Towards Model Checking Stochastic Process Algebra
Hermanns, H.; Grieskamp, W.; Santen, T.; Katoen, Joost P.; Stoddart, B.; Meyer-Kayser, J.; Siegle, M.
2000-01-01
Stochastic process algebras have been proven useful because they allow behaviour-oriented performance and reliability modelling. As opposed to traditional performance modelling techniques, the behaviour- oriented style supports composition and abstraction in a natural way. However, analysis of
Model Checking Processes Specified In Join-Calculus Algebra
Sławomir Piotr Maludziński
2014-01-01
Full Text Available This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra with its operational semantics defined by the chemical abstract machine serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, and allows the examination of more complex systems.
Algebraic model checking for Boolean gene regulatory networks.
Tran, Quoc-Nam
2011-01-01
We present a computational method in which modular and Groebner bases (GB) computation in Boolean rings are used for solving problems in Boolean gene regulatory networks (BN). In contrast to other known algebraic approaches, the degree of intermediate polynomials during the calculation of Groebner bases using our method will never grow resulting in a significant improvement in running time and memory space consumption. We also show how calculation in temporal logic for model checking can be done by means of our direct and efficient Groebner basis computation in Boolean rings. We present our experimental results in finding attractors and control strategies of Boolean networks to illustrate our theoretical arguments. The results are promising. Our algebraic approach is more efficient than the state-of-the-art model checker NuSMV on BNs. More importantly, our approach finds all solutions for the BN problems.
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; 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; 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
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...
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.
Model Checking Process Algebra of Communicating Resources for Real-time Systems
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...
Model checking process algebra of communicating resources for real-time systems
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...
Model Checking Feature Interactions
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....
The algebraic collective model
Rowe, D.J.; Turner, P.S.
2005-01-01
A recently proposed computationally tractable version of the Bohr collective model is developed to the extent that we are now justified in describing it as an algebraic collective model. The model has an SU(1,1)xSO(5) algebraic structure and a continuous set of exactly solvable limits. Moreover, it provides bases for mixed symmetry collective model calculations. However, unlike the standard realization of SU(1,1), used for computing beta wave functions and their matrix elements in a spherical basis, the algebraic collective model makes use of an SU(1,1) algebra that generates wave functions appropriate for deformed nuclei with intrinsic quadrupole moments ranging from zero to any large value. A previous paper focused on the SO(5) wave functions, as SO(5) (hyper-)spherical harmonics, and computation of their matrix elements. This paper gives analytical expressions for the beta matrix elements needed in applications of the model and illustrative results to show the remarkable gain in efficiency that is achieved by using such a basis in collective model calculations for deformed nuclei
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
Efficient probabilistic model checking on general purpose graphic processors
Bosnacki, D.; Edelkamp, S.; Sulewski, D.; Pasareanu, C.S.
2009-01-01
We present algorithms for parallel probabilistic model checking on general purpose graphic processing units (GPGPUs). For this purpose we exploit the fact that some of the basic algorithms for probabilistic model checking rely on matrix vector multiplication. Since this kind of linear algebraic
A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets
2014-11-01
linear hybrid systems by linear algebraic methods. In SAS, volume 6337 of LNCS, pages 373–389. Springer, 2010. [19] E. W. Mayr. Membership in polynomial...383–394, 2009. [31] A. Tarski. A decision method for elementary algebra and geometry. Bull. Amer. Math. Soc., 59, 1951. [32] A. Tiwari. Abstractions...A Hierarchy of Proof Rules for Checking Differential Invariance of Algebraic Sets Khalil Ghorbal1 Andrew Sogokon2 André Platzer1 November 2014 CMU
Compositional and Quantitative Model Checking
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
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...
Coverage Metrics for Model Checking
Penix, John; Visser, Willem; Norvig, Peter (Technical Monitor)
2001-01-01
When using model checking to verify programs in practice, it is not usually possible to achieve complete coverage of the system. In this position paper we describe ongoing research within the Automated Software Engineering group at NASA Ames on the use of test coverage metrics to measure partial coverage and provide heuristic guidance for program model checking. We are specifically interested in applying and developing coverage metrics for concurrent programs that might be used to support certification of next generation avionics software.
Model Checking Markov Chains: Techniques and Tools
Zapreev, I.S.
2008-01-01
This dissertation deals with four important aspects of model checking Markov chains: the development of efficient model-checking tools, the improvement of model-checking algorithms, the efficiency of the state-space reduction techniques, and the development of simulation-based model-checking
Model Checking as Static Analysis
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
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
Algebraic aspects of exact models
Gaudin, M.
1983-01-01
Spin chains, 2-D spin lattices, chemical crystals, and particles in delta function interaction share the same underlying structures: the applicability of Bethe's superposition ansatz for wave functions, the commutativity of transfer matrices, and the existence of a ternary operator algebra. The appearance of these structures and interrelations from the eight vortex model, for delta function interreacting particles of general spin, and for spin 1/2, are outlined as follows: I. Eight Vortex Model. Equivalences to Ising model and the dimer system. Transfer matrix and symmetry of the Self Conjugate model. Relation between the XYZ Hamiltonian and the transfer matrix. One parameter family of commuting transfer matrices. A representation of the symmetric group spin. Diagonalization of the transfer matrix. The Coupled Spectrum equations. II. Identical particles with Delta Function interaction. The Bethe ansatz. Yang's representation. The Ternary Algebra and intergrability. III. Identical particles with delta function interaction: general solution for two internal states. The problem of spin 1/2 fermions. The Operator method
Critical analysis of algebraic collective models
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
Model Checking Real-Time Systems
Bouyer, Patricia; Fahrenberg, Uli; Larsen, Kim Guldstrand
2018-01-01
This chapter surveys timed automata as a formalism for model checking real-time systems. We begin with introducing the model, as an extension of finite-state automata with real-valued variables for measuring time. We then present the main model-checking results in this framework, and give a hint...
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
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
Model-Checking Discrete Duration Calculus
Hansen, Michael Reichhardt
1994-01-01
can do model-checking. The subset we consider is expressive enough to formalize the requirements to the gas burner system given by A.P. Ravn (1993); but only for a discrete time domain. Model-checking is done by reducing the correctness problem ℳ|=𝒟 to the inclusion problem of regular...
Model Checking Infinite-State Markov Chains
Remke, Anne Katharina Ingrid; Haverkort, Boudewijn R.H.M.; Cloth, L.
2004-01-01
In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state
Representations of the Virasoro algebra from lattice models
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.))
Engineering Abstractions in Model Checking and Testing
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...... and implementing abstractions will improve the applicability of model checking in practice....
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
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
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
Computational algebraic geometry of epidemic models
Rodríguez Vega, Martín.
2014-06-01
Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.
UTP and Temporal Logic Model Checking
Anderson, Hugh; Ciobanu, Gabriel; Freitas, Leo
In this paper we give an additional perspective to the formal verification of programs through temporal logic model checking, which uses Hoare and He Unifying Theories of Programming (UTP). Our perspective emphasizes the use of UTP designs, an alphabetised relational calculus expressed as a pre/post condition pair of relations, to verify state or temporal assertions about programs. The temporal model checking relation is derived from a satisfaction relation between the model and its properties. The contribution of this paper is that it shows a UTP perspective to temporal logic model checking. The approach includes the notion of efficiency found in traditional model checkers, which reduced a state explosion problem through the use of efficient data structures
W algebra in the SU(3) parafermion model
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
Model checking exact cost for attack scenarios
Aslanyan, Zaruhi; Nielson, Flemming
2017-01-01
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....... 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...... 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....
A Method for Model Checking Feature Interactions
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....
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
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.
A process algebra model of QED
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)
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 the Remote Agent Planner
Khatib, Lina; Muscettola, Nicola; Havelund, Klaus; Norvig, Peter (Technical Monitor)
2001-01-01
This work tackles the problem of using Model Checking for the purpose of verifying the HSTS (Scheduling Testbed System) planning system. HSTS is the planner and scheduler of the remote agent autonomous control system deployed in Deep Space One (DS1). Model Checking allows for the verification of domain models as well as planning entries. We have chosen the real-time model checker UPPAAL for this work. We start by motivating our work in the introduction. Then we give a brief description of HSTS and UPPAAL. After that, we give a sketch for the mapping of HSTS models into UPPAAL and we present samples of plan model properties one may want to verify.
Statistical Model Checking for Biological Systems
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...
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
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:
Slicing AADL specifications for model checking
Odenbrett, M.R.; Nguyen, V.Y.; Noll, T.
2010-01-01
To combat the state-space explosion problem in model checking larger systems, abstraction techniques can be employed. Here, methods that operate on the system specification before constructing its state space are preferable to those that try to minimize the resulting transition system as they
A Simple and Practical Linear Algebra Library Interface with Static Size Checking
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.
Fusion algebras of logarithmic minimal models
Rasmussen, Joergen; Pearce, Paul A
2007-01-01
We present explicit conjectures for the chiral fusion algebras of the logarithmic minimal models LM(p,p') considering Virasoro representations with no enlarged or extended symmetry algebra. The generators of fusion are countably infinite in number but the ensuing fusion rules are quasi-rational in the sense that the fusion of a finite number of representations decomposes into a finite direct sum of representations. The fusion rules are commutative, associative and exhibit an sl(2) structure but require so-called Kac representations which are typically reducible yet indecomposable representations of rank 1. In particular, the identity of the fundamental fusion algebra p ≠ 1 is a reducible yet indecomposable Kac representation of rank 1. We make detailed comparisons of our fusion rules with the results of Gaberdiel and Kausch for p = 1 and with Eberle and Flohr for (p, p') = (2, 5) corresponding to the logarithmic Yang-Lee model. In the latter case, we confirm the appearance of indecomposable representations of rank 3. We also find that closure of a fundamental fusion algebra is achieved without the introduction of indecomposable representations of rank higher than 3. The conjectured fusion rules are supported, within our lattice approach, by extensive numerical studies of the associated integrable lattice models. Details of our lattice findings and numerical results will be presented elsewhere. The agreement of our fusion rules with the previous fusion rules lends considerable support for the identification of the logarithmic minimal models LM(p,p') with the augmented c p,p' (minimal) models defined algebraically
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.
A polynomial time algorithm for checking regularity of totally normed process algebra
Yang, F.; Huang, H.
2015-01-01
A polynomial algorithm for the regularity problem of weak and branching bisimilarity on totally normed process algebra (PA) processes is given. Its time complexity is O(n 3 +mn) O(n3+mn), where n is the number of transition rules and m is the maximal length of the rules. The algorithm works for
Coherent states and classical limit of algebraic quantum models
Scutaru, H.
1983-01-01
The algebraic models for collective motion in nuclear physics belong to a class of theories the basic observables of which generate selfadjoint representations of finite dimensional, real Lie algebras, or of the enveloping algebras of these Lie algebras. The simplest and most used for illustrations model of this kind is the Lipkin model, which is associated with the Lie algebra of the three dimensional rotations group, and which presents all characteristic features of an algebraic model. The Lipkin Hamiltonian is the image, of an element of the enveloping algebra of the algebra SO under a representation. In order to understand the structure of the algebraic models the author remarks that in both classical and quantum mechanics the dynamics is associated to a typical algebraic structure which we shall call a dynamical algebra. In this paper he shows how the constructions can be made in the case of the algebraic quantum systems. The construction of the symplectic manifold M can be made in this case using a quantum analog of the momentum map which he defines
Automata-Based CSL Model Checking
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...... probability can then be approximated in polynomial time (using uniformization). This makes the present work the centerpiece of a broadly applicable full CSL model checker. Recently, the decision algorithm by Aziz et al. was shown to be incorrect in general. In fact, it works only for stratified CTMCs...
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
Statistical Model Checking of Rich Models and Properties
Poulsen, Danny Bøgsted
in undecidability issues for the traditional model checking approaches. Statistical model checking has proven itself a valuable supplement to model checking and this thesis is concerned with extending this software validation technique to stochastic hybrid systems. The thesis consists of two parts: the first part...... 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...
Model Checking Markov Reward Models with Impulse Rewards
Cloth, Lucia; Katoen, Joost-Pieter; Khattri, Maneesh; Pulungan, Reza; Bondavalli, Andrea; Haverkort, Boudewijn; Tang, Dong
This paper considers model checking of Markov reward models (MRMs), continuous-time Markov chains with state rewards as well as impulse rewards. The reward extension of the logic CSL (Continuous Stochastic Logic) is interpreted over such MRMs, and two numerical algorithms are provided to check the
Lectures on algebraic model theory
Hart, Bradd
2001-01-01
In recent years, model theory has had remarkable success in solving important problems as well as in shedding new light on our understanding of them. The three lectures collected here present recent developments in three such areas: Anand Pillay on differential fields, Patrick Speissegger on o-minimality and Matthias Clasen and Matthew Valeriote on tame congruence theory.
An algebraic model for three-cluster giant molecules
Hess, P.O.; Bijker, R.; Misicu, S.
2001-01-01
After an introduction to the algebraic U(7) model for three bodies, we present a relation of a geometrical description of three-cluster molecule to the algebraic U(7) model. Stiffness parameters of oscillations between each of two clusters are calculated and translated to the model parameter values of the algebraic model. The model is applied to the trinuclear system l32 Sn+ α + ll6 Pd which occurs in the ternary cold fission of 252 Cf. (Author)
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.
Exchange algebra and exotic supersymmetry in the Chiral Potts model
Bernard, D.; Pasquier, V.
1989-01-01
We obtain an exchange algebra for the Chiral Potts model, the elements of which are linear in the parameters defining the rapidity curve. This enables us to connect the Chiral Potts model to a U q (GL(2)) algebra. On the other hand, looking at the model from the S-matrix point of view relates it to a Z N generalisation of the supersymmetric algebra
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
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
Isovectorial pairing in solvable and algebraic models
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.
Phase Transitions in Algebraic Cluster Models
Yepez-Martinez, H.; Cseh, J.; Hess, P.O.
2006-01-01
Complete text of publication follows. Phase transitions in nuclear systems are of utmost interest. An interesting class of phase transitions can be seen in algebraic models of nuclear structure. They are called shapephase transitions due to the following reason. These models have analytically solvable limiting cases, called dynamical symmetries, which are characterized by a chain of nested subgroups. They correspond to well-defined geometrical shape and behaviour, e.g. to rotation of an ellipsoid, or spherical vibration. The general case of the model, which includes interactions described by more than one groupchain, breaks the symmetry, and changing the relative strengths of these interactions, one can go from one shape to the other. In doing so a phase-transition can be seen. A phase transition is defined as a discontinuity of some quantity as a function of the control parameter, which gives the relative strength of the interactions of different symmetries. Real phase transitions can take place only in infinite systems, like in the classical limits of these algebraic models, when the particle number N is very large: N → ∞. For finite N the discontinuities are smoothed out, nevertheless, some indications of the phase-transitions can still be there. A controlled way of breaking the dynamical symmetries may reveal another very interesting phenomenon, i.e. the appearance of a quasidynamical (or effective) symmetry. This rather general symmetry-concept of quantum mechanics corresponds to a situation, in which the symmetry-breaking interactions are so strong that the energy-eigenfunctions are not symmetric, i.e. are not basis states of an irreducible representation of the symmetry group, rather they are linear combinations of these basis states. However, they are very special linear combinations in the sense that their coefficients are (approximately) identical for states with different spin values. When this is the case, then the underlying intrinsic state is the
Toda theories, W-algebras, and minimal models
Mansfield, P.; Spence, B.
1991-01-01
We discuss the classical W-algebra symmetries of Toda field theories in terms of the pseudo-differential Lax operator associated with the Toda Lax pair. We then show how the W-algebra transformations can be understood as the non-abelian gauge transformations which preserve the form of the Lax pair. This provides a new understanding of the W-algebras, and we discuss their closure and co-cycle structure using this approach. The quantum Lax operator is investigated, and we show that this operator, which generates the quantum W-algebra currents, is conserved in the conformally extended Toda theories. The W-algebra minimal model primary fields are shown to arise naturally in these theories, leading to the conjecture that the conformally extended Toda theories provide a lagrangian formulation of the W-algebra minimal models. (orig.)
Algebraic computability and enumeration models recursion theory and descriptive complexity
Nourani, Cyrus F
2016-01-01
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...
N=2 current algebra and coset models
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.)
Classification and checking model of pedestrian crossing
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.
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
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...
Current algebra of classical non-linear sigma models
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.)
Performability assessment by model checking of Markov reward models
Baier, Christel; Cloth, L.; Haverkort, Boudewijn R.H.M.; Hermanns, H.; Katoen, Joost P.
2010-01-01
This paper describes efficient procedures for model checking Markov reward models, that allow us to evaluate, among others, the performability of computer-communication systems. We present the logic CSRL (Continuous Stochastic Reward Logic) to specify performability measures. It provides flexibility
Algebraic models of local period maps and Yukawa algebras
Bandiera, Ruggero; Manetti, Marco
2018-02-01
We describe some L_{∞} model for the local period map of a compact Kähler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a by-product, we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.
Strategic Planning through Model Checking of ATL Formulae
Jamroga, W.J.; Rutkowski, L.; Siekmann, J.; Tadeusiewicz, R.; Zadeh, L.A.
2004-01-01
Model checking of temporal logic has already been proposed for automatic planning. In this paper, we introduce a simple adaptation of the ATL model checking algorithm that returns a strategy to achieve given goal. We point out that the algorithm generalizes minimaxing, and that ATL models generalize
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
Dynamic State Space Partitioning for External Memory Model Checking
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...
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
Partial-order reduction for GPU model checking
Neele, T.S.; Wijs, A.J.; Bošnački, D.; van de Pol, J.C.
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 explicitstate model checking, we improve memory efficiency by applying partialorder reduction. We propose
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...
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.
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.
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.
Optimisation of BPMN Business Models via Model Checking
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...
Observable algebras for the rational and trigonometric Euler-Calogero-Moser Models
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.))
Category-theoretic models of algebraic computer systems
Kovalyov, S. P.
2016-01-01
A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.
Modeling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; van den Broek, Pim
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
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.
Model checking biological systems described using ambient calculus
Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola
2005-01-01
Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005.......Model checking biological systems described using ambient calculus. In Proc. of the second International Workshop on Computational Methods in Systems Biology (CMSB04), Lecture Notes in Bioinformatics 3082:85-103, Springer, 2005....
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.
Bringing LTL Model Checking to Biologists
Ahmed, Z; Benque, D; Berezin, S; Dahl, ACE; Fisher, Jasmin; Hall, Benjamin Andrew; Ishtiaq, S; Nanavati, J; Piterman, N; Riechert, M; Skoblov, N
2017-01-01
The BioModelAnalyzer (BMA) is a web based tool for the development of discrete models of biological systems. Through a graphical user interface, it allows rapid development of complex models of gene and protein interaction networks and stability analysis without requiring users to be proficient computer programmers. Whilst stability is a useful specification for testing many systems, testing temporal specifications in BMA presently requires the user to perform simulations. Here we describe th...
Workflow Fault Tree Generation Through Model Checking
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...
Learning Markov Decision Processes for Model Checking
Mao, Hua; Chen, Yingke; Jaeger, Manfred
2012-01-01
. The proposed learning algorithm is adapted from algorithms for learning deterministic probabilistic finite automata, and extended to include both probabilistic and nondeterministic transitions. The algorithm is empirically analyzed and evaluated by learning system models of slot machines. The evaluation......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...... on learning probabilistic automata to reactive systems, where the observed system behavior is in the form of alternating sequences of inputs and outputs. We propose an algorithm for automatically learning a deterministic labeled Markov decision process model from the observed behavior of a reactive system...
Solving the nuclear shell model with an algebraic method
Feng, D.H.; Pan, X.W.; Guidry, M.
1997-01-01
We illustrate algebraic methods in the nuclear shell model through a concrete example, the fermion dynamical symmetry model (FDSM). We use this model to introduce important concepts such as dynamical symmetry, symmetry breaking, effective symmetry, and diagonalization within a higher-symmetry basis. (orig.)
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
Statistical Model Checking for Product Lines
ter Beek, Maurice H.; Legay, Axel; Lluch Lafuente, Alberto
2016-01-01
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...
Model checking meets probability: a gentle introduction
Katoen, Joost P.
2013-01-01
This paper considers fully probabilistic system models. Each transition is quantified with a probability—its likelihood of occurrence. Properties are expressed as automata that either accept or reject system runs. The central question is to determine the fraction of accepted system runs. We also
Symbolic Dependency Graphs for PCTL Model-Checking
Mariegaard, Anders; Larsen, Kim Guldstrand
2017-01-01
We consider the problem of model-checking a subset of probabilistic CTL, interpreted over (discrete-time) Markov reward models, allowing the specification of lower bounds on the probability of the set of paths satisfying a cost-bounded path formula. We first consider a reduction to fixed-point co......We consider the problem of model-checking a subset of probabilistic CTL, interpreted over (discrete-time) Markov reward models, allowing the specification of lower bounds on the probability of the set of paths satisfying a cost-bounded path formula. We first consider a reduction to fixed...
Linear Parametric Model Checking of Timed Automata
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...
Logarithmic sℓ-hat (2) CFT models from Nichols algebras: I
Semikhatov, A M; Tipunin, I Yu
2013-01-01
We construct chiral algebras that centralize rank-2 Nichols algebras with at least one fermionic generator. This gives ‘logarithmic’ W-algebra extensions of a fractional-level sℓ-hat (2) algebra. We discuss crucial aspects of the emerging general relation between Nichols algebras and logarithmic conformal field theory (CFT) models: (i) the extra input, beyond the Nichols algebra proper, needed to uniquely specify a conformal model; (ii) a relation between the CFT counterparts of Nichols algebras connected by Weyl groupoid maps; and (iii) the common double bosonization U(X) of such Nichols algebras. For an extended chiral algebra, candidates for its simple modules that are counterparts of the U(X) simple modules are proposed, as a first step toward a functorial relation between U(X) and W-algebra representation categories. (paper)
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 Bethe ansatz for 19-vertex models with reflection conditions
Utiel, Wagner
2003-01-01
In this work we solve the 19-vertex models with the use of algebraic Bethe ansatz for diagonal reflection matrices (Sklyanin K-matrices). The eigenvectors, eigenvalues and Bethe equations are given in a general form. Quantum spin chains of spin one derived from the 19-vertex models were also discussed
Generalized algebra-valued models of set theory
Löwe, B.; Tarafder, S.
2015-01-01
We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.
Model Checking Temporal Logic Formulas Using Sticker Automata
Feng, Changwei; Wu, Huanmei
2017-01-01
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. PMID:29119114
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.
Schedulability of Herschel revisited using statistical model checking
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel
2015-01-01
-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...... and blocking times of tasks. Consequently, the method may falsely declare deadline violations that will never occur during execution. This paper is a continuation of previous work of the authors in applying extended timed automata model checking (using the tool UPPAAL) to obtain more exact schedulability...... analysis, here in the presence of non-deterministic computation times of tasks given by intervals [BCET,WCET]. Computation intervals with preemptive schedulers make the schedulability analysis of the resulting task model undecidable. Our contribution is to propose a combination of model checking techniques...
An algebraic approach to modeling in software engineering
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
Directed Abelian algebras and their application to stochastic models.
Alcaraz, F C; Rittenberg, V
2008-10-01
With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma_(tau)=32 ). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma_(tau)=1.780+/-0.005 .
modelling of queuing process at airport check-in system
HOD
Key words: Airport check-in system, discrete time events, analytical models, simulation model, SimEvents toolbox. 1. ..... [6] Gross, D. and Harris, C. M. Fundamentals of. Queueing ... [11] Manataki I. E. and Zogra os K. G. “A Generic. System ...
Bayesian inference with information content model check for Langevin equations
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...
Towards Model Checking a Spi-Calculus Dialect
Gnesi, S.; Latella, D.; Lenzini, Gabriele
We present a model checking framework for a spi-calculus dialect which uses a linear time temporal logic for expressing security properties. We have provided our spi-calculus dialect, called SPID, with a semantics based on labeled transition systems (LTS), where the intruder is modeled in the
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
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
A voice-actuated wind tunnel model leak checking system
Larson, William E.
1989-01-01
A computer program has been developed that improves the efficiency of wind tunnel model leak checking. The program uses a voice recognition unit to relay a technician's commands to the computer. The computer, after receiving a command, can respond to the technician via a voice response unit. Information about the model pressure orifice being checked is displayed on a gas-plasma terminal. On command, the program records up to 30 seconds of pressure data. After the recording is complete, the raw data and a straight line fit of the data are plotted on the terminal. This allows the technician to make a decision on the integrity of the orifice being checked. All results of the leak check program are stored in a database file that can be listed on the line printer for record keeping purposes or displayed on the terminal to help the technician find unchecked orifices. This program allows one technician to check a model for leaks instead of the two or three previously required.
Algebraic approach to small-world network models
Rudolph-Lilith, Michelle; Muller, Lyle E.
2014-01-01
We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.
Polynomial algebra of discrete models in systems biology.
Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard
2010-07-01
An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.
Continual Lie algebras and noncommutative counterparts of exactly solvable models
Zuevsky, A.
2004-01-01
Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.
Model selection for contingency tables with algebraic statistics
Krampe, A.; Kuhnt, S.; Gibilisco, P.; Riccimagno, E.; Rogantin, M.P.; Wynn, H.P.
2009-01-01
Goodness-of-fit tests based on chi-square approximations are commonly used in the analysis of contingency tables. Results from algebraic statistics combined with MCMC methods provide alternatives to the chi-square approximation. However, within a model selection procedure usually a large number of
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
Model Checking Timed Automata with Priorities using DBM Subtraction
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 a non-convex set needing sets of DBMs for representation. Our subtraction algorithms are efficient in the sense that the number of generated DBMs is significantly reduced compared to a naive algorithm. The overhead in time is compensated by the gain from reducing the number of resulting DBMs since...... 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....
Consistency checks in beam emission modeling for neutral beam injectors
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
Symbolic Game Semantics for Model Checking Program Families
Dimovski, Aleksandar
2016-01-01
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...... a prototype tool implementing this approach, and we illustrate it with several examples....
Application of Model-Checking Technology to Controller Synthesis
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
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...
State Space Reduction for Model Checking Agent Programs
S.-S.T.Q. Jongmans (Sung-Shik); K.V. Hindriks; M.B. van Riemsdijk; L. Dennis; O. Boissier; R.H. Bordini (Rafael)
2012-01-01
htmlabstractState space reduction techniques have been developed to increase the efficiency of model checking in the context of imperative programming languages. Unfortunately, these techniques cannot straightforwardly be applied to agents: the nature of states in the two programming paradigms
Verifying large SDL-specifications using model checking
Sidorova, N.; Steffen, M.; Reed, R.; Reed, J.
2001-01-01
In this paper we propose a methodology for model-checking based verification of large SDL specifications. The methodology is illustrated by a case study of an industrial medium-access protocol for wireless ATM. To cope with the state space explosion, the verification exploits the layered and modular
2D sigma models and differential Poisson algebras
Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander
2015-01-01
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.
Efficient family-based model checking via variability abstractions
Dimovski, Aleksandar; Al-Sibahi, Ahmad Salim; Brabrand, Claus
2016-01-01
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......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...... of related systems), specialized family-based model checking algorithms allow efficient verification of multiple variants, simultaneously, in a single run. These algorithms, implemented in a tool Snip, scale much better than ``the brute force'' approach, where all individual systems are verified using...
Mixed Portmanteau Test for Diagnostic Checking of Time Series Models
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.
The Hamiltonian of the quantum trigonometric Calogero-Sutherland model in the exceptional algebra E8
Fernandez Nunez, J; Garcia Fuertes, W; Perelomov, A M
2009-01-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model for the Lie algebra E 8 and coupling constant κ by using the fundamental irreducible characters of the algebra as dynamical independent variables
Symbolic Model Checking and Analysis for E-Commerce Protocol
WEN Jing-Hua; ZHANG Mei; LI Xiang
2005-01-01
A new approach is proposed for analyzing non-repudiation and fairness of e-commerce protocols. The authentication e-mail protocol CMP1 is modeled as finite state machine and analyzed in two vital aspects - non-repudiation and fairness using SMV. As a result, the CMP1 protocol is not fair and we have improved it. This result shows that it is effective to analyze and check the new features of e-commerce protocols using SMV model checker
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
Soliton surfaces associated with sigma models: differential and algebraic aspects
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)
Validation of Simulation Models without Knowledge of Parameters Using Differential Algebra
Björn Haffke
2015-01-01
Full Text Available This study deals with the external validation of simulation models using methods from differential algebra. Without any system identification or iterative numerical methods, this approach provides evidence that the equations of a model can represent measured and simulated sets of data. This is very useful to check if a model is, in general, suitable. In addition, the application of this approach to verification of the similarity between the identifiable parameters of two models with different sets of input and output measurements is demonstrated. We present a discussion on how the method can be used to find parameter deviations between any two models. The advantage of this method is its applicability to nonlinear systems as well as its algorithmic nature, which makes it easy to automate.
Model Theory in Algebra, Analysis and Arithmetic
Dries, Lou; Macpherson, H Dugald; Pillay, Anand; Toffalori, Carlo; Wilkie, Alex J
2014-01-01
Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.
Geometric model of topological insulators from the Maxwell algebra
Palumbo, Giandomenico
2017-11-01
We propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincaré algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, we derive a relativistic version of the Wen-Zee term and we show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space.
Geometric Model of Topological Insulators from the Maxwell Algebra
Palumbo, Giandomenico
I propose a novel geometric model of time-reversal-invariant topological insulators in three dimensions in presence of an external electromagnetic field. Their gapped boundary supports relativistic quantum Hall states and is described by a Chern-Simons theory, where the gauge connection takes values in the Maxwell algebra. This represents a non-central extension of the Poincare' algebra and takes into account both the Lorentz and magnetic-translation symmetries of the surface states. In this way, I derive a relativistic version of the Wen-Zee term and I show that the non-minimal coupling between the background geometry and the electromagnetic field in the model is in agreement with the main properties of the relativistic quantum Hall states in the flat space. This work is part of the DITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW).
Using Stochastic Model Checking to Provision Complex Business Services
Herbert, Luke Thomas; Sharp, Robin
2012-01-01
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...
Kac-Moody algebra is not hidden symmetry of chiral models
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
The algebra of non-local charges in non-linear sigma models
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
Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
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.
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.
Using Model Checking for Analyzing Distributed Power Control Problems
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...... 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...
Algebraic fermion models and nuclear structure physics
Troltenier, Dirk; Blokhin, Andrey; Draayer, Jerry P.; Rompf, Dirk; Hirsch, Jorge G.
1996-01-01
Recent experimental and theoretical developments are generating renewed interest in the nuclear SU(3) shell model, and this extends to the symplectic model, with its Sp(6,R) symmetry, which is a natural multi-(ℎ/2π)ω extension of the SU(3) theory. First and foremost, an understanding of how the dynamics of a quantum rotor is embedded in the shell model has established it as the model of choice for describing strongly deformed systems. Second, the symplectic model extension of the 0-(ℎ/2π)ω theory can be used to probe additional degrees of freedom, like core polarization and vorticity modes that play a key role in providing a full description of quadrupole collectivity. Third, the discovery and understanding of pseudo-spin has allowed for an extension of the theory from light (A≤40) to heavy (A≥100) nuclei. Fourth, a user-friendly computer code for calculating reduced matrix elements of operators that couple SU(3) representations is now available. And finally, since the theory is designed to cope with deformation in a natural way, microscopic features of deformed systems can be probed; for example, the theory is now being employed to study double beta decay and thereby serves to probe the validity of the standard model of particles and their interactions. A subset of these topics will be considered in this course--examples cited include: a consideration of the origin of pseudo-spin symmetry; a SU(3)-based interpretation of the coupled-rotor model, early results of double beta decay studies; and some recent developments on the pseudo-SU(3) theory. Nothing will be said about other fermion-based theories; students are referred to reviews in the literature for reports on developments in these related areas
From Transition Systems to Variability Models and from Lifted Model Checking Back to UPPAAL
Dimovski, Aleksandar; Wasowski, Andrzej
2017-01-01
efficient lifted (family-based) model checking for real-time variability models. This reduces the cost of maintaining specialized family-based real-time model checkers. Real-time variability models can be model checked using the standard UPPAAL. We have implemented abstractions as syntactic source...
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
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
, 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......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...
UPPAAL-SMC: Statistical Model Checking for Priced Timed Automata
Bulychev, Petr; David, Alexandre; Larsen, Kim Guldstrand
2012-01-01
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...... 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....
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
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...
Efficient Parallel Statistical Model Checking of Biochemical Networks
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.
SoS contract verification using statistical model checking
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.
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.
An algebraic model for quark mass matrices with heavy top
Krolikowski, W.; Warsaw Univ.
1991-01-01
In terms of an intergeneration U(3) algebra, a numerical model is constructed for quark mass matrices, predicting the top-quark mass around 170 GeV and the CP-violating phase around 75 deg. The CKM matrix is nonsymmetric in moduli with |V ub | being very small. All moduli are consistent with their experimental limits. The model is motivated by the author's previous work on three replicas of the Dirac particle, presumably resulting into three generations of leptons and quarks. The paper may be also viewed as an introduction to a new method of intrinsic dynamical description of lepton and quark mass matrices. (author)
Model checking coalitional games in shortage resource scenarios
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.
Conformity checking of LPG Transportation Trucks by Modelling and Simulation
Gallab Maryam
2017-01-01
Full Text Available LPG Loading /unloading site is considered as a dangerous environment of significant risk, especially during LPG transfer operations. These risks may cause catastrophic dangers such as BLEVE (Boiling Liquid Expanding Vapour Explosion, UVCE (Unconfined Vapour Cloud Explosion, etc. The site consists of a tank (RST containing LPG and threetransfer posts. Two posts allow loading of small carrier tankers 6 tons. The other one transfer post transfer LPG contained injumbo tankers 20 tons inside the tank. The industrial site at risks chooses to demonstrate the need for a modelling-simulation approach. The aim is to check first compliance and authorization of the truck when it enters the site for loading /unloading, to verify the authorization to make the transfer, and then, to identify the driver and his training to ensure that the transfer operations are going to take place without incident. Sometimes, it may happen that Consignment Operator (CO is busy orabsent and thus the driver operates alone without being authorized, in this case the site risks a loss of control due to a lack of resources. The modelling-simulation will be done using multi-agent systems that will present the drivers, trucks, PO and loading unloading posts as agents in order to have a model facilitating this checking.
Four-parametric two-layer algebraic model of transition boundary layer at a planar plate
Labusov, A.N.; Lapin, Yu.V.
1996-01-01
Consideration is given to four-parametric two-layer algebraic model of transition boundary layer on a plane plate, based on generalization of one-parametric algebraic Prandtl-Loitsjansky-Klauzer-3 model. The algebraic model uses Prandtl formulas for mixing path with Loitsjansky damping multiplier in the internal region and the relation for turbulent viscosity, based on universal scales of external region and named the Klauzer-3 formula. 12 refs., 10 figs
Model-checking dense-time Duration Calculus
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....
Using Model Checking for Analyzing Distributed Power Control Problems
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.
Methods to model-check parallel systems software
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
Model checking as an aid to procedure design
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)
Transformation of UML Behavioral Diagrams to Support Software Model Checking
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.
The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
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.
A new (in)finite-dimensional algebra for quantum integrable models
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
Algebraic formulation of collective models. I. The mass quadrupole collective model
Rosensteel, G.; Rowe, D.J.
1979-01-01
This paper is the first in a series of three which together present a microscopic formulation of the Bohr--Mottelson (BM) collective model of the nucleus. In this article the mass quadrupole collective (MQC) model is defined and shown to be a generalization of the BM model. The MQC model eliminates the small oscillation assumption of BM and also yields the rotational and CM (3) submodels by holonomic constraints on the MQC configuration space. In addition, the MQC model is demonstrated to be an algebraic model, so that the state space of the MQC model carries an irrep of a Lie algebra of microscopic observables, the MQC algebra. An infinite class of new collective models is then given by the various inequivalent irreps of this algebra. A microscopic embedding of the BM model is achieved by decomposing the representation of the MQC algebra on many-particle state space into its irreducible components. In the second paper this decomposition is studied in detail. The third paper presents the symplectic model, which provides the realization of the collective model in the harmonic oscillator shell model
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.
Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.
2009-01-01
The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…
Algebraic Traveling Wave Solutions of a Non-local Hydrodynamic-type Model
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
Algebra for Enterprise Ontology: towards analysis and synthesis of enterprise models
Suga, Tetsuya; Iijima, Junichi
2018-03-01
Enterprise modeling methodologies have made enterprises more likely to be the object of systems engineering rather than craftsmanship. However, the current state of research in enterprise modeling methodologies lacks investigations of the mathematical background embedded in these methodologies. Abstract algebra, a broad subfield of mathematics, and the study of algebraic structures may provide interesting implications in both theory and practice. Therefore, this research gives an empirical challenge to establish an algebraic structure for one aspect model proposed in Design & Engineering Methodology for Organizations (DEMO), which is a major enterprise modeling methodology in the spotlight as a modeling principle to capture the skeleton of enterprises for developing enterprise information systems. The results show that the aspect model behaves well in the sense of algebraic operations and indeed constructs a Boolean algebra. This article also discusses comparisons with other modeling languages and suggests future work.
Behavioral Consistency of C and Verilog Programs Using Bounded Model Checking
Clarke, Edmund; Kroening, Daniel; Yorav, Karen
2003-01-01
.... We describe experimental results on various reactive present an algorithm that checks behavioral consistency between an ANSI-C program and a circuit given in Verilog using Bounded Model Checking...
su(1,2) Algebraic Structure of XYZ Antiferromagnetic Model in Linear Spin-Wave Frame
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
Anisotropic correlated electron model associated with the Temperley-Lieb algebra
Foerster, Angela; Links, Jon; Roditi, Itzhak
1997-12-01
We present and anisotropic correlated electron model on a periodic lattice, constructed from an R-matrix associated with the Temperley-Lieb algebra. By modification of the coupling of the first and last sites we obtain a model with quantum algebra invariance. (author)
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
Automatic generation of Fortran programs for algebraic simulation models
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
Phases and phase transitions in the algebraic microscopic shell model
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.
A set for relational reasoning: Facilitation of algebraic modeling by a fraction task.
DeWolf, Melissa; Bassok, Miriam; Holyoak, Keith J
2016-12-01
Recent work has identified correlations between early mastery of fractions and later math achievement, especially in algebra. However, causal connections between aspects of reasoning with fractions and improved algebra performance have yet to be established. The current study investigated whether relational reasoning with fractions facilitates subsequent algebraic reasoning using both pre-algebra students and adult college students. Participants were first given either a relational reasoning fractions task or a fraction algebra procedures control task. Then, all participants solved word problems and constructed algebraic equations in either multiplication or division format. The word problems and the equation construction tasks involved simple multiplicative comparison statements such as "There are 4 times as many students as teachers in a classroom." Performance on the algebraic equation construction task was enhanced for participants who had previously completed the relational fractions task compared with those who completed the fraction algebra procedures task. This finding suggests that relational reasoning with fractions can establish a relational set that promotes students' tendency to model relations using algebraic expressions. Copyright © 2016 Elsevier Inc. All rights reserved.
Model Checking of a Diabetes-Cancer Model
Gong, Haijun; Zuliani, Paolo; Clarke, Edmund M.
2011-06-01
Accumulating evidence suggests that cancer incidence might be associated with diabetes mellitus, especially Type II diabetes which is characterized by hyperinsulinaemia, hyperglycaemia, obesity, and overexpression of multiple WNT pathway components. These diabetes risk factors can activate a number of signaling pathways that are important in the development of different cancers. To systematically understand the signaling components that link diabetes and cancer risk, we have constructed a single-cell, Boolean network model by integrating the signaling pathways that are influenced by these risk factors to study insulin resistance, cancer cell proliferation and apoptosis. Then, we introduce and apply the Symbolic Model Verifier (SMV), a formal verification tool, to qualitatively study some temporal logic properties of our diabetes-cancer model. The verification results show that the diabetes risk factors might not increase cancer risk in normal cells, but they will promote cell proliferation if the cell is in a precancerous or cancerous stage characterized by losses of the tumor-suppressor proteins ARF and INK4a.
Independence-Based Optimization of Epistemic Model Checking
2017-02-22
favourite restaurant. Their waiter informs them that arrangements have been made with the maitre d’hotel for the bill to be paid anonymously. One of the...counter. However, some extensions will be more managable , e.g., one that requires conditionals and loops to be balanced in their timing (a...algebras. In Algo- rithms for Uncertainty and Defeasible Reasoning: Handbook of Defeasible Reasoning and Uncertainty Management Systems, volume 5
The algebra of non-local charges in non-linear sigma models
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
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.)
Modeling nanoparticle uptake and intracellular distribution using stochastic process algebras
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
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.
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
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 pa...
WCET Analysis of ARM Processors using Real-Time Model Checking
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....
Off-critical W∞ and Virasoro algebras as dynamical symmetries of the integrable models
Sotkov, G.; Stanishkov, M.
1993-01-01
An infinite set of new non commuting conserved charges in a specific class of perturbed CFT's is founded and a criterion for their existence is presented. They appear to be higher momenta of the already known commuting conserved currents. The algebra they close consists of two non commuting W ∞ algebras. Various Virasoro subalgebras of the full symmetry algebra are founded. It is shown on the examples of the perturbed Ising and Potts models that one of them plays an essential role in the computation of the correlation functions of the fields of the theory. (author)
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.
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'…
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
Checking the new IRI model: The bottomside B parameters
Mosert, M.; Buresova, D.; Miro, G.; Lazo, B.; Ezquer, R.
2003-01-01
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. (author)
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.
Development of a butterfly check valve model under natural circulation conditions
Rao, Yuxian; Yu, Lei; Fu, Shengwei; Zhang, Fan
2015-01-01
Highlights: • Bases on Lim’s swing check valve model, a butterfly check valve model was developed. • The method to quantify the friction torque T F in Li’s model was corrected. • The developed model was implemented into the RELAP5 code and verified. - Abstract: A butterfly check valve is widely used to prevent a reverse flow in the pipe lines of a marine nuclear power plant. Under some conditions, the natural circulation conditions in particular, the fluid velocity through the butterfly check valve might become too low to hold the valve disk fully open, thereby the flow resistance of the butterfly check valve varies with the location of the valve disk and as a result the fluid flow is significantly affected by the dynamic motion of the valve disk. Simulation of a pipe line that includes some butterfly check valves, especially under natural circulation conditions, is thus complicated. This paper focuses on the development of a butterfly check valve model to enhance the capability of the thermal–hydraulic system code and the developed model is implemented into the RELAP5 code. Both steady-state calculations and transient calculations were carried out for the primary loop system of a marine nuclear power plant and the calculation results are compared with the experimental data for verification purpose. The simulation results show an agreement with the experimental data
Integrating model checking with HiP-HOPS in model-based safety analysis
Sharvia, Septavera; Papadopoulos, Yiannis
2015-01-01
The ability to perform an effective and robust safety analysis on the design of modern safety–critical systems is crucial. Model-based safety analysis (MBSA) has been introduced in recent years to support the assessment of complex system design by focusing on the system model as the central artefact, and by automating the synthesis and analysis of failure-extended models. Model checking and failure logic synthesis and analysis (FLSA) are two prominent MBSA paradigms. Extensive research has placed emphasis on the development of these techniques, but discussion on their integration remains limited. In this paper, we propose a technique in which model checking and Hierarchically Performed Hazard Origin and Propagation Studies (HiP-HOPS) – an advanced FLSA technique – can be applied synergistically with benefit for the MBSA process. The application of the technique is illustrated through an example of a brake-by-wire system. - Highlights: • We propose technique to integrate HiP-HOPS and model checking. • State machines can be systematically constructed from HiP-HOPS. • The strengths of different MBSA techniques are combined. • Demonstrated through modeling and analysis of brake-by-wire system. • Root cause analysis is automated and system dynamic behaviors analyzed and verified
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...
Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking
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.
PVeStA: A Parallel Statistical Model Checking and Quantitative Analysis Tool
AlTurki, Musab; Meseguer, José
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
Algebraic Specifications, Higher-order Types and Set-theoretic Models
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......In most algebraic specification frameworks, the type system is restricted to sorts, subsorts, and first-order function types. This is in marked contrast to the so-called model-oriented frameworks, which provide higer-order types, interpreted set-theoretically as Cartesian products, function spaces...... set-theoretic models are considered, and conditions are given for the existence of initial reduct's of such models. Algebraic specifications for various set-theoretic concepts are considered....
R. Lestari; S. Linuwih
2012-01-01
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...
Phase Two Feasibility Study for Software Safety Requirements Analysis Using Model Checking
Turgeon, Gregory; Price, Petra
2010-01-01
A feasibility study was performed on a representative aerospace system to determine the following: (1) the benefits and limitations to using SCADE , a commercially available tool for model checking, in comparison to using a proprietary tool that was studied previously [1] and (2) metrics for performing the model checking and for assessing the findings. This study was performed independently of the development task by a group unfamiliar with the system, providing a fresh, external perspective free from development bias.
Model-checking statistique pour la vérification de véhicules autonomes
Barbot , Benoît; Bérard , Béatrice; Duplouy , Yann; Haddad , Serge
2017-01-01
National audience; We present an application of statistical model-checking to the verification of an autonomous vehicle controller. Our goal is to check safety properties in various traffic situations. More specifically, we focus on a traffic jam situation. The controller is specified by a C++ program. Using sensors, it registers positions and velocities of nearby vehicles and modifies the position and velocity of the controlled vehicle to avoid collisions. We model the environment using a st...
Possible check of the QCD parton model in semiinclusive μ- -production of tau/psi-meson
Bagdasaryan, I.A.; Grigoryan, S.G.; Yesaibegyan, S.V.
1982-01-01
The process of tau/psi meson production in the semi-inclusive μN → μ+tau/psi+X interaction is discussed. It is shown that the measurement of azimuthal asymmetry in semi-inclusive production of tau/psi can serve as a good test for the check of the QCD parton model. An additional method of the check of distribution gluon functions in photon-gluon fusion model is suggested
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.
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.)
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.)
Mathematical modelling in engineering: A proposal to introduce linear algebra concepts
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.
On Diagnostic Checking of Vector ARMA-GARCH Models with Gaussian and Student-t Innovations
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.
Model based feasibility study on bidirectional check valves in wave energy converters
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....../Off and bidirectional check valves. Based on the analysis it is found that the energy production may be slightly improved by using bidirectional check valves as compared to on/off valves, due to a decrease in switching losses. Furthermore a reduction in high flow peaks are realised. The downside being increased...
Abstract algebra for physicists
Zeman, J.
1975-06-01
Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)
Closing open SDL-systems for model checking with DTSpin
N. Ioustinova (Natalia); N. Sidorova; M. Steffen
2002-01-01
textabstractModel checkers like Spin can handle closed reactive systems, only. Thus to handle open systems, in particular when using assume-guarantee reasoning, we need to be able to close (sub-)systems, which is commonly done by adding an environment process. For models with asynchronous
Modelling and Analysis of Smart Grid: A Stochastic Model Checking Case Study
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
Yuksel, Ender; Nielson, Hanne Riis; Nielson, Flemming
2014-01-01
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...... 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...... consumption.We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker....
Model-Checking Real-Time Control Programs
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...
Constraint Lie algebra and local physical Hamiltonian for a generic 2D dilatonic model
Corichi, Alejandro; Karami, Asieh; Rastgoo, Saeed; Vukašinac, Tatjana
2016-01-01
We consider a class of two-dimensional dilatonic models, and revisit them from the perspective of a new set of ‘polar type’ variables. These are motivated by recently defined variables within the spherically symmetric sector of 4D general relativity. We show that for a large class of dilatonic models, including the case with matter, one can perform a series of canonical transformations in such a way that the Poisson algebra of the constraints becomes a Lie algebra. Furthermore, we construct Dirac observables and a reduced Hamiltonian that accounts for the time evolution of the system. (paper)
Abstraction and Model Checking in the PEPA Plug-in for Eclipse
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...
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…
The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems
Ng, Swee Fong; Lee, Kerry
2009-01-01
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…
Algebraic approach to q-deformed supersymmetric variants of the Hubbard model with pair hoppings
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)
Hussain, Faraz; Jha, Sumit K; Jha, Susmit; Langmead, Christopher J
2014-01-01
Stochastic models are increasingly used to study the behaviour of biochemical systems. While the structure of such models is often readily available from first principles, unknown quantitative features of the model are incorporated into the model as parameters. Algorithmic discovery of parameter values from experimentally observed facts remains a challenge for the computational systems biology community. We present a new parameter discovery algorithm that uses simulated annealing, sequential hypothesis testing, and statistical model checking to learn the parameters in a stochastic model. We apply our technique to a model of glucose and insulin metabolism used for in-silico validation of artificial pancreata and demonstrate its effectiveness by developing parallel CUDA-based implementation for parameter synthesis in this model.
COMPREHENSIVE CHECK MEASUREMENT OF KEY PARAMETERS ON MODEL BELT CONVEYOR
Vlastimil MONI
2013-07-01
Full Text Available Complex measurements of characteristic parameters realised on a long distance model belt conveyor are described. The main objective was to complete and combine the regular measurements of electric power on drives of belt conveyors operated in Czech opencast mines with measurements of other physical quantities and to gain by this way an image of their mutual relations and relations of quantities derived from them. The paper includes a short description and results of the measurements on an experimental model conveyor with a closed material transport way.
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.
Simulation-Based Model Checking for Nondeterministic Systems and Rare Events
2016-03-24
rounds of Monte Carlo sampling and Reinforcement Learning to improve the policy for nondeterminic choices with respect to satisfying a Bounded Linear ...computations for evaluating elementary functions in the Embedded GNU C Library [11]. For instance, the sine function can return values larger than 1053...Joint International Work- shop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification 9 Final Report, March 14, 2016
Algebraic partial Boolean algebras
Smith, Derek
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 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 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 8
Dynamic Delayed Duplicate Detection for External Memory Model Checking
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...
Model Checking Geographically Distributed Interlocking Systems Using UMC
Fantechi, Alessandro; Haxthausen, Anne Elisabeth; Nielsen, Michel Bøje Randahl
2017-01-01
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...
Hypersonic: Model Analysis and Checking in the Cloud
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...
CSL model checking of deterministic and stochastic Petri nets
Martinez Verdugo, J.M.; Haverkort, Boudewijn R.H.M.; German, R.; Heindl, A.
2006-01-01
Deterministic and Stochastic Petri Nets (DSPNs) are a widely used high-level formalism for modeling discrete-event systems where events may occur either without consuming time, after a deterministic time, or after an exponentially distributed time. The underlying process dened by DSPNs, under
Dynamic Delayed Duplicate Detection for External Memory Model Checking
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 typica...... significantly better than some previously published algorithms....
UML Statechart Fault Tree Generation By Model Checking
Herbert, Luke Thomas; Herbert-Hansen, Zaza Nadja Lee
of the popular Business Process Modelling and Nota-tion (BPMN) language. To capture uncertainty and unreliability in workflows, we extend this formalism with probabilistic non-deterministic branching.We present an algorithm that allows for exhaustive gen-eration of possible error states that could arise in ex...
Model checking the FlexRay startup phase
Cranen, S.
2012-01-01
This report describes a discrete-time model of the startup phase of a FlexRay network. The startup behaviour of this network is analysed in the presence of several faults. It is shown that in certain cases a faulty node can prevent the network from communicating altogether. One previously unknown
Efficient Proof Engines for Bounded Model Checking of Hybrid Systems
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...
Testing Model with "Check Technique" for Physics Education
Demir, Cihat
2016-01-01
As the number, date and form of the written tests are structured and teacher-oriented, it is considered that it creates fear and anxiety among the students. It has been found necessary and important to form a testing model which will keep the students away from the test anxiety and allows them to learn only about the lesson. For this study,…
Modeling tides and vertical tidal mixing: A reality check
Robertson, Robin
2010-01-01
Recently, there has been a great interest in the tidal contribution to vertical mixing in the ocean. In models, vertical mixing is estimated using parameterization of the sub-grid scale processes. Estimates of the vertical mixing varied widely depending on which vertical mixing parameterization was used. This study investigated the performance of ten different vertical mixing parameterizations in a terrain-following ocean model when simulating internal tides. The vertical mixing parameterization was found to have minor effects on the velocity fields at the tidal frequencies, but large effects on the estimates of vertical diffusivity of temperature. Although there was no definitive best performer for the vertical mixing parameterization, several parameterizations were eliminated based on comparison of the vertical diffusivity estimates with observations. The best performers were the new generic coefficients for the generic length scale schemes and Mellor-Yamada's 2.5 level closure scheme.
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.
Model Checking and Model-based Testing in the Railway Domain
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...... with good test strength are explained. Interlocking systems represent just one class of many others, where concrete system instances are created from generic representations, using configuration data for determining the behaviour of the instances. We explain how the systematic transition from generic...... to concrete instances in the development path is complemented by associated transitions in the verification and testing paths....
Checking Fine and Gray subdistribution hazards model with cumulative sums of residuals
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...... estimation, and only a limited contribution has been made to check the model assumptions. In this paper, we present a class of analytical methods and graphical approaches for checking the assumptions of Fine and Gray’s model. The proposed goodness-of-fit test procedures are based on the cumulative sums...
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.
Algebra of orthofermions and equivalence of their thermodynamics to the infinite U Hubbard model
Kishore, R.; Mishra, A.K.
2006-01-01
The equivalence of thermodynamics of independent orthofermions to the infinite U Hubbard model, shown earlier for the one-dimensional infinite lattice, has been extended to a finite system of two lattice sites. Regarding the algebra of orthofermions, the algebraic expressions for the number operator for a given spin and the spin raising (lowering) operators in the form of infinite series are rearranged in such a way that the ith term, having the form of an infinite series, of the number (spin raising (lowering)) operator represents the number (spin raising (lowering)) operator at the ith lattice site
Little strings, quasi-topological sigma model on loop group, and toroidal Lie algebras
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.
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...
Model-Checking Driven Design of QoS-Based Routing Protocol for Wireless Sensor Networks
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 Real Time Java Using Java PathFinder
Lindstrom, Gary; Mehlitz, Peter C.; Visser, Willem
2005-01-01
The Real Time Specification for Java (RTSJ) is an augmentation of Java for real time applications of various degrees of hardness. The central features of RTSJ are real time threads; user defined schedulers; asynchronous events, handlers, and control transfers; a priority inheritance based default scheduler; non-heap memory areas such as immortal and scoped, and non-heap real time threads whose execution is not impeded by garbage collection. The Robust Software Systems group at NASA Ames Research Center has JAVA PATHFINDER (JPF) under development, a Java model checker. JPF at its core is a state exploring JVM which can examine alternative paths in a Java program (e.g., via backtracking) by trying all nondeterministic choices, including thread scheduling order. This paper describes our implementation of an RTSJ profile (subset) in JPF, including requirements, design decisions, and current implementation status. Two examples are analyzed: jobs on a multiprogramming operating system, and a complex resource contention example involving autonomous vehicles crossing an intersection. The utility of JPF in finding logic and timing errors is illustrated, and the remaining challenges in supporting all of RTSJ are assessed.
ADAM: analysis of discrete models of biological systems using computer algebra.
Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2011-07-20
Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web
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…
Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis
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
The Virasoro algebra in integrable hierarchies and the method of matrix models
Semikhatov, A.M.
1992-01-01
The action of the Virasoro algebra on hierarchies of nonlinear integrable equations, and also the structure and consequences of Virasoro constraints on these hierarchies, are studied. It is proposed that a broad class of hierarchies, restricted by Virasoro constraints, can be defined in terms of dressing operators hidden in the structure of integrable systems. The Virasoro-algebra representation constructed on the dressing operators displays a number of analogies with structures in conformal field theory. The formulation of the Virasoro constraints that stems from this representation makes it possible to translate into the language of integrable systems a number of concepts from the method of the 'matrix models' that describe nonperturbative quantum gravity, and, in particular, to realize a 'hierarchical' version of the double scaling limit. From the Virasoro constraints written in terms of the dressing operators generalized loop equations are derived, and this makes it possible to do calculations on a reconstruction of the field-theoretical description. The reduction of the Kadomtsev-Petviashvili (KP) hierarchy, subject to Virasoro constraints, to generalized Korteweg-deVries (KdV) hierarchies is implemented, and the corresponding representation of the Virasoro algebra on these hierarchies is found both in the language of scalar differential operators and in the matrix formalism of Drinfel'd and Sokolov. The string equation in the matrix formalism does not replicate the structure of the scalar string equation. The symmetry algebras of the KP and N-KdV hierarchies restricted by Virasoro constraints are calculated: A relationship is established with algebras from the family W ∞ (J) of infinite W-algebras
Bounded Model Checking and Inductive Verification of Hybrid Discrete-Continuous Systems
Becker, Bernd; Behle, Markus; Eisenbrand, Fritz
2004-01-01
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 veri...
Lahtinen, J.; Bjoerkman, K.; Valkonen, J.; Frits, J.; Niemelae, I.
2010-12-01
Digital instrumentation and control (I and C) systems containing programmable logic controllers are challenging to verify. They enable complicated control functions and the state spaces (number of distinct values of inputs, outputs and internal memory) of the designs easily become too large for comprehensive manual inspection. Model checking is a formal method that can be used for verifying that systems have been correctly designed. A number of efficient model checking systems are available which provide analysis tools that are able to determine automatically whether a given state machine model satisfies the desired safety properties. The practical case analysed in this research project is called an 'emergency diesel generator control system' and its purpose is to provide reserve power to critical devices and computers that must be available without interruption. This report describes 1) the development of a compositional approach for checking the models in large system designs, 2) the development of a modular model checking approach for modelling function block diagrams with the Uppaal model checker and 3) the experience of utilising the new modelling approaches in practice. (orig.)
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
Variability-Specific Abstraction Refinement for Family-Based Model Checking
Dimovski, Aleksandar; Wasowski, Andrzej
2017-01-01
and property, while the number of possible scenarios is very large. In this work, we present an automatic iterative abstraction refinement procedure for family-based model checking. We use Craig interpolation to refine abstract variational models based on the obtained spurious counterexamples (traces...
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
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
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.
Monitor-Based Statistical Model Checking for Weighted Metric Temporal Logic
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 with desi......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...
DiVinE-CUDA - A Tool for GPU Accelerated LTL Model Checking
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.
Automated parameter estimation for biological models using Bayesian statistical model checking.
Hussain, Faraz; Langmead, Christopher J; Mi, Qi; Dutta-Moscato, Joyeeta; Vodovotz, Yoram; Jha, Sumit K
2015-01-01
Probabilistic models have gained widespread acceptance in the systems biology community as a useful way to represent complex biological systems. Such models are developed using existing knowledge of the structure and dynamics of the system, experimental observations, and inferences drawn from statistical analysis of empirical data. A key bottleneck in building such models is that some system variables cannot be measured experimentally. These variables are incorporated into the model as numerical parameters. Determining values of these parameters that justify existing experiments and provide reliable predictions when model simulations are performed is a key research problem. Using an agent-based model of the dynamics of acute inflammation, we demonstrate a novel parameter estimation algorithm by discovering the amount and schedule of doses of bacterial lipopolysaccharide that guarantee a set of observed clinical outcomes with high probability. We synthesized values of twenty-eight unknown parameters such that the parameterized model instantiated with these parameter values satisfies four specifications describing the dynamic behavior of the model. We have developed a new algorithmic technique for discovering parameters in complex stochastic models of biological systems given behavioral specifications written in a formal mathematical logic. Our algorithm uses Bayesian model checking, sequential hypothesis testing, and stochastic optimization to automatically synthesize parameters of probabilistic biological models.
Temporal Precedence Checking for Switched Models and its Application to a Parallel Landing Protocol
Duggirala, Parasara Sridhar; Wang, Le; Mitra, Sayan; Viswanathan, Mahesh; Munoz, Cesar A.
2014-01-01
This paper presents an algorithm for checking temporal precedence properties of nonlinear switched systems. This class of properties subsume bounded safety and capture requirements about visiting a sequence of predicates within given time intervals. The algorithm handles nonlinear predicates that arise from dynamics-based predictions used in alerting protocols for state-of-the-art transportation systems. It is sound and complete for nonlinear switch systems that robustly satisfy the given property. The algorithm is implemented in the Compare Execute Check Engine (C2E2) using validated simulations. As a case study, a simplified model of an alerting system for closely spaced parallel runways is considered. The proposed approach is applied to this model to check safety properties of the alerting logic for different operating conditions such as initial velocities, bank angles, aircraft longitudinal separation, and runway separation.
The algebras of higher order currents of the fermionic Gross-Neveu model
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
Jongen, T.; Machiels, L.; Gatski, T. B.
1997-01-01
Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.
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.
Modeling and analysis of cell membrane systems with probabilistic model checking
2011-01-01
Background Recently there has been a growing interest in the application of Probabilistic Model Checking (PMC) for the formal specification of biological systems. PMC is able to exhaustively explore all states of a stochastic model and can provide valuable insight into its behavior which are more difficult to see using only traditional methods for system analysis such as deterministic and stochastic simulation. In this work we propose a stochastic modeling for the description and analysis of sodium-potassium exchange pump. The sodium-potassium pump is a membrane transport system presents in all animal cell and capable of moving sodium and potassium ions against their concentration gradient. Results We present a quantitative formal specification of the pump mechanism in the PRISM language, taking into consideration a discrete chemistry approach and the Law of Mass Action aspects. We also present an analysis of the system using quantitative properties in order to verify the pump reversibility and understand the pump behavior using trend labels for the transition rates of the pump reactions. Conclusions Probabilistic model checking can be used along with other well established approaches such as simulation and differential equations to better understand pump behavior. Using PMC we can determine if specific events happen such as the potassium outside the cell ends in all model traces. We can also have a more detailed perspective on its behavior such as determining its reversibility and why its normal operation becomes slow over time. This knowledge can be used to direct experimental research and make it more efficient, leading to faster and more accurate scientific discoveries. PMID:22369714
Lectures on algebraic statistics
Drton, Mathias; Sullivant, Seth
2009-01-01
How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.
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
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.
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
Query Language for Location-Based Services: A Model Checking Approach
Hoareau, Christian; Satoh, Ichiro
We present a model checking approach to the rationale, implementation, and applications of a query language for location-based services. Such query mechanisms are necessary so that users, objects, and/or services can effectively benefit from the location-awareness of their surrounding environment. The underlying data model is founded on a symbolic model of space organized in a tree structure. Once extended to a semantic model for modal logic, we regard location query processing as a model checking problem, and thus define location queries as hybrid logicbased formulas. Our approach is unique to existing research because it explores the connection between location models and query processing in ubiquitous computing systems, relies on a sound theoretical basis, and provides modal logic-based query mechanisms for expressive searches over a decentralized data structure. A prototype implementation is also presented and will be discussed.
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.
Specification and Generation of Environment for Model Checking of Software Components
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
Efficient model checking for duration calculus based on branching-time approximations
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...
Combining Decision Diagrams and SAT Procedures for Efficient Symbolic Model Checking
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 algorithm...
A practical approach to model checking Duration Calculus using Presburger Arithmetic
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...... limits of the approach are illustrated by a family of examples....
Local Model Checking of Weighted CTL with Upper-Bound Constraints
Jensen, Jonas Finnemann; Larsen, Kim Guldstrand; Srba, Jiri
2013-01-01
We present a symbolic extension of dependency graphs by Liu and Smolka in order to model-check weighted Kripke structures against the logic CTL with upper-bound weight constraints. Our extension introduces a new type of edges into dependency graphs and lifts the computation of fixed-points from...
Pârvu, Ovidiu; 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
Virasoro algebra action on integrable hierarchies and Virasoro contraints in matrix models
Semikhatov, A.M.
1991-01-01
The action of the Virasoro algebra on integrable hierarchies of non-linear equations and on related objects ('Schroedinger' differential operators) is investigated. The method consists in pushing forward the Virasoro action to the wave function of a hierarchy, and then reconstructing its action on the dressing and Lax operators. This formulation allows one to observe a number of suggestive similarities between the structures involved in the description of the Virasoro algebra on the hierarchies and the structure of conformal field theory on the world-sheet. This includes, in particular, an 'off-shell' hierarchy version of operator products and of the Cauchy kernel. In relation to matrix models, which have been observed to be effectively described by integrable hierarchies subjected to Virasoro constraints, I propose to define general Virasoro-constrained hierarchies also in terms of dressing operators, by certain equations which carry the information of the hierarchy and the Virasoro algebra simultaneously and which suggest an interpretation as operator versions of recursion/loop equations in topological theories. These same equations provide a relation with integrable hierarchies with quantized spectral parameter introduced recently. The formulation in terms of dressing operators allows a scaling (continuum limit) of discrete (i.e. lattice) hierarchies with the Virasoro constraints into 'continuous' Virasoro-constrained hierarchies. In particular, the KP hierarchy subjected to the Virasoro constraints is recovered as a scaling limit of the Virasoro-constrained Toda hierarchy. The dressing operator method also makes is straightforward to identify the full symmetry algebra of Virasoro-constrained hierarchies, which is related to the family of W ∞ (J) algebras introduced recently. (orig./HS)
Entanglement in a model for Hawking radiation: An application of quadratic algebras
Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.
2013-01-01
Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: ► We examine a toy model for Hawking radiation with quantized black hole modes. ► We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. ► We study the “Dicke Superradiance” in black hole radiation using quadratically deformed su(2) algebras. ► We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.
An algebraic stress/flux model for two-phase turbulent flow
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
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...
A Csup(*)-algebra approach to the Schwinger model
Carey, A.L.; Hurst, C.A.
1981-01-01
If cutoffs are introduced then existing results in the literature show that the Schwinger model is dynamically equivalent to a boson model with quadratic Hamiltonian. However, the process of quantising the Schwinger model destroys local gauge invariance. Gauge invariance is restored by the addition of a counterterm, which may be seen as a finite renormalisation, whereupon the Schwinger model becomes dynamically equivalent to a linear boson gauge theory. This linear model is exactly soluble. We find that different treatments of the supplementary (i.e. Lorentz) condition lead to boson models with rather different properties. We choose one model and construct, from the gauge invariant subalgebra, a class of inequivalent charge sectors. We construct sectors which coincide with those found by Lowenstein and Swieca for the Schwinger model. A reconstruction of the Hilbert space on which the Schwinger model exists is described and fermion operators on this space are defined. (orig.)
Exact boson mappings for nuclear neutron (proton) shell-model algebras having SU(3) subalgebras
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
Algebraic models for the hierarchy structure of evolution equations at small x
Rembiesa, P.; Stasto, A.M.
2005-01-01
We explore several models of QCD evolution equations simplified by considering only the rapidity dependence of dipole scattering amplitudes, while provisionally neglecting their dependence on transverse coordinates. Our main focus is on the equations that include the processes of pomeron splittings. We examine the algebraic structures of the governing equation hierarchies, as well as the asymptotic behavior of their solutions in the large-rapidity limit
On the algebraic structure of self-dual gauge fields and sigma models
Bais, F.A.; Sasaki, R.
1983-01-01
An extensive and detailed analysis of self-dual gauge fields, in particular with axial symmetry, is presented, culminating in a purely algebraic procedure to generate solutions. The method which is particularly suited for the construction of multimonopole solutions for a theory with arbitrary G, is also applicable to a wide class of non-linear sigma models. The relevant symmetries as well as the associated linear problems which underly the exact solubility of the problem, are constructed and discussed in detail. (orig.)
Applications of the Local Algebras of Vector Fields to the Modelling of Physical Phenomena
Bayak, Igor V.
2015-01-01
In this paper we discuss the local algebras of linear vector fields that can be used in the mathematical modelling of physical space by building the dynamical flows of vector fields on eight-dimensional cylindrical or toroidal manifolds. It is shown that the topological features of the vector fields obey the Dirac equation when moving freely within the surface of a pseudo-sphere in the eight-dimensional pseudo-Euclidean space.
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
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.
Baek, Seong Gu; Park, Seung O.
2003-01-01
This paper provides the assessment of prediction performance of explicit algebraic stress and heat-flux models under conditions of mixed convective gas flows in a strongly-heated vertical tube. Two explicit algebraic stress models and four algebraic heat-flux models are selected for assessment. Eight combinations of explicit algebraic stress and heat-flux models are used in predicting the flows experimentally studied by Shehata and McEligot (IJHMT 41(1998) p.4333) in which property variation was significant. Among the various model combinations, the Wallin and Johansson (JFM 403(2000) p. 89) explicit algebraic stress model-Abe, Kondo, and Nagano (IJHFF 17(1996) p. 228) algebraic heat-flux model combination is found to perform best. We also found that the dimensionless wall distance y + should be calculated based on the local property rather than the property at the wall for property-variation flows. When the buoyancy or the property variation effects are so strong that the flow may relaminarize, the choice of the basic platform two-equation model is a most important factor in improving the predictions
Formal verification of dynamic hybrid systems: a NuSMV-based model checking approach
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.
Requeno, José Ignacio; Colom, José Manuel
2014-12-01
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.
Vertex algebras and algebraic curves
Frenkel, Edward
2004-01-01
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book co...
Tadesse
In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra of Xu (1993) and further we prove that it is a regular Autometrized. Algebra. Further we remark that the binary operation → on lattice implicative algebra can never be associative. Key words: Implicative ...
A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models
Kawaguchi, Io; Yoshida, Kentaroh [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
2014-06-01
We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
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
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
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2005-01-01
We reexpress the quantum Calogero-Sutherland model for the Lie algebra E 7 and the particular value of the coupling constant κ=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra
Algebraic Structure of tt * Equations for Calabi-Yau Sigma Models
Alim, Murad
2017-08-01
The tt * equations define a flat connection on the moduli spaces of {2d, \\mathcal{N}=2} quantum field theories. For conformal theories with c = 3 d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. We show that the non-holomorphic content of the tt * equations, restricted to the conformal directions, in the cases d = 1, 2, 3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space. This space parameterizes a freedom in choosing representatives of the chiral ring while preserving a constant topological metric. Geometrically, the freedom corresponds to a choice of forms on the target space respecting the Hodge filtration and having a constant pairing. Linear combinations of vector fields on that space are identified with the generators of a Lie algebra. This Lie algebra replaces the non-holomorphic derivatives of tt * and provides these with a finer and algebraic meaning. For sigma models into lattice polarized K3 manifolds, the differential ring of special functions on the moduli space is constructed, extending known structures for d = 1 and 3. The generators of the differential rings of special functions are given by quasi-modular forms for d = 1 and their generalizations in d = 2, 3. Some explicit examples are worked out including the case of the mirror of the quartic in {\\mathbbm{P}^3}, where due to further algebraic constraints, the differential ring coincides with quasi modular forms.
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
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.
HyLTL: a temporal logic for model checking hybrid systems
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.
MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable
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.
Villarreal, Rafael
2015-01-01
The book stresses the interplay between several areas of pure and applied mathematics, emphasizing the central role of monomial algebras. It unifies the classical results of commutative algebra with central results and notions from graph theory, combinatorics, linear algebra, integer programming, and combinatorial optimization. The book introduces various methods to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings and blowup algebra-emphasizing square free quadratics, hypergraph clutters, and effective computational methods.
Optlang: An algebraic modeling language for mathematical optimization
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...
Analysis of DGNB-DK criteria for BIM-based Model Checking automatization
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)....
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...
Thin-layer approximation and algebraic model for separated turbulent flows
Baldwin, B.; Lomax, H.
1978-01-01
An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.
The large N=4 superconformal W∞ algebra
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.
Model checking software for phylogenetic trees using distribution and database methods
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
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.
A rule-based approach to model checking of UML state machines
Grobelna, Iwona; Grobelny, Michał; Stefanowicz, Łukasz
2016-12-01
In the paper a new approach to formal verification of control process specification expressed by means of UML state machines in version 2.x is proposed. In contrast to other approaches from the literature, we use the abstract and universal rule-based logical model suitable both for model checking (using the nuXmv model checker), but also for logical synthesis in form of rapid prototyping. Hence, a prototype implementation in hardware description language VHDL can be obtained that fully reflects the primary, already formally verified specification in form of UML state machines. Presented approach allows to increase the assurance that implemented system meets the user-defined requirements.
Model Checking Verification and Validation at JPL and the NASA Fairmont IV and V Facility
Schneider, Frank; Easterbrook, Steve; Callahan, Jack; Montgomery, Todd
1999-01-01
We show how a technology transfer effort was carried out. The successful use of model checking on a pilot JPL flight project demonstrates the usefulness and the efficacy of the approach. The pilot project was used to model a complex spacecraft controller. Software design and implementation validation were carried out successfully. To suggest future applications we also show how the implementation validation step can be automated. The effort was followed by the formal introduction of the modeling technique as a part of the JPL Quality Assurance process.
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2003-01-01
We express the Hamiltonian of the quantum trigonometric Calogero-Sutherland model related to the Lie algebra D 4 in terms of a set of Weyl-invariant variables, namely, the characters of the fundamental representations of the Lie algebra. This parametrization allows us to solve for the energy eigenfunctions of the theory and to study properties of the system of orthogonal polynomials associated with them such as recurrence relations and generating functions
Jaynes-Cummings model and the deformed-oscillator algebra
Crnugelj, J.; Martinis, M.; Mikuta-Martinis, V.
1994-01-01
We study the time evolution of the deformed Jaynes-Cummings model (DJCM). It is shown that the standard JCM and its recent non-linear generalizations involving the intensity-dependent coupling and/or the multiphoton coupling are only particular cases of the DJCM. The time evolution of the mean phonon number and the population inversion are evaluated. A special case of the q-deformed JCM is analyzed explicitly. The long time quasi-periodic revival effects of the q-deformed JCM are observed for q∼1 and an initially large mean photon number. For other values of the deformation parameter q we observe chaotic-like behaviour of the population inversion. Photons are assumed to be initially in the deformed coherent state. ((orig.))
Polishchuk, Alexander
2005-01-01
Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.
Algebraic equations for the exceptional eigenspectrum of the generalized Rabi model
Li, Zi-Min; Batchelor, Murray T
2015-01-01
We obtain the exceptional part of the eigenspectrum of the generalized Rabi model, also known as the driven Rabi model, in terms of the roots of a set of algebraic equations. This approach provides a product form for the wavefunction components and allows an explicit connection with recent results obtained for the wavefunction in terms of truncated confluent Heun functions. Other approaches are also compared. For particular parameter values the exceptional part of the eigenspectrum consists of doubly degenerate crossing points. We give a proof for the number of roots of the constraint polynomials and discuss the number of crossing points. (paper)
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.
Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard
2014-06-26
A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for
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).
Orantin, N.
2007-09-01
The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and arrangement of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that the fine tuning of the parameters ensures that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct. (author)
Special set linear algebra and special set fuzzy linear algebra
Kandasamy, W. B. Vasantha; Smarandache, Florentin; Ilanthenral, K.
2009-01-01
The authors in this book introduce the notion of special set linear algebra and special set fuzzy Linear algebra, which is an extension of the notion set linear algebra and set fuzzy linear algebra. These concepts are best suited in the application of multi expert models and cryptology. This book has five chapters. In chapter one the basic concepts about set linear algebra is given in order to make this book a self contained one. The notion of special set linear algebra and their fuzzy analog...
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.)
Shafarevich, Igor Rostislavovich
2005-01-01
This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches
Using process algebra to develop predator-prey models of within-host parasite dynamics.
McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel
2013-07-21
As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system. Copyright © 2013 Elsevier Ltd. All rights reserved.
Contractions of quantum algebraic structures
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.)
Identification of control targets in Boolean molecular network models via computational algebra.
Murrugarra, David; Veliz-Cuba, Alan; Aguilar, Boris; Laubenbacher, Reinhard
2016-09-23
Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.
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.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
Cirilo António, N., E-mail: nantonio@math.ist.utl.pt [Centro de Análise Funcional e Aplicações, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Manojlović, N., E-mail: nmanoj@ualg.pt [Grupo de Física Matemática da Universidade de Lisboa, Av. Prof. Gama Pinto 2, PT-1649-003 Lisboa (Portugal); Departamento de Matemática, F.C.T., Universidade do Algarve, Campus de Gambelas, PT-8005-139 Faro (Portugal); Salom, I., E-mail: isalom@ipb.ac.rs [Institute of Physics, University of Belgrade, P.O. Box 57, 11080 Belgrade (Serbia)
2014-12-15
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.
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.
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 U(1) invariant integrable models: Compact and non-compact applications
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.
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
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.
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.
MODELING IN MAPLE AS THE RESEARCHING MEANS OF FUNDAMENTAL CONCEPTS AND PROCEDURES IN LINEAR ALGEBRA
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
Combining Static Model Checking with Dynamic Enforcement Using the Statecall Policy Language
Madhavapeddy, Anil
Internet protocols encapsulate a significant amount of state, making implementing the host software complex. In this paper, we define the Statecall Policy Language (SPL) which provides a usable middle ground between ad-hoc coding and formal reasoning. It enables programmers to embed automata in their code which can be statically model-checked using SPIN and dynamically enforced. The performance overheads are minimal, and the automata also provide higher-level debugging capabilities. We also describe some practical uses of SPL by describing the automata used in an SSH server written entirely in OCaml/SPL.
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.
Misbah Razzaq
Full Text Available Internet worms are analogous to biological viruses since they can infect a host and have the ability to propagate through a chosen medium. To prevent the spread of a worm or to grasp how to regulate a prevailing worm, compartmental models are commonly used as a means to examine and understand the patterns and mechanisms of a worm spread. However, one of the greatest challenge is to produce methods to verify and validate the behavioural properties of a compartmental model. This is why in this study we suggest a framework based on Petri Nets and Model Checking through which we can meticulously examine and validate these models. We investigate Susceptible-Exposed-Infectious-Recovered (SEIR model and propose a new model Susceptible-Exposed-Infectious-Recovered-Delayed-Quarantined (Susceptible/Recovered (SEIDQR(S/I along with hybrid quarantine strategy, which is then constructed and analysed using Stochastic Petri Nets and Continuous Time Markov Chain. The analysis shows that the hybrid quarantine strategy is extremely effective in reducing the risk of propagating the worm. Through Model Checking, we gained insight into the functionality of compartmental models. Model Checking results validate simulation ones well, which fully support the proposed framework.
The quantum Rabi model and Lie algebra representations of sl2
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)
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 Integrated Approach of Model checking and Temporal Fault Tree for System Safety Analysis
Koh, Kwang Yong; Seong, Poong Hyun [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of)
2009-10-15
Digitalization of instruments and control systems in nuclear power plants offers the potential to improve plant safety and reliability through features such as increased hardware reliability and stability, and improved failure detection capability. It however makes the systems and their safety analysis more complex. Originally, safety analysis was applied to hardware system components and formal methods mainly to software. For software-controlled or digitalized systems, it is necessary to integrate both. Fault tree analysis (FTA) which has been one of the most widely used safety analysis technique in nuclear industry suffers from several drawbacks as described in. 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.
Jordan algebras versus C*- algebras
Stormer, E.
1976-01-01
The axiomatic formulation of quantum mechanics and the problem of whether the observables form self-adjoint operators on a Hilbert space, are discussed. The relation between C*- algebras and Jordan algebras is studied using spectral theory. (P.D.)
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
Process algebra and Markov chains
Brinksma, E.; Hermanns, H.; Brinksma, E.; Hermanns, H.; Katoen, J.P.
2001-01-01
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
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.
An Efficient Explicit-time Description Method for Timed Model Checking
Hao Wang
2009-12-01
Full Text Available Timed model checking, the method to formally verify real-time systems, is attracting increasing attention from both the model checking community and the real-time community. Explicit-time description methods verify real-time systems using general model constructs found in standard un-timed model checkers. Lamport proposed an explicit-time description method using a clock-ticking process (Tick to simulate the passage of time together with a group of global variables to model time requirements. Two methods, the Sync-based Explicit-time Description Method using rendezvous synchronization steps and the Semaphore-based Explicit-time Description Method using only one global variable were proposed; they both achieve better modularity than Lamport's method in modeling the real-time systems. In contrast to timed automata based model checkers like UPPAAL, explicit-time description methods can access and store the current time instant for future calculations necessary for many real-time systems, especially those with pre-emptive scheduling. However, the Tick process in the above three methods increments the time by one unit in each tick; the state spaces therefore grow relatively fast as the time parameters increase, a problem when the system's time period is relatively long. In this paper, we propose a more efficient method which enables the Tick process to leap multiple time units in one tick. Preliminary experimental results in a high performance computing environment show that this new method significantly reduces the state space and improves both the time and memory efficiency.
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.
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
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)
Equations of motion for a spectrum-generating algebra: Lipkin-Meshkov-Glick model
Rosensteel, G; Rowe, D J; Ho, S Y
2008-01-01
For a spectrum-generating Lie algebra, a generalized equations-of-motion scheme determines numerical values of excitation energies and algebra matrix elements. In the approach to the infinite particle number limit or, more generally, whenever the dimension of the quantum state space is very large, the equations-of-motion method may achieve results that are impractical to obtain by diagonalization of the Hamiltonian matrix. To test the method's effectiveness, we apply it to the well-known Lipkin-Meshkov-Glick (LMG) model to find its low-energy spectrum and associated generator matrix elements in the eigenenergy basis. When the dimension of the LMG representation space is 10 6 , computation time on a notebook computer is a few minutes. For a large particle number in the LMG model, the low-energy spectrum makes a quantum phase transition from a nondegenerate harmonic vibrator to a twofold degenerate harmonic oscillator. The equations-of-motion method computes critical exponents at the transition point
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson
2013-01-01
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 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.
Location Contexts of User Check-Ins to Model Urban Geo Life-Style Patterns
Hasan, Samiul; Ukkusuri, Satish V.
2015-01-01
Geo-location data from social media offers us information, in new ways, to understand people's attitudes and interests through their activity choices. In this paper, we explore the idea of inferring individual life-style patterns from activity-location choices revealed in social media. We present a model to understand life-style patterns using the contextual information (e. g. location categories) of user check-ins. Probabilistic topic models are developed to infer individual geo life-style patterns from two perspectives: i) to characterize the patterns of user interests to different types of places and ii) to characterize the patterns of user visits to different neighborhoods. The method is applied to a dataset of Foursquare check-ins of the users from New York City. The co-existence of several location contexts and the corresponding probabilities in a given pattern provide useful information about user interests and choices. It is found that geo life-style patterns have similar items—either nearby neighborhoods or similar location categories. The semantic and geographic proximity of the items in a pattern reflects the hidden regularity in user preferences and location choice behavior. PMID:25970430
McCaig, Chris; Begon, Mike; Norman, Rachel; Shankland, Carron
2011-03-01
Changing scale, for example, the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper, we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interactions.
The Einstein action for algebras of matrix valued functions - Toy models
Hajac, P.M.
1995-10-01
Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for M 4 (R). It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made. (author). 14 refs
The Einstein action for algebras of matrix valued functions - Toy models
Hajac, P M
1995-10-01
Two toy models are considered within the framework of noncommutative differential geometry. In the first one, the Einstein action of the Levi-Civita connection is computed for the algebra of matrix valued functions on a torus. It is shown that, assuming some constraints on the metric, this action splits into a classical-like, a quantum-like and a mixed term. In the second model, an analogue of the Palatini method of variation is applied to obtain critical points of the Einstein action functional for M{sub 4}(R). It is pointed out that a solution to the Palatini variational problem is not necessarily a Levi-Civita connection. In this model, no additional assumptions regarding metrics are made. (author). 14 refs.
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.
Finite automata over algebraic structures: models and some methods of analysis
Volodymyr V. Skobelev
2015-10-01
Full Text Available In this paper some results of research in two new trends of finite automata theory are presented. For understanding the value and the aim of these researches some short retrospective analysis of development of finite automata theory is given. The first trend deals with families of finite automata defined via recurrence relations on algebraic structures over finite rings. The problem of design of some algorithm that simulates with some accuracy any element of given family of automata is investigated. Some general scheme for design of families of hash functions defined by outputless automata is elaborated. Computational security of these families of hash functions is analyzed. Automata defined on varieties with some algebra are presented and their homomorphisms are characterized. Special case of these automata, namely automata on elliptic curves, are investigated in detail. The second trend deals with quantum automata. Languages accepted by some basic models of quantum automata under supposition that unitary operators associated with input alphabet commute each with the others are characterized.
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…
Klapisch, M.; Bar-Shalom, A.
1997-12-01
Busquet's RADIOM model for effective ionization temperature Tz is an appealing and simple way to introduce non LTE effects in hydrocodes. The authors report checking the validity of RADIOM in the optically thin case by comparison with two collisional radiative models, MICCRON (level-by-level) for C and Al and SCROLL (superconfiguration- by-superconfiguration) for Lu and Au. MICCRON is described in detail. The agreement between the average ion charge >ZBusquet is very good in most cases. There is however room for improvement when the departure from LTE is more pronounced for heavy atoms and for emissivity. Improvement appears possible because the concept of ionization temperature seems to hold in a broader range of parameters.
A Formal Approach for RT-DVS Algorithms Evaluation Based on Statistical Model Checking
Shengxin Dai
2015-01-01
Full Text Available Energy saving is a crucial concern in embedded real time systems. Many RT-DVS algorithms have been proposed to save energy while preserving deadline guarantees. This paper presents a novel approach to evaluate RT-DVS algorithms using statistical model checking. A scalable framework is proposed for RT-DVS algorithms evaluation, in which the relevant components are modeled as stochastic timed automata, and the evaluation metrics including utilization bound, energy efficiency, battery awareness, and temperature awareness are expressed as statistical queries. Evaluation of these metrics is performed by verifying the corresponding queries using UPPAAL-SMC and analyzing the statistical information provided by the tool. We demonstrate the applicability of our framework via a case study of five classical RT-DVS algorithms.
Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
Chamseddine, Ali H.; Connes, Alain
2007-01-01
The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input
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.
Study of the 'non-Abelian' current algebra of a non-linear σ-model
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
Remenska, D.; Templon, J.A.; Willemse, T.A.C.; Homburg, P.; Verstoep, K.; Casajus, A.; Bal, H.E.; Brat, G.; Rungta, N.; Venet, A.
2013-01-01
One of the challenges in concurrent software development is early discovery of design errors which could lead to deadlocks or race-conditions. For safety-critical and complex distributed applications, traditional testing does not always expose such problems. Performing more rigorous formal analysis
Lashkevich, Michael; Pugai, Yaroslav
2013-01-01
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [1]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show that the singular vectors are expressed in terms of the degenerate Macdonald polynomials with rectangular partitions. We study the matrix elements that contain a singular vector in one chirality and a cosingular vector in the other chirality and find them to lead to the resonance identities already known in the conformal perturbation theory. Besides, we give a new derivation of the equation of motion in the sinh-Gordon theory, and a new representation for conserved currents
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.
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
Enabling model checking for collaborative process analysis: from BPMN to `Network of Timed Automata'
Mallek, Sihem; Daclin, Nicolas; Chapurlat, Vincent; Vallespir, Bruno
2015-04-01
Interoperability is a prerequisite for partners involved in performing collaboration. As a consequence, the lack of interoperability is now considered a major obstacle. The research work presented in this paper aims to develop an approach that allows specifying and verifying a set of interoperability requirements to be satisfied by each partner in the collaborative process prior to process implementation. To enable the verification of these interoperability requirements, it is necessary first and foremost to generate a model of the targeted collaborative process; for this research effort, the standardised language BPMN 2.0 is used. Afterwards, a verification technique must be introduced, and model checking is the preferred option herein. This paper focuses on application of the model checker UPPAAL in order to verify interoperability requirements for the given collaborative process model. At first, this step entails translating the collaborative process model from BPMN into a UPPAAL modelling language called 'Network of Timed Automata'. Second, it becomes necessary to formalise interoperability requirements into properties with the dedicated UPPAAL language, i.e. the temporal logic TCTL.
Verification of communication protocols in web services model-checking service compositions
Tari, Zahir; Mukherjee, Anshuman
2014-01-01
Gathers recent advancements in the field of self-organizing wireless sensor networks and provides readers with the essential, state-of-the-art information about sensor networking. In the near future, wireless sensor networks will become an integral part of our day-to-day life. To solve different sensor networking related issues, researchers have put a great deal of effort into coming up with innovative ideas. Verification of Communication Protocols in Web Services: Model-Checking Service Compositions gathers recent advancements in the field of self-organizing wireless sensor networks and provides readers with integral information about sensor networking. It introduces current technological trends, particularly in node organization, and provides implementation details of each networking type to help readers set up sensor networks in their related job fields. In addition, it identifies the limitations of current technologies, as well as future research directions.
Model Checking A Self-Stabilizing Synchronization Protocol for Arbitrary Digraphs
Malekpour, Mahyar R.
2012-01-01
This report presents the mechanical verification of a self-stabilizing distributed clock synchronization protocol for arbitrary digraphs in the absence of faults. This protocol does not rely on assumptions about the initial state of the system, other than the presence of at least one node, and no central clock or a centrally generated signal, pulse, or message is used. The system under study is an arbitrary, non-partitioned digraph ranging from fully connected to 1-connected networks of nodes while allowing for differences in the network elements. Nodes are anonymous, i.e., they do not have unique identities. There is no theoretical limit on the maximum number of participating nodes. The only constraint on the behavior of the node is that the interactions with other nodes are restricted to defined links and interfaces. This protocol deterministically converges within a time bound that is a linear function of the self-stabilization period. A bounded model of the protocol is verified using the Symbolic Model Verifier (SMV) for a subset of digraphs. Modeling challenges of the protocol and the system are addressed. The model checking effort is focused on verifying correctness of the bounded model of the protocol as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period.
Fluid Petri Nets and hybrid model-checking: a comparative case study
Gribaudo, M.; Horvath, A.; Bobbio, A.; Tronci, E.; Ciancamerla, E.; Minichino, M.
2003-01-01
The modeling and analysis of hybrid systems is a recent and challenging research area which is actually dominated by two main lines: a functional analysis based on the description of the system in terms of discrete state (hybrid) automata (whose goal is to ascertain conformity and reachability properties), and a stochastic analysis (whose aim is to provide performance and dependability measures). This paper investigates a unifying view between formal methods and stochastic methods by proposing an analysis methodology of hybrid systems based on Fluid Petri Nets (FPNs). FPNs can be analyzed directly using appropriate tools. Our paper shows that the same FPN model can be fed to different functional analyzers for model checking. In order to extensively explore the capability of the technique, we have converted the original FPN into languages for discrete as well as hybrid as well as stochastic model checkers. In this way, a first comparison among the modeling power of well known tools can be carried out. Our approach is illustrated by means of a 'real world' hybrid system: the temperature control system of a co-generative plant
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)
New insights in the standard model of quantum physics in Clifford algebra
Daviau, Claude
2013-01-01
Why Clifford algebra is the true mathematical frame of the standard model of quantum physics. Why the time is everywhere oriented and why the left side shall never become the right side. Why positrons have also a positive proper energy. Why there is a Planck constant. Why a mass is not a charge. Why a system of particles implies the existence of the inverse of the individual wave function. Why a fourth neutrino should be a good candidate for black matter. Why concepts as “parity” and “reverse” are essential. Why the electron of a H atom is in only one bound state. Plus 2 very remarkable identities, and the invariant wave equations that they imply. Plus 3 generations and 4 neutrinos. Plus 5 dimensions in the space and 6 dimensions in space-time…
Approach method of the solutions of algebraic models of the N body problem
Dufour, M.
1986-09-01
We have studied a class of algebraic eigenvalue problems that generate tridiagonal matrices. The Lipkin Hamiltonian was chosen as representative. Three methods have been implemented, whose extension to more general many body problems seems possible i) Degenerate Linked Cluster Theory (LCT), which disregards special symmetries of the interaction and defines a hierarchy of approximation based on model spaces at fixed number of particle-hole excitation of the unperturbed Hamiltonian. The method works for small perturbations but does not yield a complete description. ii) A new linearization method that replaces the matrix to be diagonalized by local (tangent) approximations by harmonic matrices. This method generalizes LCT and is a posteriori reminiscent of semi-classical ones. However of is simpler, more precise and yields a complete description of spectra. iii) A global way to characterize spectra based on Gershgorine-Hadamard disks [fr
Schlingemann, D.
1996-10-01
Several two dimensional quantum field theory models have more than one vacuum state. An investigation of super selection sectors in two dimensions from an axiomatic point of view suggests that there should be also states, called soliton or kink states, which interpolate different vacua. Familiar quantum field theory models, for which the existence of kink states have been proven, are the Sine-Gordon and the φ 4 2 -model. In order to establish the existence of kink states for a larger class of models, we investigate the following question: Which are sufficient conditions a pair of vacuum states has to fulfill, such that an interpolating kink state can be constructed? We discuss the problem in the framework of algebraic quantum field theory which includes, for example, the P(φ) 2 -models. We identify a large class of vacuum states, including the vacua of the P(φ) 2 -models, the Yukawa 2 -like models and special types of Wess-Zumino models, for which there is a natural way to construct an interpolating kink state. In two space-time dimensions, massive particle states are kink states. We apply the Haag-Ruelle collision theory to kink sectors in order to analyze the asymptotic scattering states. We show that for special configurations of n kinks the scattering states describe n freely moving non interacting particles. (orig.)
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
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
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)
Fukui, Hirokazu [Institute of Nuclear Safety System Inc., Seika, Kyoto (Japan); Yoshida, Michio; Yamaura, Kazuho [Japan Institute for Group Dynamics, Fukuoka (Japan)
2000-09-01
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
Almini, A. A.; Kulahci, Murat; Montgomery, D. C.
2009-01-01
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......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...... 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...
The Moyal momentum algebra applied to θ-deformed 2d conformal models and KdV-hierarchies
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)
The algebra of the general Markov model on phylogenetic trees and networks.
Sumner, J G; Holland, B R; Jarvis, P D
2012-04-01
It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.
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...
Herbert, L.T.; Hansen, Z.N.L.
2016-01-01
This paper 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 is explored by means of an evolutionary algorithm, where the goals for improvement are defined in terms of optimising quantities, typically employed to model resources, associated with a workflow. The approach is fully automated and only the modelling of the production workflows, potential faults and the expression of the goals require manual input. We present the design of a software tool implementing this framework and explore the practical utility of this approach through an industrial case study in which the risk of production failures and their impact are reduced by restructuring the workflow. - Highlights: • We present a framework which allows for the automated restructuring of workflows. • This framework seeks to minimise the impact of errors on the workflow. • We illustrate a scalable software implementation of this framework. • We explore the practical utility of this approach through an industry case. • The impact of errors can be substantially reduced by restructuring the workflow.
Chen, Hui; Deng, Ju-Zhi; Yin, Min; Yin, Chang-Chun; Tang, Wen-Wu
2017-03-01
To speed up three-dimensional (3D) DC resistivity modeling, we present a new multigrid method, the aggregation-based algebraic multigrid method (AGMG). We first discretize the differential equation of the secondary potential field with mixed boundary conditions by using a seven-point finite-difference method to obtain a large sparse system of linear equations. Then, we introduce the theory behind the pairwise aggregation algorithms for AGMG and use the conjugate-gradient method with the V-cycle AGMG preconditioner (AGMG-CG) to solve the linear equations. We use typical geoelectrical models to test the proposed AGMG-CG method and compare the results with analytical solutions and the 3DDCXH algorithm for 3D DC modeling (3DDCXH). In addition, we apply the AGMG-CG method to different grid sizes and geoelectrical models and compare it to different iterative methods, such as ILU-BICGSTAB, ILU-GCR, and SSOR-CG. The AGMG-CG method yields nearly linearly decreasing errors, whereas the number of iterations increases slowly with increasing grid size. The AGMG-CG method is precise and converges fast, and thus can improve the computational efficiency in forward modeling of three-dimensional DC resistivity.
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
Simulation Modeling of a Check-in and Medication Reconciliation Ambulatory Clinic Kiosk
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.
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
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.
Algebraic stress model for axial flow in a bare rod-bundle
de Lemos, M.J.S.
1987-01-01
The problem of predicting transport properties for momentum and heat across the boundaries of interconnected channels has been the subject of many investigations. In the particular case of axial flow through rod-bundles, transport coefficients for channel faces aligned with rod centers are known to be considerably higher than those calculated by simple isotropic theories. And yet, it was been found that secondary flows play only a minor role in this overall transport, being turbulence highly enhanced across that hypothetical surface. In order to numerically predict the correct amount of the quantity being transported, the approach taken by many investigators was then to artificially increase the diffusion coefficient obtained via a simple isopropic theory (usually the standard k-ε model) and numerically match the correct experimentally observed mixing rates. The present paper reports an attempt to describe the turbulent stresses by means of an Algebraic Stress Model for turbulence. Relative turbulent kinetic energy distribution in all three directions are presented and compared with experiments in a square lattice. The strong directional dependence of transport terms are then obtained via a model for the Reynolds stresses. The results identify a need for a better representation of the mean-flow field part of the pressure-strain correlation term
Living on the edge: a toy model for holographic reconstruction of algebras with centers
Donnelly, William; Marolf, Donald; Michel, Ben; Wien, Jason
2017-01-01
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 boundary regions. In addition, the entropy of boundary regions receives both Ryu-Takayanagi-like contributions and further corrections that model the ((δArea)/(4G N )) term of Faulkner, Lewkowycz, and Maldacena. Comparison with Yang-Mills theory then suggests that this ((δArea)/(4G N )) term can be reinterpreted as a part of the bulk entropy of gravitons under an appropriate extension of the physical bulk Hilbert space.
Calculus domains modelled using an original bool algebra based on polygons
Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.
2016-08-01
Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.
Saldarriaga Vargas, Clarita
When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.
Upton, H.A.; Garcia, P.
1999-08-24
A check valve for use in a GDCS of a nuclear reactor and having a motor driven disk including a rotatable armature for rotating the check valve disk over its entire range of motion is described. In one embodiment, the check valve includes a valve body having a coolant flow channel extending therethrough. The coolant flow channel includes an inlet end and an outlet end. A valve body seat is located on an inner surface of the valve body. The check valve further includes a disk assembly, sometimes referred to as the motor driven disc, having a counterweight and a disk shaped valve. The disk valve includes a disk base having a seat for seating with the valve body seat. The disk assembly further includes a first hinge pin member which extends at least partially through the disk assembly and is engaged to the disk. The disk valve is rotatable relative to the first hinge pin member. The check valve also includes a motor having a stator frame with a stator bore therein. An armature is rotatably positioned within the stator bore and the armature is coupled to the disk valve to cause the disk valve to rotate about its full range of motion. 5 figs.
Upton, H.A.; Garcia, P.
1999-01-01
A check valve for use in a GDCS of a nuclear reactor and having a motor driven disk including a rotatable armature for rotating the check valve disk over its entire range of motion is described. In one embodiment, the check valve includes a valve body having a coolant flow channel extending therethrough. The coolant flow channel includes an inlet end and an outlet end. A valve body seat is located on an inner surface of the valve body. The check valve further includes a disk assembly, sometimes referred to as the motor driven disc, having a counterweight and a disk shaped valve. The disk valve includes a disk base having a seat for seating with the valve body seat. The disk assembly further includes a first hinge pin member which extends at least partially through the disk assembly and is engaged to the disk. The disk valve is rotatable relative to the first hinge pin member. The check valve also includes a motor having a stator frame with a stator bore therein. An armature is rotatably positioned within the stator bore and the armature is coupled to the disk valve to cause the disk valve to rotate about its full range of motion. 5 figs
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.
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...
A new algebraic turbulence model for accurate description of airfoil flows
Xiao, Meng-Juan; She, Zhen-Su
2017-11-01
We report a new algebraic turbulence model (SED-SL) based on the SED theory, a symmetry-based approach to quantifying wall turbulence. The model specifies a multi-layer profile of a stress length (SL) function in both the streamwise and wall-normal directions, which thus define the eddy viscosity in the RANS equation (e.g. a zero-equation model). After a successful simulation of flat plate flow (APS meeting, 2016), we report here further applications of the model to the flow around airfoil, with significant improvement of the prediction accuracy of the lift (CL) and drag (CD) coefficients compared to other popular models (e.g. BL, SA, etc.). Two airfoils, namely RAE2822 airfoil and NACA0012 airfoil, are computed for over 50 cases. The results are compared to experimental data from AGARD report, which shows deviations of CL bounded within 2%, and CD within 2 counts (10-4) for RAE2822 and 6 counts for NACA0012 respectively (under a systematic adjustment of the flow conditions). In all these calculations, only one parameter (proportional to the Karmen constant) shows slight variation with Mach number. The most remarkable outcome is, for the first time, the accurate prediction of the drag coefficient. The other interesting outcome is the physical interpretation of the multi-layer parameters: they specify the corresponding multi-layer structure of turbulent boundary layer; when used together with simulation data, the SED-SL enables one to extract physical information from empirical data, and to understand the variation of the turbulent boundary layer.
Entropy correlation and entanglement for mixed states in an algebraic model
Hou Xiwen; Chen Jinghua; Wan Mingfang; Ma Zhongqi
2009-01-01
As an alternative with potential connections to actual experiments, other than the systems more usually used in the field of entanglement, the dynamics of entropy correlation and entanglement between two anharmonic vibrations in a well-established algebraic model, with parameters extracted from fitting to highly excited spectral experimental results for molecules H 2 O and SO 2 , is studied in terms of the linear entropy and two negativities for various initial states that are respectively taken to be the mixed density matrices of thermal states and squeezed states on each mode. For a suitable parameter in initial states the entropies in two stretches can show positive correlation or anti-correlation. And the linear entropy of each mode is positively correlated with the negativities just for the mixed-squeezed states with small parameters in H 2 O while they do not display any correlation in other cases. For the mixed-squeezed states the negativities exhibit dominantly positive correlations with an effective mutual entropy. The differences in the linear entropy and the negativities between H 2 O and SO 2 are discussed as well. Those are useful for molecular quantum computing and quantum information processing
Yuan-Shyi Peter Chiu; Chien-Hua Lee; Nong Pan; Singa Wang Chiu
2013-01-01
This study uses mathematical modeling along with an algebraic technique to resolve the production-distribution policy for a single-producer multi-retailer integrated inventory system with scrap in production. We assume that a product is manufactured through an imperfect production process where all nonconforming items will be picked up and scrapped in each production cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in ...
Algebraic entropy for algebraic maps
Hone, A N W; Ragnisco, Orlando; Zullo, Federico
2016-01-01
We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)
Fusion rules of chiral algebras
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.)
Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA.
Yang, Xian; Han, Rui; Guo, Yike; Bradley, Jeremy; Cox, Benita; Dickinson, Robert; Kitney, Richard
2012-01-01
Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of clinical pathway, thereby assisting
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.
Jafarizadeh, M. A.; Ranjbar, Z.; Fouladi, N.; Ghapanvari, M.
2018-01-01
In this paper, a successful algebraic method based on the dual algebraic structure for three level pairing model in the framework of sdg IBM is proposed for transitional nuclei which show transitional behavior from spherical to gamma-unstable quantum shape phase transition. In this method complicated sdg Hamiltonian, which is a three level pairing Hamiltonian is determined easily via the exactly solvable method. This description provides a better interpretation of some observables such as BE (4) in nuclei which exhibits the necessity of inclusion of g boson in the sd IBM, while BE (4) cannot be explained in the sd boson model. Some observables such as Energy levels, BE (2), BE (4), the two neutron separation energies signature splitting of the γ-vibrational band and expectation values of the g-boson number operator are calculated and examined for 46 104 - 110Pd isotopes.
MacCallum, M.A.H.
1990-01-01
The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one general relativity meeting and the next, despite which there have been significant changes in the period since the last report. The introductory remarks aim to give a brief survey of capabilities of the principal available systems and highlight one or two trends. The reference to the most recent full survey of computer algebra in relativity and brief descriptions of the Maple, REDUCE and SHEEP and other applications are given. (author)
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
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
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
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
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.
Djurfeldt, Mikael
2012-07-01
The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31-42, 2008b) and an implementation in Python has been publicly released.
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…
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.).
Deligne, Mumford and Artin [DM, Ar2]) and consider algebraic stacks, then we can cons- truct the 'moduli ... the moduli scheme and the moduli stack of vector bundles. First I will give ... 1–31. © Printed in India. 1 ...... Cultura, Spain. References.
Rossi, R., E-mail: riccardo.rossi12@unibo.i [Laboratorio di Termofluidodinamica Computazionale Seconda Facolta di Ingegneria di Forli, Universita di Bologna Via Fontanelle 40, 47100 Forli (Italy); Center for Turbulence Research Department of Mechanical Engineering Stanford University, CA 94305 (United States); Philips, D.A.; Iaccarino, G. [Center for Turbulence Research Department of Mechanical Engineering Stanford University, CA 94305 (United States)
2010-10-15
Research highlights: {yields} The computed DNS statistics indicate that a gradient-transport scheme can be applied to the vertical and spanwise scalar flux components. {yields} The streamwise scalar flux is characterized by a counter-gradient transport mechanism in the wake region close to the obstacle. {yields} The wake profiles of scalar fluctuations and the shape of probability density functions do not suggest a significant flapping movement of the scalar plume. {yields} The evaluation of scalar dispersion models must include a careful assessment of the computed mean velocity field and Reynolds stress tensor. {yields} Algebraic models provide an improved prediction of the mean concentration field as compared to the standard eddy-diffusivity model. -- Abstract: The dispersion of a passive scalar downstream of a wall-mounted cube is examined using direct numerical simulations and turbulence models applied to the Reynolds equations. The scalar is released from a circular source located on top of the obstacle, which is immersed in a developing boundary-layer flow. Direct simulations are performed to give insight into the mixing process and to provide a reference database for turbulence closures. Algebraic flux models are evaluated against the standard eddy-diffusivity representation. Coherent structures periodically released from the cube top are responsible for a counter-diffusion mechanism appearing in the streamwise scalar flux. Alternating vortex pairs form from the lateral edges of the cube, but the intensity profiles and probability density functions of scalar fluctuations suggest that they do not cause a significant flapping movement of the scalar plume. The gradient-transport scheme is consistent with the vertical and spanwise scalar flux components. From the comparative study with our direct simulations, we further stress that Reynolds stress predictions must be carefully evaluated along with scalar flux closures in order to establish the reliability of
Rossi, R.; Philips, D.A.; Iaccarino, G.
2010-01-01
Research highlights: → The computed DNS statistics indicate that a gradient-transport scheme can be applied to the vertical and spanwise scalar flux components. → The streamwise scalar flux is characterized by a counter-gradient transport mechanism in the wake region close to the obstacle. → The wake profiles of scalar fluctuations and the shape of probability density functions do not suggest a significant flapping movement of the scalar plume. → The evaluation of scalar dispersion models must include a careful assessment of the computed mean velocity field and Reynolds stress tensor. → Algebraic models provide an improved prediction of the mean concentration field as compared to the standard eddy-diffusivity model. -- Abstract: The dispersion of a passive scalar downstream of a wall-mounted cube is examined using direct numerical simulations and turbulence models applied to the Reynolds equations. The scalar is released from a circular source located on top of the obstacle, which is immersed in a developing boundary-layer flow. Direct simulations are performed to give insight into the mixing process and to provide a reference database for turbulence closures. Algebraic flux models are evaluated against the standard eddy-diffusivity representation. Coherent structures periodically released from the cube top are responsible for a counter-diffusion mechanism appearing in the streamwise scalar flux. Alternating vortex pairs form from the lateral edges of the cube, but the intensity profiles and probability density functions of scalar fluctuations suggest that they do not cause a significant flapping movement of the scalar plume. The gradient-transport scheme is consistent with the vertical and spanwise scalar flux components. From the comparative study with our direct simulations, we further stress that Reynolds stress predictions must be carefully evaluated along with scalar flux closures in order to establish the reliability of Reynolds
Characteristic Dynkin diagrams and W algebras
Ragoucy, E.
1993-01-01
We present a classification of characteristic Dynkin diagrams for the A N , B N , C N and D N algebras. This classification is related to the classification of W(G, K) algebras arising from non-abelian Toda models, and we argue that it can give new insight on the structure of W algebras. (orig.)
The Das-Popowicz Moyal momentum algebra
Boulahoual, A.; Sedra, M.B.
2002-08-01
We introduce in this short note some aspects of the Moyal momentum algebra that we call the Das-Popowicz Mm algebra. Our interest on this algebra is motivated by the central role that it can play in the formulation of integrable models and in higher conformal spin theories. (author)
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.
Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)
2010-02-26
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.
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.
Algebraic characterizations of measure algebras
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
Comments on two-loop Kac-Moody algebras
Ferreira, L A; Gomes, J F; Zimerman, A H [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Schwimmer, A [Istituto Nazionale di Fisica Nucleare, Trieste (Italy)
1991-10-01
It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decouple {beta}-{gamma} 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.
Quantum W-algebras and elliptic algebras
Feigin, B.; Kyoto Univ.; Frenkel, E.
1996-01-01
We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)
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,…
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
Type checking by domain analysis in Ampersand
Joosten, S.M.M.; Joosten, S.J.C.; Kahl, W.; Winter, M.; Oliveira, J.N.
2015-01-01
In the process of incorporating subtyping in relation algebra, an algorithm was found to derive the subtyping relation from the program to be checked. By using domain analysis rather than type inference, this algorithm offers an attractive visualization of the type derivation process. This
1983-03-01
Tic, equals to (NI/ Nic ) where Nic , defined as the net chemical production rate of i-th species, is in general the algebraic sum of terms which are...detailed analysis has shown that in preignition regions the chemical rates which make a significant contribution to any of the Nic are such that at least...Elkton Division Lab., Inc. ATTN. R. Biddle ATTN: M. Summeitield Tech Lib. 1041 US Hlighway One North P. 0. Box 241 Princeton, NJ 08540 Elkton, MD
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)
Classical Exchange Algebra of the Nonlinear Sigma Model on a Supercoset Target with Z2n Grading
Ke San-Min; Li Xin-Ying; Wang Chun; Yue Rui-Hong
2011-01-01
The classical exchange algebra satisfied by the monodromy matrix of the nonlinear sigma model on a supercoset target with Z 2n grading is derived using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution. When n = 2, our results coincide with the results given by Magro for the pure spinor description of AdS 5 × S 5 string theory (when the ghost terms are omitted). (the physics of elementary particles and fields)
Fu Chuanji; Zhu Qinsheng; Wu Shaoyi
2010-01-01
Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external held. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external held. (general)
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
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.
Jacob, M.
1967-01-01
The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( ΔI = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [fr
José, Marco V; Morgado, Eberto R; Govezensky, Tzipe
2011-07-01
Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The Extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. Since the dimensions of remarkable subsets of the Genetic Hotels are not necessarily integer numbers, we also introduce the concept of algebraic fractal dimension. A general decoding function which maps each codon to its corresponding amino acid or the stop signals is also derived. The Phenotypic Hotel of amino acids is also illustrated. The proposed evolutionary paths are discussed in terms of the existing theories of the evolution of the SGC. The adoption of 3-dimensional models of the Genetic and Phenotypic Hotels will facilitate the understanding of the biological properties of the SGC.
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.
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
Kleyn, Aleks
2007-01-01
The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.
Construction and decoding of a class of algebraic geometry codes
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...... is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH decoder codes......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...
Physical modelling of sediment transport in mountain torrents upstream of open check dams
Schwindt, Sebastian; Franca, Mario J.; Schleiss, Anton J.
2015-04-01
Dynamic morphological processes in mountain torrents do not only attract the attention of many contemporary researchers, but are also a relevant issue for the design of flood protection measures in the downstream sections where dwellers may be threatened by the important potential of flows with high concentration of sediments. Events which have a morphodynamic effect are simulated at the Laboratory of Hydraulic Constructions (LCH) in order to optimize the design of a flood protection measure, notably open check dams. Different scenarios with a fix bed consisting of boulders as well as mobile beds are studied and the influence of flow constrictions, i.e. distinct geometric configurations of open check dams are analysed. Three varying water pumped discharges in the order of 5 to 20 l/s are tested with progressively increasing solid discharges of 1, 3 and 6 % of the liquid discharge according to the transport capacity. The moistened sediments are introduced via a system of conveyor belts and are then mixed with the liquid discharge in an about 3 m long rough trapezoidal channel with a base width of 24 cm. The mean diameter Dm of the injected sediments is 0.86 cm and the dimensionless grain size distribution is in line with a normalized shape derived from over 60 streams in the Alps. A wide range of frequent floods in morphologically diverging types of mountain torrents is covered, in particular regarding the sediment availability in the catchment area and along the river. A basic assumption here is considering that the frequent floods are floods with return periods between 1 to 5 years and are the most important process in terms of amounts of sediment transport. This may be arguable for some mountain torrents and landscape effective processes which are driven by floods with return periods of more than several decades. In order to identify benchmarks for hydraulic parameters which lead to the obstruction of flow restrictions at mountain torrents, the water depth is
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.
Salvador Lucas
2015-12-01
Full Text Available Recent developments in termination analysis for declarative programs emphasize the use of appropriate models for the logical theory representing the program at stake as a generic approach to prove termination of declarative programs. In this setting, Order-Sorted First-Order Logic provides a powerful framework to represent declarative programs. It also provides a target logic to obtain models for other logics via transformations. We investigate the automatic generation of numerical models for order-sorted first-order logics and its use in program analysis, in particular in termination analysis of declarative programs. We use convex domains to give domains to the different sorts of an order-sorted signature; we interpret the ranked symbols of sorted signatures by means of appropriately adapted convex matrix interpretations. Such numerical interpretations permit the use of existing algorithms and tools from linear algebra and arithmetic constraint solving to synthesize the models.
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.
Sugiyama, Hitoshi; Akiyama, Mitsunobu; Shinohara, Yasunori; Hitomi, Daisuke
1997-01-01
A numerical analysis has been performed for three dimensional developing turbulent flow in a 90deg bent tube with straight inlet and outlet sections by an algebraic Reynolds stress model. To our knowledge, very little has been reported about detailed comparison between calculated results and experimental data containing Reynolds stresses. In calculation, an algebraic Reynolds stress model together with a boundary-fitted coordinate system is applied to a 90deg bent tube in order to solve anisotropic turbulent flow precisely. The calculated results display comparatively good agreement with the experimental data of time averaged velocity and secondary vectors. In addition, the present method predicts as a characteristic feature that the intensity of secondary flow near the inner wall is increased immediately downstream from the bend outlet by the pressure gradient. With regard to comparison of Reynolds stresses, the present method is able to reproduce well the distributions of streamwise normal stress and shear stress defined streamwise and radial velocity fluctuation except for the shear stress defined streamwise and circumferential velocity fluctuation. The present calculation has been found to simulate many features of the developing flow in bent tube satisfactorily, but it has a tendency to underpredict the Reynolds stresses. (author)
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Samuel Belliard
2013-11-01
Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.
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.
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...
Model Checking the Logic of Allen's Relations Meets and Started-by is P^NP-Complete
Laura Bozzelli
2016-09-01
Full Text Available In the plethora of fragments of Halpern and Shoham's modal logic of time intervals (HS, the logic AB of Allen's relations Meets and Started-by is at a central position. Statements that may be true at certain intervals, but at no sub-interval of them, such as accomplishments, as well as metric constraints about the length of intervals, that force, for instance, an interval to be at least (resp., at most, exactly k points long, can be expressed in AB. Moreover, over the linear order of the natural numbers N, it subsumes the (point-based logic LTL, as it can easily encode the next and until modalities. Finally, it is expressive enough to capture the ω-regular languages, that is, for each ω-regular expression R there exists an AB formula Φ such that the language defined by R coincides with the set of models of Φ over N. It has been shown that the satisfiability problem for AB over N is EXPSPACE-complete. Here we prove that, under the homogeneity assumption, its model checking problem is Δ^p_2 = P^NP-complete (for the sake of comparison, the model checking problem for full HS is EXPSPACE-hard, and the only known decision procedure is nonelementary. Moreover, we show that the modality for the Allen relation Met-by can be added to AB at no extra cost (AA'B is P^NP-complete as well.
Vertex algebras and mirror symmetry
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.)
Dragon, N.
1979-01-01
The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)
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.
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
Iterated Leavitt Path Algebras
Hazrat, R.
2009-11-01
Leavitt path algebras associate to directed graphs a Z-graded algebra and in their simplest form recover the Leavitt algebras L(1,k). In this note, we introduce iterated Leavitt path algebras associated to directed weighted graphs which have natural ± Z grading and in their simplest form recover the Leavitt algebras L(n,k). We also characterize Leavitt path algebras which are strongly graded. (author)
Neumann, U.; Puzalowski, R.; Grimm, I.
1985-01-01
Numerical valve models for simulation of selfactuating safety valves and damped check valves are introduced for the computer programs TRAC-PF1 and ROLAST. As examples of application post-test calculations and stability analysis are given. (orig.)
Wahyu Budi Wicaksono
2017-08-01
Full Text Available The purpose of this research was to know the effectiveness of Pair Checks cooperative model towards students’ learning result and learning motivation of eight grade. Population of this research were students of eight grade Junior High School 2 Pati in the academic year 2016/1017. The research used cluster random sampling technique.Where the selected samples were students of class VIII H as experimental class and class VIII G as control class. The data collected by the method of documentation, test methods, and scale methods. The analyzed of data used completeness test and average different test. The results showed that: (1 students’ learning result who join Pair Checks cooperative model have classical study completeness; (2 students’ mathematics learning result who join Pair Checks cooperative model is better than students mathematics learning result who join ekspository learning; (3 students’ learning motivation who join Pair Checks cooperative model is better than students’ learning motivation who join ekspository learning.
Quantum affine algebras and deformations of the virasoro and W-algebras
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.)
2010-01-01
...-case holds) C-19Notice at automated teller machines C-20Notice at automated teller machines (delayed... would like a list of the routing numbers for these institutions. C-9—Automated Teller Machine Deposits (Extended Hold) Deposits at Automated Teller Machines Funds from any deposits (cash or checks) made at...
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...
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.
Filiform Lie algebras of order 3
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
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 ...
The bubble algebra: structure of a two-colour Temperley-Lieb Algebra
Grimm, Uwe; Martin, Paul P
2003-01-01
We define new diagram algebras providing a sequence of multiparameter generalizations of the Temperley-Lieb algebra, suitable for the modelling of dilute lattice systems of two-dimensional statistical mechanics. These algebras give a rigorous foundation to the various 'multi-colour algebras' of Grimm, Pearce and others. We determine the generic representation theory of the simplest of these algebras, and locate the nongeneric cases (at roots of unity of the corresponding parameters). We show by this example how the method used (Martin's general procedure for diagram algebras) may be applied to a wide variety of such algebras occurring in statistical mechanics. We demonstrate how these algebras may be used to solve the Yang-Baxter equations
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...
Twisted boundary states and representation of generalized fusion algebra
Ishikawa, Hiroshi; Tani, Taro
2006-01-01
The mutual consistency of boundary conditions twisted by an automorphism group G of the chiral algebra is studied for general modular invariants of rational conformal field theories. We show that a consistent set of twisted boundary states associated with any modular invariant realizes a non-negative integer matrix representation (NIM-rep) of the generalized fusion algebra, an extension of the fusion algebra by representations of the twisted chiral algebra associated with the automorphism group G. We check this result for several concrete cases. In particular, we find that two NIM-reps of the fusion algebra for su(3) k (k=3,5) are organized into a NIM-rep of the generalized fusion algebra for the charge-conjugation automorphism of su(3) k . We point out that the generalized fusion algebra is non-commutative if G is non-Abelian and provide some examples for G-bar S 3 . Finally, we give an argument that the graph fusion algebra associated with simple current extensions coincides with the generalized fusion algebra for the extended chiral algebra, and thereby explain that the graph fusion algebra contains the fusion algebra of the extended theory as a subalgebra
Li, X Y; Yang, G W; Zheng, D S; Guo, W S; Hung, W N N
2015-04-28
Genetic regulatory networks are the key to understanding biochemical systems. One condition of the genetic regulatory network under different living environments can be modeled as a synchronous Boolean network. The attractors of these Boolean networks will help biologists to identify determinant and stable factors. Existing methods identify attractors based on a random initial state or the entire state simultaneously. They cannot identify the fixed length attractors directly. The complexity of including time increases exponentially with respect to the attractor number and length of attractors. This study used the bounded model checking to quickly locate fixed length attractors. Based on the SAT solver, we propose a new algorithm for efficiently computing the fixed length attractors, which is more suitable for large Boolean networks and numerous attractors' networks. After comparison using the tool BooleNet, empirical experiments involving biochemical systems demonstrated the feasibility and efficiency of our approach.
A 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...
Learning and Model-checking Networks of I/O Automata
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...... learn generic models for network entities in the form of automata templates. As is characteristic for SRL techniques, the abstraction level aorded by learning generic templates enables one to apply the learned model to new domains. A main benet of learning models based on nite automata lies in the fact...
Logic Model Checking of Time-Periodic Real-Time Systems
Florian, Mihai; Gamble, Ed; Holzmann, Gerard
2012-01-01
In this paper we report on the work we performed to extend the logic model checker SPIN with built-in support for the verification of periodic, real-time embedded software systems, as commonly used in aircraft, automobiles, and spacecraft. We first extended the SPIN verification algorithms to model priority based scheduling policies. Next, we added a library to support the modeling of periodic tasks. This library was used in a recent application of the SPIN model checker to verify the engine control software of an automobile, to study the feasibility of software triggers for unintended acceleration events.
Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.
1999-01-01
This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.
Hopf algebras and topological recursion
Esteves, João N
2015-01-01
We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293–309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347–452). (paper)
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)
Automated evolutionary restructuring of workflows to minimise errors via stochastic model checking
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...
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...
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...
Scalable and Accurate SMT-Based Model Checking of Data Flow Systems
2013-10-31
of variable x is always less than that of variable y) can be represented in this theory. • A theory of inductive datatypes . Modeling software... datatypes can be done directly in this theory. • A theory of arrays. Software that uses arrays can be modeled with constraints in this theory, as can...Arithmetic (and specialized fragments) Arrays Inductive datatypes Bit-vectors Uninterpreted functions SMT Engine Input interfaces FEATURES Support for
The Yoneda algebra of a K2 algebra need not be another K2 algebra
Cassidy, T.; Phan, C.; Shelton, B.
2010-01-01
The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K2 algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K2 algebra would be another K2 algebra. We show that this is not necessarily the case by constructing a monomial K2 algebra for which the corresponding Yoneda algebra is not K2.
Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches
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.
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.
Ke Sanmin; Yang Wenli; Shi Kangjie; Wang Chun; Jiang Kexia
2011-01-01
We investigate the classical exchange algebra of the monodromy matrix for a Green-Schwarz sigma model on supercoset target space with Z 4m grading by using a first-order Hamiltonian formulation and by adding to the Lax connection terms proportional to constraints. This enables us to show that the conserved charges of the theory are in involution in the Poisson bracket sense. Our calculation is based on a general world-sheet metric. Taking a particular case of m= 1 (and a particular choice of supergroup), our results coincide with those of the Green-Schwarz superstring theory in AdS 5 xS 5 background obtained by Magro [J. High Energy Phys. 0901, 021 (2009)].
Rahmouni, Adib N.
2004-01-01
In 1994, Berenger [Journal of Computational Physics 114 (1994) 185] proposed a new layer method: perfectly matched layer, PML, for electromagnetism. This new method is based on the truncation of the computational domain by a layer which absorbs waves regardless of their frequency and angle of incidence. Unfortunately, the technique proposed by Berenger (loc. cit.) leads to a system which has lost the most important properties of the original one: strong hyperbolicity and symmetry. We present in this paper an algebraic technique leading to well-known PML model [IEEE Transactions on Antennas and Propagation 44 (1996) 1630] for the linearized Euler equations, strongly well-posed, preserving the advantages of the initial method, and retaining symmetry. The technique proposed in this paper can be extended to various hyperbolic problems
Study of phase transition of even and odd nuclei based on q-deforme SU(1,1) algebraic model
Jafarizadeh, M. A.; Amiri, N.; Fouladi, N.; Ghapanvari, M.; Ranjbar, Z.
2018-04-01
The q-deformed Hamiltonian for the SO (6) ↔ U (5) transitional case in s, d interaction boson model (IBM) can be constructed by using affine SUq (1 , 1) Lie algebra in the both IBM-1 and 2 versions and IBFM. In this research paper, we have studied the energy spectra of 120-128Xe isotopes and 123-131Xe isotopes and B(E2) transition probabilities of 120-128Xe isotopes in the shape phase transition region between the spherical and gamma unstable deformed shapes of the theory of quantum deformation. The theoretical results agree with the experimental data fairly well. It is shown that the q-deformed SO (6) ↔ U (5) transitional dynamical symmetry remains after deformation.
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 ...
Algebraic structure of chiral anomalies
Stora, R.
1985-09-01
I will describe first the algebraic aspects of chiral anomalies, exercising however due care about the topological delicacies. I will illustrate the structure and methods in the context of gauge anomalies and will eventually make contact with results obtained from index theory. I will go into two sorts of generalizations: on the one hand, generalizing the algebraic set up yields e.g. gravitational and mixed gauge anomalies, supersymmetric gauge anomalies, anomalies in supergravity theories; on the other hand most constructions applied to the cohomologies which characterize anomalies easily extend to higher cohomologies. Section II is devoted to a description of the general set up as it applies to gauge anomalies. Section III deals with a number of algebraic set ups which characterize more general types of anomalies: gravitational and mixed gauge anomalies, supersymmetric gauge anomalies, anomalies in supergravity theories. It also includes brief remarks on σ models and a reminder on the full BRST algebra of quantized gauge theories
A Framework for Relating Timed Transition Systems and Preserving TCTL Model Checking
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....
Can We Efficiently Check Concurrent Programs Under Relaxed Memory Models in Maude?
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......Relaxed memory models offer suitable abstractions of the actual optimizations offered by multi-core architectures and by compilers of concurrent programming languages. Using such abstractions for verification purposes is challenging in part due to their inherent non-determinism which contributes...