heidergott, Bernd; van der Woude, Jacob
2014-01-01
Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, compu
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
International Nuclear Information System (INIS)
Read, N.; Saleur, H.
2007-01-01
The symmetry algebras of certain families of quantum spin chains are considered in detail. The simplest examples possess m states per site (m>=2), with nearest-neighbor interactions with U(m) symmetry, under which the sites transform alternately along the chain in the fundamental m and its conjugate representation m-bar. We find that these spin chains, even with arbitrary coefficients of these interactions, have a symmetry algebra A m much larger than U(m), which implies that the energy eigenstates fall into sectors that for open chains (i.e., free boundary conditions) can be labeled by j=0,1,...,L, for the 2L-site chain such that the degeneracies of all eigenvalues in the jth sector are generically the same and increase rapidly with j. For large j, these degeneracies are much larger than those that would be expected from the U(m) symmetry alone. The enlarged symmetry algebra A m (2L) consists of operators that commute in this space of states with the Temperley-Lieb algebra that is generated by the set of nearest-neighbor interaction terms; A m (2L) is not a Yangian. There are similar results for supersymmetric chains with gl(m+n|n) symmetry of nearest-neighbor interactions, and a richer representation structure for closed chains (i.e., periodic boundary conditions). The symmetries also apply to the loop models that can be obtained from the spin chains in a spacetime or transfer matrix picture. In the loop language, the symmetries arise because the loops cannot cross. We further define tensor products of representations (for the open chains) by joining chains end to end. The fusion rules for decomposing the tensor product of representations labeled j 1 and j 2 take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra A m into a ribbon Hopf algebra, and we show that this is 'Morita equivalent' to the quantum group U q (sl 2 ) for m=q+q -1 . The open-chain results are extended to the cases vertical bar m vertical
Colloquium: An algebraic model of localized surface plasmons and their interactions
Davis, T. J.; Gómez, D. E.
2017-01-01
Although localized surface plasmons in metal nanoparticles can be modeled by Maxwells equations, the difficulty in solving them forces many researchers to use numerical methods. Such methods give accurate results but rarely provide much insight into the complex behaviors of the surface plasmons, nor do they provide a means to choose a configuration of metal nanoparticles to achieve a desired optical response. This Colloquium presents a simple algebraic approach for modeling localized surface plasmons, their excitation by light, and their interactions with one another. Although the method is not numerically accurate it yields useful insight into plasmon behavior and provides a basis for the design of complex plasmonic devices. The approach relies on a description of the surface plasmons in terms of a set of eigenmodes. However, the functional form of these modes is not usually required and the entire problem is reduced to a simple algebra involving the plasmon amplitudes, resonance terms, and their mutual coupling. The algebraic method is derived from an electrostatic formalism, appropriate for near-field interactions at optical frequencies, which is then used to demonstrate a variety of optical effects associated with localized surface plasmons, such as plasmon hybridization, induced transparency, Fano resonances, optical phase detection, and all-optical modulation, among others.
Model checking optimal finite-horizon control for probabilistic gene regulatory networks.
Wei, Ou; Guo, Zonghao; Niu, Yun; Liao, Wenyuan
2017-12-14
Probabilistic Boolean networks (PBNs) have been proposed for analyzing external control in gene regulatory networks with incorporation of uncertainty. A context-sensitive PBN with perturbation (CS-PBNp), extending a PBN with context-sensitivity to reflect the inherent biological stability and random perturbations to express the impact of external stimuli, is considered to be more suitable for modeling small biological systems intervened by conditions from the outside. In this paper, we apply probabilistic model checking, a formal verification technique, to optimal control for a CS-PBNp that minimizes the expected cost over a finite control horizon. We first describe a procedure of modeling a CS-PBNp using the language provided by a widely used probabilistic model checker PRISM. We then analyze the reward-based temporal properties and the computation in probabilistic model checking; based on the analysis, we provide a method to formulate the optimal control problem as minimum reachability reward properties. Furthermore, we incorporate control and state cost information into the PRISM code of a CS-PBNp such that automated model checking a minimum reachability reward property on the code gives the solution to the optimal control problem. We conduct experiments on two examples, an apoptosis network and a WNT5A network. Preliminary experiment results show the feasibility and effectiveness of our approach. The approach based on probabilistic model checking for optimal control avoids explicit computation of large-size state transition relations associated with PBNs. It enables a natural depiction of the dynamics of gene regulatory networks, and provides a canonical form to formulate optimal control problems using temporal properties that can be automated solved by leveraging the analysis power of underlying model checking engines. This work will be helpful for further utilization of the advances in formal verification techniques in system biology.
The large N=4 superconformal W∞ algebra
International Nuclear Information System (INIS)
Beccaria, Matteo; Candu, Constantin; Gaberdiel, Matthias R.
2014-01-01
The most general large N=4 superconformal W ∞ algebra, containing in addition to the superconformal algebra one supermultiplet for each integer spin, is analysed in detail. It is found that the W ∞ algebra is uniquely determined by the levels of the two su(2) algebras, a conclusion that holds both for the linear and the non-linear case. We also perform various cross-checks of our analysis, and exhibit two different types of truncations in some detail.
A branch-and-bound methodology within algebraic modelling systems
Bisschop, J.J.; Heerink, J.B.J.; Kloosterman, G.
1998-01-01
Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\\sc Minto} is an
Design of Installing Check Dam Using RAMMS Model in Seorak National Park of South Korea
Jun, K.; Tak, W.; JUN, B. H.; Lee, H. J.; KIM, S. D.
2016-12-01
Design of Installing Check Dam Using RAMMS Model in Seorak National Park of South Korea Kye-Won Jun*, Won-Jun Tak*, Byong-Hee Jun**, Ho-Jin Lee***, Soung-Doug Kim* *Graduate School of Disaster Prevention, Kangwon National University, 346 Joogang-ro, Samcheok-si, Gangwon-do, Korea **School of Fire and Disaster Protection, Kangwon National University, 346 Joogang-ro, Samcheok-si, Gangwon-do, Korea ***School of Civil Engineering, Chungbuk National University, 1 Chungdae-ro, Seowon-gu, Cheongju, Korea Abstract As more than 64% of the land in South Korea is mountainous area, so many regions in South Korea are exposed to the danger of landslide and debris flow. So it is important to understand the behavior of debris flow in mountainous terrains, the various methods and models are being presented and developed based on the mathematical concept. The purpose of this study is to investigate the regions that experienced the debris flow due to typhoon called Ewiniar and to perform numerical modeling to design and layout of the Check dam for reducing the damage by the debris flow. For the performance of numerical modeling, on-site measurement of the research area was conducted including: topographic investigation, research on bridges in the downstream, and precision LiDAR 3D scanning for composed basic data of numerical modeling. The numerical simulation of this study was performed using RAMMS (Rapid Mass Movements Simulation) model for the analysis of the debris flow. This model applied to the conditions of the Check dam which was installed in the upstream, midstream, and downstream. Considering the reduction effect of debris flow, the expansion of debris flow, and the influence on the bridges in the downstream, proper location of the Check dam was designated. The result of present numerical model showed that when the Check dam was installed in the downstream section, 50 m above the bridge, the reduction effect of the debris flow was higher compared to when the Check dam were
Specification and Generation of Environment for Model Checking of Software Components
Czech Academy of Sciences Publication Activity Database
Pařízek, P.; Plášil, František
2007-01-01
Roč. 176, - (2007), s. 143-154 ISSN 1571-0661 R&D Projects: GA AV ČR 1ET400300504 Institutional research plan: CEZ:AV0Z10300504 Keywords : software components * behavior protocols * model checking * automated generation of environment Subject RIV: JC - Computer Hardware ; Software
Local Model Checking of Weighted CTL with Upper-Bound Constraints
DEFF Research Database (Denmark)
Jensen, Jonas Finnemann; Larsen, Kim Guldstrand; Srba, Jiri
2013-01-01
boolean domain to nonnegative integers in order to cope with the weights. We present both global and local algorithms for the fixed-point computation on symbolic dependency graphs and argue for the advantages of our approach compared to the direct encoding of the model checking problem into dependency...
Model based feasibility study on bidirectional check valves in wave energy converters
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik C.; Andersen, Torben Ole
2014-01-01
Discrete fluid power force systems have been proposed as the primary stage for Wave Energy Converters (WEC’s) when converting ocean waves into electricity, this to improve the overall efficiency of wave energy devices. This paper presents a model based feasibility study of using bidirectional check...... structural loads in the WEC....
Combining Decision Diagrams and SAT Procedures for Efficient Symbolic Model Checking
DEFF Research Database (Denmark)
Williams, Poul Frederick; Biere, Armin; Clarke, Edmund M.
2000-01-01
In this paper we show how to do symbolic model checking using Boolean Expression Diagrams (BEDs), a non-canonical representation for Boolean formulas, instead of Binary Decision Diagrams (BDDs), the traditionally used canonical representation. The method is based on standard fixed point algorithms...
Lin, T.
2014-01-01
In this paper, we settle a problem in probabilistic verification of infinite--state process (specifically, {\\it probabilistic pushdown process}). We show that model checking {\\it stateless probabilistic pushdown process} (pBPA) against {\\it probabilistic computational tree logic} (PCTL) is undecidable.
A practical approach to model checking Duration Calculus using Presburger Arithmetic
DEFF Research Database (Denmark)
Hansen, Michael Reichhardt; Dung, Phan Anh; Brekling, Aske Wiid
2014-01-01
This paper investigates the feasibility of reducing a model-checking problem K ⊧ ϕ for discrete time Duration Calculus to the decision problem for Presburger Arithmetic. Theoretical results point at severe limitations of this approach: (1) the reduction in Fränzle and Hansen (Int J Softw Inform 3...
Model checking for combined logics with an application to mobile systems
Franceschet, M.; Montanari, A.; de Rijke, M.
2004-01-01
In this paper, we develop model checking procedures for three ways of combining (temporal) logics: temporalization, independent combination, and join.We prove that they are terminating, sound, and complete, we analyze their computational complexity, and we report on experiments with
Efficient model checking for duration calculus based on branching-time approximations
DEFF Research Database (Denmark)
Fränzle, Martin; Hansen, Michael Reichhardt
2008-01-01
Duration Calculus (abbreviated to DC) is an interval-based, metric-time temporal logic designed for reasoning about embedded real-time systems at a high level of abstraction. But the complexity of model checking any decidable fragment featuring both negation and chop, DC's only modality, is non...
Gilbert, David
2016-01-01
Insights gained from multilevel computational models of biological systems can be translated into real-life applications only if the model correctness has been verified first. One of the most frequently employed in silico techniques for computational model verification is model checking. Traditional model checking approaches only consider the evolution of numeric values, such as concentrations, over time and are appropriate for computational models of small scale systems (e.g. intracellular networks). However for gaining a systems level understanding of how biological organisms function it is essential to consider more complex large scale biological systems (e.g. organs). Verifying computational models of such systems requires capturing both how numeric values and properties of (emergent) spatial structures (e.g. area of multicellular population) change over time and across multiple levels of organization, which are not considered by existing model checking approaches. To address this limitation we have developed a novel approximate probabilistic multiscale spatio-temporal meta model checking methodology for verifying multilevel computational models relative to specifications describing the desired/expected system behaviour. The methodology is generic and supports computational models encoded using various high-level modelling formalisms because it is defined relative to time series data and not the models used to generate it. In addition, the methodology can be automatically adapted to case study specific types of spatial structures and properties using the spatio-temporal meta model checking concept. To automate the computational model verification process we have implemented the model checking approach in the software tool Mule (http://mule.modelchecking.org). Its applicability is illustrated against four systems biology computational models previously published in the literature encoding the rat cardiovascular system dynamics, the uterine contractions of labour
Compositional Model Checking of Interlocking Systems for Lines with Multiple Stations
DEFF Research Database (Denmark)
Macedo, Hugo Daniel dos Santos; Fantechi, Alessandro; Haxthausen, Anne Elisabeth
2017-01-01
In the railway domain safety is guaranteed by an interlocking system which translates operational decisions into commands leading to field operations. Such a system is safety critical and demands thorough formal verification during its development process. Within this context, our work has focused...... on the extension of a compositional model checking approach to formally verify interlocking system models for lines with multiple stations. The idea of the approach is to decompose a model of the interlocking system by applying cuts at the network modelling level. The paper introduces an alternative cut (the...... linear cut) to a previously proposed cut (border cut). Powered with the linear cut, the model checking approach is then applied to the verification of an interlocking system controlling a real-world multiple station line....
An algebraic model for nuclear molecules of two and three clusters
International Nuclear Information System (INIS)
Yepez M, H.
2003-01-01
In this work we present a phenomenological algebraic model for nuclear rnolecules with two and three nuclei. This model takes into account the inner structures of the nuclei. For the case of nuclear molecules with two clusters the Hamiltonian of the model has a UC 1 (6) UC 2 (6) U R (4) SU C1 ,(3) SU C2 (3) SU R (3) dynamical symmetry. We also obtain the geometrical potential associated with the algebraic Hamiltonian applying a geometrical mapping with coherent states. The relation between the parameter of the coherent state and the relative distance of the clusters was deduced. The algebraic model was applied to the molecular system 12 C + 12 C the molecular spectrum of this system was reproduced fitting the parameters of the model and, the geometrical potential associated with this parameters was obtained. In this case the geometrical potential and the double folding potential show a similar behavior in the proximities of the potential minima. Following the inverse procedure i.e. if we first reproduce some general characteristics of the molecular potential with the geometrical potential associated with the Hamiltonian and then we try to obtain the values of the parameters of the Hamiltonian, some restrictions for this parameters were obtained. Some typical molecular spectra were obtained with the allowed values of the Hamiltonian parameters. For the nuclear molecule 12 C + 12 C for some of this allowed values the molecular spectrum of this system was reproduced. For the case of the hypothetical nuclear molecule 96 Sr + 146 Ba we also obtained some typical molecular spectra. This last procedure is very important for nuclear molecules for which there is no experimental data of their molecular spectrum. Because if we know the double-folding potential it is possible to obtain typical energy spectra obtaining the parameters of the model by reproducing these potentials. For the case of nuclear molecules with three clusters we present an extension of the two cluster
Application of the algebraic RNG model for transition simulation. [renormalization group theory
Lund, Thomas S.
1990-01-01
The algebraic form of the RNG model of Yakhot and Orszag (1986) is investigated as a transition model for the Reynolds averaged boundary layer equations. It is found that the cubic equation for the eddy viscosity contains both a jump discontinuity and one spurious root. A yet unpublished transformation to a quartic equation is shown to remove the numerical difficulties associated with the discontinuity, but only at the expense of merging both the physical and spurious root of the cubic. Jumps between the branches of the resulting multiple-valued solution are found to lead to oscillations in flat plate transition calculations. Aside from the oscillations, the transition behavior is qualitatively correct.
Contractions of quantum algebraic structures
International Nuclear Information System (INIS)
Doikou, A.; Sfetsos, K.
2010-01-01
A general framework for obtaining certain types of contracted and centrally extended algebras is reviewed. The whole process relies on the existence of quadratic algebras, which appear in the context of boundary integrable models. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
International Nuclear Information System (INIS)
Forger, M.; Mannheim Univ.; Laartz, J.; Schaeper, U.
1994-01-01
The recently derived current algrbra of classical non-linear sigma models on arbitrary Riemannian manifolds is extended to include the energy-momentum tensor. It is found that in two dimensions the energy-momentum tensor θ μv , the Noether current j μ associated with the global symmetry of the theory and the composite field j appearing as the coefficient of the Schwinger term in the current algebra, together with the derivatives of j μ and j, generte a closed algebra. The subalgebra generated by the light-cone components of the energy-momentum tensor consists of two commuting copies of the Virasoro algebra, with central charge c=0, reflecting the classical conformal invariance of the theory, but the current algebra part and the semidirect product structure are quite different from the usual Kac-Moody/Sugawara type contruction. (orig.)
Warner, Seth
1990-01-01
Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Goodstein, R L
2007-01-01
This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.
Formal verification of dynamic hybrid systems: a NuSMV-based model checking approach
Directory of Open Access Journals (Sweden)
Xu Zhi
2018-01-01
Full Text Available Software security is an important and challenging research topic in developing dynamic hybrid embedded software systems. Ensuring the correct behavior of these systems is particularly difficult due to the interactions between the continuous subsystem and the discrete subsystem. Currently available security analysis methods for system risks have been limited, as they rely on manual inspections of the individual subsystems under simplifying assumptions. To improve this situation, a new approach is proposed that is based on the symbolic model checking tool NuSMV. A dual PID system is used as an example system, for which the logical part and the computational part of the system are modeled in a unified manner. Constraints are constructed on the controlled object, and a counter-example path is ultimately generated, indicating that the hybrid system can be analyzed by the model checking tool.
Directory of Open Access Journals (Sweden)
Requeno José Ignacio
2014-12-01
Full Text Available Model checking is a generic verification technique that allows the phylogeneticist to focus on models and specifications instead of on implementation issues. Phylogenetic trees are considered as transition systems over which we interrogate phylogenetic questions written as formulas of temporal logic. Nonetheless, standard logics become insufficient for certain practices of phylogenetic analysis since they do not allow the inclusion of explicit time and probabilities. The aim of this paper is to extend the application of model checking techniques beyond qualitative phylogenetic properties and adapt the existing logical extensions and tools to the field of phylogeny. The introduction of time and probabilities in phylogenetic specifications is motivated by the study of a real example: the analysis of the ratio of lactose intolerance in some populations and the date of appearance of this phenotype.
Thermodiffusion in Multicomponent Mixtures Thermodynamic, Algebraic, and Neuro-Computing Models
Srinivasan, Seshasai
2013-01-01
Thermodiffusion in Multicomponent Mixtures presents the computational approaches that are employed in the study of thermodiffusion in various types of mixtures, namely, hydrocarbons, polymers, water-alcohol, molten metals, and so forth. We present a detailed formalism of these methods that are based on non-equilibrium thermodynamics or algebraic correlations or principles of the artificial neural network. The book will serve as single complete reference to understand the theoretical derivations of thermodiffusion models and its application to different types of multi-component mixtures. An exhaustive discussion of these is used to give a complete perspective of the principles and the key factors that govern the thermodiffusion process.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
Cirilo António, N.; Manojlović, N.; Salom, I.
2014-12-01
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.
Directory of Open Access Journals (Sweden)
Ian D. Washington
2015-07-01
Full Text Available A technique for optimizing large-scale differential-algebraic process models under uncertainty using a parallel embedded model approach is developed in this article. A combined multi-period multiple-shooting discretization scheme is proposed, which creates a significant number of independent numerical integration tasks for each shooting interval over all scenario/period realizations. Each independent integration task is able to be solved in parallel as part of the function evaluations within a gradient-based non-linear programming solver. The focus of this paper is on demonstrating potential computation performance improvement when the embedded differential-algebraic equation model solution of the multi-period discretization is implemented in parallel. We assess our parallel dynamic optimization approach on two case studies; the first is a benchmark literature problem, while the second is a large-scale air separation problem that considers a robust set-point transition under parametric uncertainty. Results indicate that focusing on the speed-up of the embedded model evaluation can significantly decrease the overall computation time; however, as the multi-period formulation grows with increased realizations, the computational burden quickly shifts to the internal computation performed within the non-linear programming algorithm. This highlights the need for further decomposition, structure exploitation and parallelization within the non-linear programming algorithm and is the subject for further investigation.
Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications
International Nuclear Information System (INIS)
Martins, M.J.; Melo, C.S.
2009-01-01
We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U q [SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.
Algebraic Bethe ansatz for U(1) invariant integrable models: Compact and non-compact applications
Martins, M. J.; Melo, C. S.
2009-10-01
We apply the algebraic Bethe ansatz developed in our previous paper [C.S. Melo, M.J. Martins, Nucl. Phys. B 806 (2009) 567] to three different families of U(1) integrable vertex models with arbitrary N bond states. These statistical mechanics systems are based on the higher spin representations of the quantum group U[SU(2)] for both generic and non-generic values of q as well as on the non-compact discrete representation of the SL(2,R) algebra. We present for all these models the explicit expressions for both the on-shell and the off-shell properties associated to the respective transfer matrices eigenvalue problems. The amplitudes governing the vectors not parallel to the Bethe states are shown to factorize in terms of elementary building blocks functions. The results for the non-compact SL(2,R) model are argued to be derived from those obtained for the compact systems by taking suitable N→∞ limits. This permits us to study the properties of the non-compact SL(2,R) model starting from systems with finite degrees of freedom.
International Nuclear Information System (INIS)
Koh, Kwang Yong; Seong, Poong Hyun
2010-01-01
Fault tree analysis (FTA) has suffered from several drawbacks such that it uses only static gates and hence can not capture dynamic behaviors of the complex system precisely, and it is in lack of rigorous semantics, and reasoning process which is to check whether basic events really cause top events is done manually and hence very labor-intensive and time-consuming for the complex systems while it has been one of the most widely used safety analysis technique in nuclear industry. Although several attempts have been made to overcome this problem, they can not still do absolute or actual time modeling because they adapt relative time concept and can capture only sequential behaviors of the system. In this work, to resolve the problems, FTA and model checking are integrated to provide formal, automated and qualitative assistance to informal and/or quantitative safety analysis. Our approach proposes to build a formal model of the system together with fault trees. We introduce several temporal gates based on timed computational tree logic (TCTL) to capture absolute time behaviors of the system and to give concrete semantics to fault tree gates to reduce errors during the analysis, and use model checking technique to automate the reasoning process of FTA
Genetic coding and united-hypercomplex systems in the models of algebraic biology.
Petoukhov, Sergey V
2017-08-01
Structured alphabets of DNA and RNA in their matrix form of representations are connected with Walsh functions and a new type of systems of multidimensional numbers. This type generalizes systems of complex numbers and hypercomplex numbers, which serve as the basis of mathematical natural sciences and many technologies. The new systems of multi-dimensional numbers have interesting mathematical properties and are called in a general case as "systems of united-hypercomplex numbers" (or briefly "U-hypercomplex numbers"). They can be widely used in models of multi-parametrical systems in the field of algebraic biology, artificial life, devices of biological inspired artificial intelligence, etc. In particular, an application of U-hypercomplex numbers reveals hidden properties of genetic alphabets under cyclic permutations in their doublets and triplets. A special attention is devoted to the author's hypothesis about a multi-linguistic in DNA-sequences in a relation with an ensemble of U-numerical sub-alphabets. Genetic multi-linguistic is considered as an important factor to provide noise-immunity properties of the multi-channel genetic coding. Our results attest to the conformity of the algebraic properties of the U-numerical systems with phenomenological properties of the DNA-alphabets and with the complementary device of the double DNA-helix. It seems that in the modeling field of algebraic biology the genetic-informational organization of living bodies can be considered as a set of united-hypercomplex numbers in some association with the famous slogan of Pythagoras "the numbers rule the world". Copyright © 2017 Elsevier B.V. All rights reserved.
MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable
Directory of Open Access Journals (Sweden)
Karin Quaas
2014-03-01
Full Text Available Parametric timed automata extend timed automata (Alur and Dill, 1991 in that they allow the specification of parametric bounds on the clock values. Since their introduction in 1993 by Alur, Henzinger, and Vardi, it is known that the emptiness problem for parametric timed automata with one clock is decidable, whereas it is undecidable if the automaton uses three or more parametric clocks. The problem is open for parametric timed automata with two parametric clocks. Metric temporal logic, MTL for short, is a widely used specification language for real-time systems. MTL-model checking of timed automata is decidable, no matter how many clocks are used in the timed automaton. In this paper, we prove that MTL-model checking for parametric timed automata is undecidable, even if the automaton uses only one clock and one parameter and is deterministic.
HyLTL: a temporal logic for model checking hybrid systems
Directory of Open Access Journals (Sweden)
Davide Bresolin
2013-08-01
Full Text Available The model-checking problem for hybrid systems is a well known challenge in the scientific community. Most of the existing approaches and tools are limited to safety properties only, or operates by transforming the hybrid system to be verified into a discrete one, thus loosing information on the continuous dynamics of the system. In this paper we present a logic for specifying complex properties of hybrid systems called HyLTL, and we show how it is possible to solve the model checking problem by translating the formula into an equivalent hybrid automaton. In this way the problem is reduced to a reachability problem on hybrid automata that can be solved by using existing tools.
Directory of Open Access Journals (Sweden)
Gina Belmonte
2016-07-01
Full Text Available Recent research on formal verification for Collective Adaptive Systems (CAS pushed advancements in spatial and spatio-temporal model checking, and as a side result provided novel image analysis methodologies, rooted in logical methods for topological spaces. Medical Imaging (MI is a field where such technologies show potential for ground-breaking innovation. In this position paper, we present a preliminary investigation centred on applications of spatial model checking to MI. The focus is shifted from pure logics to a mixture of logical, statistical and algorithmic approaches, driven by the logical nature intrinsic to the specification of the properties of interest in the field. As a result, novel operators are introduced, that could as well be brought back to the setting of CAS.
MODELING IN MAPLE AS THE RESEARCHING MEANS OF FUNDAMENTAL CONCEPTS AND PROCEDURES IN LINEAR ALGEBRA
Directory of Open Access Journals (Sweden)
Vasil Kushnir
2016-05-01
-th degree of a square matrix, to calculate matrix exponent, etc. The author creates four basic forms of canonical models of matrices and shows how to design matrices of similar transformations to these four forms. We introduce the programs-procedures for square matrices construction based on the selected models of canonical matrices. Then you can create a certain amount of various square matrices based on canonical matrix models, it allows to use individual learning technologies. The use of Maple-technology allows to automate the cumbersome and complex procedures for finding the transformation matrices of canonical form of a matrix, values of matrices functions, etc., which not only saves time but also attracts attention and efforts on understanding the above mentioned fundamental concepts of linear algebra and procedures for investigation of their properties. All these create favorable conditions for the use of fundamental concepts of linear algebra in scientific and research work of students and undergraduates using Maple-technology
Numerical Modeling of Debris Flow Force Caused by Climate Change and Its application to Check Dam
KIM, S. D.; Jun, K.; JUN, B. H.; Lee, H. J.; TAK, W. J.
2016-12-01
Due to global warming, climate change cause a super hurricane and heavy rainfall frequently. Heavy rainfall cause by debris flow in mountainous terrains, and disasters by debris flow force have continuously increased. The purpose of this study is to analyze the characteristics of debris flow force acting on the check dam. The numerical approach to the debris flow force was performed by the Finite Difference Method (FDM) based on the erosion-deposition combination model including the equation of continuity, mass conservation, and momentum conservation. In order to investigate behavior of the debris flow force according to the variance of supplying water discharge and channel slope angle, a rectangular straight channel and one closed type check dam was set up for conducting numerical simulations. As the supply water discharges increase, the curve of the impact force by debris flow becomes unstable and fluctuation with high impact force occurred as time passes. And the peak impact force showed a steeper slope and appeared more quickly, the high impact force undergoes a fluctuation with high speed, and acting on the check dam. At the mountainous upstream, strong rainfall energy provoke a repeat erosion and deposition which results in debris flow force causing much damage along the check dam at the mountainous place. The analyses of the present study help provide information to predict future debris flow force and how to design for the check dam. This research was supported by a grant [MPSS-NH-2014-74] through the Disaster and Safety Management Institute funded by Ministry of Public Safety and Security of Korean government
Model-Checking of Linear-Time Properties in Multi-Valued Systems
Li, Yongming; Droste, Manfred; Lei, Lihui
2012-01-01
In this paper, we study model-checking of linear-time properties in multi-valued systems. Safety property, invariant property, liveness property, persistence and dual-persistence properties in multi-valued logic systems are introduced. Some algorithms related to the above multi-valued linear-time properties are discussed. The verification of multi-valued regular safety properties and multi-valued $\\omega$-regular properties using lattice-valued automata are thoroughly studied. Since the law o...
Analysis of DGNB-DK criteria for BIM-based Model Checking automatization
DEFF Research Database (Denmark)
Gade, Peter Nørkjær; Svidt, Kjeld; Jensen, Rasmus Lund
This report includes the results of an analysis of the automation potential of the Danish edition of building sustainability assessment method Deutsche Gesellschaft für Nachhaltiges Bauen (DGNB) for office buildings version 2014 1.1. The analysis investigate the criteria related to DGNB-DK and if......-DK and if they would be suited for automation through the technological concept BIM-based Model Checking (BMC)....
Numerical algebraic geometry for model selection and its application to the life sciences
Gross, Elizabeth
2016-10-12
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology.
Numerical algebraic geometry for model selection and its application to the life sciences.
Gross, Elizabeth; Davis, Brent; Ho, Kenneth L; Bates, Daniel J; Harrington, Heather A
2016-10-01
Researchers working with mathematical models are often confronted by the related problems of parameter estimation, model validation and model selection. These are all optimization problems, well known to be challenging due to nonlinearity, non-convexity and multiple local optima. Furthermore, the challenges are compounded when only partial data are available. Here, we consider polynomial models (e.g. mass-action chemical reaction networks at steady state) and describe a framework for their analysis based on optimization using numerical algebraic geometry. Specifically, we use probability-one polynomial homotopy continuation methods to compute all critical points of the objective function, then filter to recover the global optima. Our approach exploits the geometrical structures relating models and data, and we demonstrate its utility on examples from cell signalling, synthetic biology and epidemiology. © 2016 The Author(s).
The quantum Rabi model and Lie algebra representations of sl2
International Nuclear Information System (INIS)
Wakayama, Masato; Yamasaki, Taishi
2014-01-01
The aim of the present paper is to understand the spectral problem of the quantum Rabi model in terms of Lie algebra representations of sl 2 (R). We define a second order element of the universal enveloping algebra U(sl 2 ) of sl 2 (R), which, through the image of a principal series representation of sl 2 (R), provides a picture equivalent to the quantum Rabi model drawn by confluent Heun differential equations. By this description, in particular, we give a representation theoretic interpretation of the degenerate part of the spectrum (i.e., Judd's eigenstates) of the Rabi Hamiltonian due to Kuś in 1985, which is a part of the exceptional spectrum parameterized by integers. We also discuss the non-degenerate part of the exceptional spectrum of the model, in addition to the Judd eigenstates, from a viewpoint of infinite dimensional irreducible submodules (or subquotients) of the non-unitary principal series such as holomorphic discrete series representations of sl 2 (R). (paper)
Model checking software for phylogenetic trees using distribution and database methods.
Requeno, José Ignacio; Colom, José Manuel
2013-12-01
Model checking, a generic and formal paradigm stemming from computer science based on temporal logics, has been proposed for the study of biological properties that emerge from the labeling of the states defined over the phylogenetic tree. This strategy allows us to use generic software tools already present in the industry. However, the performance of traditional model checking is penalized when scaling the system for large phylogenies. To this end, two strategies are presented here. The first one consists of partitioning the phylogenetic tree into a set of subgraphs each one representing a subproblem to be verified so as to speed up the computation time and distribute the memory consumption. The second strategy is based on uncoupling the information associated to each state of the phylogenetic tree (mainly, the DNA sequence) and exporting it to an external tool for the management of large information systems. The integration of all these approaches outperforms the results of monolithic model checking and helps us to execute the verification of properties in a real phylogenetic tree.
Model checking software for phylogenetic trees using distribution and database methods
Directory of Open Access Journals (Sweden)
Requeno José Ignacio
2013-12-01
Full Text Available Model checking, a generic and formal paradigm stemming from computer science based on temporal logics, has been proposed for the study of biological properties that emerge from the labeling of the states defined over the phylogenetic tree. This strategy allows us to use generic software tools already present in the industry. However, the performance of traditional model checking is penalized when scaling the system for large phylogenies. To this end, two strategies are presented here. The first one consists of partitioning the phylogenetic tree into a set of subgraphs each one representing a subproblem to be verified so as to speed up the computation time and distribute the memory consumption. The second strategy is based on uncoupling the information associated to each state of the phylogenetic tree (mainly, the DNA sequence and exporting it to an external tool for the management of large information systems. The integration of all these approaches outperforms the results of monolithic model checking and helps us to execute the verification of properties in a real phylogenetic tree.
A Novel Algorithm for Intrusion Detection Based on RASL Model Checking
Directory of Open Access Journals (Sweden)
Weijun Zhu
2013-01-01
Full Text Available The interval temporal logic (ITL model checking (MC technique enhances the power of intrusion detection systems (IDSs to detect concurrent attacks due to the strong expressive power of ITL. However, an ITL formula suffers from difficulty in the description of the time constraints between different actions in the same attack. To address this problem, we formalize a novel real-time interval temporal logic—real-time attack signature logic (RASL. Based on such a new logic, we put forward a RASL model checking algorithm. Furthermore, we use RASL formulas to describe attack signatures and employ discrete timed automata to create an audit log. As a result, RASL model checking algorithm can be used to automatically verify whether the automata satisfy the formulas, that is, whether the audit log coincides with the attack signatures. The simulation experiments show that the new approach effectively enhances the detection power of the MC-based intrusion detection methods for a number of telnet attacks, p-trace attacks, and the other sixteen types of attacks. And these experiments indicate that the new algorithm can find several types of real-time attacks, whereas the existing MC-based intrusion detection approaches cannot do that.
Process Algebra and Markov Chains
Brinksma, Hendrik; Hermanns, H.; Brinksma, Hendrik; Hermanns, H.; Katoen, Joost P.
This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study
Leibniz Algebras and Lie Algebras
Directory of Open Access Journals (Sweden)
Geoffrey Mason
2013-10-01
Full Text Available This paper concerns the algebraic structure of finite-dimensional complex Leibniz algebras. In particular, we introduce left central and symmetric Leibniz algebras, and study the poset of Lie subalgebras using an associative bilinear pairing taking values in the Leibniz kernel.
Construction and decoding of a class of algebraic geometry codes
DEFF Research Database (Denmark)
Justesen, Jørn; Larsen, Knud J.; Jensen, Helge Elbrønd
1989-01-01
A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decod......A class of codes derived from algebraic plane curves is constructed. The concepts and results from algebraic geometry that were used are explained in detail; no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result...
Visual Predictive Check in Models with Time-Varying Input Function.
Largajolli, Anna; Bertoldo, Alessandra; Campioni, Marco; Cobelli, Claudio
2015-11-01
The nonlinear mixed effects models are commonly used modeling techniques in the pharmaceutical research as they enable the characterization of the individual profiles together with the population to which the individuals belong. To ensure a correct use of them is fundamental to provide powerful diagnostic tools that are able to evaluate the predictive performance of the models. The visual predictive check (VPC) is a commonly used tool that helps the user to check by visual inspection if the model is able to reproduce the variability and the main trend of the observed data. However, the simulation from the model is not always trivial, for example, when using models with time-varying input function (IF). In this class of models, there is a potential mismatch between each set of simulated parameters and the associated individual IF which can cause an incorrect profile simulation. We introduce a refinement of the VPC by taking in consideration a correlation term (the Mahalanobis or normalized Euclidean distance) that helps the association of the correct IF with the individual set of simulated parameters. We investigate and compare its performance with the standard VPC in models of the glucose and insulin system applied on real and simulated data and in a simulated pharmacokinetic/pharmacodynamic (PK/PD) example. The newly proposed VPC performance appears to be better with respect to the standard VPC especially for the models with big variability in the IF where the probability of simulating incorrect profiles is higher.
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
Energy Technology Data Exchange (ETDEWEB)
Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil); Universidade Federal de Juiz de Fora, MG (Brazil)
2013-07-01
Full text: In current theoretical physics there is a relevant number of theoretical investigations that lead to believe that at the first moments of our Universe, the geometry was not commutative and the dominating physics at that time was ruled by the laws of noncommutative (NC) geometry. Therefore, the idea is that the physics of the early moments can be constructed based on these concepts. The first published work using the idea of a NC spacetime were carried out by Snyder who believed that NC principles could make the quantum field theory infinities disappear. However, it did not occur and Snyder's ideas were put to sleep for a long time. The main modern motivations that rekindle the investigation about NC field theories came from string theory and quantum gravity. In the context of quantum mechanics for example, R. Banerjee discussed how NC structures appear in planar quantum mechanics providing a useful way for obtaining them. The analysis was based on the NC algebra used in planar quantum mechanics that was originated from 't Hooft's analysis on dissipation and quantization. In this work we carry out a NC algebra analysis of the Friedmann-Robert-Walker model, coupled to a perfect fluid and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. (author)
Model-Checking the Higher-Dimensional Modal mu-Calculus
Directory of Open Access Journals (Sweden)
Martin Lange
2012-02-01
Full Text Available The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in polynomial time, and conversely every polynomial-time decidable problem that has a bisimulation-invariant encoding into labeled transition systems can also be defined in the higher-dimensional modal mu-calculus. We exemplify the latter connection by giving several examples of decision problems which reduce to model checking of the higher-dimensional modal mu-calculus for some fixed formulas. This way generic model checking algorithms for the logic can then be used via partial evaluation in order to obtain algorithms for theses problems which may benefit from improvements that are well-established in the field of program verification, namely on-the-fly and symbolic techniques. The aim of this work is to extend such techniques to other fields as well, here exemplarily done for process equivalences, automata theory, parsing, string problems, and games.
Sediment depositions upstream of open check dams: new elements from small scale models
Piton, Guillaume; Le Guern, Jules; Carbonari, Costanza; Recking, Alain
2015-04-01
numbers that the flows tend to adopt? New small scale model experiments have been undertaken focusing on depositions processes and their related hydraulics. Accurate photogrammetric measurements allowed us to better describe the deposition processes3. Large Scale Particle Image Velocimetry (LS-PIV) was performed to determine surface velocity fields in highly active channels with low grain submersion4. We will present preliminary results of our experiments showing the new elements we observed in massive deposit dynamics. REFERENCES 1.Armanini, A., Dellagiacoma, F. & Ferrari, L. From the check dam to the development of functional check dams. Fluvial Hydraulics of Mountain Regions 37, 331-344 (1991). 2.Piton, G. & Recking, A. Design of sediment traps with open check dams: a review, part I: hydraulic and deposition processes. (Accepted by the) Journal of Hydraulic Engineering 1-23 (2015). 3.Le Guern, J. Ms Thesis: Modélisation physique des plages de depot : analyse de la dynamique de remplissage.(2014) . 4.Carbonari, C. Ms Thesis: Small scale experiments of deposition processes occuring in sediment traps, LS-PIV measurments and geomorphological descriptions. (in preparation).
Two Remarks to Bifullness of Centers of Archimedean Atomic Lattice Effect Algebras
Directory of Open Access Journals (Sweden)
M. Kalina
2011-01-01
Full Text Available Lattice effect algebras generalize orthomodular lattices as well as MV-algebras. This means that within lattice effect algebras it is possible to model such effects as unsharpness (fuzziness and/or non-compatibility. The main problem is the existence of a state. There are lattice effect algebras with no state. For this reason we need some conditions that simplify checking the existence of a state. If we know that the center C(E of an atomic Archimedean lattice effect algebra E (which is again atomic is a bifull sublattice of E, then we are able to represent E as a subdirect product of lattice effect algebras Ei where the top element of each one of Ei is an atom of C(E. In this case it is enough if we find a state at least in one of Ei and we are able to extend this state to the whole lattice effect algebra E. In [8] an atomic lattice effect algebra E (in fact, an atomic orthomodular lattice with atomic center C(E was constructed, where C(E is not a bifull sublattice of E. In this paper we show that for atomic lattice effect algebras E (atomic orthomodular lattices neither completeness (and atomicity of C(E nor σ-completeness of E are sufficient conditions for C(E to be a bifull sublattice of E.
Bounded Model Checking and Inductive Verification of Hybrid Discrete-Continuous Systems
DEFF Research Database (Denmark)
Becker, Bernd; Behle, Markus; Eisenbrand, Fritz
2004-01-01
verication, bounded plan- ning and heuristic search, combinatorial optimization and integer programming. Af- ter sketching the overall verication ow we present rst results indicating that the combination and tight integration of dierent verication engines is a rst step to pave the way to fully automated BMC......We present a concept to signicantly advance the state of the art for bounded model checking (BMC) and inductive verication (IV) of hybrid discrete-continuous systems. Our approach combines the expertise of partners coming from dierent domains, like hybrid systems modeling and digital circuit...
A conceptual model of the hydraulics of check dam for gully control
Castillo, C.; Pérez, R.; Gómez, J. A.
2012-04-01
Check dams have been long recognized as useful structures to minimize concentrated flow erosion by reducing the original gradient of the gully channel and, consequently, the erosive power of run-off (FAO, 1986). Careful attention must be paid to the design of the structures in order to avoid negative effects such as bypassing or scouring that might lead to the parcial or total collapse of the structure (Nyssen,2004). This study attempts to offer a conceptual model to explain the fundamental hydraulics of the flow regime modifications produced by these structures on rectagular-shaped gullies, before and after the filling by sediment of the small volume created by the check dam. The factors affecting the characteristics (location and amount of dissipated energy) of the hydraulic jump and the role played by the steepness of the gully on the hydraulic influence are discussed through a geometric and energetic approach. The shear stress reduction efficiency of the structure is evaluated against flow conditions (subcritical and supercritical), steepness factor, effective height and check dam spacing. HEC RAS 4.0 model (U.S. Army Corps of Engineers, 2008) has been used for validation purposes. In addition, apron protection measures (riprap stone and gabions) have been discussed in order to determine the limits of the discharge and drop height to prevent scouring. The model presented a good performance on the prediction of hydraulic variables, and especially estimating shear stress reduction by the check dam structure. Steepness factor is the key parameter defining the hydraulic influence and ultimate slope and, therefore, the efficiency of the structure. The effective control of the flow erosivity requires the selection of a steepness factor value close to or higher than 1, showing similarities with natural stabilised channels as step-pools morphologies (Abrahams, 1995). The requirements for an efficient reduction of the shear stress and for assuring the stability of the
Warner, Zachary B.
2013-01-01
This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…
Ford, Timothy J
2017-01-01
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Anomaly in RTT relation for DIM algebra and network matrix models
Awata, Hidetoshi; Kanno, Hiroaki; Mironov, Andrei; Morozov, Alexei; Morozov, Andrey; Ohkubo, Yusuke; Zenkevich, Yegor
2017-05-01
We discuss the recent proposal of arxiv:arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q-deformed conformal block and its 5 d / 6 d gauge theory counterpart, i.e. the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4d Nekrasov functions), which breaks the spectral duality.
Anomaly in RTT relation for DIM algebra and network matrix models
Directory of Open Access Journals (Sweden)
Hidetoshi Awata
2017-05-01
Full Text Available We discuss the recent proposal of arXiv:1608.05351 about generalization of the RTT relation to network matrix models. We show that the RTT relation in these models is modified by a nontrivial, but essentially abelian anomaly cocycle, which we explicitly evaluate for the free field representations of the quantum toroidal algebra. This cocycle is responsible for the braiding, which permutes the external legs in the q-deformed conformal block and its 5d/6d gauge theory counterpart, i.e. the non-perturbative Nekrasov functions. Thus, it defines their modular properties and symmetry. We show how to cancel the anomaly using a construction somewhat similar to the anomaly matching condition in gauge theory. We also describe the singular limit to the affine Yangian (4d Nekrasov functions, which breaks the spectral duality.
Sulis, William H
2017-10-01
Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.
Diagnostic models of intelligent tutor system for teaching skills to solve algebraic equations
Directory of Open Access Journals (Sweden)
Andrey Grigoriyevich Chukhray
2007-10-01
Full Text Available In this paper one solution for teaching skills to solve n-power algebraic equation by Lobachevsky-Greffe-Dandelen method is described. StudentÃ¢Â€Â™s mistakes are discovered and classified. Based on signal-parametric approach to fault diagnosis in dynamic systems mathematical diagnostic models which allow detecting mistake classes by comparing student calculated results and system calculated results are created. Features of proposed diagnostic models application are presented. Intelligent tutor system is developed and used on Ã¢Â€ÂœAutomatic Control TheoryÃ¢Â€Â practical training by third year students of National Aerospace University.
Study of the 'non-Abelian' current algebra of a non-linear σ-model
International Nuclear Information System (INIS)
Ghosh, Subir
2006-01-01
A particular form of non-linear σ-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-Abelian nature of the invariance, with field dependent structure functions. Reduction of the field theory to a point particle framework yields a non-linear harmonic oscillator, which is a special case of similar models studied before in [J.F. Carinena et al., Nonlinearity 17 (2004) 1941, math-ph/0406002; J.F. Carinena et al., in: Proceedings of 10th International Conference in Modern Group Analysis, Larnaca, Cyprus, 2004, p. 39, math-ph/0505028; J.F. Carinena et al., Rep. Math. Phys. 54 (2004) 285, hep-th/0501106]. The connection with non-commutative geometry is also established
Constructing a coherent problem model to facilitate algebra problem solving in a chemistry context
Hiong Ngu, Bing; Seeshing Yeung, Alexander; Phan, Huy P.
2015-04-01
An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant information for reaching a solution. Worked examples direct students to follow steps toward the solution, and its emphasis is on computation instead of the formation of a coherent problem model. Text editing yielded higher scores in a transfer test (which shared the same solution procedure as in the acquisition problems but differed in contexts), but not a similar test (which resembled acquisition problems in terms of both solution procedure and context). Results provide some theoretical support and practical implications for using text editing to develop a coherent problem model to facilitate problem-solving skills in chemistry.
An algebraic approach for solving evolution problems in some nonlinear quantum models
International Nuclear Information System (INIS)
Karassiov, Valery P.; Klimov, Andrei B.
1994-01-01
A new general Lie-algebraic approach is proposed for solving evolution tasks in some nonlinear problems of quantum physics with polynomially deformed Lie algebras su pd (2) as their dynamic symmetry algebras. The method makes use of an expansion of the evolution operators by power series in the su pd (2) shift operators and a (recursive) reduction finding coefficient functions for solving auxiliary exactly solvable su(2) problems with quadratic Hamiltonians. ((orig.))
International Nuclear Information System (INIS)
Odesskii, A V
2002-01-01
This survey is devoted to associative Z ≥0 -graded algebras presented by n generators and n(n-1)/2 quadratic relations and satisfying the so-called Poincare-Birkhoff-Witt condition (PBW-algebras). Examples are considered of such algebras, depending on two continuous parameters (namely, on an elliptic curve and a point on it), that are flat deformations of the polynomial ring in n variables. Diverse properties of these algebras are described, together with their relations to integrable systems, deformation quantization, moduli spaces, and other directions of modern investigations
National Research Council Canada - National Science Library
Hartshorne, Robin
1977-01-01
.... 141 BECKERIWEISPFENNINGIKREDEL. Grabner Bases. A Computational Approach to Commutative Algebra. 142 LANG. Real and Functional Analysis. 3rd ed. 143 DOOB. Measure Theory. 144 DENNIS/FARB. Noncommutat...
Jorgensen, Palle E T
1987-01-01
Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e
Lochbihler, Andreas
2012-01-01
The Java programming language provides safety and security guarantees such as type safety and its security architecture. They distinguish it from other mainstream programming languages like C and C++. In this work, we develop a machine-checked model of concurrent Java and the Java memory model and investigate the impact of concurrency on these guarantees. From the formal model, we automatically obtain an executable verified compiler to bytecode and a validated virtual machine.
Directory of Open Access Journals (Sweden)
Marcus Völp
2012-11-01
Full Text Available Reliability in terms of functional properties from the safety-liveness spectrum is an indispensable requirement of low-level operating-system (OS code. However, with evermore complex and thus less predictable hardware, quantitative and probabilistic guarantees become more and more important. Probabilistic model checking is one technique to automatically obtain these guarantees. First experiences with the automated quantitative analysis of low-level operating-system code confirm the expectation that the naive probabilistic model checking approach rapidly reaches its limits when increasing the numbers of processes. This paper reports on our work-in-progress to tackle the state explosion problem for low-level OS-code caused by the exponential blow-up of the model size when the number of processes grows. We studied the symmetry reduction approach and carried out our experiments with a simple test-and-test-and-set lock case study as a representative example for a wide range of protocols with natural inter-process dependencies and long-run properties. We quickly see a state-space explosion for scenarios where inter-process dependencies are insignificant. However, once inter-process dependencies dominate the picture models with hundred and more processes can be constructed and analysed.
Model checking of safety-critical software in the nuclear engineering domain
International Nuclear Information System (INIS)
Lahtinen, J.; Valkonen, J.; Björkman, K.; Frits, J.; Niemelä, I.; Heljanko, K.
2012-01-01
Instrumentation and control (I and C) systems play a vital role in the operation of safety-critical processes. Digital programmable logic controllers (PLC) enable sophisticated control tasks which sets high requirements for system validation and verification methods. Testing and simulation have an important role in the overall verification of a system but are not suitable for comprehensive evaluation because only a limited number of system behaviors can be analyzed due to time limitations. Testing is also performed too late in the development lifecycle and thus the correction of design errors is expensive. This paper discusses the role of formal methods in software development in the area of nuclear engineering. It puts forward model checking, a computer-aided formal method for verifying the correctness of a system design model, as a promising approach to system verification. The main contribution of the paper is the development of systematic methodology for modeling safety critical systems in the nuclear domain. Two case studies are reviewed, in which we have found errors that were previously not detected. We also discuss the actions that should be taken in order to increase confidence in the model checking process.
Monitor-Based Statistical Model Checking for Weighted Metric Temporal Logic
DEFF Research Database (Denmark)
Bulychev, Petr; David, Alexandre; Larsen, Kim Guldstrand
2012-01-01
We present a novel approach and implementation for ana- lysing weighted timed automata (WTA) with respect to the weighted metric temporal logic (WMTL≤ ). Based on a stochastic semantics of WTAs, we apply statistical model checking (SMC) to estimate and test probabilities of satisfaction...... often exact and ex- perimentally tight. The technique is implemented in the new tool Casaal that we seamlessly connect to Uppaal-smc in a tool chain. We demon- strate the applicability of our technique and the efficiency of our imple- mentation through a number of case-studies....
Bringing Automated Model Checking to PLC Program Development - A CERN Case Study
Fernandez Adiego, B; Tournier, J-C; Blanco Vinuela, E; Gonzalez Suarez, V M
2014-01-01
Verification of critical software is a high priority but a challenging task for industrial control systems. Model checking appears to be an appropriate approach for this purpose. However, this technique is not widely used in industry yet, due to some obstacles. The main obstacles encountered when trying to apply formal verification techniques at industrial installations are the difficulty of creating models out of PLC programs and defining formally the specification requirements. In addition, models produced out of real-life programs have a huge state space, thus preventing the verification due to performance issues. Our work at CERN (European Organization for Nuclear Research) focuses on developing efficient automatic verification methods for industrial critical installations based on PLC (Programmable Logic Controller) control systems. In this paper, we present a tool generating automatically formal models out of PLC code. The tool implements a general methodology which can support several input languages, ...
An Evaluation Framework for Energy Aware Buildings using Statistical Model Checking
DEFF Research Database (Denmark)
David, Alexandre; Du, DeHui; Larsen, Kim Guldstrand
2012-01-01
Cyber-physical systems are to be found in numerous applications throughout society. The principal barrier to develop trustworthy cyber-physical systems is the lack of expressive modelling and specification for- malisms supported by efficient tools and methodologies. To overcome this barrier, we...... extend in this paper the modelling formalism of the tool Uppaal-smc to stochastic hybrid automata, thus providing the expressive power required for modeling complex cyber-physical systems. The application of Statistical Model Checking provides a highly scalable technique for analyzing performance...... properties of this formalisms. A particular kind of cyber-physical systems are Smart Grids which together with Intelligent, Energy Aware Buildings will play a major role in achieving an energy efficient society of the future. In this paper we present a framework in Uppaal-smc for energy aware buildings...
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Hansen, Zaza Nadja Lee
2016-01-01
This article presents a framework for the automated restructuring of stochastic workflows to reduce the impact of faults. The framework allows for the modelling of workflows by means of a formalised subset of the BPMN workflow language. We extend this modelling formalism to describe faults...... and incorporate an intention preserving stochastic semantics able to model both probabilistic- and non-deterministic behaviour. Stochastic model checking techniques are employed to generate the state-space of a given workflow. Possible improvements obtained by restructuring are measured by employing the framework......'s capacity for tracking real-valued quantities associated with states and transitions of the workflow. The space of possible restructurings of a workflow are explored by means of an evolutionary algorithm, where the goals for improvement are defined in terms of optimising quantities, typically employed...
Algebraic geometry methods associated to the one-dimensional Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Martins, M.J., E-mail: martins@df.ufscar.br
2016-06-15
In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.
Syafari
2017-01-01
This research was purposed to develop module and learning model and instrument of proofing ability in algebra structure through cooperative learning with helping map concept media for students of mathematic major and mathematics education in State University and Private University in North Sumatra province. The subject of this research was the…
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
International Nuclear Information System (INIS)
Aoyama, Shogo
2014-01-01
The Poisson brackets for non-linear σ-models on G/H are set up on the light-like plane. A quantity which transforms irreducibly by the Killing vectors, called Killing scalar, is constructed in an arbitrary representation of G. It is shown to satisfy the classical exchange algebra
Directory of Open Access Journals (Sweden)
G. Bussi
2013-08-01
Full Text Available Soil loss and sediment transport in Mediterranean areas are driven by complex non-linear processes which have been only partially understood. Distributed models can be very helpful tools for understanding the catchment-scale phenomena which lead to soil erosion and sediment transport. In this study, a modelling approach is proposed to reproduce and evaluate erosion and sediment yield processes in a Mediterranean catchment (Rambla del Poyo, Valencia, Spain. Due to the lack of sediment transport records for model calibration and validation, a detailed description of the alluvial stratigraphy infilling a check dam that drains a 12.9 km2 sub-catchment was used as indirect information of sediment yield data. These dam infill sediments showed evidences of at least 15 depositional events (floods over the time period 1990–2009. The TETIS model, a distributed conceptual hydrological and sediment model, was coupled to the Sediment Trap Efficiency for Small Ponds (STEP model for reproducing reservoir retention, and it was calibrated and validated using the sedimentation volume estimated for the depositional units associated with discrete runoff events. The results show relatively low net erosion rates compared to other Mediterranean catchments (0.136 Mg ha−1 yr−1, probably due to the extensive outcrops of limestone bedrock, thin soils and rather homogeneous vegetation cover. The simulated sediment production and transport rates offer model satisfactory results, further supported by in-site palaeohydrological evidences and spatial validation using additional check dams, showing the great potential of the presented data assimilation methodology for the quantitative analysis of sediment dynamics in ungauged Mediterranean basins.
Re-engineering pre-employment check-up systems: a model for improving health services.
Rateb, Said Abdel Hakim; El Nouman, Azza Abdel Razek; Rateb, Moshira Abdel Hakim; Asar, Mohamed Naguib; El Amin, Ayman Mohammed; Gad, Saad abdel Aziz; Mohamed, Mohamed Salah Eldin
2011-01-01
The purpose of this paper is to develop a model for improving health services provided by the pre-employment medical fitness check-up system affiliated to Egypt's Health Insurance Organization (HIO). Operations research, notably system re-engineering, is used in six randomly selected centers and findings before and after re-engineering are compared. The re-engineering model follows a systems approach, focusing on three areas: structure, process and outcome. The model is based on six main components: electronic booking, standardized check-up processes, protected medical documents, advanced archiving through an electronic content management (ECM) system, infrastructure development, and capacity building. The model originates mainly from customer needs and expectations. The centers' monthly customer flow increased significantly after re-engineering. The mean time spent per customer cycle improved after re-engineering--18.3 +/- 5.5 minutes as compared to 48.8 +/- 14.5 minutes before. Appointment delay was also significantly decreased from an average 18 to 6.2 days. Both beneficiaries and service providers were significantly more satisfied with the services after re-engineering. The model proves that re-engineering program costs are exceeded by increased revenue. Re-engineering in this study involved multiple structure and process elements. The literature review did not reveal similar re-engineering healthcare packages. Therefore, each element was compared separately. This model is highly recommended for improving service effectiveness and efficiency. This research is the first in Egypt to apply the re-engineering approach to public health systems. Developing user-friendly models for service improvement is an added value.
African Journals Online (AJOL)
Tadesse
Department of Mathematics, Faculty of Computer and Mathematical Sciences, Addis Ababa. University, Addis Ababa, Ethiopia(*drkvenkateswarlu@gmail.com, **berhanufk@yahoo.co.uk). ABSTRACT. In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra ...
African Journals Online (AJOL)
Tadesse
metric space. Also we prove that every implicative algebra can be made into a regular. Autometrized Algebra of Swamy (1964) (see theorem 2.9). We recall the definition of Xu (1993). Defintion [2]: Let (L,∨,∧,0,1) be a bounded lattice with order reversing involution. “ ' ”and a binary operation → satisfying the following ...
Linear Algebra and Smarandache Linear Algebra
Vasantha, Kandasamy
2003-01-01
The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...
Model Checking Artificial Intelligence Based Planners: Even the Best Laid Plans Must Be Verified
Smith, Margaret H.; Holzmann, Gerard J.; Cucullu, Gordon C., III; Smith, Benjamin D.
2005-01-01
Automated planning systems (APS) are gaining acceptance for use on NASA missions as evidenced by APS flown On missions such as Orbiter and Deep Space 1 both of which were commanded by onboard planning systems. The planning system takes high level goals and expands them onboard into a detailed of action fiat the spacecraft executes. The system must be verified to ensure that the automatically generated plans achieve the goals as expected and do not generate actions that would harm the spacecraft or mission. These systems are typically tested using empirical methods. Formal methods, such as model checking, offer exhaustive or measurable test coverage which leads to much greater confidence in correctness. This paper describes a formal method based on the SPIN model checker. This method guarantees that possible plans meet certain desirable properties. We express the input model in Promela, the language of SPIN and express the properties of desirable plans formally.
Using cumulative sums of martingale residuals for model checking in nested case-control studies.
Borgan, Ørnulf; Zhang, Ying
2015-09-01
Standard use of Cox regression requires collection of covariate information for all individuals in a cohort even when only a small fraction of them experiences the event of interest (fail). This may be very expensive for large cohorts. Further in biomarker studies, it will imply a waste of valuable biological material that one may want to save for future studies. A nested case-control study offers a useful alternative. For this design, covariate information is only needed for the failing individuals (cases) and a sample of controls selected from the cases' at-risk sets. Methods based on martingale residuals are useful for checking the fit of Cox's regression model for cohort data. But similar methods have so far not been developed for nested case-control data. In this article, it is described how one may define martingale residuals for nested case-control data, and it is shown how plots and tests based on cumulative sums of martingale residuals may be used to check model fit. The plots and tests may be obtained using available software. © 2015, The International Biometric Society.
The Moyal momentum algebra applied to θ-deformed 2d conformal models and KdV-hierarchies
International Nuclear Information System (INIS)
Boulahoual, A.; Sedra, M.B.
2002-08-01
The properties of the Das-Popowicz Moyal momentum algebra that we introduce in hep-th/0207242 are reexamined in detail and used to discuss some aspects of integrable models and 2d conformal field theories. Among the results presented we setup some useful convention notations which lead to extract some non trivial properties of the Moyal momentum algebra. We use the particular sub-algebra sl n -Σ-tilde n (0,n) to construct the sl 2 -Liouville conformal model δδ-barΦ=2/θe -1/θΦ and its sl 3 -Toda extension δδ-bar 1 =Ae -1/2θ(Φ 1 +1/2Φ 2 ) and δδ-barΦ 2 =Be -1/2 / θ (Φ 1 +2Φ 2 ) . We also show that the central charge, a la Feigin-Fuchs, associated to the spin-2 conformal current of the θ-Liouville model is given by c θ =(1+24θ 2 ). Moreover, the results obtained for the Das-Popowicz Mm algebra are applied to study systematically some properties of the Moyal KdV and Boussinesq hierarchies generalizing some known results. We also discuss the primarily condition of conformal w θ -currents and interpret this condition as being a dressing gauge symmetry in the Moyal momentum space. Some computations related to the dressing gauge group are explicitly presented. (author)
White, Michael J; Harmel, R Daren; Arnold, Jeff G; Williams, Jimmy R
2014-01-01
The Soil and Water Assessment Tool (SWAT) is a basin-scale hydrologic model developed by the United States Department of Agriculture Agricultural Research Service. SWAT's broad applicability, user-friendly model interfaces, and automatic calibration software have led to a rapid increase in the number of new users. These advancements also allow less experienced users to conduct SWAT modeling applications. In particular, the use of automated calibration software may produce simulated values that appear appropriate because they adequately mimic measured data used in calibration and validation. Autocalibrated model applications (and often those of unexperienced modelers) may contain input data errors and inappropriate parameter adjustments not readily identified by users or the autocalibration software. The objective of this research was to develop a program to assist users in the identification of potential model application problems. The resulting "SWAT Check" is a stand-alone Microsoft Windows program that (i) reads selected SWAT output and alerts users of values outside the typical range; (ii) creates process-based figures for visualization of the appropriateness of output values, including important outputs that are commonly ignored; and (iii) detects and alerts users of common model application errors. By alerting users to potential model application problems, this software should assist the SWAT community in developing more reliable modeling applications. Copyright © by the American Society of Agronomy, Crop Science Society of America, and Soil Science Society of America, Inc.
International Nuclear Information System (INIS)
Littlefield, R.J.; Maschhoff, K.J.
1991-04-01
Many linear algebra algorithms utilize an array of processors across which matrices are distributed. Given a particular matrix size and a maximum number of processors, what configuration of processors, i.e., what size and shape array, will execute the fastest? The answer to this question depends on tradeoffs between load balancing, communication startup and transfer costs, and computational overhead. In this paper we analyze in detail one algorithm: the blocked factored Jacobi method for solving dense eigensystems. A performance model is developed to predict execution time as a function of the processor array and matrix sizes, plus the basic computation and communication speeds of the underlying computer system. In experiments on a large hypercube (up to 512 processors), this model has been found to be highly accurate (mean error ∼ 2%) over a wide range of matrix sizes (10 x 10 through 200 x 200) and processor counts (1 to 512). The model reveals, and direct experiment confirms, that the tradeoffs mentioned above can be surprisingly complex and counterintuitive. We propose decision procedures based directly on the performance model to choose configurations for fastest execution. The model-based decision procedures are compared to a heuristic strategy and shown to be significantly better. 7 refs., 8 figs., 1 tab
Fine, Henry Burchard
2005-01-01
At the beginning of the twentieth century, college algebra was taught differently than it is nowadays. There are many topics that are now part of calculus or analysis classes. Other topics are covered only in abstract form in a modern algebra class on field theory. Fine's College Algebra offers the reader a chance to learn the origins of a variety of topics taught in today's curriculum, while also learning valuable techniques that, in some cases, are almost forgotten. In the early 1900s, methods were often emphasized, rather than abstract principles. In this book, Fine includes detailed discus
Garrett, Paul B
2007-01-01
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal
Living on the edge: a toy model for holographic reconstruction of algebras with centers
Energy Technology Data Exchange (ETDEWEB)
Donnelly, William; Marolf, Donald; Michel, Ben; Wien, Jason [Department of Physics, University of California,Santa Barbara, CA 93106 (United States)
2017-04-18
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the ((δArea)/(4G{sub N})) term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this ((δArea)/(4G{sub N})) term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
Living on the edge: a toy model for holographic reconstruction of algebras with centers
Donnelly, William; Marolf, Donald; Michel, Ben; Wien, Jason
2017-04-01
We generalize the Pastawski-Yoshida-Harlow-Preskill (HaPPY) holographic quantum error-correcting code to provide a toy model for bulk gauge fields or linearized gravitons. The key new elements are the introduction of degrees of freedom on the links (edges) of the associated tensor network and their connection to further copies of the HaPPY code by an appropriate isometry. The result is a model in which boundary regions allow the reconstruction of bulk algebras with central elements living on the interior edges of the (greedy) entanglement wedge, and where these central elements can also be reconstructed from complementary bounda ry regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the δ Area/4{G_N} term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this δ Area/4{G_N} term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
Evaluation of A Resilience Embedded System Using Probabilistic Model-Checking
Directory of Open Access Journals (Sweden)
Ling Fang
2014-05-01
Full Text Available If a Micro Processor Unit (MPU receives an external electric signal as noise, the system function will freeze or malfunction easily. A new resilience strategy is implemented in order to reset the MPU automatically and stop the MPU from freezing or malfunctioning. The technique is useful for embedded systems which work in non-human environments. However, evaluating resilience strategies is difficult because their effectiveness depends on numerous, complex, interacting factors. In this paper, we use probabilistic model checking to evaluate the embedded systems installed with the above mentioned new resilience strategy. Qualitative evaluations are implemented with 6 PCTL formulas, and quantitative evaluations use two kinds of evaluation. One is system failure reduction, and the other is ADT (Average Down Time, the industry standard. Our work demonstrates the benefits brought by the resilience strategy. Experimental results indicate that our evaluation is cost-effective and reliable.
Holme, Audun
1988-01-01
This volume presents selected papers resulting from the meeting at Sundance on enumerative algebraic geometry. The papers are original research articles and concentrate on the underlying geometry of the subject.
Energy Technology Data Exchange (ETDEWEB)
Pires, Luis F.G.; Barreto, Claudio V.; Sarmento, Renata C. [Pontificia Univ. Catolica do Rio de Janeiro, RJ (Brazil). Dept. de Engenharia Mecanica. Nucleo de Simulacao Termohidraulica de Dutos (SIMDUT)
2005-07-01
As usual a shipping terminal contains a header and its diameter is smaller than the main pipeline diameter. This diameter reduction amplifies the effects caused by hydraulic transients. It was noticed during simulations that check valves without dynamic modeling may introduce some error in the maximum pressure results without a dynamic model approach. The current paper uses commercial pipeline simulation software to model the dynamic behavior of the check valves. It was studied the header diameter influence and how the check valve model type may change the maximum pressure in the pipeline. It was proved that even a pipeline that works with low pressure and small elevation drop needs a detailed valve modeling to prevent the calculation of unreal pressure values in the region with diameter reduction. (author)
McKeague, Charles P
1986-01-01
Elementary Algebra, Third Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first ponders on the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the elimination method, solving linear systems by graphing, word problems, addition property of equality, solving linear equations, linear inequalities, addition and subtraction of real numbers, and properties of real numbers. The text then takes a look at exponents and polynomials, factoring, and rational expressions. Topics include reducing ra
McKeague, Charles P
1981-01-01
Elementary Algebra 2e, Second Edition focuses on the basic principles, operations, and approaches involved in elementary algebra. The book first tackles the basics, linear equations and inequalities, and graphing and linear systems. Discussions focus on the substitution method, solving linear systems by graphing, solutions to linear equations in two variables, multiplication property of equality, word problems, addition property of equality, and subtraction, addition, multiplication, and division of real numbers. The manuscript then examines exponents and polynomials, factoring, and rational e
International Nuclear Information System (INIS)
Fukui, Hirokazu; Yoshida, Michio; Yamaura, Kazuho
2000-01-01
For those who run an organization, it is critical to identify the causal relationship between the organization's characteristics and the safety-checking action of its staff, in order to effectively implement activities for promoting safety. In this research. a causal model of the safety-checking action was developed and factors affecting it were studied. A questionnaire survey, which includes safety awareness, attitude toward safety, safety culture and others, was conducted at three nuclear power plants and eight factors were extracted by means of factor analysis of the questionnaire items. The extracted eight interrelated factors were as follows: work norm, supervisory action, interest in training, recognition of importance, safety-checking action, the subject of safety, knowledge/skills, and the attitude of an organization. Among them, seven factors except the recognition of importance were defined as latent variables and a causal model of safety-checking action was constructed. By means of covariance structure analysis, it was found that the three factors: the attitude of an organization, supervisory action and the subject of safety, have a significant effect on the safety-checking action. Moreover, it was also studied that workplaces in which these three factors are highly regarded form social environment where safety-checking action is fully supported by the workplace as a whole, while workplaces in which these three factors are poorly regarded do not fully form social environment where safety-checking action is supported. Therefore, the workplaces form an organizational environment where safety-checking action tends to depend strongly upon the knowledge or skills of individuals. On top of these, it was noted that the attitude of an organization and supervisory action are important factors that serve as the first trigger affecting the formation of the organizational climate for safety. (author)
Checking the Adequacy of Fit of Models from Split-Plot Designs
DEFF Research Database (Denmark)
Almini, A. A.; Kulahci, Murat; Montgomery, D. C.
2009-01-01
One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split......-plot models. In this article, we propose the computation of two R-2, R-2-adjusted, prediction error sums of squares (PRESS), and R-2-prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types...... of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have...
Fusion rules of chiral algebras
International Nuclear Information System (INIS)
Gaberdiel, M.
1994-01-01
Recently we showed that for the case of the WZW and the minimal models fusion can be understood as a certain ring-like tensor product of the symmetry algebra. In this paper we generalize this analysis to arbitrary chiral algebras. We define the tensor product of conformal field theory in the general case and prove that it is associative and symmetric up to equivalence. We also determine explicitly the action of the chiral algebra on this tensor product. In the second part of the paper we demonstrate that this framework provides a powerful tool for calculating restrictions for the fusion rules of chiral algebras. We exhibit this for the case of the W 3 algebra and the N=1 and N=2 NS superconformal algebras. (orig.)
Applications of Computer Algebra Conference
Martínez-Moro, Edgar
2017-01-01
The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.
Applied matrix algebra in the statistical sciences
Basilevsky, Alexander
2005-01-01
This comprehensive text offers teachings relevant to both applied and theoretical branches of matrix algebra and provides a bridge between linear algebra and statistical models. Appropriate for advanced undergraduate and graduate students. 1983 edition.
A new model for algebraic Rossby solitary waves in rotation fluid and its solution
Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru
2015-09-01
A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.
Simulation Modeling of a Check-in and Medication Reconciliation Ambulatory Clinic Kiosk
Directory of Open Access Journals (Sweden)
Blake Lesselroth
2011-01-01
Full Text Available Gaps in information about patient medication adherence may contribute to preventable adverse drug events and patient harm. Hence, health-quality advocacy groups, including the Joint Commission, have called for the implementation of standardized processes to collect and compare patient medication lists. This manuscript describes the implementation of a self-service patient kiosk intended to check in patients for a clinic appointment and collect a medication adherence history, which is then available through the electronic health record. We used business process engineering and simulation modeling to analyze existing workflow, evaluate technology impact on clinic throughput, and predict future infrastructure needs. Our empiric data indicated that a multi-function healthcare kiosk offers a feasible platform to collect medical history data. Furthermore, our simulation model showed a non-linear association between patient arrival rate, kiosk number, and estimated patient wait times. This study provides important data to help administrators and healthcare executives predict infrastructure needs when considering the use of self-service kiosks.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Edwards, Harold M
1995-01-01
In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject
Bell, Eric T
1927-01-01
The central topic of this book is the presentation of the author's principle of arithmetical paraphrases, which won him the BÃ´cher Prize in 1924. This general principle served to unify and extend many isolated results in the theory of numbers. The author successfully provides a systematic attempt to find a unified theory for each of various classes of related important problems in the theory of numbers, including its interrelations with algebra and analysis. This book will be of interest to advanced students in various branches of mathematics, including number theory, abstract algebra, ellipti
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Jacobson, Nathan
2009-01-01
A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L
Falkenberg, Anna; Nyfjäll, Mats; Bildt, Carina; Vingård, Eva
2009-01-01
To predict sickness absence by three health check-up models. A study group of 821 participants from the public sector in Sweden where three health check-up models were compared 1) the limited variable model including smoking, body mass index, blood pressure, and cholesterol, 2) the several variable model including smoking, waist-hip ratio, blood pressure, relation between low density lipoproteins and high density lipoproteins, serum triglycerides, and fitness test, and 3) Self-rated health measured by one single question. Sickness absence data during 1 year was delivered from the employer. The three models served their purpose to predict sickness absence. The self-rated health-model with one single question has as good quality in predestination as more complicated models. This may have an implication for cost-effective procedures in occupational health services.
Antoni, Sven-Thomas; Rinast, Jonas; Ma, Xintao; Schupp, Sibylle; Schlaefer, Alexander
2016-11-01
Correlation between internal and external motion is critical for respiratory motion compensation in radiosurgery. Artifacts like coughing, sneezing or yawning or changes in the breathing pattern can lead to misalignment between beam and tumor and need to be detected to interrupt the treatment. We propose online model checking (OMC), a model-based verification approach from the field of formal methods, to verify that the breathing motion is regular and the correlation holds. We demonstrate that OMC may be more suitable for artifact detection than the prediction error. We established a sinusoidal model to apply OMC to the verification of respiratory motion. The method was parameterized to detect deviations from typical breathing motion. We analyzed the performance on synthetic data and on clinical episodes showing large correlation error. In comparison, we considered the prediction error of different state-of-the-art methods based on least mean squares (LMS; normalized LMS, nLMS; wavelet-based multiscale autoregression, wLMS), recursive least squares (RLSpred) and support vector regression (SVRpred). On synthetic data, OMC outperformed wLMS by at least 30 % and SVRpred by at least 141 %, detecting 70 % of transitions. No artifacts were detected by nLMS and RLSpred. On patient data, OMC detected 23-49 % of the episodes correctly, outperforming nLMS, wLMS, RLSpred and SVRpred by up to 544, 491, 408 and 258 %, respectively. On selected episodes, OMC detected up to 94 % of all events. OMC is able to detect changes in breathing as well as artifacts which previously would have gone undetected, outperforming prediction error-based detection. Synthetic data analysis supports the assumption that prediction is very insensitive to specific changes in breathing. We suggest using OMC as an additional safety measure ensuring reliable and fast stopping of irradiation.
Norman, Laura M.; Niraula, Rewati
2016-01-01
The objective of this study was to evaluate the effect of check dam infrastructure on soil and water conservation at the catchment scale using the Soil and Water Assessment Tool (SWAT). This paired watershed study includes a watershed treated with over 2000 check dams and a Control watershed which has none, in the West Turkey Creek watershed, Southeast Arizona, USA. SWAT was calibrated for streamflow using discharge documented during the summer of 2013 at the Control site. Model results depict the necessity to eliminate lateral flow from SWAT models of aridland environments, the urgency to standardize geospatial soils data, and the care for which modelers must document altering parameters when presenting findings. Performance was assessed using the percent bias (PBIAS), with values of ±2.34%. The calibrated model was then used to examine the impacts of check dams at the Treated watershed. Approximately 630 tons of sediment is estimated to be stored behind check dams in the Treated watershed over the 3-year simulation, increasing water quality for fish habitat. A minimum precipitation event of 15 mm was necessary to instigate the detachment of soil, sediments, or rock from the study area, which occurred 2% of the time. The resulting watershed model is useful as a predictive framework and decision-support tool to consider long-term impacts of restoration and potential for future restoration.
Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang
2016-01-01
A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively.
Current and Future Tests of the Algebraic Cluster Model of12C
Gai, Moshe
2017-07-01
A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts, in12C, rotation-vibration structure with rotational bands of an oblate equilateral triangular symmetric spinning top with a D 3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with a degenerate 4+ and 4- (parity doublet) states. Our newly measured {2}2+ state in12C allows the first study of rotation-vibration structure in12C. The newly measured 5- state and 4- states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D 3h symmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of12C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in12C such as the (0+) Hoyle band and the (1-) bending mode with prediction of (“missing 3- and 4-”) states that may shed new light on clustering in12C and light nuclei. In particular, the observation (or non observation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in12C. We discuss proposed research programs at the Darmstadt S- DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon.
Risnawati; Khairinnisa, S.; Darwis, A. H.
2018-01-01
The purpose of this study was to develop a CORE model-based worksheet with recitation task that were valid and practical and could facilitate students’ communication skills in Linear Algebra course. This study was conducted in mathematics education department of one public university in Riau, Indonesia. Participants of the study were media and subject matter experts as validators as well as students from mathematics education department. The objects of this study are students’ worksheet and students’ mathematical communication skills. The results of study showed that: (1) based on validation of the experts, the developed students’ worksheet was valid and could be applied for students in Linear Algebra courses; (2) based on the group trial, the practicality percentage was 92.14% in small group and 90.19% in large group, so the worksheet was very practical and could attract students to learn; and (3) based on the post test, the average percentage of ideals was 87.83%. In addition, the results showed that the students’ worksheet was able to facilitate students’ mathematical communication skills in linear algebra course.
DEFF Research Database (Denmark)
Vester, Steen
2015-01-01
We study the complexity of the model-checking problem for the branching-time logic CTL ∗ and the alternating-time temporal logics ATL/ATL ∗ in one-counter processes and one-counter games respectively. The complexity is determined for all three logics when integer weights are input in unary (non...
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
Caglayan, Günhan
2013-01-01
This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…
A verification of the bakery protocol combining algebraic and model-oriented techniques
C. Brovedani; A.S. Klusener (Steven)
1996-01-01
textabstractIn this paper we give a specification of the so called Bakery protocol in an extension of the process algebra ACP with abstract datatypes. We prove that this protocol is equal to a Queue, modulo branching bisimulation equivalence. The verification is as follows. First we give a linear
Proposing and Testing a Model to Explain Traits of Algebra Preparedness
Venenciano, Linda; Heck, Ronald
2016-01-01
Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…
Developing Pre-Algebraic Thinking in Generalizing Repeating Pattern Using SOLO Model
Lian, Lim Hooi; Yew, Wun Thiam
2011-01-01
In this paper, researchers discussed the application of the generalization perspective in helping the primary school pupils to develop their pre-algebraic thinking in generalizing repeating pattern. There are two main stages of the generalization perspective had been adapted, namely investigating and generalizing the pattern. Since the Biggs and…
Model checks for Cox-type regression models based on optimally weighted martingale residuals.
Gandy, Axel; Jensen, Uwe
2009-12-01
We introduce directed goodness-of-fit tests for Cox-type regression models in survival analysis. "Directed" means that one may choose against which alternatives the tests are particularly powerful. The tests are based on sums of weighted martingale residuals and their asymptotic distributions.We derive optimal tests against certain competing models which include Cox-type regression models with different covariates and/or a different link function. We report results from several simulation studies and apply our test to a real dataset.
On Elementary and Algebraic Cellular Automata
Gulak, Yuriy
In this paper we study elementary cellular automata from an algebraic viewpoint. The goal is to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures. We introduce algebraic cellular automata as a natural generalization of elementary ones and discuss their applications as generic models of complex systems.
Kollár, János
1997-01-01
This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.
International Nuclear Information System (INIS)
Christian, J M; McDonald, G S; Chamorro-Posada, P
2010-01-01
We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.
Comments on two-loop Kac-Moody algebras
International Nuclear Information System (INIS)
Ferreira, L.A.; Gomes, J.F.; Zimerman, A.H.; Schwimmer, A.
1991-10-01
It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decouple β-γ system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity to versions of the corresponding ordinary models and decoupled Abelian fields. (author). 15 refs
QuickChecking Static Analysis Properties
DEFF Research Database (Denmark)
Midtgaard, Jan; Møller, Anders
2015-01-01
A static analysis can check programs for potential errors. A natural question that arises is therefore: who checks the checker? Researchers have given this question varying attention, ranging from basic testing techniques, informal monotonicity arguments, thorough pen-and-paper soundness proofs......, to verified fixed point checking. In this paper we demonstrate how quickchecking can be useful for testing a range of static analysis properties with limited effort. We show how to check a range of algebraic lattice properties, to help ensure that an implementation follows the formal specification...
QuickChecking static analysis properties
DEFF Research Database (Denmark)
Midtgaard, Jan; Møller, Anders
2017-01-01
A static analysis can check programs for potential errors. A natural question that arises is therefore: who checks the checker? Researchers have given this question varying attention, ranging from basic testing techniques, informal monotonicity arguments, thorough pen-and-paper soundness proofs......, to verified fixed point checking. In this paper, we demonstrate how quickchecking can be useful to test a range of static analysis properties with limited effort. We show how to check a range of algebraic lattice properties, to help ensure that an implementation follows the formal specification of a lattice...
Algebraic characterizations of measure algebras
Czech Academy of Sciences Publication Activity Database
Jech, Thomas
2008-01-01
Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008
Model Checking for a Class of Performance Properties of Fluid Stochastic Models
Bujorianu, L.M.; Bujorianu, M.C.; Horváth, A.; Telek, M.
2006-01-01
Recently, there is an explosive development of fluid approa- ches to computer and distributed systems. These approaches are inherently stochastic and generate continuous state space models. Usually, the performance measures for these systems are defined using probabilities of reaching certain sets
International Nuclear Information System (INIS)
Mohammad, N.; Siddiqui, A.H.
1987-11-01
The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs
Thinking Visually about Algebra
Baroudi, Ziad
2015-01-01
Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…
Energy Technology Data Exchange (ETDEWEB)
Mukhamedov, Farrukh, E-mail: far75m@yandex.ru, E-mail: farrukh.m@uaeu.ac.ae [International Islamic University Malaysia, Department of Computational and Theoretical Sciences, Faculty of Science (Malaysia); Barhoumi, Abdessatar, E-mail: abdessatar.barhoumi@ipein.rnu.tn [Carthage University, Department of Mathematics, Nabeul Preparatory Engineering Institute (Tunisia); Souissi, Abdessatar, E-mail: s.abdessatar@hotmail.fr [Carthage University, Department of Mathematics, Marsa Preparatory Institute for Scientific and Technical Studies (Tunisia)
2016-12-15
It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC’s on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains.
International Nuclear Information System (INIS)
Ribeiro, Rafael S.; Hermes, Christian J.L.
2014-01-01
In this study, the method of entropy generation minimization (i.e., design aimed at facilitating both heat, mass and fluid flows) is used to assess the evaporator design (aspect ratio and fin density) considering the thermodynamic losses due to heat and mass transfer, and viscous flow processes. A fully algebraic model was put forward to simulate the thermal-hydraulic behavior of tube-fin evaporator coils running under frosting conditions. The model predictions were validated against experimental data, showing a good agreement between calculated and measured counterparts. The optimization exercise has pointed out that high aspect ratio heat exchanger designs lead to lower entropy generation in cases of fixed cooling capacity and air flow rate constrained by the characteristic curve of the fan. - Highlights: • An algebraic model for frost accumulation on tube-fin heat exchangers was advanced. • Model predictions for cooling capacity and air flow rate were compared with experimental data, with errors within ±5% band. • Minimum entropy generation criterion was used to optimize the evaporator geometry. • Thermodynamic analysis led to slender designs for fixed cooling capacity and fan characteristics
Iachello, F
1995-01-01
1. The Wave Mechanics of Diatomic Molecules. 2. Summary of Elements of Algebraic Theory. 3. Mechanics of Molecules. 4. Three-Body Algebraic Theory. 5. Four-Body Algebraic Theory. 6. Classical Limit and Coordinate Representation. 8. Prologue to the Future. Appendices. Properties of Lie Algebras; Coupling of Algebras; Hamiltonian Parameters
International Nuclear Information System (INIS)
Gulshani, P.; So, C.B.
1986-10-01
In a number of postulated accident scenarios in a CANDU reactor, some of the horizontal fuel channels are predicted to experience periods of stratified channel coolant condition which can lead to a circumferential temperature gradient around the pressure tube. To study pressure tube strain and integrity under stratified flow channel conditions, it is, necessary to determine the pressure tube circumferential temperature distribution. This paper presents an algebraic model, called AMPTRACT (Algebraic Model for Pressure Tube TRAnsient Circumferential Temperature), developed to give the transient temperature distribution in a closed form. AMPTRACT models the following modes of heat transfer: radiation from the outermost elements to the pressure tube and from the pressure to calandria tube, convection between the fuel elements and the pressure tube and superheated steam, and circumferential conduction from the exposed to submerged part of the pressure tube. An iterative procedure is used to solve the mass and energy equations in closed form for axial steam and fuel-sheath transient temperature distributions. The one-dimensional conduction equation is then solved to obtain the pressure tube circumferential transient temperature distribution in a cosine series expansion. In the limit of large times and in the absence of convection and radiation to the calandria tube, the predicted pressure tube temperature distribution reduces identically to a parabolic profile. In this limit, however, radiation cannot be ignored because the temperatures are generally high. Convection and radiation tend to flatten the parabolic distribution
Rudiger, Jesper
2013-01-01
A characteristic of the news market is that consumers often cross-check information, i.e. observe several news outlets. At the same time, data on political media suggest that more partisan consumers are more likely to cross-check. We explore these phenomena by building a model of horizontal competition in newspaper endorsements. Without cross-checking, outlets are unbiased and minimally differentiated. When cross-checking is allowed, we show that cross-checkers are indeed more partisan than ...
Lie algebra in quantum physics by means of computer algebra
Kikuchi, Ichio; Kikuchi, Akihito
2017-01-01
This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...
1998-01-01
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Vertex algebras and mirror symmetry
International Nuclear Information System (INIS)
Borisov, L.A.
2001-01-01
Mirror Symmetry for Calabi-Yau hypersurfaces in toric varieties is by now well established. However, previous approaches to it did not uncover the underlying reason for mirror varieties to be mirror. We are able to calculate explicitly vertex algebras that correspond to holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in toric varieties. We establish the relation between these vertex algebras for mirror Calabi-Yau manifolds. This should eventually allow us to rewrite the whole story of toric mirror symmetry in the language of sheaves of vertex algebras. Our approach is purely algebraic and involves simple techniques from toric geometry and homological algebra, as well as some basic results of the theory of vertex algebras. Ideas of this paper may also be useful in other problems related to maps from curves to algebraic varieties.This paper could also be of interest to physicists, because it contains explicit description of holomorphic parts of A and B models of Calabi-Yau hypersurfaces and complete intersections in terms of free bosons and fermions. (orig.)
Mahé, Louis; Roy, Marie-Françoise
1992-01-01
Ten years after the first Rennes international meeting on real algebraic geometry, the second one looked at the developments in the subject during the intervening decade - see the 6 survey papers listed below. Further contributions from the participants on recent research covered real algebra and geometry, topology of real algebraic varieties and 16thHilbert problem, classical algebraic geometry, techniques in real algebraic geometry, algorithms in real algebraic geometry, semialgebraic geometry, real analytic geometry. CONTENTS: Survey papers: M. Knebusch: Semialgebraic topology in the last ten years.- R. Parimala: Algebraic and topological invariants of real algebraic varieties.- Polotovskii, G.M.: On the classification of decomposing plane algebraic curves.- Scheiderer, C.: Real algebra and its applications to geometry in the last ten years: some major developments and results.- Shustin, E.L.: Topology of real plane algebraic curves.- Silhol, R.: Moduli problems in real algebraic geometry. Further contribu...
International Nuclear Information System (INIS)
Yau, Donald
2011-01-01
We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.
Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.
José, Marco V; Morgado, Eberto R; Guimarães, Romeu Cardoso; Zamudio, Gabriel S; de Farías, Sávio Torres; Bobadilla, Juan R; Sosa, Daniela
2014-08-11
Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state.
Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi
2014-03-01
In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.
Bliss, Gilbert Ames
1933-01-01
This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t
An Ada Linear-Algebra Software Package Modeled After HAL/S
Klumpp, Allan R.; Lawson, Charles L.
1990-01-01
New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.
Quantum affine algebras and deformations of the virasoro and W-algebras
International Nuclear Information System (INIS)
Frenkel, E.; Reshetikhin, N.
1996-01-01
Using the Wakimoto realization of quantum affine algebras we define new Poisson algebras, which are q-deformations of the classical W-algebras. We also define their free field realizations, i.e. homomorphisms into some Heisenberg-Poisson algebras. The formulas for these homomorphisms coincide with formulas for spectra of transfer-matrices in the corresponding quantum integrable models derived by the Bethe-Ansatz method. (orig.)
Grätzer, George
1979-01-01
Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...
Filiform Lie algebras of order 3
International Nuclear Information System (INIS)
Navarro, R. M.
2014-01-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases
Filiform Lie algebras of order 3
Navarro, R. M.
2014-04-01
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, "Cohomologie des algèbres de Lie nilpotentes. Application à l'étude de la variété des algèbres de Lie nilpotentes," Bull. Soc. Math. France 98, 81-116 (1970)]. Also we give the dimension, using an adaptation of the {sl}(2,{C})-module Method, and a basis of such infinitesimal deformations in some generic cases.
Yoneda algebras of almost Koszul algebras
Indian Academy of Sciences (India)
Abstract. Let k be an algebraically closed field, A a finite dimensional connected. (p,q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, we prove that the. Yoneda algebra of A is isomorphic to a twisted polynomial algebra A![t; β] in one inde- terminate t of degree q +1 in which A! is the quadratic dual of A, β is an ...
NonpModelCheck: An R Package for Nonparametric Lack-of-Fit Testing and Variable Selection
Directory of Open Access Journals (Sweden)
Adriano Zanin Zambom
2017-05-01
Full Text Available We describe the R package NonpModelCheck for hypothesis testing and variable selection in nonparametric regression. This package implements functions to perform hypothesis testing for the significance of a predictor or a group of predictors in a fully nonparametric heteroscedastic regression model using high-dimensional one-way ANOVA. Based on the p values from the test of each covariate, three different algorithms allow the user to perform variable selection using false discovery rate corrections. A function for classical local polynomial regression is implemented for the multivariate context, where the degree of the polynomial can be as large as needed and bandwidth selection strategies are built in.
Miyanishi, Masayoshi
2000-01-01
Open algebraic surfaces are a synonym for algebraic surfaces that are not necessarily complete. An open algebraic surface is understood as a Zariski open set of a projective algebraic surface. There is a long history of research on projective algebraic surfaces, and there exists a beautiful Enriques-Kodaira classification of such surfaces. The research accumulated by Ramanujan, Abhyankar, Moh, and Nagata and others has established a classification theory of open algebraic surfaces comparable to the Enriques-Kodaira theory. This research provides powerful methods to study the geometry and topology of open algebraic surfaces. The theory of open algebraic surfaces is applicable not only to algebraic geometry, but also to other fields, such as commutative algebra, invariant theory, and singularities. This book contains a comprehensive account of the theory of open algebraic surfaces, as well as several applications, in particular to the study of affine surfaces. Prerequisite to understanding the text is a basic b...
Generalized Hermitian Algebras
Foulis, David J.; Pulmannová, Sylvia
2009-05-01
We refer to the real Jordan Banach algebra of bounded Hermitian operators on a Hilbert space as a Hermitian algebra. In this paper we define and launch a study of a class of generalized Hermitian (GH) algebras. Among the examples of GH-algebras are ordered special Jordan algebras, JW-algebras, and AJW-algebras, but unlike these more restricted cases, a GH-algebra is not necessarily a Banach space and its lattice of projections is not necessarily complete. In this paper we develop the basic theory of GH-algebras, identify their unit intervals as effect algebras, and observe that their projection lattices are sigma-complete orthomodular lattices. We show that GH-algebras are spectral order-unit spaces and that they admit a substantial spectral theory.
Universal enveloping algebras for Malcev color algebras
de-la-Concepción, Daniel
2015-01-01
In this paper we give a construction of the universal enveloping algebra of a Malcev algebra in categories of group algebra comodules with a symmetry given by a bicharacter of the group. A particular example of such categories is the category of super vector spaces.
An algebraic approach to analysis of recursive and concurrent programs
DEFF Research Database (Denmark)
Terepeta, Michal Tomasz
This thesis focuses on formal techniques based on static program analysis, model checking and abstract interpretation that offer means for reasoning about software, verification of its properties and discovering potential bugs. First, we investigate an algebraic approach to static analysis...... implementing those algorithms, which also provides a lot of flexibility with respect to, e.g., various constraints solvers. Finally, we describe one such experimental solver based on Newton’s method. It allows solving equation systems over abstract domains that were not accommodated by other solving techniques...
International Nuclear Information System (INIS)
Neuhaus, Thorsten; Schaffrath, Andreas
2009-01-01
In this contribution the analysis and calculation of a compensator burst after a pump start and check valve slam with the pressure surge code DYVRO mod. 3 are presented. The compensator burst occurred in the essential service water system (ESWS) of a pressurized water reactor (PWR) in a deviant operation mode. Due to lack of knowledge about the causes a systematic investigation has been performed by TUV NORD SysTec GmbH and Co. KG. The following scenario was identified as most likely: Because of maintenance a heat exchanger was shut off from the ESWS by a closed valve. Due to the hydrostatic pressure profile air had been sucked in through this leaky closed valve forming an air bubble. After the pump start the water was accelerated against the closed valve where the air bubble was compressed. The subsequent backflow resulted in a fast closing of a check valve and a pressure surge that caused the compensator burst. Calculations have been performed with the self developed and validated pressure surge computer code DYVRO mod. 3. The present paper is focussed on the modelling of the pipe system, the pump, the check valve and the behaviour of the air bubble as well as the simulation of the incident. The calculated maximum pressure in the ESWS is above 3 MPa, which is approx. four times higher than the design pressure of 0.7 MPa. This pressure increase has led most likely to the abrupt compensator failure. (author)
Directory of Open Access Journals (Sweden)
Katie Ovens
2012-01-01
Full Text Available Introduction: Delta checks use two specimen test results taken in succession in order to detect test result changes greater than expected physiological variation. One of the most common and serious errors detected by delta checks is specimen mix-up errors. The positive and negative predictive values of delta checks for detecting specimen mix-up errors, however, are largely unknown. Materials and Methods: We addressed this question by first constructing a stochastic dynamic model using repeat test values for five analytes from approximately 8000 inpatients in Calgary, Alberta, Canada. The analytes examined were sodium, potassium, chloride, bicarbonate, and creatinine. The model simulated specimen mix-up errors by randomly switching a set number of pairs of second test results. Sensitivities and specificities were then calculated for each analyte for six combinations of delta check equations and cut-off values from the published literature. Results: Delta check specificities obtained from this model ranged from 50% to 99%; however the sensitivities were generally below 20% with the exception of creatinine for which the best performing delta check had a sensitivity of 82.8%. Within a plausible incidence range of specimen mix-ups the positive predictive values of even the best performing delta check equation and analyte became negligible. Conclusion: This finding casts doubt on the ongoing clinical utility of delta checks in the setting of low rates of specimen mix-ups.
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Indian Academy of Sciences (India)
Introduction and preliminaries. The class of Malcev algebras contains one of the Lie algebras and so a question arises whether some known results on Lie algebras can be extended to the framework of Malcev algebras (see [4, 7, 9, 10]). In the present paper, we are interested in studying the structure of arbitrary Malcev ...
Embeddings of Heyting Algebras
Jongh, D.H.J. de; Visser, A.
In this paper we study embeddings of Heyting Algebras. It is pointed out that such embeddings are naturally connected with Derived Rules. We compare the Heyting Algebras embeddable in the Heyting Algebra of the Intuitionistic Propositional Calculus (IPC), i.e. the free Heyting Algebra on countably
Dzhumadil'daev, A. S.
2002-01-01
Algebras with identity $(a\\star b)\\star (c\\star d) -(a\\star d)\\star(c\\star b)$ $=(a,b,c)\\star d-(a,d,c)\\star b$ are studied. Novikov algebras under Jordan multiplication and Leibniz dual algebras satisfy this identity. If algebra with such identity has unit, then it is associative and commutative.
Free probability on Hecke algebras and certain group C^{*}-algebras induced by Hecke algebras
Directory of Open Access Journals (Sweden)
Ilwoo Cho
2016-01-01
Full Text Available In this paper, by establishing free-probabilistic models on the Hecke algebras \\(\\mathcal{H}\\left(GL_{2}(\\mathbb{Q}_{p}\\right\\ induced by \\(p\\-adic number fields \\(\\mathbb{Q}_{p}\\, we construct free probability spaces for all primes \\(p\\. Hilbert-space representations are induced by such free-probabilistic structures. We study \\(C^{*}\\-algebras induced by certain partial isometries realized under the representations.
Introduction to relation algebras relation algebras
Givant, Steven
2017-01-01
The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...
International Nuclear Information System (INIS)
Ludu, A.; Greiner, M.
1995-09-01
A non-linear associative algebra is realized in terms of translation and dilation operators, and a wavelet structure generating algebra is obtained. We show that this algebra is a q-deformation of the Fourier series generating algebra, and reduces to this for certain value of the deformation parameter. This algebra is also homeomorphic with the q-deformed su q (2) algebra and some of its extensions. Through this algebraic approach new methods for obtaining the wavelets are introduced. (author). 20 refs
Directory of Open Access Journals (Sweden)
Cătălin Dima
2010-06-01
Full Text Available We present a variant of ATL with distributed knowledge operators based on a synchronous and perfect recall semantics. The coalition modalities in this logic are based on partial observation of the full history, and incorporate a form of cooperation between members of the coalition in which agents issue their actions based on the distributed knowledge, for that coalition, of the system history. We show that model-checking is decidable for this logic. The technique utilizes two variants of games with imperfect information and partially observable objectives, as well as a subset construction for identifying states whose histories are indistinguishable to the considered coalition.
Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches
Directory of Open Access Journals (Sweden)
Ning Zhou
2013-01-01
Full Text Available This work presents an efficient solution using computer algebra system to perform linear temporal properties verification for synchronous digital systems. The method is essentially based on both Groebner bases approaches and symbolic simulation. A mechanism for constructing canonical polynomial set based symbolic representations for both circuit descriptions and assertions is studied. We then present a complete checking algorithm framework based on these algebraic representations by using Groebner bases. The computational experience result in this work shows that the algebraic approach is a quite competitive checking method and will be a useful supplement to the existent verification methods based on simulation.
Bochnak, Jacek; Roy, Marie-Françoise
1998-01-01
This book is a systematic treatment of real algebraic geometry, a subject that has strong interrelation with other areas of mathematics: singularity theory, differential topology, quadratic forms, commutative algebra, model theory, complexity theory etc. The careful and clearly written account covers both basic concepts and up-to-date research topics. It may be used as text for a graduate course. The present edition is a substantially revised and expanded English version of the book "Géometrie algébrique réelle" originally published in French, in 1987, as Volume 12 of ERGEBNISSE. Since the publication of the French version the theory has made advances in several directions. Many of these are included in this English version. Thus the English book may be regarded as a completely new treatment of the subject.
International Nuclear Information System (INIS)
Grimm, Uwe; Schuetz, Gunter
1992-09-01
The finite-size spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with central charge c q [sl(2)] quantum algebra transformations. (author)
The algebras of large N matrix mechanics
Energy Technology Data Exchange (ETDEWEB)
Halpern, M.B.; Schwartz, C.
1999-09-16
Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.
International Nuclear Information System (INIS)
Wang, Dan; Wang, Linxiang; Melnik, Roderick
2016-01-01
In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature. - Highlights: • Predict the polycrystalline hysteresis effectively. • Sub hysteresis loop can be captured. • Frequency dependence is naturally included.
Energy Technology Data Exchange (ETDEWEB)
Wang, Dan [State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou (China); Wang, Linxiang, E-mail: wanglx236@zju.edu.cn [State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou (China); Melnik, Roderick [MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo, ON, Canada N2L 3L5 (Canada)
2016-07-15
In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature. - Highlights: • Predict the polycrystalline hysteresis effectively. • Sub hysteresis loop can be captured. • Frequency dependence is naturally included.
Model Pembelajaran Kooperatif Tipe Pair Check untuk Membangun Keterampilan Bertanya Produktif Siswa
Directory of Open Access Journals (Sweden)
Dwi Ermavianti
2016-05-01
Full Text Available This study aimed for (1 developing the students’ productive questioning ability in the subject of Anatomy and Physiology and (2 improving the students’ productive cognitive learning. This classroom action study was conducted for the X grade students of the Department of Make up and Beauty Teraphy II. It was undertaken during the odd semester of the academic year of 2014/2015. The data was collected by participatory monitoring, questionnaires, and documentary study. The data resulted from the observation, the interviews, and the discussions with collaborators were analysed, identified, interpreted, validated, and inferred descriptively. The results revealed the students’ productive questioning ability development in the subject of Anatomy consists of 9 stages: the concept explanation, groups division, texts distribution, pair-check assignments, role shifts, answers validation, counseling and directing, correct answers validation, and rewards distribution. In the preliminary condition, the students’ questioning ability was scored and categorised as fair. In the second cycle, it achieved higher score and was categorised as good. It was proved by the higher frequency of questions and the more productive reading ability of the students. The students’ performance in the first cycle that was categorised as good and very good were 61.3% and 9.67% respectively. While in the second cycle, 12 students with the percentage of 38.70% were categorised as good and 15 students with the percentage of 48.30% were categorised as very good in productive questioning. Penelitian ini bertujuan untuk (1 membangun keterampilan bertanya produktif siswa pada mata pelajaran anatomi dan fisiologi dan (2 mengembangkan cara berpikir siswa agar terampil secara produktif. Penelitian ini menggunakan disain Penelitian Tindakan Kelas, dengan setting kegiatan pembelajaran dilaksanakan pada semester ganjil bagi siswa kelas X Tata Kecantikan 2 tahun ajaran 2014
Cluster algebras in mathematical physics
International Nuclear Information System (INIS)
Francesco, Philippe Di; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito
2014-01-01
identities in conformal field theory and so forth. It is remarkable that the key ingredients in such a variety of theories and models are captured and described universally in the common language of cluster algebras. This special issue provides a bird's-eye view of the known and latest results in various topics in mathematical physics where cluster algebras have played an essential role. The contributed articles are themselves an eloquent illustration of the breadth and depth of the subject of cluster algebras. We are confident that the issue will stimulate both newcomers and experts, since the applications to physics still seem to be growing
A division algebra classification of generalized supersymmetries
International Nuclear Information System (INIS)
Toppan, Francesco
2004-10-01
Generalized supersymmetries admitting bosonic tensor central charges are classified in accordance with their division algebra properties. Division algebra consistent constraints lead (in the complex and quaternionic cases) to the classes of hermitian and holomorphic generalized supersymmetries. Applications to the analytic continuation of the M-algebra to the Euclidean and the systematic investigation of certain classes of models in generic space-times are briefly mentioned. (author)
Goldmann, H
1990-01-01
The first part of this monograph is an elementary introduction to the theory of Fréchet algebras. Important examples of Fréchet algebras, which are among those considered, are the algebra of all holomorphic functions on a (hemicompact) reduced complex space, and the algebra of all continuous functions on a suitable topological space.The problem of finding analytic structure in the spectrum of a Fréchet algebra is the subject of the second part of the book. In particular, the author pays attention to function algebraic characterizations of certain Stein algebras (= algebras of holomorphic functions on Stein spaces) within the class of Fréchet algebras.
Abrams, Gene; Siles Molina, Mercedes
2017-01-01
This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume. Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry. Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and...
Directory of Open Access Journals (Sweden)
Zhe Dong
2015-01-01
Full Text Available Small modular reactors (SMRs are those fission reactors whose electrical output power is no more than 300 MWe. SMRs usually have the inherent safety feature that can be applicable to power plants of any desired power rating by applying the multimodular operation scheme. Due to its strong inherent safety feature, the modular high temperature gas-cooled reactor (MHTGR, which uses helium as coolant and graphite as moderator and structural material, is a typical SMR for building the next generation of nuclear plants (NGNPs. The once-through steam generator (OTSG is the basis of realizing the multimodular scheme, and modeling of the OTSG is meaningful to study the dynamic behavior of the multimodular plants and to design the operation and control strategy. In this paper, based upon the conservation laws of mass, energy, and momentum, a new differential-algebraic model for the OTSGs of the MHTGR-based multimodular nuclear plants is given. This newly-built model can describe the dynamic behavior of the OTSG in both the cases of providing superheated steam and generating saturated steam. Numerical simulation results show the feasibility and satisfactory performance of this model. Moreover, this model has been applied to develop the real-time simulation software for the operation and regulation features of the world first underconstructed MHTGR-based commercial nuclear plant—HTR-PM.
Energy Technology Data Exchange (ETDEWEB)
Finch, P.E. [Centre for Mathematical Physics, School of Mathematics and Physics, University of Queensland, 4072 (Australia); Dancer, K.A., E-mail: dancer@maths.uq.edu.a [Centre for Mathematical Physics, School of Mathematics and Physics, University of Queensland, 4072 (Australia); Isaac, P.S.; Links, J. [Centre for Mathematical Physics, School of Mathematics and Physics, University of Queensland, 4072 (Australia)
2011-06-11
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the two-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.
Modeling and simulation in inquiry learning: Checking solutions and giving intelligent advice
Bravo, C.; van Joolingen, W.R.; de Jong, T.
2006-01-01
Inquiry learning is a didactic approach in which students acquire knowledge and skills through processes of theory building and experimentation. Computer modeling and simulation can play a prominent role within this approach. Students construct representations of physical systems using modeling.
Coping with Algebraic Constraints in Power Networks
Monshizadeh, Nima; De Persis, Claudio; van der Schaft, Abraham; Scherpen, Jacquelien M.A.
2016-01-01
In the intuitive modelling of the power network, the generators and the loads are located at different subset of nodes. This corresponds to the so-called structure preserving model which is naturally expressed in terms of differential algebraic equations (DAE). The algebraic constraints in the
International Nuclear Information System (INIS)
Demichev, A.; Kryukov, A.; Rodionov, A.
2002-01-01
We propose an XML-based standard for formulation of field theoretical models. The goal of creation of such a standard is to provide a way for an unambiguous exchange and cross-checking of results of computer calculations in high energy physics. At the moment, the suggested standard implies that models under consideration are of the SM or MSSM type (i.e., they are just SM or MSSM, their submodels, smooth modifications or straightforward generalizations). (author)
Samuel, Pierre
2008-01-01
Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal
Osborn, J
1989-01-01
During the academic year 1987-1988 the University of Wisconsin in Madison hosted a Special Year of Lie Algebras. A Workshop on Lie Algebras, of which these are the proceedings, inaugurated the special year. The principal focus of the year and of the workshop was the long-standing problem of classifying the simple finite-dimensional Lie algebras over algebraically closed field of prime characteristic. However, other lectures at the workshop dealt with the related areas of algebraic groups, representation theory, and Kac-Moody Lie algebras. Fourteen papers were presented and nine of these (eight research articles and one expository article) make up this volume.
A Model-Based Framework for Legal Policy Simulation and Compliance Checking
Soltana, Ghanem
2017-01-01
Information systems implementing requirements from laws and regulations, such as taxes and social benefits, need to be thoroughly verified to demonstrate their compliance. Several Verification and Validation (V&V) techniques, such as reliability testing, and modeling and simulation, can be used for assessing that such systems meet their legal. Typically, one has to model the expected (legal) behavior of the system in a form that can be executed (simulated), subject the resulting models and th...
Relation between dual S-algebras and BE-algebras
Directory of Open Access Journals (Sweden)
Arsham Borumand Saeid
2015-05-01
Full Text Available In this paper, we investigate the relationship between dual (Weak Subtraction algebras, Heyting algebras and BE-algebras. In fact, the purpose of this paper is to show that BE-algebra is a generalization of Heyting algebra and dual (Weak Subtraction algebras. Also, we show that a bounded commutative self distributive BE-algebra is equivalent to the Heyting algebra.
modelling of queuing process at airport check-in system: a case ...
African Journals Online (AJOL)
HOD
memoryless) process described by Poisson distribution. Service times are independently and identically distributed or exponentially distributed random variables; the process is expressed by Erlange model [17, 19 - 21]. Queuing models are described using probability distribution of inter-arrivals and service times, number.
Checking Fine and Gray subdistribution hazards model with cumulative sums of residuals
DEFF Research Database (Denmark)
Li, Jianing; Scheike, Thomas; Zhang, Mei Jie
2015-01-01
Recently, Fine and Gray (J Am Stat Assoc 94:496–509, 1999) proposed a semi-parametric proportional regression model for the subdistribution hazard function which has been used extensively for analyzing competing risks data. However, failure of model adequacy could lead to severe bias in parameter...
Automated evolutionary restructuring of workflows to minimise errors via stochastic model checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Hansen, Zaza Nadja Lee; Jacobsen, Peter
2014-01-01
This paper presents a framework for the automated restructuring of workflows that allows one to minimise the impact of errors on a production workflow. The framework allows for the modelling of workflows by means of a formalised subset of the Business Process Modelling and Notation (BPMN) language......, a well-established visual language for modelling workflows in a business context. The framework’s modelling language is extended to include the tracking of real-valued quantities associated with the process (such as time, cost, temperature). In addition, this language also allows for an intention...... by means of a case study from the food industry. Through this case study we explore the extent to which the risk of production faults can be reduced and the impact of these can be minimised, primarily through restructuring of the production workflows. This approach is fully automated and only the modelling...
Boundary Lax pairs from non-ultra-local Poisson algebras
International Nuclear Information System (INIS)
Avan, Jean; Doikou, Anastasia
2009-01-01
We consider non-ultra-local linear Poisson algebras on a continuous line. Suitable combinations of representations of these algebras yield representations of novel generalized linear Poisson algebras or 'boundary' extensions. They are parametrized by a boundary scalar matrix and depend, in addition, on the choice of an antiautomorphism. The new algebras are the classical-linear counterparts of the known quadratic quantum boundary algebras. For any choice of parameters, the non-ultra-local contribution of the original Poisson algebra disappears. We also systematically construct the associated classical Lax pair. The classical boundary principal chiral model is examined as a physical example.
Icardi, Matteo
2014-09-01
The inhomogeneous generalized population balance equation, which is discretized with the direct quadrature method of moment (DQMOM), is solved to predict the bubble size distribution (BSD) in a vertical pipe flow. The proposed model is compared with a more classical approach where bubbles are characterized with a constant mean size. The turbulent two-phase flow field, which is modeled using a Reynolds-Averaged Navier-Stokes equation approach, is assumed to be in local equilibrium, thus the relative gas and liquid (slip) velocities can be calculated with the algebraic slip model, thereby accounting for the drag, lift, and lubrication forces. The complex relationship between the bubble size distribution and the resulting forces is described accurately by the DQMOM. Each quadrature node and weight represents a class of bubbles with characteristic size and number density, which change dynamically in time and space to preserve the first moments of the BSD. The predictions obtained are validated against previously published experimental data, thereby demonstrating the advantages of this approach for large-scale systems as well as suggesting future extensions to long piping systems and more complex geometries. © 2014 Elsevier Inc.
Müller, Dirk K; Pampel, André; Möller, Harald E
2013-05-01
Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data. Copyright © 2013 Elsevier Inc. All rights reserved.
Bolton, Matthew L; Bass, Ellen J; Siminiceanu, Radu I
2012-11-01
Breakdowns in complex systems often occur as a result of system elements interacting in unanticipated ways. In systems with human operators, human-automation interaction associated with both normative and erroneous human behavior can contribute to such failures. Model-driven design and analysis techniques provide engineers with formal methods tools and techniques capable of evaluating how human behavior can contribute to system failures. This paper presents a novel method for automatically generating task analytic models encompassing both normative and erroneous human behavior from normative task models. The generated erroneous behavior is capable of replicating Hollnagel's zero-order phenotypes of erroneous action for omissions, jumps, repetitions, and intrusions. Multiple phenotypical acts can occur in sequence, thus allowing for the generation of higher order phenotypes. The task behavior model pattern capable of generating erroneous behavior can be integrated into a formal system model so that system safety properties can be formally verified with a model checker. This allows analysts to prove that a human-automation interactive system (as represented by the model) will or will not satisfy safety properties with both normative and generated erroneous human behavior. We present benchmarks related to the size of the statespace and verification time of models to show how the erroneous human behavior generation process scales. We demonstrate the method with a case study: the operation of a radiation therapy machine. A potential problem resulting from a generated erroneous human action is discovered. A design intervention is presented which prevents this problem from occurring. We discuss how our method could be used to evaluate larger applications and recommend future paths of development.
Bolton, Matthew L.; Bass, Ellen J.; Siminiceanu, Radu I.
2012-01-01
Breakdowns in complex systems often occur as a result of system elements interacting in unanticipated ways. In systems with human operators, human-automation interaction associated with both normative and erroneous human behavior can contribute to such failures. Model-driven design and analysis techniques provide engineers with formal methods tools and techniques capable of evaluating how human behavior can contribute to system failures. This paper presents a novel method for automatically generating task analytic models encompassing both normative and erroneous human behavior from normative task models. The generated erroneous behavior is capable of replicating Hollnagel’s zero-order phenotypes of erroneous action for omissions, jumps, repetitions, and intrusions. Multiple phenotypical acts can occur in sequence, thus allowing for the generation of higher order phenotypes. The task behavior model pattern capable of generating erroneous behavior can be integrated into a formal system model so that system safety properties can be formally verified with a model checker. This allows analysts to prove that a human-automation interactive system (as represented by the model) will or will not satisfy safety properties with both normative and generated erroneous human behavior. We present benchmarks related to the size of the statespace and verification time of models to show how the erroneous human behavior generation process scales. We demonstrate the method with a case study: the operation of a radiation therapy machine. A potential problem resulting from a generated erroneous human action is discovered. A design intervention is presented which prevents this problem from occurring. We discuss how our method could be used to evaluate larger applications and recommend future paths of development. PMID:23105914
Algebraic isotopy in genetics.
Campos, T M; Holgate, P
1987-01-01
It is shown that many of the algebras arising in nonselective genetics are isotopes of the algebras for particularly simple systems of inheritance. Moreover, interesting aspects of the structure are preserved under the relevant isotopies.
Rudiments of algebraic geometry
Jenner, WE
2017-01-01
Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
A Framework for Relating Timed Transition Systems and Preserving TCTL Model Checking
DEFF Research Database (Denmark)
Jacobsen, Lasse; Jacobsen, Morten; Møller, Mikael Harkjær
2010-01-01
Many formal translations between time dependent models have been proposed over the years. While some of them produce timed bisimilar models, others preserve only reachability or (weak) trace equivalence. We suggest a general framework for arguing when a translation preserves Timed Computation Tree...... Logic (TCTL) or its safety fragment.The framework works at the level of timed transition systems, making it independent of the modeling formalisms and applicable to many of the translations published in the literature. Finally, we present a novel translation from extended Timed-Arc Petri Nets...... to Networks of Timed Automata and using the framework argue that itpreserves the full TCTL. The translation has been implemented in the verification tool TAPAAL....
International Nuclear Information System (INIS)
Gladchenkov, E V; Kolyubin, V A; Nedosekin, P G; Zaharchenko, K V; Ibragimov, R F; Kadilin, V V; Tyurin, E M
2017-01-01
Were conducted a series of experiments, the purpose of which had to verify the mathematical model of the radiation environment sensor. Theoretical values of the beta particles count rate from 90 Sr - 90 Y source registered by radiation environment sensor was compared with the experimental one. Theoretical (calculated) count rate of beta particles was found with using the developed mathematical model of the radiation environment sensor. Deviation of the calculated values of the beta particle count rate does not exceed 10% from the experimental. (paper)
Cylindric-like algebras and algebraic logic
Ferenczi, Miklós; Németi, István
2013-01-01
Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics. Tarski’s quest for finding structure in logic leads to cylindric-like algebras as studied in this book, they are among the main players in Tarskian algebraic logic. Cylindric algebra theory can be viewed in many ways: as an algebraic form of definability theory, as a study of higher-dimensional relations, as an enrichment of Boolean Algebra theory, or, as logic in geometric form (“cylindric” in the name refers to geometric aspects). Cylindric-like algebras have a wide range of applications, in, e.g., natural language theory, data-base theory, stochastics, and even in relativity theory. The present volume, consisting of 18 survey papers, intends to give an overview of the main achievements and new research directions in the past 30 years, since the publication of the Henkin-Monk-Tarski monographs. It is dedicated to the memory of Leon Henkin.
Addressing challenges in obtaining high coverage when model checking android applications
CSIR Research Space (South Africa)
Botha, Heila-Marie
2017-07-01
Full Text Available -state-comparator and can be excluded from the state using JPF’s @FilterField annotation or other conguration options discussed in [5]. JPF-Android further optimizes state-matching by pre-loading all application classes and application specic models. It also rede...
Can We Efficiently Check Concurrent Programs Under Relaxed Memory Models in Maude?
DEFF Research Database (Denmark)
Arrahman, Yehia Abd; Andric, Marina; Beggiato, Alessandro
2014-01-01
to the state space explosion. Several techniques have been proposed to mitigate those problems so to make verification under relaxed memory models feasible. We discuss how to adopt some of those techniques in a Maude-based approach to language prototyping, and suggest the use of other techniques that have been...
Interval Abstraction Refinement for Model Checking of Timed-Arc Petri Nets
DEFF Research Database (Denmark)
Viesmose, Sine Lyhne; Jacobsen, Thomas Stig; Jensen, Jacob Jon
2014-01-01
can be considerably faster but it does not in general guarantee conclusive answers. We implement the algorithms within the open-source model checker TAPAAL and demonstrate on a number of experiments that our approximation techniques often result in a significant speed-up of the verification....
Model checking a cache coherence protocol for a Java DSM implementation
J. Pang; W.J. Fokkink (Wan); R. Hofman (Rutger); R. Veldema
2007-01-01
textabstractJackal is a fine-grained distributed shared memory implementation of the Java programming language. It aims to implement Java's memory model and allows multithreaded Java programs to run unmodified on a distributed memory system. It employs a multiple-writer cache coherence
Model checking a cache coherence protocol of a Java DSM implementation
Pang, J.; Fokkink, W.J.; Hofman, R.; Veldema, R.S.
2007-01-01
Jackal is a fine-grained distributed shared memory implementation of the Java programming language. It aims to implement Java's memory model and allows multithreaded Java programs to run unmodified on a distributed memory system. It employs a multiple-writer cache coherence protocol. In this paper,
Learning and Model-checking Networks of I/O Automata
DEFF Research Database (Denmark)
Mao, Hua; Jaeger, Manfred
2012-01-01
We introduce a new statistical relational learning (SRL) approach in which models for structured data, especially network data, are constructed as networks of communicating nite probabilistic automata. Leveraging existing automata learning methods from the area of grammatical inference, we can le...
New applications of graded Lie algebras to Lie algebras, generalized Lie algebras and cohomology
Pinczon, Georges; Ushirobira, Rosane
2005-01-01
We give new applications of graded Lie algebras to: identities of standard polynomials, deformation theory of quadratic Lie algebras, cyclic cohomology of quadratic Lie algebras, $2k$-Lie algebras, generalized Poisson brackets and so on.
Yin, Ken-Ming
An algebraic one-dimensional model on the membrane-electrode-assembly (MEA) of direct methanol fuel cell (DMFC) is proposed. Non-linear regression procedure was imposed on the model to retrieve important parameters: solid polymer electrolyte conductivity κ m, exchange current density of methanol electro-oxidation at anode catalyst surface i oM,ref, and mass diffusivity of methanol in aqueous phase within the porous electrode D a that correspond to the experimentally measured polarization curves. Although numerical iteration is required for a complete solution, the explicit relationships of methanol concentration, methanol crossover rate, oxygen concentration and cell discharge current density do provide a clear picture of the mass transport and electrochemical kinetics within the various porous media in the MEA. It is shown the cathode mixed potential induced by the parallel reactions of oxygen reduction and oxidation of crossover methanol elucidates the potential drop of the cathode and the decrease of the cell open circuit voltage (OCV). Methanol transport in the membrane is described by the diffusion, electro-osmosis, and pressure induced convection. Detailed accounts of the effects of anode methanol and cathode oxygen feed concentrations on the cell discharge performance are given with correlation to the physical structure and chemical compositions of the catalyst layers (CLs).
Planar algebra of the subgroup-subfactor
Indian Academy of Sciences (India)
The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of the standard invariant of R ⋊ H ⊂ R ⋊ G in terms of operator matrices. We also obtain an identification between the planar algebra of the fixed algebra subfactor R G ⊂ R H and the -invariant planar subalgebra ...
Singularity Theory for W-Algebra Potentials
Gaite, J
1994-01-01
The Landau potentials of W3-algebra models are analyzed with algebraic-geometric methods. The number of ground states and the number of independent perturbations of every potential coincide and can be computed. This number agrees with the structure of ground states obtained in a previous paper,
A process algebra software engineering environment
Diertens, B.
2008-01-01
In previous work we described how the process algebra based language PSF can be used in software engineering, using the ToolBus, a coordination architecture also based on process algebra, as implementation model. In this article we summarize that work and describe the software development process
The data type variety of stack algebras
Bergstra, J.A.; Tucker, J.V.
1995-01-01
We define and study the class of all stack algebras as the class of all minimal algebras in a variety defined by an infinite recursively enumerable set of equations. Among a number of results, we show that the initial model of the variety is computable, that its equational theory is decidable,
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Linear Algebra introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduction to
Indian Academy of Sciences (India)
We study the structure of split Malcev algebras of arbitrary dimension over an algebraically closed field of characteristic zero. We show that any such algebras is of the form M = U + ∑ j I j with U a subspace of the abelian Malcev subalgebra and any I j a well described ideal of satisfying [ I j , I k ] = 0 if ≠ .
Foundations of algebraic geometry
Weil, A
1946-01-01
This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Noguera, Carlos; Loiret, Frédéric
2009-01-01
Acceptance rate: 38%; International audience; Software components are used in various application domains, and many component models and frameworks have been proposed to fulfill domain-specific requirements. The ad-hoc development of these component frameworks hampers the reuse of tools and abstractions across different frameworks. We believe that in order to promote the reuse of components within various domain contexts an homogeneous design approach is needed. A key requirement of such an a...
Nourani, Cyrus F
2014-01-01
IntroductionCategorical PreliminariesCategories and FunctorsMorphismsFunctorsCategorical ProductsNatural TransformationsProducts on Models Preservation of LimitsModel Theory and Topoi More on Universal ConstructionsChapter ExercisesInfinite Language CategoriesBasicsLimits and Infinitary Languages Generic Functors and Language String ModelsFunctorial Morphic Ordered Structure ModelsChapter ExercisesFunctorial Morphic Ordered Structure ModelsFunctorial Fragment M
Discrete event systems in dioid algebra and conventional algebra
Declerck, Philippe
2013-01-01
This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i
Quintana, César; Ramos, Gonzalo; Moral, Andoni; Rodriguez, Jose Antonio; Pérez, Carlos; Hutchinson, Ian; INGLEY, Richard; Rull, Fernando
2016-10-01
Raman Laser Spectrometer (RLS) is one of the Pasteur payload instruments located at the Rover of the ExoMars mission and within the ESA's Aurora Exploration Programme. RLS will explore the Mars surface composition through the Raman spectroscopy technique. The instrument is divided into several units: a laser for Raman emission stimulation, an internal optical head (iOH) for sample excitation and for Raman emission recovering, a spectrometer with a CCD located at its output (SPU), the optical harness (OH) for the units connection, from the laser to the excitation path of the iOH and from the iOH reception path to the spectrometer, and the corresponding electronics for the CCD operation.Due to the variability of the samples to be analyzed on Mars, a radiometry prediction for the instrument performance results to be of the critical importance. In such a framework, and taking into account the SNR (signal to noise ratio) required for the achievement of successful results from the scientific point of view (a proper information about the Mars surface composition), a radiometric model has been developed to provide the requirements for the different units, i.e. the laser irradiance, the iOH, OH, and SPU throughputs, and the samples that will be possible to be analyzed in terms of its Raman emission and the relationship of the Raman signal with respect to fluorescence emission, among others.The radiometric model fundamentals (calculations and approximations), as well as the first results obtained during the bread board characterization campaign are here reported on.
International Nuclear Information System (INIS)
Krivonos, S.O.; Sorin, A.S.
1994-06-01
We show that the Zamolodchikov's and Polyakov-Bershadsky nonlinear algebras W 3 and W (2) 3 can be embedded as subalgebras into some linear algebras with finite set of currents. Using these linear algebras we find new field realizations of W (2) 3 and W 3 which could be a starting point for constructing new versions of W-string theories. We also reveal a number of hidden relationships between W 3 and W (2) 3 . We conjecture that similar linear algebras can exist for other W-algebra as well. (author). 10 refs
Algorithms in Algebraic Geometry
Dickenstein, Alicia; Sommese, Andrew J
2008-01-01
In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its
Parameter Estimation and Prediction of a Nonlinear Storage Model: an algebraic approach
Doeswijk, T.G.; Keesman, K.J.
2005-01-01
Generally, parameters that are nonlinear in system models are estimated by nonlinear least-squares optimization algorithms. In this paper, if a nonlinear discrete-time model with a polynomial quotient structure in input, output, and parameters, a method is proposed to re-parameterize the model such
Chouika, Nabil; Mezrag, Cédric; Moutarde, Hervé; Rodríguez-Quintero, José
2017-07-01
We briefly report on a recent computation, with the help of a fruitful algebraic model, sketching the pion valence dressed-quark generalized parton distribution. Then, preliminary, we introduce on a sensible procedure to get reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Efremov-Radyushkin-Brodsky-Lepage kinematical regions, grounded on the GPD overlap representation and its parametrization of a Radon transform of the so-called double distribution.
Directory of Open Access Journals (Sweden)
Wanda Vrasti
2012-03-01
Full Text Available Over the past couple of months history has been unfolding with dizzying speed. The #occupy model of leaderless, demandless direct action, which in the beginning no one with only a slim understanding of how capitalism works thought could become anything more than a facile if charming jab at anti-corporate activism, has gone viral. Every morning we wake up to new reports about ‘occupying X’, where X can be anything from cities, campuses, boardrooms, buildings, highways, and public events, all the way to academic disciplines. What originally seemed like a romantic fantasy about temporary autonomous zones now feels like history. And no one likes to find themselves on thewrong side of history, especially not intellectuals, let alone intellectuals in the business of explaining global politics.
Algebraic geometry and effective lagrangians
International Nuclear Information System (INIS)
Martinec, E.J.; Chicago Univ., IL
1989-01-01
N=2 supersymmetric Landau-Ginsburg fixed points describe nonlinear models whose target spaces are algebraic varieties in certain generalized projective spaces; the defining equation is precisely the zero set of the superpotential, considered as a condition in the projective space. The ADE classification of modular invariants arises as the classification of projective descriptions of P 1 ; in general, the hierarchy of fixed points is conjectured to be isomorphic to the classification of quasihomogeneous singularities. The condition of vanishing first Chern class is an integrality condition on the Virasoro central charge; the central charge is determined by the superpotential. The operator algebra is given by the algebra of Wick contractions of perturbations of the superpotential. (orig.)
Computational triadic algebras of signs
Energy Technology Data Exchange (ETDEWEB)
Zadrozny, W. [T.J. Watson Research Center, Yorktown Heights, NY (United States)
1996-12-31
We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.
International Nuclear Information System (INIS)
Feigin, B.L.; Semikhatov, A.M.
2004-01-01
We construct W-algebra generalizations of the sl-circumflex(2) algebra-W algebras W n (2) generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky-Polyakov W 3 (2) algebra. We define these algebras as a centralizer (commutant) of the Uqs-bar (n vertical bar 1) quantum supergroup and explicitly find the generators in a factored, 'Miura-like' form. Another construction of the W n (2) algebras is in terms of the coset sl-circumflex(n vertical bar 1)/sl-circumflex(n). The relation between the two constructions involves the 'duality' (k+n-1)(k'+n-1)=1 between levels k and k' of two sl-circumflex(n) algebras
Algebraic conformal field theory
International Nuclear Information System (INIS)
Fuchs, J.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1991-11-01
Many conformal field theory features are special versions of structures which are present in arbitrary 2-dimensional quantum field theories. So it makes sense to describe 2-dimensional conformal field theories in context of algebraic theory of superselection sectors. While most of the results of the algebraic theory are rather abstract, conformal field theories offer the possibility to work out many formulae explicitly. In particular, one can construct the full algebra A-bar of global observables and the endomorphisms of A-bar which represent the superselection sectors. Some explicit results are presented for the level 1 so(N) WZW theories; the algebra A-bar is found to be the enveloping algebra of a Lie algebra L-bar which is an extension of the chiral symmetry algebra of the WZW theory. (author). 21 refs., 6 figs
Discrete Minimal Surface Algebras
Directory of Open Access Journals (Sweden)
Joakim Arnlind
2010-05-01
Full Text Available We consider discrete minimal surface algebras (DMSA as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sl_n (any semi-simple Lie algebra providing a trivial example by itself. A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.
Bicovariant quantum algebras and quantum Lie algebras
International Nuclear Information System (INIS)
Schupp, P.; Watts, P.; Zumino, B.
1993-01-01
A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)
The Boolean algebra and central Galois algebras
Directory of Open Access Journals (Sweden)
George Szeto
2001-01-01
Full Text Available Let B be a Galois algebra with Galois group G, Jg={b∈B∣bx=g(xb for all x∈B} for g∈G, and BJg=Beg for a central idempotent eg. Then a relation is given between the set of elements in the Boolean algebra (Ba,≤ generated by {0,eg∣g∈G} and a set of subgroups of G, and a central Galois algebra Be with a Galois subgroup of G is characterized for an e∈Ba.
The ABCDEFG of instantons and W-algebras
Keller, Christoph A.; Mekareeya, Noppadol; Song, Jaewon; Tachikawa, Yuji
2012-03-01
For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure mathcal{N} = {2} super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.
The ABCDEFG of instantons and W-algebras
Keller, Christoph A.; Mekareeya, Noppadol; Song, Jaewon; Tachikawa, Yuji
2012-01-01
For arbitrary gauge groups, we check at the one-instanton level that the Nekrasov partition function of pure N = 2 super Yang-Mills is equal to the norm of a certain coherent state of the corresponding W-algebra. For non-simply-laced gauge groups, we confirm in particular that the coherent state is in the twisted sector of a simply-laced W-algebra.
Hurwitz Algebras and the Octonion Algebra
Burdik, Čestmir; Catto, Sultan
2018-02-01
We explore some consequences of a theory of internal symmetries for elementary particles constructed on exceptional quantum mechanical spaces based on Jordan algebra formulation that admit exceptional groups as gauge groups.
DEFF Research Database (Denmark)
Grønhøj Larsen, Christian; Jørgensen, Karsten Juhl; Gøtzsche, Peter C
2012-01-01
To investigate whether Danish providers of general health checks present a balanced account of possible benefits and harms on their websites and whether the health checks are evidence-based.......To investigate whether Danish providers of general health checks present a balanced account of possible benefits and harms on their websites and whether the health checks are evidence-based....
International Nuclear Information System (INIS)
Kedem, Rinat
2008-01-01
Q-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211-21, 301). Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497-529), and discuss the relation of the polynomiality property of the solutions of the Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119-44)