Model Checking Processes Specified In Join-Calculus Algebra
Directory of Open Access Journals (Sweden)
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.
Model Checking Processes Specified In Join-Calculus Algebra
Sławomir Piotr Maludziński; Grzegorz Dobrowolski
2014-01-01
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.
Analysis of DIRAC's behavior using model checking with process algebra
International Nuclear Information System (INIS)
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.
Optimizing algebraic petri net model checking by slicing
Khan, Yasir Imtiaz; Risoldi, Matteo
2013-01-01
High-level Petri nets make models more concise and read- able as compared to low-level Petri nets. However, usual verification techniques such as state space analysis remain an open challenge for both because of state space explosion. The contribution of this paper is to propose an approach for property based reduction of the state space of Algebraic Petri nets (a variant of high-level Petri nets). To achieve the objective, we propose a slicing algorithm for Algebraic Petri ...
Model Checking Process Algebra of Communicating Resources for Real-time Systems
DEFF Research Database (Denmark)
Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand;
2014-01-01
This paper presents a new process algebra, called PACOR, for real-time systems which deals with resource constrained timed behavior as an improved version of the ACSR algebra. We define PACOR as a Process Algebra of Communicating Resources which allows to express preemptiveness, urgent ness and...... original semantics of PACOR and enables the verification of PACOR systems using symbolic model checking in UPPAAL and statistical model checking UPPAAL SMC. Finally we provide an example to illustrate system specification in PACOR, translation and verification....
Model checking process algebra of communicating resources for real-time systems
DEFF Research Database (Denmark)
Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand;
2014-01-01
This paper presents a new process algebra, called PACoR, for real-time systems which deals with resource- constrained timed behavior as an improved version of the ACSR algebra. We define PACoR as a Process Algebra of Communicating Resources which allows to explicitly express preemptiveness...... preserves the original semantics of PACoR and enables the verification of PACoR systems using symbolic model checking in Uppaal and statistical model checking UppaalSMC. Finally we provide an example to illustrate system specification in PACoR, translation and verification....
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...
Model composition in model checking
Felscher, Ingo
2014-01-01
Model-checking allows one to formally check properties of systems: these properties are modeled as logic formulas and the systems as structures like transition systems. These transition systems are often composed, i.e., they arise in form of products or sums. The composition technique allows us to deduce the truth of a formula in the composed system from "interface information": the truth of formulas for the component systems and information in which components which of these formulas hold. W...
Institute of Scientific and Technical Information of China (English)
Zhi-Hong Tao; Cong-Hua Zhou; Zhong Chen; Li-Fu Wang
2007-01-01
Bounded Model Checking has been recently introduced as an efficient verification method for reactive systems.This technique reduces model checking of linear temporal logic to propositional satisfiability.In this paper we first present how quantified Boolean decision procedures can replace BDDs.We introduce a bounded model checking procedure for temporal logic CTL* which reduces model checking to the satisfiability of quantified Boolean formulas.Our new technique avoids the space blow up of BDDs, and extends the concept of bounded model checking.
Energy Technology Data Exchange (ETDEWEB)
Ritter, Patricia [Centro de Estudios Científicos (CECs),Avenida Arturo Prat 514, Valdivia (Chile); Sämann, Christian [Maxwell Institute for Mathematical Sciences,Department of Mathematics, Heriot-Watt University,Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom)
2014-04-09
In this paper, we begin the study of zero-dimensional field theories with fields taking values in a semistrict Lie 2-algebra. These theories contain the IKKT matrix model and various M-brane related models as special cases. They feature solutions that can be interpreted as quantized 2-plectic manifolds. In particular, we find solutions corresponding to quantizations of ℝ{sup 3}, S{sup 3} and a five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie 2-algebra models around the solution corresponding to quantized ℝ{sup 3}, we obtain higher BF-theory on this quantized space.
International Nuclear Information System (INIS)
In this paper, we begin the study of zero-dimensional field theories with fields taking values in a semistrict Lie 2-algebra. These theories contain the IKKT matrix model and various M-brane related models as special cases. They feature solutions that can be interpreted as quantized 2-plectic manifolds. In particular, we find solutions corresponding to quantizations of ℝ3, S3 and a five-dimensional Hpp-wave. Moreover, by expanding a certain class of Lie 2-algebra models around the solution corresponding to quantized ℝ3, we obtain higher BF-theory on this quantized space
Compositional and Quantitative Model Checking
DEFF Research Database (Denmark)
Larsen, Kim Guldstrand
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 on...
Model Checking as Static Analysis
DEFF Research Database (Denmark)
Zhang, Fuyuan
properties which can predict safe approximations to program behaviors. In this thesis, we have developed several static analysis based techniques to solve model checking problems, aiming at showing the link between static analysis and model checking. We focus on logical approaches to static analysis......Both model checking and static analysis are prominent approaches to detecting software errors. Model Checking is a successful formal method for verifying properties specified in temporal logics with respect to transition systems. Static analysis is also a powerful method for validating program...... multi-valued setting, and we therefore obtain a multivalued analysis for temporal properties specied by CTL formulas. In particular, we have shown that the three-valued CTL model checking problem over Kripke modal transition systems can be exactly encoded in three-valued ALFP. Last, we come back to two...
Checking Model Transformation Refinement
Büttner, Fabian; Egea, Marina; Guerra, Esther; Lara, Juan De
2013-01-01
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-38883-5_15 Proceedings of 6th International Conference, ICMT 2013, Budapest, Hungary, June 18-19, 2013 Refinement is a central notion in computer science, meaning that some artefact S can be safely replaced by a refinement R, which preserves S’s properties. Having available techniques and tools to check transformation refinement would enable (a) the reasoning on whether a transformation correctly impl...
MODEL IDENTIFICATION AND COMPUTER ALGEBRA.
Bollen, Kenneth A; Bauldry, Shawn
2010-10-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158
Model Checking Algorithms for CTMDPs
DEFF Research Database (Denmark)
Buchholz, Peter; Hahn, Ernst Moritz; Hermanns, Holger;
2011-01-01
Continuous Stochastic Logic (CSL) can be interpreted over continuoustime Markov decision processes (CTMDPs) to specify quantitative properties of stochastic systems that allow some external control. Model checking CSL formulae over CTMDPs requires then the computation of optimal control strategie...
Advances in Probabilistic Model Checking
Kwiatkowska, Marta; Parker, David
2012-01-01
Probabilistic model checking is an automated verification method that aims to establish the correctness of probabilistic systems. Probability may arise, for example, due to failures of unreliable components, communication across lossy media, or through the use of randomisation in distributed protocols. Probabilistic model checking enables a range of exhaustive, quantitative analyses of properties such as "the probability of a message being delivered within 5ms is at least 0.89". In the last t...
Model checking PSL safety properties
Launiainen, Tuomas
2009-01-01
Model checking is a modern, efficient approach to gaining confidence of the correctness of complex systems. It outperforms conventional testing methods especially in cases where a high degree of confidence in the correctness of the system is required, or when the test runs of the system are difficult to reproduce accurately. In model checking the system is verified against a specification that is expressed in a formal specification language. The main challenges are that the process requires q...
Jansen, D.N.
2002-01-01
The logic ATCTL is a convenient logic to specify properties with actions and real-time. It is intended as a property language for Lightweight UML models [12], which consist mainly of simplified class diagrams and statecharts. ATCTL combines two known extensions of CTL, namely ACTL and TCTL. The reas
Direct Model Checking Matrix Algorithm
Institute of Scientific and Technical Information of China (English)
Zhi-Hong Tao; Hans Kleine Büning; Li-Fu Wang
2006-01-01
During the last decade, Model Checking has proven its efficacy and power in circuit design, network protocol analysis and bug hunting. Recent research on automatic verification has shown that no single model-checking technique has the edge over all others in all application areas. So, it is very difficult to determine which technique is the most suitable for a given model. It is thus sensible to apply different techniques to the same model. However, this is a very tedious and time-consuming task, for each algorithm uses its own description language. Applying Model Checking in software design and verification has been proved very difficult. Software architectures (SA) are engineering artifacts that provide high-level and abstract descriptions of complex software systems. In this paper a Direct Model Checking (DMC) method based on Kripke Structure and Matrix Algorithm is provided. Combined and integrated with domain specific software architecture description languages (ADLs), DMC can be used for computing consistency and other critical properties.
Observable Algebra in Field Algebra of G-spin Models
Institute of Scientific and Technical Information of China (English)
蒋立宁
2003-01-01
Field algebra of G-spin models can provide the simplest examples of lattice field theory exhibiting quantum symmetry. Let D(G) be the double algebra of a finite group G and D(H), a sub-algebra of D(G) determined by subgroup H of G. This paper gives concrete generators and the structure of the observable algebra AH, which is a D(H)-invariant sub-algebra in the field algebra of G-spin models F, and shows that AH is a C*-algebra. The correspondence between H and AH is strictly monotonic. Finally, a duality between D(H) and AH is given via an irreducible vacuum C*-representation of F.
FOUNDATION OF NUCLEAR ALGEBRAIC MODELS
Institute of Scientific and Technical Information of China (English)
周孝谦
1990-01-01
Based upon Tomonoga-Rowe's many body theory, we find that the algebraic models, including IBM and FDSM are simplest extension of Rowe-Rosensteel's sp(3R).Dynkin-Gruber's subalgebra embedding method is applied to find an appropriate algebra and it's reduction chains conforming to physical requirement. The separated cases sp(6) and so(8) now appear as two branches stemming from the same root D6-O(12). Transitional ease between sp(6) and so(8) is inherently include.
From model checking to model measuring
Henzinger, Thomas A.; Otop, Jan
2013-01-01
We define the model-measuring problem: given a model $M$ and specification~$\\varphi$, what is the maximal distance $\\rho$ such that all models $M'$ within distance $\\rho$ from $M$ satisfy (or violate)~$\\varphi$. The model measuring problem presupposes a distance function on models. We concentrate on automatic distance functions, which are defined by weighted automata. The model-measuring problem subsumes several generalizations of the classical model-checking problem, in particular, qu...
Heteroscedasticity checks for regression models
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the nonparametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach may readily be extended to handle partial linear, and linear autoregressive models.
Heteroscedasticity checks for regression models
Institute of Scientific and Technical Information of China (English)
ZHU; Lixing
2001-01-01
［1］Carroll, R. J., Ruppert, D., Transformation and Weighting in Regression, New York: Chapman and Hall, 1988.［2］Cook, R. D., Weisberg, S., Diagnostics for heteroscedasticity in regression, Biometrika, 1988, 70: 1—10.［3］Davidian, M., Carroll, R. J., Variance function estimation, J. Amer. Statist. Assoc., 1987, 82: 1079—1091.［4］Bickel, P., Using residuals robustly I: Tests for heteroscedasticity, Ann. Statist., 1978, 6: 266—291.［5］Carroll, R. J., Ruppert, D., On robust tests for heteroscedasticity, Ann. Statist., 1981, 9: 205—209.［6］Eubank, R. L., Thomas, W., Detecting heteroscedasticity in nonparametric regression, J. Roy. Statist. Soc., Ser. B, 1993, 55: 145—155.［7］Diblasi, A., Bowman, A., Testing for constant variance in a linear model, Statist. and Probab. Letters, 1997, 33: 95—103.［8］Dette, H., Munk, A., Testing heteoscedasticity in nonparametric regression, J. R. Statist. Soc. B, 1998, 60: 693—708.［9］Müller, H. G., Zhao, P. L., On a semi-parametric variance function model and a test for heteroscedasticity, Ann. Statist., 1995, 23: 946—967.［10］Stute, W., Manteiga, G., Quindimil, M. P., Bootstrap approximations in model checks for regression, J. Amer. Statist. Asso., 1998, 93: 141—149.［11］Stute, W., Thies, G., Zhu, L. X., Model checks for regression: An innovation approach, Ann. Statist., 1998, 26: 1916—1939.［12］Shorack, G. R., Wellner, J. A., Empirical Processes with Applications to Statistics, New York: Wiley, 1986.［13］Efron, B., Bootstrap methods: Another look at the jackknife, Ann. Statist., 1979, 7: 1—26.［14］Wu, C. F. J., Jackknife, bootstrap and other re-sampling methods in regression analysis, Ann. Statist., 1986, 14: 1261—1295.［15］H rdle, W., Mammen, E., Comparing non-parametric versus parametric regression fits, Ann. Statist., 1993, 21: 1926—1947.［16］Liu, R. Y., Bootstrap procedures under some non-i.i.d. models, Ann. Statist., 1988, 16: 1696—1708.［17
Shashidhar, K C; Catthoor, Francky; Janssens, Gerda
2011-01-01
Development of energy and performance-efficient embedded software is increasingly relying on application of complex transformations on the critical parts of the source code. Designers applying such nontrivial source code transformations are often faced with the problem of ensuring functional equivalence of the original and transformed programs. Currently they have to rely on incomplete and time-consuming simulation. Formal automatic verification of the transformed program against the original is instead desirable. This calls for equivalence checking tools similar to the ones available for comparing digital circuits. We present such a tool to compare array-intensive programs related through a combination of important global transformations like expression propagations, loop and algebraic transformations. When the transformed program fails to pass the equivalence check, the tool provides specific feedback on the possible locations of errors.
The model checking fingerprints of CTL operators
Krebs, Andreas; Meier, Arne; Mundhenk, Martin
2015-01-01
The aim of this study is to understand the inherent expressive power of CTL operators. We investigate the complexity of model checking for all CTL fragments with one CTL operator and arbitrary Boolean operators. This gives us a fingerprint of each CTL operator. The comparison between the fingerprints yields a hierarchy of the operators that mirrors their strength with respect to model checking.
Program Analysis as Model Checking
DEFF Research Database (Denmark)
Olesen, Mads Chr.
of an abstract interpretation. For the generalisation to lattice automata to have benefit it is important that efficient tools exist. This thesis presents multi-core tools for efficient and scalable reachability and Büchi emptiness checking of timed/lattice automata. Finally, a number of case studies...... overapproximation of the hardware is needed; the case of identifying timing anomalous hardware for which such abstractions are hard to find is considered....
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 implicati...
MODEL IDENTIFICATION AND COMPUTER ALGEBRA
Bollen, Kenneth A.; Bauldry, Shawn
2010-01-01
Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local a...
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
Bethe algebra of Gaudin model, Calogero-Moser space and Cherednik algebra
Mukhin, E.; Tarasov, V.; Varchenko, A.
2009-01-01
We identify the Bethe algebra of the Gaudin model associated to gl(N) acting on a suitable representation with the center of the rational Cherednik algebra and with the algebra of regular functions on the Calogero-Moser space.
Model Checking Discounted Temporal Properties
Alfaro, de Luca; Faella, Marco; Henzinger, Thomas A.; Majumdar, Rupak; Stoelinga, Mariëlle
2004-01-01
Temporal logic is two-valued: formulas are interpreted as 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
Model Checking Discounted Temporal Properties
Alfaro, de Luca; Faella, Marco; Henzinger, Thomas A.; Majumdar, Rupak; Stoelinga, Mariëlle
2005-01-01
Temporal logic is two-valued: formulas are interpreted as 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
Model Checking Implantable Cardioverter Defibrillators
Abbas, Houssam; Jang, Kuk Jin; Jiang, Zhihao; Mangharam, Rahul
2015-01-01
Ventricular Fibrillation is a disorganized electrical excitation of the heart that results in inadequate blood flow to the body. It usually ends in death within seconds. The most common way to treat the symptoms of fibrillation is to implant a medical device, known as an Implantable Cardioverter Defibrillator (ICD), in the patient's body. Model-based verification can supply rigorous proofs of safety and efficacy. In this paper, we build a hybrid system model of the human heart+ICD closed loop...
Graded CTL Model Checking for Test Generation
Napoli, Margherita
2011-01-01
Recently there has been a great attention from the scientific community towards the use of the model-checking technique as a tool for test generation in the simulation field. This paper aims to provide a useful mean to get more insights along these lines. By applying recent results in the field of graded temporal logics, we present a new efficient model-checking algorithm for Hierarchical Finite State Machines (HSM), a well established symbolism long and widely used for representing hierarchical models of discrete systems. Performing model-checking against specifications expressed using graded temporal logics has the peculiarity of returning more counterexamples within a unique run. We think that this can greatly improve the efficacy of automatically getting test cases. In particular we verify two different models of HSM against branching time temporal properties.
Engineering Abstractions in Model Checking and Testing
DEFF Research Database (Denmark)
Achenbach, Michael; Ostermann, Klaus
2009-01-01
Abstractions are used in model checking to tackle problems like state space explosion or modeling of IO. The application of these abstractions in real software development processes, however, lacks engineering support. This is one reason why model checking is not widely used in practice yet and...... testing is still state of the art in falsification. We show how user-defined abstractions can be integrated into a Java PathFinder setting with tools like AspectJ or Javassist and discuss implications of remaining weaknesses of these tools. We believe that a principled engineering approach to designing...
A PSL Bounded Model Checking Method
Institute of Scientific and Technical Information of China (English)
YU Lei; ZHAO Zongtao
2012-01-01
SAT-based bounded model checking （BMC） is introduced as an important complementary technique to OBDD-based symbolic model checking, and is an efficient verification method for parallel and reactive systems. However, until now the properties verified by bounded model checking are very finite. Temporal logic PSL is a property specification language （IEEE-1850） describing parallel systems and is divided into two parts, i.e. the linear time logic FL and the branch time logic OBE. In this paper, the specification checked by BMC is extended to PSL and its algorithm is also proposed. Firstly, define the bounded semantics of PSL, and then reduce the bounded semantics into SAT by translating PSL specification formula and the state transition relation of the system to the propositional formula A and B, respectively. Finally, verify the satisfiability of the conjunction propositional formula of A and B. The algorithm results in the translation of the existential model checking of the temporal logic PSL into the satisfiability problem of propositional formula. An example of a queue controlling circuit is used to interpret detailedly the executing procedure of the algorithm.
A Metric Encoding for Bounded Model Checking
Pradella, Matteo; Morzenti, Angelo; San Pietro, Pierluigi
In Bounded Model Checking, both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative future and past metric temporal operators, typically found in properties of hard real time systems. The encoding is simple and intuitive in principle, but it is made more complex by the presence, typical of the Bounded Model Checking technique, of backward and forward loops used to represent an ultimately periodic infinite domain by a finite structure. We report and comment on the new encoding technique and on an extensive set of experiments carried out to assess its feasibility and effectiveness.
Statistical Model Checking for Biological Systems
DEFF Research Database (Denmark)
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel;
2014-01-01
Statistical Model Checking (SMC) is a highly scalable simulation-based verification approach for testing and estimating the probability that a stochastic system satisfies a given linear temporal property. The technique has been applied to (discrete and continuous time) Markov chains, stochastic...
Using chemical organization theory for model checking
Kaleta, Christoph; Richter, Stephan; Dittrich, Peter
2009-01-01
Motivation: The increasing number and complexity of biomodels makes automatic procedures for checking the models' properties and quality necessary. Approaches like elementary mode analysis, flux balance analysis, deficiency analysis and chemical organization theory (OT) require only the stoichiometric structure of the reaction network for derivation of valuable information. In formalisms like Systems Biology Markup Language (SBML), however, information about the stoichiometric coefficients re...
Efficient CSL Model Checking Using Stratification
DEFF Research Database (Denmark)
Zhang, Lijun; Jansen, David N.; Nielson, Flemming; Hermanns, Holger
2012-01-01
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 [ 1, 2]. Their proof can be turned into an approximation algorithm with worse than...
Automata-Based CSL Model Checking
DEFF Research Database (Denmark)
Zhang, Lijun; Jansen, David N.; Nielson, Flemming; Hermanns, Holger
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...
Statistical Model Checking for Stochastic Hybrid Systems
DEFF Research Database (Denmark)
David, Alexandre; Du, Dehui; Larsen, Kim Guldstrand; Legay, Axel; Mikučionis, Marius; Poulsen, Danny Bøgsted; Sedwards, Sean
This paper presents novel extensions and applications of the UPPAAL-SMC model checker. The extensions allow for statistical model checking of stochastic hybrid systems. We show how our race-based stochastic semantics extends to networks of hybrid systems, and indicate the integration technique...... applied for implementing this semantics in the UPPAAL-SMC simulation engine. We report on two applications of the resulting tool-set coming from systems biology and energy aware buildings....
An algebraic model of software evolution
Keller, Benjamin J.d
1990-01-01
A model of the software evolution process, called the Abstraction Refinement Model, is described which builds on the algebraic influence of the Laws of Programming and the transformational Draco Paradigm. The result is an algebraic structure consisting of the states of the software product (system descriptions) ordered by a relation of relative correctness with transformations defined between the system descriptions. This structure is interpreted as the software evolution space, ...
Howard, Y; Gravell, A; Ferreira, C; Augusto, J C
2011-01-01
Trace analysis can be a useful way to discover problems in a program under test. Rather than writing a special purpose trace analysis tool, this paper proposes that traces can usefully be analysed by checking them against a formal model using a standard model-checker or else an animator for executable specifications. These techniques are illustrated using a Travel Agent case study implemented in J2EE. We added trace beans to this code that write trace information to a database. The traces are then extracted and converted into a form suitable for analysis by Spin, a popular model-checker, and Pro-B, a model-checker and animator for the B notation. This illustrates the technique, and also the fact that such a system can have a variety of models, in different notations, that capture different features. These experiments have demonstrated that model-based trace-checking is feasible. Future work is focussed on scaling up the approach to larger systems by increasing the level of automation.
Model Checking over Paraconsistent Temporal Logic
Institute of Scientific and Technical Information of China (English)
CHEN Dong-huo; WANG Lin-zhang; CUI Jia-lin
2008-01-01
Classical logic cannot be used to effectively reason about concurrent systems with inconsistencies (inconsistencies often occur, especially in the early stage of the development, when large and complex concurrent systems are developed). In this paper, we propose the use of a guasi-classical temporal logic (QCTL) for supporting the verification of temporal properties of such systems even where the consistent model is not available. Our models are paraKripke structures ( extended standard Kripke structures), in which both a formula and its negation are satisfied in a same state, and properties to be verified are expressed by QCTL with paraKripke structures semantics. We introduce a novel notion of paraKripke models, which grasps the paraconsistent character of the entailment relation of QCTL. Furthermore, we explore the methodology of model checking over QCTL, and describe the detailed algorithm of implementing QCTL model checker. In the sequel, a simple example is presented, showing how to exploit the proposed model checking technique to verify the temporal properties of inconsistent concurrent systems.
Statistical Model Checking of Rich Models and Properties
DEFF Research Database (Denmark)
Poulsen, Danny Bøgsted
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 for...... 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...
SAT-Based Model Checking without Unrolling
Bradley, Aaron R.
A new form of SAT-based symbolic model checking is described. Instead of unrolling the transition relation, it incrementally generates clauses that are inductive relative to (and augment) stepwise approximate reachability information. In this way, the algorithm gradually refines the property, eventually producing either an inductive strengthening of the property or a counterexample trace. Our experimental studies show that induction is a powerful tool for generalizing the unreachability of given error states: it can refine away many states at once, and it is effective at focusing the proof search on aspects of the transition system relevant to the property. Furthermore, the incremental structure of the algorithm lends itself to a parallel implementation.
Distributed Parametric and Statistical Model Checking
Directory of Open Access Journals (Sweden)
Peter Bulychev
2011-10-01
Full Text Available Statistical Model Checking (SMC is a trade-off between testing and formal verification. The core idea of the approach is to conduct some simulations of the system and verify if they satisfy some given property. In this paper we show that SMC is easily parallelizable on a master/slaves architecture by introducing a series of algorithms that scale almost linearly with respect to the number of slave computers. Our approach has been implemented in the UPPAAL SMC toolset and applied on non-trivial case studies.
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.
Workflow Fault Tree Generation Through Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2014-01-01
probabilistic structure of the system being modelled. From these calculations, a comprehensive fault tree is generated. Further, we show that annotating the model with rewards (data) allows the expected mean values of reward structures to be calculated at points of failure....... with probabilistic non-deterministic branching. We present an algorithm that allows for exhaustive generation of possible error states that could arise in execution of the model, where the generated error states allow for both fail-stop behaviour and continued system execution. We employ stochastic...... model checking to calculate the probabilities of reaching each non-error system state. Each generated error state is assigned a variable indicating its individual probability of occurrence. Our method can determine the probability of combined faults occurring, while accounting for the basic...
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.
Model Checking Is Static Analysis of Modal Logic
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis
2010-01-01
it can give an exact characterisation of the semantics of formulae in a modal logic. This shows that model checking can be performed by means of state-of-the-art approaches to static analysis and allow us to conclude that the problems of model checking and static analysis are reducible to each other....... In terms of computational complexity we show that model checking by means of static analysis gives the same complexity bounds as are known for traditional approaches to model checking....
Solving stochastic epidemiological models using computer algebra
Hincapie, Doracelly; Ospina, Juan
2011-06-01
Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.
Probabilistic Model--Checking of Quantum Protocols
Gay, S; Papanikolaou, N; Gay, Simon; Nagarajan, Rajagopal; Papanikolaou, Nikolaos
2005-01-01
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using present-day technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of PRISM, a probabilistic model-checking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniqu...
Model Checking of Boolean Process Models
Schneider, Christoph; Wehler, Joachim
2011-01-01
In the field of Business Process Management formal models for the control flow of business processes have been designed since more than 15 years. Which methods are best suited to verify the bulk of these models? The first step is to select a formal language which fixes the semantics of the models. We adopt the language of Boolean systems as reference language for Boolean process models. Boolean systems form a simple subclass of coloured Petri nets. Their characteristics are low tokens to mode...
Tomino, Dan
2010-01-01
1-loop vacuum energies of (fuzzy) spacetimes from a supersymmetric reduced model with Filippov 3-algebra are discussed. A_{2,2} algebra, Nambu-Poisson algebra in flat spacetime, and a Lorentzian 3-algebra are examined as 3-algebras.
Probabilistic and hybrid model checking deployments for wireless sensor networks
International Nuclear Information System (INIS)
In the early stages of system development, model checking is a good practice for examining the WSNs (Wireless Sensor Networks). Model checking involves verifying a system's properties based on the system's finite state model. For varying applications like computers and wireless communication prior to expensive simulations, model checking has become a vital requirement in order to investigate the performance and reliability. In this paper for the first time, we are presenting probabilistic and hybrid model checking tools which are being implemented to analyse and verify the WSN applications and their examples. Here we are categorizing the model checking tools and presenting how they have been used for the investigation of various behaviours of WSN solutions. Consequently, this paper helps readers/researchers to choose the appropriate model checking tool and to get benefited in shape of validating their solutions. The paper has also highlighted the problems of existing model checking tools within WSN domain. (author)
Conformant Planning via Symbolic Model Checking
Cimatti, A; 10.1613/jair.774
2011-01-01
We tackle the problem of planning in nondeterministic domains, by presenting a new approach to conformant planning. Conformant planning is the problem of finding a sequence of actions that is guaranteed to achieve the goal despite the nondeterminism of the domain. Our approach is based on the representation of the planning domain as a finite state automaton. We use Symbolic Model Checking techniques, in particular Binary Decision Diagrams, to compactly represent and efficiently search the automaton. In this paper we make the following contributions. First, we present a general planning algorithm for conformant planning, which applies to fully nondeterministic domains, with uncertainty in the initial condition and in action effects. The algorithm is based on a breadth-first, backward search, and returns conformant plans of minimal length, if a solution to the planning problem exists, otherwise it terminates concluding that the problem admits no conformant solution. Second, we provide a symbolic representation ...
A process algebra model of QED
Sulis, William
2016-03-01
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.
Using Model Checking to Validate AI Planner Domain Models
Penix, John; Pecheur, Charles; Havelund, Klaus
1999-01-01
This report describes an investigation into using model checking to assist validation of domain models for the HSTS planner. The planner models are specified using a qualitative temporal interval logic with quantitative duration constraints. We conducted several experiments to translate the domain modeling language into the SMV, Spin and Murphi model checkers. This allowed a direct comparison of how the different systems would support specific types of validation tasks. The preliminary results indicate that model checking is useful for finding faults in models that may not be easily identified by generating test plans.
Sigma-models and Homotopy Algebras
Zeitlin, Anton M
2015-01-01
We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein equations with extra fields, as generalized Maurer-Cartan equations.
Fusion algebras of logarithmic minimal models
Energy Technology Data Exchange (ETDEWEB)
Rasmussen, Joergen; Pearce, Paul A [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)
2007-11-09
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 {ne} 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{sub p,p'} (minimal) models defined algebraically.
An algebraic approach to the Hubbard model
de Leeuw, Marius
2015-01-01
We study the algebraic structure of an integrable Hubbard-Shastry type lattice model associated with the centrally extended su(2|2) superalgebra. This superalgebra underlies Beisert's AdS/CFT worldsheet R-matrix and Shastry's R-matrix. The considered model specializes to the one-dimensional Hubbard model in a certain limit. We demonstrate that Yangian symmetries of the R-matrix specialize to the Yangian symmetry of the Hubbard model found by Korepin and Uglov. Moreover, we show that the Hubbard model Hamiltonian has an algebraic interpretation as the so-called secret symmetry. We also discuss Yangian symmetries of the A and B models introduced by Frolov and Quinn.
Phase transitions in algebraic cluster models
International Nuclear Information System (INIS)
We study the phase transitions of two algebraic cluster models, which have similar interactions, but differ from each other in their model spaces. The semimicroscopical model incorporates the Pauli exclusion principle, while the phenomenological one does not. The appearance of the quasidynamical SU(3) symmetry is also investigated in the presence of an explicitly symmetry-breaking interaction. Examples of binary cluster configurations with two, one, or zero closed-shell clusters are studied
Analyzing Interoperability of Protocols Using Model Checking
Institute of Scientific and Technical Information of China (English)
WUPeng
2005-01-01
In practical terms, protocol interoperability testing is still laborious and error-prone with little effect, even for those products that have passed conformance testing. Deadlock and unsymmetrical data communication are familiar in interoperability testing, and it is always very hard to trace their causes. The previous work has not provided a coherent way to analyze why the interoperability was broken among protocol implementations under test. In this paper, an alternative approach is presented to analyzing these problems from a viewpoint of implementation structures. Sequential and concurrent structures are both representative implementation structures, especially in event-driven development model. Our research mainly discusses the influence of sequential and concurrent structures on interoperability, with two instructive conclusions: (a) a sequential structure may lead to deadlock; (b) a concurrent structure may lead to unsymmetrical data communication. Therefore, implementation structures carry weight on interoperability, which may not gain much attention before. To some extent, they are decisive on the result of interoperability testing. Moreover, a concurrent structure with a sound task-scheduling strategy may contribute to the interoperability of a protocol implementation. Herein model checking technique is introduced into interoperability analysis for the first time. As the paper shows, it is an effective way to validate developers' selections on implementation structures or strategies.
Abstraction and Model Checking in the PEPA Plug-in for Eclipse
DEFF Research Database (Denmark)
Smith, Michael James Andrew
2010-01-01
The stochastic process algebra PEPA is a widely used language for performance modelling, and a large part of its success is due to the rich tool support that is available. As a compositional Markovian formalism, however, it suffers from the state space explosion problem, where even small models can...... 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...
Checking for normality in linear mixed models
Institute of Scientific and Technical Information of China (English)
WU Ping; ZHU LiXing; FANG Yun
2012-01-01
Linear mixed models are popularly used to fit continuous longitudinal data,and the random effects are commonly assumed to have normal distribution.However,this assumption needs to be tested so that further analysis can be proceeded well.In this paper,we consider the Baringhaus-Henze-Epps-Pulley (BHEP) tests,which are based on an empirical characteristic function.Differing from their case,we consider the normality checking for the random effects which are unobservable and the test should be based on their predictors.The test is consistent against global alternatives,and is sensitive to the local alternatives converging to the null at a certain rate arbitrarily close to 1/(√)n where n is sample size.Furthermore,to overcome the problem that the limiting null distribution of the test is not tractable,we suggest a new method:use a conditional Monte Carlo test (CMCT) to approximate the null distribution,and then to simulate p-values.The test is compared with existing methods,the power is examined,and several examples are applied to illustrate the usefulness of our test in the analysis of longitudinal data.
Modelling Chinese Smart Grid : A stochastic model checking case study
Energy Technology Data Exchange (ETDEWEB)
Yuksel, E.; Nielson, H.R.; Nielson, F. (Technical Univ. of Denmark. DTU Informatics, Kgs. Lyngby (Denmark)); Zhu, H. (East China Normal Univ. (China)); Huang, H. (Wuxi SensingNet Industrialization Research Institute (China))
2012-07-01
In this document, we consider a specific Chinese Smart Grid implementation and try to address the verification problem for certain quantitative properties including performance and battery consumption. We employ stochastic model checking approach and present our modelling and analysis study using PRISM model checker. (Author)
Verifying Multi-Agent Systems via Unbounded Model Checking
Kacprzak, M.; Lomuscio, A.; Lasica, T.; Penczek, W.; Szreter, M.
2004-01-01
We present an approach to the problem of verification of epistemic properties in multi-agent systems by means of symbolic model checking. In particular, it is shown how to extend the technique of unbounded model checking from a purely temporal setting to a temporal-epistemic one. In order to achieve this, we base our discussion on interpreted systems semantics, a popular semantics used in multi-agent systems literature. We give details of the technique and show how it can be applied to the well known train, gate and controller problem. Keywords: model checking, unbounded model checking, multi-agent systems
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 Method for Model Checking Feature Interactions
DEFF Research Database (Denmark)
Pedersen, Thomas; Le Guilly, Thibaut; Ravn, Anders Peter; Skou, Arne Joachim
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 ...
Algebraic analysis of a model of two-dimensional gravity
Frolov, A M; Kuzmin, S V
2009-01-01
An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian $H_{c}$ are obtained and explicitly written in closed form.
Graph model of the Heisenberg-Weyl algebra
Blasiak, P.; Horzela, A.; Duchamp, G. H. E.; Penson, K. A.; Solomon, A. I.
2007-01-01
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs. This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.
Graph model of the Heisenberg-Weyl algebra
International Nuclear Information System (INIS)
We consider an algebraic formulation of Quantum Theory and develop a combinatorial model of the Heisenberg-Weyl algebra structure. It is shown that by lifting this structure to the richer algebra of graph operator calculus, we gain a simple interpretation involving, for example, the natural composition of graphs. This provides a deeper insight into the algebraic structure of Quantum Theory and sheds light on the intrinsic combinatorial underpinning of its abstract formalism.
Phase transitions in algebraic cluster models
International Nuclear Information System (INIS)
Complete text of publication follows. There has been much interest recently in phase transitions in various nuclear systems. The phases are defined as (local) minima of the potential energy surface (PES) defined in terms of parameters characterizing the nuclear system. Phase transitions occur when some relevant parameter is changed gradually and the system moves from one phase to another one. In the analysis of such systems the key questions are the number of phases and the order of phase transition between them. Algebraic nuclear structure models are especially interesting from the phase transition point of view, because the different phases may be characterized by different symmetries of the system. Much work has been done recently on models based on the interacting boson approximation (IBA). In these studies the potential energy surface is constructed from the algebraic Hamiltonian by its geometric mapping using the coherent state formalism. Inspired by these studies we performed a similar analysis of a family of algebraic cluster models based on the semimicroscopic algebraic cluster model (SACM). This model has two dynamical symmetries: the SU(3) and SO(4) limits are believed to correspond to vibration around a spherical equilibrium shape and static dipole deformation, respectively. The semimicroscopic nature of this model is reflected by the fact that a fully antisymmetrized microscopic model space is combined with a phenomenologic Hamiltonian that describes excitations of the (typically) two-cluster system. The microscopic model space is necessary to take into account the Pauli exclusion principle acting between the nucleons of the closely interacting clusters. In practice this means that the number of excitation quanta in the relative motion of the clusters has to exceed a certain number n0 characterizing the system. This is clearly a novelty with respect to other algebraic models, and it complicates the formalism considerably. We thus introduced as a
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
Through most of Greek history, mathematicians concentrated on geometry, although Euclid considered the theory of numbers. The Greek mathematician Diophantus (3rd century),however, presented problems that had to be solved by what we would today call algebra. His book is thus the first algebra text.
Modeling Environment for Component Model Checking from Hierarchical Architecture
Czech Academy of Sciences Publication Activity Database
Pařízek, P.; Plášil, František
2007-01-01
Roč. 182, - (2007), s. 139-153. ISSN 1571-0661 R&D Projects: GA ČR GA201/06/0770 Institutional research plan: CEZ:AV0Z10300504 Keywords : software components * behavior protocols * environment model checking * hierarchical component architecture Subject RIV: JC - Computer Hardware ; Software
Quantum spin models and extended conformal algebras
Honecker, A
1995-01-01
First, an algebraic criterion for integrability is discussed -the so-called `superintegrability'- and some results on the classification of superintegrable quantum spin Hamiltonians based on sl(2) are obtained. Next, the massive phases of the Z_n-chiral Potts quantum spin chain (a model that violates parity) are studied in detail. It is shown that the excitation spectrum of the massive high-temperature phase can be explained in terms of n-1 fundamental quasiparticles. We compute correlation functions from a perturbative and numerical evaluation of the groundstate for the Z_3-chain. In addition to an exponential decay we observe an oscillating contribution. The oscillation length seems to be related to the asymmetry of the dispersion relations. We show that this relation is exact at special values of the parameters for general Z_n using a form factor expansion. Finally, we discuss several aspects of extended conformal algebras (W-algebras). We observe an analogy between boundary conditions for Z_n-spin chains ...
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
Algebraic model theory for languages without equality
Elgueta Montó, Raimon
1994-01-01
In our opinion, it is fair to distinguish two separate branches in the origins of model theory. The first one, the model theory of first-order logic, can be traced back to the pioneering work of L. Lowenheim, T. Skolem, K. Gödel, A. Tarski and A.I. MaI 'cev, published before the mid 30's. This branch was put forward during the 40s' and 50s’ by several authors, including A. Tarski, L. Henkin, A. Robinson, J. Los. Their contribution, however, was rather influenced by modern algebra, a disciplin...
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.
Kimura, Yusuke
2015-07-01
It has been understood that correlation functions of multi-trace operators in SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand, such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.
Application of non-commutative algebra to a soluble fermionic model
International Nuclear Information System (INIS)
We explore the properties of the non-commutative Grassmann algebra to obtain the high-temperature expansion of the grand canonical partition function for self-interacting fermionic systems. As an application, we consider the anharmonic fermionic oscillator, the simplest model in Quantum Mechanics with self-interacting fermions that is exactly soluble. The knowledge of the exact expression for its grand canonical partition function enables us to check the β-expansion obtained using our Grassmann-algebra-based technique. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Efficient Checking of Individual Rewards Properties in Markov Population Models
Bortolussi, Luca; Hillston, Jane
2015-01-01
In recent years fluid approaches to the analysis of Markov populations models have been demonstrated to have great pragmatic value. Initially developed to estimate the behaviour of the system in terms of the expected values of population counts, the fluid approach has subsequently been extended to more sophisticated interrogations of models through its embedding within model checking procedures. In this paper we extend recent work on checking CSL properties of individual agents within a Marko...
Isovectorial pairing in solvable and algebraic models
International Nuclear Information System (INIS)
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 44Ti. 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.
Dynamic State Space Partitioning for External Memory Model Checking
DEFF Research Database (Denmark)
Evangelista, Sami; Kristensen, Lars Michael
2009-01-01
We describe a dynamic partitioning scheme usable by model checking techniques that divide the state space into partitions, such as most external memory and distributed model checking algorithms. The goal of the scheme is to reduce the number of transitions that link states belonging to different...... partitions, and thereby limit the amount of disk access and network communication. We report on several experiments made with our verification platform ASAP that implements the dynamic partitioning scheme proposed in this paper....
Model checking biological systems described using ambient calculus
DEFF Research Database (Denmark)
Mardare, Radu Iulian; Priami, Corrado; Qualia, Paola; Vagin, Oleksander
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....
Improved Bounded Model Checking for the Universal Fragment of CTL
Institute of Scientific and Technical Information of China (English)
Liang Xu; Wei Chen; Yan-Yan Xu; Wen-Hui Zhang
2009-01-01
SAT-based bounded model checking (BMC) has been introduced as a complementary technique to BDD-based symbolic model checking in recent years, and a lot of successful work has been done in this direction. The approach was first introduced by A. Biere et al. in checking linear temporal logic (LTL) formulae and then also adapted to check formulae of the universal fragment of computation tree logic (ACTL) by W. Penczek et al. As the efficiency of model checking is still an important issue, we present an improved BMC approach for ACTL based on Penczek's method. We consider two aspects of the approach. One is reduction of the number of variables and transitions in the k-model by distinguishing the temporal operator EX from the others. The other is simplification of the transformation of formulae by using uniform path encoding instead of a disjunction of all paths needed in the k-model. With these improvements, for an ACTI, formula, the length of the final encoding of the formula in the worst case is reduced. The improved approach is implemented in the tool BMV and is compared with the original one by applying both to two well known examples, mutual exclusion and dining philosophers. The comparison shows the advantages of the improved approach with respect to the efficiency of model checking.
Model Checking-Based Testing of Web Applications
Institute of Scientific and Technical Information of China (English)
ZENG Hongwei; MIAO Huaikou
2007-01-01
A formal model representing the navigation behavior of a Web application as the Kripke structure is proposed and an approach that applies model checking to test case generation is presented. The Object Relation Diagram as the object model is employed to describe the object structure of a Web application design and can be translated into the behavior model. A key problem of model checking-based test generation for a Web application is how to construct a set of trap properties that intend to cause the violations of model checking against the behavior model and output of counterexamples used to construct the test sequences.We give an algorithm that derives trap properties from the object model with respect to node and edge coverage criteria.
Symmetries of faces models and the double triangle algebra
Trinchero, R
2005-01-01
Symmetries of trigonometric integrable two dimensional statistical face models are considered. The corresponding symmetry operators on the Hilbert space of states of the quantum version of these models define a weak *-Hopf algebra isomorphic to the Ocneanu double triangle algebra(DTA).
Learning Markov Decision Processes for Model Checking
Directory of Open Access Journals (Sweden)
Hua Mao
2012-12-01
Full Text Available 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. 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 is performed by analyzing the probabilistic linear temporal logic properties of the system as well as by analyzing the schedulers, in particular the optimal schedulers, induced by the learned models.
Learning Markov Decision Processes for Model Checking
DEFF Research Database (Denmark)
Mao, Hua; Chen, Yingke; Jaeger, Manfred;
2012-01-01
Constructing an accurate system model for formal model verification can be both resource demanding and time-consuming. To alleviate this shortcoming, algorithms have been proposed for automatically learning system models based on observed system behaviors. In this paper we extend the algorithm 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....... 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...
A spatial operator algebra for manipulator modeling and control
Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.
1991-01-01
A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.
Linear Parametric Model Checking of Timed Automata
DEFF Research Database (Denmark)
Hune, Tohmas Seidelin; Romijn, Judi; Stoelinga, Mariëlle; Vaandrager, Frits W.
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...
Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra
Jung, Hyunyi; Mintos, Alexia; Newton, Jill
2015-01-01
This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…
Diagnostic checking for conditional heteroscedasticity models
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We suggest the score type tests for goodness-of-fit of conditional heteroscedasticity models in both univariate and multivariate time series.The tests can detect the alternatives converging to the null at a parametric rate.Weight functions are involved in the construction of the tests,which provides us with the flexibility to choose scores,especially under directional alternatives,for enhancing power performance.Furthermore,when the alternatives are not directional,we construct asymptotically distribution-free maximin tests for a large class of alternatives.A possibility to construct score-based omnibus tests is discussed when the alternative is saturated.The power performance is also investigated.A simulation study is carried out and a real data is analyzed.
A Metric Encoding for Bounded Model Checking (extended version)
Pradella, Matteo; Pietro, Pierluigi San
2009-01-01
In Bounded Model Checking both the system model and the checked property are translated into a Boolean formula to be analyzed by a SAT-solver. We introduce a new encoding technique which is particularly optimized for managing quantitative future and past metric temporal operators, typically found in properties of hard real time systems. The encoding is simple and intuitive in principle, but it is made more complex by the presence, typical of the Bounded Model Checking technique, of backward and forward loops used to represent an ultimately periodic infinite domain by a finite structure. We report and comment on the new encoding technique and on an extensive set of experiments carried out to assess its feasibility and effectiveness.
Applied Bounded Model Checking for Interlocking System Designs
DEFF Research Database (Denmark)
Haxthausen, Anne Elisabeth; Peleska, Jan; Pinger, Ralf
2013-01-01
In this article the verification and validation of interlocking systems is investigated. Reviewing both geographical and route-related interlocking, the verification objectives can be structured from a perspective of computer science into (1) verification of static semantics, and (2) verification...... of behavioural (operational) semantics. The former checks that the plant model – that is, the software components reflecting the physical components of the interlocking system – has been set up in an adequate way. The latter investigates trains moving through the network, with the objective to uncover potential...... safety violations. From a formal methods perspective, these verification objectives can be approached by theorem proving, global, or bounded model checking. This article explains the techniques for application of bounded model checking techniques, and discusses their advantages in comparison...
Applied Bounded Model Checking for Interlocking System Designs
DEFF Research Database (Denmark)
Haxthausen, Anne Elisabeth; Peleska, Jan; Pinger, Ralf
2014-01-01
In this paper the verification and validation of interlocking systems is investigated. Reviewing both geographical and route-related interlocking, the verification objectives can be structured from a perspective of computer science into (1) verification of static semantics, and (2) verification of...... behavioural (operational) semantics. The former checks that the plant model – that is, the software components reflecting the physical components of the interlocking system – has been set up in an adequate way. The latter investigates trains moving through the network, with the objective to uncover potential...... safety violations. From a formal methods perspective, these verification objectives can be approached by theorem proving, global, or bounded model checking. This paper explains the techniques for application of bounded model checking techniques, and discusses their advantages in comparison to the...
Bounded Model Checking of Temporal Formulas with Alloy
Cunha, Alcino
2012-01-01
Alloy is formal modeling language based on first-order relational logic, with no specific support for specifying reactive systems. We propose the usage of temporal logic to specify such systems, and show how bounded model checking can be performed with the Alloy Analyzer.
Towards Model Checking a Spi-Calculus Dialect
Gnesi, S.; Latella, D.; Lenzini, G.
2002-01-01
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 Dolev-
Using Model Checking for Analyzing Distributed Power Control Problems
DEFF Research Database (Denmark)
Brihaye, Thomas; Jungers, Marc; Lasaulce, Samson; Markey, Nicolas; Oreiby, Ghassan
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...
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
Fermi resonance-algebraic model for molecular vibrational spectra
Institute of Scientific and Technical Information of China (English)
侯喜文; 董世海; 谢汨; 马中骐
1999-01-01
A Fermi resonance-algebraic model is proposed for molecular vibrations, where a U(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent molecule XY2 and a molecule XY3 is successfully applied to fitting the recently observed vibrational spectrum of the water molecule and arsine (AsH3), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations.
Modelling Software Evolution using Algebraic Graph Rewriting
Ciraci, Selim; Broek, van den, PR Peter; Avgeriou, P.; Zdun, U.; Borne, I
2006-01-01
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 relations in UML interaction diagrams. Then, we provide a set of algebraic graph rewrite rules that formalizes the changes that may be caused by an evolution request, using the pushout construction ...
W-algebras and superalgebras from constrained WZW models
International Nuclear Information System (INIS)
A classification of W algebras and superalgebras arising in Abelian as well as non Abelian Toda theories is presented. Each model, obtained from a constrained WZW action, is related with an Sl(2) subalgebra (resp. OSp(1/2) superalgebra) of a simple Lie algebra (resp. superalgebra) G. However, the determination of an U(1)Y factor, commuting with Sl(2) (resp. OSp(1/2)), appears, when it exists, particularly useful to characterize the corresponding W algebra. The (super) conformal spin contents of each W (super)algebra is performed. The class of all the superconformal algebras (i.e. with conformal spins s≤2) is easily obtained as a byproduct of our general results. (author) 26 refs.; 21 tabs
Algebra model and security analysis for cryptographic protocols
Institute of Scientific and Technical Information of China (English)
HUAI Jinpeng; LI Xianxian
2004-01-01
More and more cryptographic protocols have been used to achieve various security requirements of distributed systems in the open network environment. However cryptographic protocols are very difficult to design and analyze due to the complexity of the cryptographic protocol execution, and a large number of problems are unsolved that range from the theory framework to the concrete analysis technique. In this paper, we build a new algebra called cryptographic protocol algebra (CPA) for describing the message operations with many cryptographic primitives, and proposed a new algebra model for cryptographic protocols based on the CPA. In the model, expanding processes of the participant's knowledge on the protocol runs are characterized with some algebraic notions such as subalgebra, free generator and polynomial algebra, and attack processes are modeled with a new notion similar to that of the exact sequence used in homological algebra. Then we develope a mathematical approach to the cryptographic protocol security analysis. By using algebraic techniques, we have shown that for those cryptographic protocols with some symmetric properties, the execution space generated by an arbitrary number of participants may boil down to a smaller space generated by several honest participants and attackers. Furthermore we discuss the composability problem of cryptographic protocols and give a sufficient condition under which the protocol composed of two correct cryptographic protocols is still correct, and we finally offer a counterexample to show that the statement may not be true when the condition is not met.
Model checking conditional CSL for continuous-time Markov chains
DEFF Research Database (Denmark)
Gao, Yang; Xu, Ming; Zhan, Naijun;
2013-01-01
probabilistic operator. CCSL allows us to express a richer class of properties for CTMCs. Based on a parameterized product obtained from the CTMC and an automaton extracted from a given CCSL formula, we propose an approximate model checking algorithm and analyse its complexity....
An Extended Ontology Model and Ontology Checking Based on Description Logics
Institute of Scientific and Technical Information of China (English)
王洪伟; 蒋馥; 吴家春
2004-01-01
Ontology is defined as an explicit specification of a conceptualization. In this paper, an extended ontology model was constructed using description logics, which is a 5-tuples including term set, individual set, term definition set, instantiation assertion set and term restriction set. Based on the extended model, the issue on ontology checking was studied with the conclusion that the four kinds of term checking, including term satisfiability checking, term subsumption checking, term equivalence checking and term disjointness checking, can be reduced to the satisfiability checking, and satisfiability checking can be transformed into instantiation consistence checking.
Computing Small 1-Homological Models for Commutative Differential Graded Algebras
Alvarez, Victor; Armario, Jose Andres; Frau, Maria Dolores; Gonzalez-Diaz, Rocio; Jimenez, Maria Jose; Real, Pedro; Silva, Beatriz
2001-01-01
We use homological perturbation machinery specific for the algebra category [P. Real. Homological Perturbation Theory and Associativity. Homology, Homotopy and Applications vol. 2, n. 5 (2000) 51-88] to give an algorithm for computing the differential structure of a small 1--homological model for commutative differential graded algebras (briefly, CDGAs). The complexity of the procedure is studied and a computer package in Mathematica is described for determining such models.
Mixed Portmanteau Test for Diagnostic Checking of Time Series Models
Directory of Open Access Journals (Sweden)
Sohail Chand
2014-01-01
Full Text Available Model criticism is an important stage of model building and thus goodness of fit tests provides a set of tools for diagnostic checking of the fitted model. Several tests are suggested in literature for diagnostic checking. These tests use autocorrelation or partial autocorrelation in the residuals to criticize the adequacy of fitted model. The main idea underlying these portmanteau tests is to identify if there is any dependence structure which is yet unexplained by the fitted model. In this paper, we suggest mixed portmanteau tests based on autocorrelation and partial autocorrelation functions of the residuals. We derived the asymptotic distribution of the mixture test and studied its size and power using Monte Carlo simulations.
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.
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
Symbolic Model Checking and Analysis for E-Commerce Protocol
Institute of Scientific and Technical Information of China (English)
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
Quantum matrix algebra for the SU(n) WZNW model
Furlan, Paolo; Isaev, A P; Ogievetsky, O V; Pyatov, P N; Todorov, I T
2003-01-01
The zero modes of the chiral SU(n) WZNW model give rise to an intertwining quantum matrix algebra A generated by an n x n matrix a=(a^i_\\alpha) (with noncommuting entries) and by rational functions of n commuting elements q^{p_i}. We study a generalization of the Fock space (F) representation of A for generic q (q not a root of unity) and demonstrate that it gives rise to a model of the quantum universal enveloping algebra U_q(sl_n), each irreducible representation entering F with multiplicity 1. For an integer level k the complex parameter q is an even root of unity, q^h=-1 (h=k+n) and the algebra A has an ideal I_h such that the factor algebra A_h = A/I_h is finite dimensional.
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.
Observable algebras for the rational and trigonometric Euler-Calogero-Moser Models
International Nuclear Information System (INIS)
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.))
Schedulability of Herschel revisited using statistical model checking
DEFF Research Database (Denmark)
David, Alexandre; Larsen, Kim Guldstrand; Legay, Axel;
2015-01-01
Schedulability analysis is a main concern for several embedded applications due to their safety-critical nature. The classical method of response time analysis provides an efficient technique used in industrial practice. However, the method is based on conservative assumptions related to execution...... 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...
Performance modeling and prediction for linear algebra algorithms
Iakymchuk, Roman
2012-01-01
This dissertation incorporates two research projects: performance modeling and prediction for dense linear algebra algorithms, and high-performance computing on clouds. The first project is focused on dense matrix computations, which are often used as computational kernels for numerous scientific applications. To solve a particular mathematical operation, linear algebra libraries provide a variety of algorithms. The algorithm of choice depends, obviously, on its performance. Performance of su...
Detecting feature interactions in Web services with model checking techniques
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
As a platform-independent software system, a Web service is designed to offer interoperability among diverse and heterogeneous applications.With the introduction of service composition in the Web service creation, various message interactions among the atomic services result in a problem resembling the feature interaction problem in the telecommunication area.This article defines the problem as feature interaction in Web services and proposes a model checking-based detection method.In the method, the Web service description is translated to the Promela language - the input language of the model checker simple promela interpreter (SPIN), and the specific properties, expressed as linear temporal logic (LTL) formulas, are formulated according to our classification of feature interaction.Then, SPIN is used to check these specific properties to detect the feature interaction in Web services.
SMT-based Bounded Model Checking with Difference Logic Constraints
Bersani, Marcello M; Morzenti, Angelo; Pradella, Matteo; Rossi, Matteo; Pietro, Pierluigi San
2010-01-01
Traditional Bounded Model Checking (BMC) is based on translating the model checking problem into SAT, the Boolean satisfiability problem. This paper introduces an encoding of Linear Temporal Logic with Past operators (PLTL) into the Quantifier-Free Difference Logic with Uninterpreted Functions (QF-UFIDL). The resulting encoding is a simpler and more concise version of existing SATbased encodings, currently used in BMC. In addition, we present an extension of PLTL augmented with arithmetic relations over integers, which can express unbounded counters; as such, the extended logic is more expressive than PLTL. We introduce suitable restrictions and assumptions that are shown to make the verification problem for the extended logic decidable, and we define an encoding of the new logic into QF-UFIDL. Finally, a performance comparison with the SAT-based approach on purely PLTL examples shows significant improvements in terms of both execution time and memory occupation.
Boundary algebras and Kac modules for logarithmic minimal models
Morin-Duchesne, Alexi; Ridout, David
2015-01-01
Virasoro Kac modules were initially introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be...
A Graphical μ-Calculus and Local Model Checking
Institute of Scientific and Technical Information of China (English)
林惠民
2002-01-01
A graphical notation for the propositionalμ-calculus, called modal graphs, ispresented. It is shown that both the textual and equational presentations of theμ-calculus canbe translated into modal graphs. A model checking algorithm based on such graphs is proposed.The algorithm is truly local in the sense that it only generates the parts of the underlyingsearch space which are necessary for the computation of the final result. The correctness of thealgorithm is proven and its complexity analysed.
Model Checking for Licensing Support in the Finnish Nuclear Industry
Energy Technology Data Exchange (ETDEWEB)
Antti, Pakonen; Janne, Valkonen [VTT Technical Research, VTT (Finland); Sami, Matinaho; Markus, Hartikainen [Protum Power and Heat, Fortum (Finland)
2014-08-15
This paper examines how model checking can be used to support the qualification of digital I and C software in nuclear power plants, in a way that is consistent with regulatory demands specifically, the common position of seven European nuclear regulators and authorised technical support organisations. As a practical example, we discuss the third-party review service provided by VTT for the power company Fortum in the I and C renewal project of the Loviisa plant in southern Finland.
Parallel State Space Construction for Model-Checking
Garavel, Hubert; Mateescu, Radu; Smarandache, Irina
2001-01-01
The verification of concurrent finite-state systems by model-checking often requires to generate (a large part of) the state space of the system under analysis. Because of the state explosion problem, this may be a resource-consuming operation, both in terms of memory and CPU time. In this report, we aim at improving the performances of state space construction by using parallelization techniques. We present parallel algorithms for constructing state spaces (or Labeled Transition Systems) on ...
A comparison between algebraic models of molecular spectroscopy
Bijker, R; Lemus, R; Arias, J M; Pérez-Bernal, F
1998-01-01
We discuss a symmetry-adapted algebraic (or vibron) model for molecular spectroscopy. The model is formulated in terms of tensor operators under the molecular point group. In this way, we have identified interactions that are absent in previous versions of the vibron model, in which the Hamiltonian is expressed in terms of Casimir operators and their products. The inclusion of these new interactions leads to reliable spectroscopic predictions. As an example we study the vibrational excitations of the methane molecule, and compare our results with those obtained in other algebraic models.
Correctness of Sensor Network Applications by Software Bounded Model Checking
Werner, Frank; Faragó, David
We investigate the application of the software bounded model checking tool CBMC to the domain of wireless sensor networks (WSNs). We automatically generate a software behavior model from a network protocol (ESAWN) implementation in a WSN development and deployment platform (TinyOS), which is used to rigorously verify the protocol. Our work is a proof of concept that automatic verification of programs of practical size (≈ 21 000 LoC) and complexity is possible with CBMC and can be integrated into TinyOS. The developer can automatically check for pointer dereference and array index out of bound errors. She can also check additional, e.g., functional, properties that she provides by assume- and assert-statements. This experience paper shows that our approach is in general feasible since we managed to verify about half of the properties. We made the verification process scalable in the size of the code by abstraction (eg, from hardware) and by simplification heuristics. The latter also achieved scalability in data type complexity for the properties that were verifiable. The others require technical advancements for complex data types within CBMC's core.
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. PMID:11890304
Model-Checking Linear-Time Properties of Quantum Systems
Ying, Mingsheng; Yu, Nengkun; Feng, Yuan
2011-01-01
We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain closed subspaces of state (Hilbert) spaces are used as the atomic propositions about the behavior of systems. We provide an algorithm for verifying invariants of quantum automata. Then automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and omega-properties recognizable by reversible Buechi automata.
Model Checking Data Consistency for Cache Coherence Protocols
Institute of Scientific and Technical Information of China (English)
Hong Pan; Hui-Min Lin; Yi Lv
2006-01-01
A method for automatic verification of cache coherence protocols is presented, in which cache coherence protocols are modeled as concurrent value-passing processes, and control and data consistency requirement are described as formulas in first-orderμ-calculus. A model checker is employed to check if the protocol under investigation satisfies the required properties. Using this method a data consistency error has been revealed in a well-known cache coherence protocol.The error has been corrected, and the revised protocol has been shown free from data consistency error for any data domain size, by appealing to data independence technique.
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...
SoS contract verification using statistical model checking
Directory of Open Access Journals (Sweden)
Alessandro Mignogna
2013-11-01
Full Text Available Exhaustive formal verification for systems of systems (SoS is impractical and cannot be applied on a large scale. In this paper we propose to use statistical model checking for efficient verification of SoS. We address three relevant aspects for systems of systems: 1 the model of the SoS, which includes stochastic aspects; 2 the formalization of the SoS requirements in the form of contracts; 3 the tool-chain to support statistical model checking for SoS. We adapt the SMC technique for application to heterogeneous SoS. We extend the UPDM/SysML specification language to express the SoS requirements that the implemented strategies over the SoS must satisfy. The requirements are specified with a new contract language specifically designed for SoS, targeting a high-level English- pattern language, but relying on an accurate semantics given by the standard temporal logics. The contracts are verified against the UPDM/SysML specification using the Statistical Model Checker (SMC PLASMA combined with the simulation engine DESYRE, which integrates heterogeneous behavioral models through the functional mock-up interface (FMI standard. The tool-chain allows computing an estimation of the satisfiability of the contracts by the SoS. The results help the system architect to trade-off different solutions to guide the evolution of the SoS.
Laser modeling a numerical approach with algebra and calculus
Csele, Mark Steven
2014-01-01
Offering a fresh take on laser engineering, Laser Modeling: A Numerical Approach with Algebra and Calculus presents algebraic models and traditional calculus-based methods in tandem to make concepts easier to digest and apply in the real world. Each technique is introduced alongside a practical, solved example based on a commercial laser. Assuming some knowledge of the nature of light, emission of radiation, and basic atomic physics, the text:Explains how to formulate an accurate gain threshold equation as well as determine small-signal gainDiscusses gain saturation and introduces a novel pass
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.
Logarithmic sℓ-hat (2) CFT models from Nichols algebras: I
International Nuclear Information System (INIS)
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)
Stochastic Model Checking of the Stochastic Quality Calculus
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis; Zeng, Kebin
2015-01-01
The Quality Calculus uses quality binders for input to express strategies for continuing the computation even when the desired input has not been received. The Stochastic Quality Calculus adds generally distributed delays for output actions and real-time constraints on the quality binders for inp...... based on stochastic model checking and we compute closed form solutions for a number of interesting scenarios. The analyses are applied to the design of an intelligent smart electrical meter of the kind to be installed in European households by 2020....
Symbolic Game Semantics for Model Checking Program Families
DEFF Research Database (Denmark)
Dimovski, Aleksandar
this paper, we propose an efficient game semantics based approach for verifying open program families, i.e. program families with free (undefined) identifiers. We use symbolic representation of algorithmic game semantics, where concrete values are replaced with symbolic ones. In this way, we can...... compactly represent program families with infinite integers as so-called (finite-state) featured symbolic automata. Specifically designed model checking algorithms are then employed to verify safety of all programs from a family at once and pinpoint those programs that are unsafe (respectively, safe). We...
Model Checking Degrees of Belief in a System of Agents
Raimondi, Franco; Primero, Giuseppe; Rungta, Neha
2014-01-01
Reasoning about degrees of belief has been investigated in the past by a number of authors and has a number of practical applications in real life. In this paper we present a unified framework to model and verify degrees of belief in a system of agents. In particular, we describe an extension of the temporal-epistemic logic CTLK and we introduce a semantics based on interpreted systems for this extension. In this way, degrees of beliefs do not need to be provided externally, but can be derived automatically from the possible executions of the system, thereby providing a computationally grounded formalism. We leverage the semantics to (a) construct a model checking algorithm, (b) investigate its complexity, (c) provide a Java implementation of the model checking algorithm, and (d) evaluate our approach using the standard benchmark of the dining cryptographers. Finally, we provide a detailed case study: using our framework and our implementation, we assess and verify the situational awareness of the pilot of Air France 447 flying in off-nominal conditions.
Generalized Symbolic Execution for Model Checking and Testing
Khurshid, Sarfraz; Pasareanu, Corina; Visser, Willem; Kofmeyer, David (Technical Monitor)
2003-01-01
Modern software systems, which often are concurrent and manipulate complex data structures must be extremely reliable. We present a novel framework based on symbolic execution, for automated checking of such systems. We provide a two-fold generalization of traditional symbolic execution based approaches: one, we define a program instrumentation, which enables standard model checkers to perform symbolic execution; two, we give a novel symbolic execution algorithm that handles dynamically allocated structures (e.g., lists and trees), method preconditions (e.g., acyclicity of lists), data (e.g., integers and strings) and concurrency. The program instrumentation enables a model checker to automatically explore program heap configurations (using a systematic treatment of aliasing) and manipulate logical formulae on program data values (using a decision procedure). We illustrate two applications of our framework: checking correctness of multi-threaded programs that take inputs from unbounded domains with complex structure and generation of non-isomorphic test inputs that satisfy a testing criterion. Our implementation for Java uses the Java PathFinder model checker.
An algebraic approach to modeling in software engineering
International Nuclear Information System (INIS)
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
Fully Analyzing an Algebraic Polya Urn Model
Morcrette, Basile
2012-01-01
This paper introduces and analyzes a particular class of Polya urns: balls are of two colors, can only be added (the urns are said to be additive) and at every step the same constant number of balls is added, thus only the color compositions varies (the urns are said to be balanced). These properties make this class of urns ideally suited for analysis from an "analytic combinatorics" point-of-view, following in the footsteps of Flajolet-Dumas-Puyhaubert, 2006. Through an algebraic generating function to which we apply a multiple coalescing saddle-point method, we are able to give precise asymptotic results for the probability distribution of the composition of the urn, as well as local limit law and large deviation bounds.
Model checking as an aid to procedure design
International Nuclear Information System (INIS)
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)
Reasoning About Strategies: On the Model-Checking Problem
Mogavero, Fabio; Perelli, Giuseppe; Vardi, Moshe Y
2011-01-01
In open systems verification, to formally check for reliability, one needs an appropriate formalism to model the interaction between agents and express the correctness of the system no matter how the environment behaves. An important contribution in this context is given by modal logics for strategic ability, in the setting of multi-agent games, such as ATL, ATL*, and the like. Recently, Chatterjee, Henzinger, and Piterman introduced Strategy Logic (CHP-SL), with the aim of getting a powerful framework for reasoning explicitly about strategies. CHP-SL is obtained by using first-order quantifications over strategies and it has been investigated in the setting of two-agents turned-based games, where a non-elementary model-checking algorithm has been provided. While CHP-SL is a very expressive logic, we claim that it does not fully capture the strategic aspects of multi-agent systems. In this paper, we introduce and study a more general strategy logic, denoted SL, for reasoning about strategies in multi-agent co...
Using Model Checking for Analyzing Distributed Power Control Problems
Directory of Open Access Journals (Sweden)
Thomas Brihaye
2010-01-01
Full Text Available Model checking (MC is a formal verification technique which has been known and still knows a resounding success in the computer science community. Realizing that the distributed power control (PC problem can be modeled by a timed game between a given transmitter and its environment, the authors wanted to know whether this approach can be applied to distributed PC. It turns out that it can be applied successfully and allows one to analyze realistic scenarios including the case of discrete transmit powers and games with incomplete information. The proposed methodology is as follows. We state some objectives a transmitter-receiver pair would like to reach. The network is modeled by a game where transmitters are considered as timed automata interacting with each other. The objectives are then translated into timed alternating-time temporal logic formulae and MC is exploited to know whether the desired properties are verified and determine a winning strategy.
Model-checking dense-time Duration Calculus
DEFF Research Database (Denmark)
Fränzle, Martin
2004-01-01
Since the seminal work of Zhou Chaochen, M. R. Hansen, and P. Sestoft on decidability of dense-time Duration Calculus [Zhou, Hansen, Sestoft, 1993] it is well-known that decidable fragments of Duration Calculus can only be obtained through withdrawal of much of the interesting vocabulary of this...... logic. While this was formerly taken as an indication that key-press verification of implementations with respect to elaborate Duration Calculus specifications were also impossible, we show that the model property is well decidable for realistic designs which feature natural constraints on their...... 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....
Methods to model-check parallel systems software.
Energy Technology Data Exchange (ETDEWEB)
Matlin, O. S.; McCune, W.; Lusk, E.
2003-12-15
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.
Weak quasitriangular Quasi-Hopf algebra structure of minimal models
Teschner, J. A.
1995-01-01
The chiral vertex operators for the minimal models are constructed and used to define a fusion product of representations. The existence of commutativity and associativity operations is proved. The matrix elements of the associativity operations are shown to be given in terms of the 6-j symbols of the weak quasitriangular quasi-Hopf algebra obtained by truncating $\\usl$ at roots of unity.
Supersymmetry and DLCQ Limit of Lie 3-algebra Model of M-theory
Sato, Matsuo
2011-01-01
In arXiv:1003.4694, we proposed two models of M-theory, Hermitian 3-algebra model and Lie 3-algebra model. In this paper, we study the Lie 3-algebra model with a Lorentzian Lie 3-algebra. This model is ghost-free despite the Lorentzian 3-algebra. We show that our model satisfies two criteria as a model of M-theory. First, we show that the model possesses N=1 supersymmetry in eleven dimensions. Second, we show the model reduces to BFSS matrix theory with finite size matrices in a DLCQ limit.
A conceptual model of check dam hydraulics for gully control
Directory of Open Access Journals (Sweden)
C. Castillo
2013-09-01
Full Text Available There is little information in scientific literature regarding the modifications induced by check dam systems in flow regimes in restored gully reaches, despite it being a crucial issue for the design of conservation measures. Here, we develop a conceptual model to classify flow regimes in straight rectangular channels for initial and dam-filling conditions as well as a method of estimating efficiency in order to provide guidelines for optimal design. The model integrates several previous mathematical approaches for assessing the main processes involved (hydraulic jump HJ, impact flow, gradually varied flows. Its performance was compared with the simulations obtained from IBER, a bi-dimensional hydrodynamic model. The impact of check dam spacing (defined by the geometric factor of influence c on efficiency was explored. Eleven main classifications of flow regimes were identified depending on the element and level of influence. The model produced similar results when compared with IBER, but led to higher estimations of HJ and impact lengths. Total influence guaranteed maximum efficiency and HJ control defining the location of the optimal c. Geometric total influence (c = 1 was a valid criterion for the different stages of the structures in a wide range of situations provided that hydraulic roughness conditions remained high within the gully, e.g. through revegetation. Our total influence criterion involved shorter spacing than that habitually recommended in technical manuals for restoration, but was in line with those values found in spontaneous and stable step-pools systems, which might serve as a reference for man-made interventions.
How algebraic Bethe ansatz works for integrable model
Fadeev, L
1996-01-01
I study the technique of Algebraic Bethe Ansatz for solving integrable models and show how it works in detail on the simplest example of spin 1/2 XXX magnetic chain. Several other models are treated more superficially, only the specific details are given. Several parameters, appearing in these generalizations: spin s, anisotropy parameter \\ga, shift \\om in the alternating chain, allow to include in our treatment most known examples of soliton theory, including relativistic model of Quantum Field Theory.
Generalization of Richardson-Gaudin models to rank-2 algebras
Energy Technology Data Exchange (ETDEWEB)
Errea, B; Lerma, S; Dukelsky, J; Dimitrova, S S; Pittel, S; Van Isacker, P; Gueorguiev, V G
2006-07-20
A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained.
Modelling and Analysis of Network Security - an Algebraic Approach
Qian ZHANG; Jiang, Ying; Wu, Peng
2015-01-01
Game theory has been applied to investigate network security. But different security scenarios were often modeled via different types of games and analyzed in an ad-hoc manner. In this paper, we propose an algebraic approach for modeling and analyzing uniformly several types of network security games. This approach is based on a probabilistic extension of the value-passing Calculus of Communicating Systems (CCS) which is regarded as a Generative model for Probabilistic Value-passing CCS (PVCC...
Algebraic turbulence modeling for unstructured and adaptive meshes
Mavriplis, Dimitri J.
1990-01-01
An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.
The BC1 quantum elliptic model: algebraic forms, hidden algebra sl(2), polynomial eigenfunctions
International Nuclear Information System (INIS)
The potential of the BC1 quantum elliptic model is a superposition of two Weierstrass functions with a doubling of both periods (two coupling constants). The BC1 elliptic model degenerates to an A1 elliptic model characterized by the Lamé Hamiltonian. It is shown that in the space of the BC1 elliptic invariant, the potential becomes a rational function, while the flat space metric becomes a polynomial. The model possesses the hidden sl(2) algebra for arbitrary coupling constants: it is equivalent to the sl(2) quantum top in three different magnetic fields. It is shown that three one-parametric families of coupling constants exist, for which a finite number of polynomial eigenfunctions (up to a factor) occur. (paper)
Combining Decision Diagrams and SAT Procedures for Efficient Symbolic Model Checking
DEFF Research Database (Denmark)
Williams, Poul Frederick; Biere, Armin; Clarke, Edmund M.;
2000-01-01
, combined with BDDs and SAT-solvers to perform satisfiability checking. As a result we are able to model check systems for which standard BDD-based methods fail. For example, we model check a liveness property of a 256 bit shift-and-add multiplier and we are able to find a previously undetected bug...
A Succinct Approach to Static Analysis and Model Checking
DEFF Research Database (Denmark)
Filipiuk, Piotr
In a number of areas software correctness is crucial, therefore it is often desirable to formally verify the presence of various properties or the absence of errors. This thesis presents a framework for concisely expressing static analysis and model checking problems. The framework facilitates...... guarantees that there always is single best solution for a problem under consideration. We also develop a solving algorithm, based on a dierential worklist, that computes the least solution guaranteed by the Moore Family result. Furthermore, we present a logic for specifying analysis problems called Layered...... Fixed Point Logic. Its most prominent feature is the direct support for both inductive computations of behaviors as well as co-inductive specications of properties. Two main theoretical contributions are a Moore Family result and a parametrized worst-case time complexity result. We develop a BDD...
Analysis of the Security of BB84 by Model Checking
Elboukhari, Mohamed; Azizi, Abdelmalek; 10.5121/ijnsa.2010.2207
2010-01-01
Quantum Cryptography or Quantum key distribution (QKD) is a technique that allows the secure distribution of a bit string, used as key in cryptographic protocols. When it was noted that quantum computers could break public key cryptosystems based on number theory extensive studies have been undertaken on QKD. Based on quantum mechanics, QKD offers unconditionally secure communication. Now, the progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years. Efforts are made to improve the performance and reliability of the implemented technologies. But several challenges remain despite this big progress. The task of how to test the apparatuses of QKD For example did not yet receive enough attention. These devises become complex and demand a big verification effort. In this paper we are interested in an approach based on the technique of probabilistic model checking for studying quantum information. Precisely, we use the PRISM tool to analyze ...
Boundary algebras and Kac modules for logarithmic minimal models
Morin-Duchesne, Alexi; Rasmussen, Jørgen; Ridout, David
2015-10-01
Virasoro Kac modules were originally introduced indirectly as representations whose characters arise in the continuum scaling limits of certain transfer matrices in logarithmic minimal models, described using Temperley-Lieb algebras. The lattice transfer operators include seams on the boundary that use Wenzl-Jones projectors. If the projectors are singular, the original prescription is to select a subspace of the Temperley-Lieb modules on which the action of the transfer operators is non-singular. However, this prescription does not, in general, yield representations of the Temperley-Lieb algebras and the Virasoro Kac modules have remained largely unidentified. Here, we introduce the appropriate algebraic framework for the lattice analysis as a quotient of the one-boundary Temperley-Lieb algebra. The corresponding standard modules are introduced and examined using invariant bilinear forms and their Gram determinants. The structures of the Virasoro Kac modules are inferred from these results and are found to be given by finitely generated submodules of Feigin-Fuchs modules. Additional evidence for this identification is obtained by comparing the formalism of lattice fusion with the fusion rules of the Virasoro Kac modules. These are obtained, at the character level, in complete generality by applying a Verlinde-like formula and, at the module level, in many explicit examples by applying the Nahm-Gaberdiel-Kausch fusion algorithm.
The Hidden Quantum Group of the 8-vertex Free Fermion Model: q-Clifford Algebras
Cuerno, Rodolfo; Gómez, César; López Manzanares, Esperanza; Sierra, Germán
1993-01-01
We prove in this paper that the elliptic $R$--matrix of the eight vertex free fermion model is the intertwiner $R$--matrix of a quantum deformed Clifford--Hopf algebra. This algebra is constructed by affinization of a quantum Hopf deformation of the Clifford algebra.
Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
Khachatryan, Sh.; Ferraz, A.; Klümper, A.; Sedrakyan, A.
2015-10-01
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.
Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
Directory of Open Access Journals (Sweden)
Sh. Khachatryan
2015-10-01
Full Text Available We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy with Yang–Baxter or tetrahedron equations. The basic ingredient of our models is the R-matrix, which describes the scattering of a pair of particles over another pair of particles, the quark-anti-quark (meson scattering on another quark-anti-quark state. We show that the Kitaev model belongs to this class of models and its R-matrix fulfills well-defined equations for integrability.
Algebraic fermion models and nuclear structure physics
International Nuclear Information System (INIS)
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
Analysis of the Security of BB84 by Model Checking
Directory of Open Access Journals (Sweden)
Mohamed Elboukhari
2010-04-01
Full Text Available Quantum Cryptography or Quantum key distribution (QKD is a technique that allows the secure distribution of a bit string, used as key in cryptographic protocols. When it was noted that quantum computers could break public key cryptosystems based on number theory extensive studies have been undertaken on QKD. Based on quantum mechanics, QKD offers unconditionally secure communication. Now, the progress of research in this field allows the anticipation of QKD to be available outside of laboratories within the next few years. Efforts are made to improve the performance and reliability of the implemented technologies. But several challenges remain despite this big progress. The task of how to test the apparatuses of QKD For example did not yet receive enough attention. These devises become complex and demand a big verification effort. In this paper we are interested in an approach based on the technique of probabilistic model checking for studying quantum information. Precisely, we use the PRISM tool to analyze the security of BB84 protocol and we are focused on the specific security property of eavesdropping detection. We show that this property is affected by the parameters of quantum channel and the power of eavesdropper
Optimisation of BPMN Business Models via Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2013-01-01
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...
Algebraic Turbulence-Chemistry Interaction Model
Norris, Andrew T.
2012-01-01
The results of a series of Perfectly Stirred Reactor (PSR) and Partially Stirred Reactor (PaSR) simulations are compared to each other over a wide range of operating conditions. It is found that the PaSR results can be simulated by a PSR solution with just an adjusted chemical reaction rate. A simple expression has been developed that gives the required change in reaction rate for a PSR solution to simulate the PaSR results. This expression is the basis of a simple turbulence-chemistry interaction model. The interaction model that has been developed is intended for use with simple one-step global reaction mechanisms and for steady-state flow simulations. Due to the simplicity of the model there is very little additional computational cost in adding it to existing CFD codes.
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.
Algebraic spin liquid in an exactly solvable spin model
Energy Technology Data Exchange (ETDEWEB)
Yao, Hong; Zhang, Shou-Cheng; Kivelson, Steven A.; /Stanford U., Phys. Dept.
2010-03-25
We have proposed an exactly solvable quantum spin-3/2 model on a square lattice. Its ground state is a quantum spin liquid with a half integer spin per unit cell. The fermionic excitations are gapless with a linear dispersion, while the topological 'vison' excitations are gapped. Moreover, the massless Dirac fermions are stable. Thus, this model is, to the best of our knowledge, the first exactly solvable model of half-integer spins whose ground state is an 'algebraic spin liquid.'
Model Checking Classes of Metric LTL Properties of Object-Oriented Real-Time Maude Specifications
Erika Ábrahám; Peter Csaba Ölveczky; Daniela Lepri
2010-01-01
This paper presents a transformational approach for model checking two important classes of metric temporal logic (MTL) properties, namely, bounded response and minimum separation, for nonhierarchical object-oriented Real-Time Maude specifications. We prove the correctness of our model checking algorithms, which terminate under reasonable non-Zeno-ness assumptions when the reachable state space is finite. These new model checking features have been integrated into Real-Time Maude, and are use...
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
The Modeling Library of Eavesdropping Methods in Quantum Cryptography Protocols by Model Checking
Yang, Fan; Yang, Guowu; Hao, Yujie
2016-07-01
The most crucial issue of quantum cryptography protocols is its security. There exists many ways to attack the quantum communication process. In this paper, we present a model checking method for modeling the eavesdropping in quantum information protocols. So when the security properties of a certain protocol are needed to be verified, we can directly use the models which are already built. Here we adopt the probabilistic model checking tool—PRISM to model these attack methods. The verification results show that the detection rate of eavesdropping is approximately close to 1 when enough photons are transmitted.
The Modeling Library of Eavesdropping Methods in Quantum Cryptography Protocols by Model Checking
Yang, Fan; Yang, Guowu; Hao, Yujie
2016-03-01
The most crucial issue of quantum cryptography protocols is its security. There exists many ways to attack the quantum communication process. In this paper, we present a model checking method for modeling the eavesdropping in quantum information protocols. So when the security properties of a certain protocol are needed to be verified, we can directly use the models which are already built. Here we adopt the probabilistic model checking tool—PRISM to model these attack methods. The verification results show that the detection rate of eavesdropping is approximately close to 1 when enough photons are transmitted.
The supersymmetry extended Weyl algebra and Casalbuoni's G4 model
International Nuclear Information System (INIS)
We briefly review the classical version of Casalbuoni's G4 supersymmetric model (i.e. the single particle version of the scalar chiral supermultiplet) with particular emphasis on the role played by the chirality. We show that the off-mass-shell commutators of the quantum model can be derived from the Lie algebra of the Weyl (i.e. Poincare plus dilatations) group extended by supersymmetry. The proper-time wavefunctions of the off-mass-shell states satisfy equations which clarify the role of the auxiliary fields of quantum field theory. (orig.)
A Multiple—Valued Algebra for Modeling MOS VLSI Circuits at Switch—Level
Institute of Scientific and Technical Information of China (English)
胡谋
1992-01-01
A multiple-valued algebra for modeling MOS VLSI circuits at switch-level is proposed in this paper,Its structure and properties are studied.This algebra can be used to transform a MOS digital circuit to a swith-level algebraic expression so as to generate the truth table for the circuit and to derive a Boolean expression for it.In the paper,methods to construct a switch-level algebraic expression for a circuit and methods to simplify expressions are given.This algebra provides a new tool for MOS VLSI circuit design and analysis.
Applications Of Algebraic Image Operators To Model-Based Vision
Lerner, Bao-Ting; Morelli, Michael V.; Thomas, Hans J.
1989-03-01
This paper extends our previous research on a highly structured and compact algebraic representation of grey-level images. Addition and multiplication are defined for the set of all grey-level images, which can then be described as polynomials of two variables. Utilizing this new algebraic structure, we have devised an innovative, efficient edge detection scheme.We have developed a robust method for linear feature extraction by combining the techniques of a Hough transform and a line follower with this new edge detection scheme. The major advantage of this feature extractor is its general, object-independent nature. Target attributes, such as line segment lengths, intersections, angles of intersection, and endpoints are derived by the feature extraction algorithm and employed during model matching. The feature extractor and model matcher are being incorporated into a distributed robot control system. Model matching is accomplished using both top-down and bottom-up processing: a priori sensor and world model information are used to constrain the search of the image space for features, while extracted image information is used to update the model.
Clifford algebra and the projective model of Hyperbolic spaces
Sokolov, Andrey
2016-01-01
I apply the algebraic framework developed in [1] to study geometry of hyperbolic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is described in [2].
Family-Based Model Checking Without a Family-Based Model Checker
DEFF Research Database (Denmark)
Dimovski, Aleksandar; Al-Sibahi, Ahmad Salim; Brabrand, Claus; Wasowski, Andrzej
Many software systems are variational: they can be configured to meet diverse sets of requirements. Variability is found in both communication protocols and discrete controllers of embedded systems. In these areas, model checking is an important verification technique. For variational models...
Proceedings Second International Workshop on Algebraic Methods in Model-based Software Engineering
Durán, Francisco
2011-01-01
Over the past years there has been quite a lot of activity in the algebraic community about using algebraic methods for providing support to model-driven software engineering. The aim of this workshop is to gather researchers working on the development and application of algebraic methods to provide rigorous support to model-based software engineering. The topics relevant to the workshop are all those related to the use of algebraic methods in software engineering, including but not limited to: formally specifying and verifying model-based software engineering concepts and related ones (MDE, UML, OCL, MOF, DSLs, ...); tool support for the above; integration of formal and informal methods; and theoretical frameworks (algebraic, rewriting-based, category theory-based, ...). The workshop's main goal is to examine, discuss, and relate the existing projects within the algebraic community that address common open-issues in model-driven software engineering.
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.
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
A U(1) Current Algebra Model Coupled to 2D-Gravity
Stoilov, M.; Zaikov, R.
1993-01-01
We consider a simple model of a scalar field with $U(1)$ current algebra gauge symmetry coupled to $2D$-gravity in order to clarify the origin of Stuckelberg symmetry in the $w_{\\infty}$-gravity theory. An analogous symmetry takes place in our model too. The possible central extension of the complete symmetry algebra and the corresponding critical dimension have been found. The analysis of the Hamiltonian and the constraints shows that the generators of the current algebra, the reparametrizat...
A New Algebraic Modelling Approach to Distributed Problem-Solving in MAS
Institute of Scientific and Technical Information of China (English)
帅典勋; 邓志东
2002-01-01
This paper is devoted to a new algebraic modelling approach to distributed problem-solving in multi-agent systems (MAS), which is featured by a unified framework for describing and treating social behaviors, social dynamics and social intelligence. A conceptual architecture of algebraic modelling is presented. The algebraic modelling of typical social behaviors, social situation and social dynamics is discussed in the context of distributed problemsolving in MAS. The comparison and simulation on distributed task allocations and resource assignments in MAS show more advantages of the algebraic approach than other conventional methods.
Clifford algebras geometric modelling and chain geometries with application in kinematics
Klawitter, Daniel
2015-01-01
After revising known representations of the group of Euclidean displacements Daniel Klawitter gives a comprehensive introduction into Clifford algebras. The Clifford algebra calculus is used to construct new models that allow descriptions of the group of projective transformations and inversions with respect to hyperquadrics. Afterwards, chain geometries over Clifford algebras and their subchain geometries are examined. The author applies this theory and the developed methods to the homogeneous Clifford algebra model corresponding to Euclidean geometry. Moreover, kinematic mappings for special Cayley-Klein geometries are developed. These mappings allow a description of existing kinematic mappings in a unifying framework. Contents Models and representations of classical groups Clifford algebras, chain geometries over Clifford algebras Kinematic mappings for Pin and Spin groups Cayley-Klein geometries Target Groups Researchers and students in the field of mathematics, physics, and mechanical engineering About...
Algebraic Traveling Wave Solutions of a Non-local Hydrodynamic-type Model
International Nuclear Information System (INIS)
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
Model checking and strategy synthesis for stochastic games: from theory to practice
Kwiatkowska, MZ
2016-01-01
Probabilistic model checking is an automatic procedure for establishing if a desired property holds in a probabilistic model, aimed at verifying quantitative probabilistic specifications such as the probability of a critical failure occurring or expected time to termination. Much progress has been made in recent years in algorithms, tools and applications of probabilistic model checking, as exemplified by the probabilistic model checker PRISM (www.prismmodelchecker.org). However, the unstoppa...
Checking Fine and Gray Subdistribution Hazards Model with Cumulative Sums of Residuals
Li, Jianing; Scheike, Thomas H.; Zhang, Mei-Jie
2014-01-01
Recently, Fine and Gray (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. T...
A logic for model-checking of mean-field models
Kolesnichenko, Anna; Remke, Anne; Boer, de, J.W.; Haverkort, Boudewijn R.
2012-01-01
Recently, many systems consisting of a large number of interacting objects were analysed using the mean-field method, which has only been used for performance evaluation. In this short paper, we apply it to model checking. We define logic, which allows to describe the overall properties of the large system.
Algebraic model for single-particle energies of $\\Lambda$ hypernuclei
Fortunato, L
2016-01-01
A model is proposed for the spectrum of $\\Lambda$ hypernuclei based on the $u(3)\\times u(2)$ Lie algebra, in which the internal degrees of freedom of the spin-1/2 $\\Lambda$ particle are treated in the Fermionic $u(2)$ scheme, while the motion of the hyperon inside a nucleus is described in the Bosonic $u(3)$ harmonic oscillator scheme. Within this model, a simple formula for single-particle energies of the $\\Lambda$ particle is obtained from the natural dynamical symmetry. The formula is applied to the experimental data on the reaction spectroscopy for the $^{89}_\\Lambda$Y and $^{51}_\\Lambda$V hypernuclei, providing a clear theoretical interpretation of the observed structures.
Development of a butterfly check valve model under natural circulation conditions
International Nuclear Information System (INIS)
Highlights: • Bases on Lim’s swing check valve model, a butterfly check valve model was developed. • The method to quantify the friction torque TF 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
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.
Model Checking and Model-based Testing in the Railway Domain
DEFF Research Database (Denmark)
Haxthausen, Anne Elisabeth; Peleska, Jan
2015-01-01
This chapter describes some approaches and emerging trends for verification and model-based testing of railway control systems. We describe state-of-the-art methods and associated tools for verifying interlocking systems and their configuration data, using bounded model checking and k-induction. ......This chapter describes some approaches and emerging trends for verification and model-based testing of railway control systems. We describe state-of-the-art methods and associated tools for verifying interlocking systems and their configuration data, using bounded model checking and k......-induction. Using real-world models of novel Danish interlocking systems, it is exemplified how this method scales up and is suitable for industrial application. For verification of the integrated HW/SW system performing the interlocking control tasks, a modelbased hardware-in-the-loop testing approach is presented...
Algebraic models of deviant modal operators based on de Morgan and Kleene lattices
Cattaneo, G.; Ciucci, DE; Dubois, D.
2011-01-01
An algebraic model of a kind of modal extension of de Morgan logic is described under the name MDS5 algebra. The main properties of this algebra can be summarized as follows: (1) it is based on a de Morgan lattice, rather than a Boolean algebra; (2) a modal necessity operator that satisfies the axioms N, K, T, and 5 (and as a consequence also B and 4) of modal logic is introduced; it allows one to introduce a modal possibility by the usual combination of necessity operation and...
Phases and phase transitions in the algebraic microscopic shell model
Directory of Open Access Journals (Sweden)
Georgieva A. I.
2016-01-01
Full Text Available We explore the dynamical symmetries of the shell model number conserving algebra, which define three types of pairing and quadrupole phases, with the aim to obtain the prevailing phase or phase transition for the real nuclear systems in a single shell. This is achieved by establishing a correspondence between each of the pairing bases with the Elliott’s SU(3 basis that describes collective rotation of nuclear systems. This allows for a complete classification of the basis states of different number of particles in all the limiting cases. The probability distribution of the SU(3 basis states within theirs corresponding pairing states is also obtained. The relative strengths of dynamically symmetric quadrupole-quadrupole interaction in respect to the isoscalar, isovector and total pairing interactions define a control parameter, which estimates the importance of each term of the Hamiltonian in the correct reproduction of the experimental data for the considered nuclei.
Model Checking of Software Components: Combining Java PathFinder and Behavior Protocol Model Checker
Czech Academy of Sciences Publication Activity Database
Pařízek, P.; Plášil, František; Kofroň, Jan
Los Alamitos: IEEE Computer Society, 2006, s. 133-141. ISBN 0-7695-2624-1. [SEW 2006. Annual IEEE/NASA Software Engineering Workshop /30./. Loyola College Graduate Center, Columbia (US), 24.04.2006-28.04.2006] R&D Projects: GA ČR GA201/06/0770 Institutional research plan: CEZ:AV0Z10300504 Keywords : software components * behavior protocols * model checking * cooperation of model checkers Subject RIV: JC - Computer Hardware ; Software
An Approach to Checking 3D Model with Related Engineering Drawings
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
For some reasons, engineers build their product 3D mo del according to a set of related engineering drawings. The problem is how we ca n know the 3D model is correct. The manual checking is very boring and time cons uming, and still could not avoid mistakes. Thus, we could not confirm the model, maybe try checking again. It will effect the production preparing cycle greatly , and should be solved in a intelligent way. The difficulties are quite obvious, unlike word checking in a word processing package, ...
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Hinkelmann, Franziska; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard
2010-01-01
Motivation: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, bounded Petri nets, and agent-based models. Simulation is a common practice for analyzing discrete models, but many systems are far too large to capture all the relevant dynamical features through simulation alone. Results: We convert discrete models into algebraic models and apply tools from computational algebra to analyze their dynamics. The key feature of biological systems that is exploited by our algorithms is their sparsity: while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes. In our experience with models arising in systems biology and random models, this structure leads to fast computations when using algebraic models, and thus efficient analysis. Availability: All algorithms and methods are available in our package Analysis of Dynamic Algebraic Models (ADAM), a user friendly web-interf...
Efficient model checking for duration calculus based on branching-time approximations
DEFF Research Database (Denmark)
Fränzle, Martin; Hansen, Michael Reichhardt
2008-01-01
Duration Calculus (abbreviated to DC) is an interval-based, metric-time temporal logic designed for reasoning about embedded real-time systems at a high level of abstraction. But the complexity of model checking any decidable fragment featuring both negation and chop, DC's only modality, is non......-elementary and thus impractical. We here investigate a similar approximation as frequently employed in model checking situation-based temporal logics, where linear-time problems are safely approximated by branching-time counterparts amenable to more efficient model-checking algorithms. Mimicking the role that a...... situation has in (A)CTL as origin of a set of linear traces, we define a branching-time counterpart to interval-based temporal logics building on situation pairs spanning sets of intervals. While this branching-time interval semantics yields the desired reduction in complexity of the model-checking problem...
Efficient Symmetry Reduction and the Use of State Symmetries for Symbolic Model Checking
Directory of Open Access Journals (Sweden)
Christian Appold
2010-06-01
Full Text Available One technique to reduce the state-space explosion problem in temporal logic model checking is symmetry reduction. The combination of symmetry reduction and symbolic model checking by using BDDs suffered a long time from the prohibitively large BDD for the orbit relation. Dynamic symmetry reduction calculates representatives of equivalence classes of states dynamically and thus avoids the construction of the orbit relation. In this paper, we present a new efficient model checking algorithm based on dynamic symmetry reduction. Our experiments show that the algorithm is very fast and allows the verification of larger systems. We additionally implemented the use of state symmetries for symbolic symmetry reduction. To our knowledge we are the first who investigated state symmetries in combination with BDD based symbolic model checking.
Validation of mission critical software design and implementation using model checking
Pingree, P. J.; Mikk, E.; Holzmann, G.; Smith, M.; Dams, D.
2002-01-01
Model Checking conducts an exhaustive exploration of all possible behaviors of a software system design and as such can be used to detect defects in designs that are typically difficult to discover with conventional testing approaches.
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...
Re"modeling" College Algebra: An Active Learning Approach
Pinzon, D.; Pinzon, K.; Stackpole, M.
2016-01-01
In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…
Towards Symbolic Model Checking for Multi-Agent Systems via OBDDs
Raimondi, Franco; Lomunscio, Alessio
2004-01-01
We present an algorithm for model checking temporal-epistemic properties of multi-agent systems, expressed in the formalism of interpreted systems. We first introduce a technique for the translation of interpreted systems into boolean formulae, and then present a model-checking algorithm based on this translation. The algorithm is based on OBDD's, as they offer a compact and efficient representation for boolean formulae.
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.
Algebraic structures generating reaction-diffusion models: the activator-substrate system
Palese, Marcella
2015-01-01
We shall construct a class of nonlinear reaction-diffusion equations starting from an infinitesimal algebraic skeleton. Our aim is to explore the possibility of an algebraic foundation of integrability properties and of stability of equilibrium states associated with nonlinear models describing patterns formation.
Sigma-model Solutions and Intersecting p-Branes Related to Lie Algebras
Grebeniuk, M. A.; Ivashchuk, V. D.
1998-01-01
A family of Majumdar-Papapetrou type solutions in sigma-model of p-brane origin is obtained for all direct sums of finite-dimensional simple Lie algebras. Several examples of p-brane dyonic configurations in D=10 (IIA) and D=11 supergravities corresponding to the Lie algebra sl(3,C) are considered.
Energy Technology Data Exchange (ETDEWEB)
Lahtinen, J. [VTT Technical Research Centre of Finland, Espoo (Finland); Launiainen, T.; Heljanko, K.; Ropponen, J. [Aalto Univ., Espoo (Finland). Dept. of Information and Computer Science
2012-07-01
Digital instrumentation and control (I and C) systems are challenging to verify. They enable complicated control functions, and the state spaces of the models easily become too large for comprehensive verification through traditional methods. Model checking is a formal method that can be used for system verification. A number of efficient model checking systems are available that provide analysis tools to determine automatically whether a given state machine model satisfies the desired safety properties. This report reviews the work performed in the Safety Evaluation and Reliability Analysis of Nuclear Automation (SARANA) project in 2011 regarding model checking. We have developed new, more exact modelling methods that are able to capture the behaviour of a system more realistically. In particular, we have developed more detailed fault models depicting the hardware configuration of a system, and methodology to model function-block-based systems asynchronously. In order to improve the usability of our model checking methods, we have developed an algorithm for model checking large modular systems. The algorithm can be used to verify properties of a model that could otherwise not be verified in a straightforward manner. (orig.)
Index-aware model order reduction methods applications to differential-algebraic equations
Banagaaya, N; Schilders, W H A
2016-01-01
The main aim of this book is to discuss model order reduction (MOR) methods for differential-algebraic equations (DAEs) with linear coefficients that make use of splitting techniques before applying model order reduction. The splitting produces a system of ordinary differential equations (ODE) and a system of algebraic equations, which are then reduced separately. For the reduction of the ODE system, conventional MOR methods can be used, whereas for the reduction of the algebraic systems new methods are discussed. The discussion focuses on the index-aware model order reduction method (IMOR) and its variations, methods for which the so-called index of the original model is automatically preserved after reduction.
Verifying Real-time Commit Protocols Using Dense-time Model Checking Technology
Al-Bataineh, Omar I.; Reynolds, Mark; French, Tim; Woodings, Terry
2012-01-01
The timed-based automata model, introduced by Alur and Dill, provides a useful formalism for describing real-time systems. Over the last two decades, several dense-time model checking tools have been developed based on that model. The paper considers the verification of real-time distributed commit protocols using dense-time model checking technology. More precisely, we model and verify the well-known timed two phase commit protocol in three different state-of-the-art real-time model checkers...
Verifying Real-time Commit Protocols Using Dense-time Model Checking Technology
Al-Bataineh, Omar I; French, Tim; Woodings, Terry
2012-01-01
The timed-based automata model, introduced by Alur and Dill, provides a useful formalism for describing real-time systems. Over the last two decades, several dense-time model checking tools have been developed based on that model. The paper considers the verification of real-time distributed commit protocols using dense-time model checking technology. More precisely, we model and verify the well-known timed two phase commit protocol in three different state-of-the-art real-time model checkers: UPPAAL, Rabbit, and RED, and compare the results.
Energy Technology Data Exchange (ETDEWEB)
Bracken, Anthony J.; Ge Xiangyu; Gould, Mark D.; Links, Jon; Zhou Huanqiang [Centre for Mathematical Physics, University of Queensland, Brisbane, QLD (Australia)
2001-06-01
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded quantum inverse scattering method. The Bethe ansatz equations for all these models are derived by using the algebraic Bethe ansatz method. (author)
PKreport: report generation for checking population pharmacokinetic model assumptions
Directory of Open Access Journals (Sweden)
Li Jun
2011-05-01
Full Text Available Abstract Background Graphics play an important and unique role in population pharmacokinetic (PopPK model building by exploring hidden structure among data before modeling, evaluating model fit, and validating results after modeling. Results The work described in this paper is about a new R package called PKreport, which is able to generate a collection of plots and statistics for testing model assumptions, visualizing data and diagnosing models. The metric system is utilized as the currency for communicating between data sets and the package to generate special-purpose plots. It provides ways to match output from diverse software such as NONMEM, Monolix, R nlme package, etc. The package is implemented with S4 class hierarchy, and offers an efficient way to access the output from NONMEM 7. The final reports take advantage of the web browser as user interface to manage and visualize plots. Conclusions PKreport provides 1 a flexible and efficient R class to store and retrieve NONMEM 7 output, 2 automate plots for users to visualize data and models, 3 automatically generated R scripts that are used to create the plots; 4 an archive-oriented management tool for users to store, retrieve and modify figures, 5 high-quality graphs based on the R packages, lattice and ggplot2. The general architecture, running environment and statistical methods can be readily extended with R class hierarchy. PKreport is free to download at http://cran.r-project.org/web/packages/PKreport/index.html.
Model-Checking Real-Time Control Programs
DEFF Research Database (Denmark)
Iversen, T. K.; Kristoffersen, K. J.; Larsen, Kim Guldstrand; Laursen, M.; Madsen, R. G.; Mortensen, S. K.; Pettersson, P.; Thomasen, C. B.
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...
Practical Application of Model Checking in Software Verification
Havelund, Klaus; Skakkebaek, Jens Ulrik
1999-01-01
This paper presents our experiences in applying the JAVA PATHFINDER (J(sub PF)), a recently developed JAVA to SPIN translator, in the finding of synchronization bugs in a Chinese Chess game server application written in JAVA. We give an overview of J(sub PF) and the subset of JAVA that it supports and describe the abstraction and verification of the game server. Finally, we analyze the results of the effort. We argue that abstraction by under-approximation is necessary for abstracting sufficiently smaller models for verification purposes; that user guidance is crucial for effective abstraction; and that current model checkers do not conveniently support the computational models of software in general and JAVA in particular.
Application of Model-Checking Technology to Controller Synthesis
DEFF Research Database (Denmark)
David, Alexandre; Grunnet, Jacob Deleuran; Jessen, Jan Jacob;
2011-01-01
its continuous environment, which is modelled and taken care of in our frameworks. Our first technique does it by using Matlab to discretise the problem and then Uppaal-tiga to solve the obtained timed game. This is implemented as a toolbox. The second technique relies on the user defining a timed...... game model in Uppaal- tiga. Then the strategy is automatically imported in Simulink as an S-function for simulation and validation purposes. We demonstrate the effectiveness of these frameworks in different case-studies....
Model Checking Electronic Commerce Security Protocols Based on CTL
Institute of Scientific and Technical Information of China (English)
XIAO De-qin; ZHANG Huan-guo
2005-01-01
We present a model based on Computational Temporal Logic (CTL) methods for verifying security requirements of electronic commerce protocols. The model describes formally the authentication, confidentiality integrity,non-repudiation, denial of service and access control of the electronic commerce protocols. We illustrate as case study a variant of the Lu-Smolka protocol proposed by Lu-Smolka.Moreover, we have discovered two attacks that allow a dishonest user to purchase a good debiting the amount to another user. And also, we compared our work with relative research works and found that the formal way of this paper is more general to specify security protocols for E-Commerce.
VERIFICATION OF CONFLICTION AND UNREACHABILITY IN RULE-BASED EXPERT SYSTEMS WITH MODEL CHECKING
Directory of Open Access Journals (Sweden)
Einollah pira
2014-03-01
Full Text Available It is important to find optimal solutions for structural errors in rule-based expert systems .Solutions to discovering such errors by using model checking techniques have already been proposed, but these solutions have problems such as state space explosion. In this paper, to overcome these problems, we model the rule-based systems as finite state transition systems and express confliction and unreachabilityas Computation Tree Logic (CTL logic formula and then use the technique of model checking to detect confliction and unreachability in rule-based systems with the model checker UPPAAL.
Y(sl(2)) Algebra Application in Extended Hydrogen Atom and Monopole Models
Institute of Scientific and Technical Information of China (English)
TIAN Li-Jun; ZHANG Hong-Biao; JIN Shuo; XUE Kang
2004-01-01
We present the extended hydrogen atom and monopole-hydrogen atom theory through generalizing the usual hydrogen atom model and with a monopole model respectively, in which Y (sl(2) ) algebras are realized. We derive the Hamiltonians of the two models based on the Y(sl(2) ) and the generalized Pauli equation. The energy spectra of the systems are also given in terms of Yangian algebra and quantum mechanics.
Efficient Proof Engines for Bounded Model Checking of Hybrid Systems
DEFF Research Database (Denmark)
Fränzle, Martin; Herde, Christian
2005-01-01
In this paper we present HySat, a new bounded model checker for linear hybrid systems, incorporating a tight integration of a DPLL-based pseudo-Boolean SAT solver and a linear programming routine as core engine. In contrast to related tools like MathSAT, ICS, or CVC, our tool exploits all of the...
Hypersonic: Model Analysis and Checking in the Cloud
DEFF Research Database (Denmark)
Acretoaie, Vlad; Störrle, Harald
2014-01-01
”. Objective: In this paper we investigate the conceptual and technical feasibility of a new software architecture for modeling tools, where certain advanced features are factored out of the client and moved towards the Cloud. With this approach we plan to address the above mentioned drawbacks of existing...
Membrane Matrix models and non-perturbative checks of gauge/gravity duality
O'Connor, Denjoe
2016-01-01
We compare the bosonic and maximally supersymmetric membrane models. We find that in Hoppe regulated form the bosonic membrane is well approximated by massive Gaussian quantum matrix models. In contrast the similarly regulated supersymmetric membrane, which is equivalent to the BFSS model, has a gravity dual description. We sketch recent progress in checking gauge/gravity duality in this context.
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 of E-Commerce Protocol using Casper FDR
Dantuluri Sravanthi
2013-01-01
In present days the popularity of electronic commerce applications are motivated the development of new e-commerce protocols. By using these new protocols the secrecy and agreement properties are achieved. This paper mainly focuses on how to model the e-commerce protocol in CSP using SPL and verified using CasperFDR whether the protocol satisfies the properties specified. Attacks are identified in this version. The specifications through which these attacks are found are presented.
Using Stochastic Model Checking to Provision Complex Business Services
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2012-01-01
We present a framework for modelling and analysis of real-world business workflows. Business processes regularly form the basis for the design of software services, and frequently display complex stochastic behaviour. The accurate evaluation of their qualitative aspects can allow for determining ...... of business processes including transient probabilities, timing, occurrence and ordering of events, and best- and worst-case scenarios. The developments presented are illustrated using an example from the health-care industry.......We present a framework for modelling and analysis of real-world business workflows. Business processes regularly form the basis for the design of software services, and frequently display complex stochastic behaviour. The accurate evaluation of their qualitative aspects can allow for determining...... bounds on resources consumed during execution of business processes. Accurate resource provisioning is often central to ensuring the safe execution of a process. We first introduce a formalised core subset of the Business Process Modelling and Notation (BPMN), which we extend with probabilistic and non...
Numerical modelling of granular flows: a reality check
Windows-Yule, C. R. K.; Tunuguntla, D. R.; Parker, D. J.
2016-07-01
Discrete particle simulations provide a powerful tool for the advancement of our understanding of granular media, and the development and refinement of the multitudinous techniques used to handle and process these ubiquitous materials. However, in order to ensure that this tool can be successfully utilised in a meaningful and reliable manner, it is of paramount importance that we fully understand the degree to which numerical models can be trusted to accurately and quantitatively recreate and predict the behaviours of the real-world systems they are designed to emulate. Due to the complexity and diverse variety of physical states and dynamical behaviours exhibited by granular media, a simulation algorithm capable of closely reproducing the behaviours of a given system may be entirely unsuitable for other systems with different physical properties, or even similar systems exposed to differing control parameters. In this paper, we focus on two widely used forms of granular flow, for which discrete particle simulations are shown to provide a full, quantitative replication of the behaviours of real industrial and experimental systems. We identify also situations for which quantitative agreement may fail are identified, but important general, qualitative trends are still recreated, as well as cases for which computational models are entirely unsuitable. By assembling this information into a single document, we hope not only to provide researchers with a useful point of reference when designing and executing future studies, but also to equip those involved in the design of simulation algorithms with a clear picture of the current strengths and shortcomings of contemporary models, and hence an improved knowledge of the most valuable areas on which to focus their work.
Numerical modelling of granular flows: a reality check
Windows-Yule, C. R. K.; Tunuguntla, D. R.; Parker, D. J.
2015-12-01
Discrete particle simulations provide a powerful tool for the advancement of our understanding of granular media, and the development and refinement of the multitudinous techniques used to handle and process these ubiquitous materials. However, in order to ensure that this tool can be successfully utilised in a meaningful and reliable manner, it is of paramount importance that we fully understand the degree to which numerical models can be trusted to accurately and quantitatively recreate and predict the behaviours of the real-world systems they are designed to emulate. Due to the complexity and diverse variety of physical states and dynamical behaviours exhibited by granular media, a simulation algorithm capable of closely reproducing the behaviours of a given system may be entirely unsuitable for other systems with different physical properties, or even similar systems exposed to differing control parameters. In this paper, we focus on two widely used forms of granular flow, for which discrete particle simulations are shown to provide a full, quantitative replication of the behaviours of real industrial and experimental systems. We identify also situations for which quantitative agreement may fail are identified, but important general, qualitative trends are still recreated, as well as cases for which computational models are entirely unsuitable. By assembling this information into a single document, we hope not only to provide researchers with a useful point of reference when designing and executing future studies, but also to equip those involved in the design of simulation algorithms with a clear picture of the current strengths and shortcomings of contemporary models, and hence an improved knowledge of the most valuable areas on which to focus their work.
Currents algebra for an atom-molecule Bose-Einstein condensate model
Filho, Gilberto N. Santos
2016-01-01
I present an interconversion currents algebra for an atom-molecule Bose-Einstein condensate model and use it to get the quantum dynamics of the currents. For different choices of the Hamiltonian parameters I get different currents dynamics.
A Check-up for the Statistical Parton Model
Buccella, Franco
2014-01-01
We compare the parton distributions deduced in the framework of a quantum statistical approach for both the longitudinal and transverse degrees of freedom with the unpolarized distributions measured at Hera and with the polarized ones proposed in a previous paper, which have been shown to be in very good agreement also with the results of experiments performed after that proposal. The agreement with Hera data in correspondence of very similar values for the 'temperature' and the 'potentials' found in the previous work gives a robust confirm of the statistical model. The feature of describing both unpolarized and polarized parton distributions in terms of few parameters fixed by data with large statistics and small systematic errors makes very attractive the parametrization proposed here.
A check-up for the statistical Parton model
Buccella, Franco; Sohaily, Sozha
2015-11-01
We compare the Parton distributions deduced in the framework of a quantum statistical approach for both the longitudinal and transverse degrees of freedom with the unpolarized distributions measured at HERA and with the polarized ones proposed in a previous paper, which have been shown to be in very good agreement also with the results of experiments performed after that proposal. The agreement with HERA data in correspondence to very similar values for the “temperature” and the “potentials” found in the previous work gives a robust confirm of the statistical model. The unpolarized distributions are compared also with the result of NNPDF. The free parameters are fixed mainly by data in the range (0.1, 0.5) for the x variable, where the valence Partons dominate, and in the small x region for the diffractive contribution. This feature makes the parametrization proposed here very attractive.
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...
Cascading Verification: An Integrated Method for Domain-Specific Model Checking
Zervoudakis, F.
2014-01-01
Model checking is an established formal method for verifying the desired behavioral properties of system models. But popular model checkers tend to support low-level modeling languages that require intricate models to represent even the simplest systems. Modeling complexity arises in part from the need to encode domain knowledge, including domain objects and concepts, and their relationships, at relatively low levels of abstraction. We will demonstrate that, once formalized, domain knowledge ...
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.
Clifford algebra-based spatio-temporal modelling and analysis for complex geo-simulation data
Luo, Wen; Yu, Zhaoyuan; Hu, Yong; Yuan, Linwang
2013-10-01
The spatio-temporal data simulating Ice-Land-Ocean interaction of Antarctic are used to demonstrate the Clifford algebra-based data model construction, spatio-temporal query and data analysis. The results suggest that Clifford algebra provides a powerful mathematical tool for the whole modelling and analysis chains for complex geo-simulation data. It can also help implement spatio-temporal analysis algorithms more clearly and simply.
Heinicke, C; Heinicke, Christian; Hehl, Friedrich W.
2001-01-01
We survey the application of computer algebra in the context of gravitational theories. After some general remarks, we show of how to check the second Bianchi-identity by means of the Reduce package Excalc. Subsequently we list some computer algebra systems and packages relevant to applications in gravitational physics. We conclude by presenting a couple of typical examples.
Gamble, Ed; Holzmann, Gerard
2011-01-01
Part of the US DOT investigation of Toyota SUA involved analysis of the throttle control software. JPL LaRS applied several techniques, including static analysis and logic model checking, to the software. A handful of logic models were built. Some weaknesses were identified; however, no cause for SUA was found. The full NASA report includes numerous other analyses
Requirements-level semantics and model checking of object-oriented statecharts
Eshuis, Rik; Jansen, David N.; Wieringa, Roel
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 te
Random Testing and Model Checking: Building a Common Framework for Nondeterministic Exploration
Groce, Alex; Joshi, Rajeev
2008-01-01
Two popular forms of dynamic analysis, random testing and explicit-state software model checking, are perhaps best viewed as search strategies for exploring the state spaces introduced by nondeterminism in program inputs. We present an approach that enables this nondeterminism to be expressed in the SPIN model checker's PROMELA language, and then lets users generate either model checkers or random testers from a single harness for a tested C program. Our approach makes it easy to compare model checking and random testing for models with precisely the same input ranges and probabilities and allows us to mix random testing with model checking's exhaustive exploration of non-determinism. The PROMELA language, as intended in its design, serves as a convenient notation for expressing nondeterminism and mixing random choices with nondeterministic choices. We present and discuss a comparison of random testing and model checking. The results derive from using our framework to test a C program with an effectively infinite state space, a module in JPL's next Mars rover mission. More generally, we show how the ability of the SPIN model checker to call C code can be used to extend SPIN's features, and hope to inspire others to use the same methods to implement dynamic analyses that can make use of efficient state storage, matching, and backtracking.
Directory of Open Access Journals (Sweden)
R. Lestari
2012-12-01
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
Off-critical W∞ and Virasoro algebras as dynamical symmetries of the integrable models
International Nuclear Information System (INIS)
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)
DiVinE-CUDA - A Tool for GPU Accelerated LTL Model Checking
Directory of Open Access Journals (Sweden)
Jiří Barnat
2009-12-01
Full Text Available In this paper we present a tool that performs CUDA accelerated LTL Model Checking. The tool exploits parallel algorithm MAP adjusted to the NVIDIA CUDA architecture in order to efficiently detect the presence of accepting cycles in a directed graph. Accepting cycle detection is the core algorithmic procedure in automata-based LTL Model Checking. We demonstrate that the tool outperforms non-accelerated version of the algorithm and we discuss where the limits of the tool are and what we intend to do in the future to avoid them.
Local Model Checking of Weighted CTL with Upper-Bound Constraints
DEFF Research Database (Denmark)
Jensen, Jonas Finnemann; Larsen, Kim Guldstrand; Srba, Jiri; Østergaard, Lars
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...... boolean domain to nonnegative integers in order to cope with the weights. We present both global and local algorithms for the fixed-point computation on symbolic dependency graphs and argue for the advantages of our approach compared to the direct encoding of the model checking problem into dependency...
Application safety enhancement model using self-checking with software enzymes
Subramaniam, Chandrasekaran; Ravishankar, Arthi; Gopal, Deepthi; Subramanian, Dhaarini
2011-12-01
The objective of the paper is to propose a safety enhancement model for application software in accelerating the respective self checking strategies similar to bio enzymatic actions. The application software components which are safety critical may have to be assessed periodically or on demand to achieve not only the functional correctness but also the safety specifications or features while getting executed. The design and deployment of such software modules can be formally verified for possible safety flaws using self checking capabilities and software enzymatic actions. The self checks must sense the safety holes in the software and decide to activate the built-in software components called enzymes to do the safe guard operations in a timely manner to mitigate the safety faults using the proposed enzyme calculus. The various application hazards due to the boolean faults in the functional and behavioral model that lead to software safety issues are considered in this approach.
Algebraic multigrid preconditioner for the cardiac bidomain model.
Plank, Gernot; Liebmann, Manfred; Weber dos Santos, Rodrigo; Vigmond, Edward J; Haase, Gundolf
2007-04-01
The bidomain equations are considered to be one of the most complete descriptions of the electrical activity in cardiac tissue, but large scale simulations, as resulting from discretization of an entire heart, remain a computational challenge due to the elliptic portion of the problem, the part associated with solving the extracellular potential. In such cases, the use of iterative solvers and parallel computing environments are mandatory to make parameter studies feasible. The preconditioned conjugate gradient (PCG) method is a standard choice for this problem. Although robust, its efficiency greatly depends on the choice of preconditioner. On structured grids, it has been demonstrated that a geometric multigrid preconditioner performs significantly better than an incomplete LU (ILU) preconditioner. However, unstructured grids are often preferred to better represent organ boundaries and allow for coarser discretization in the bath far from cardiac surfaces. Under these circumstances, algebraic multigrid (AMG) methods are advantageous since they compute coarser levels directly from the system matrix itself, thus avoiding the complexity of explicitly generating coarser, geometric grids. In this paper, the performance of an AMG preconditioner (BoomerAMG) is compared with that of the standard ILU preconditioner and a direct solver. BoomerAMG is used in two different ways, as a preconditioner and as a standalone solver. Two 3-D simulation examples modeling the induction of arrhythmias in rabbit ventricles were used to measure performance in both sequential and parallel simulations. It is shown that the AMG preconditioner is very well suited for the solution of the bidomain equation, being clearly superior to ILU preconditioning in all regards, with speedups by factors in the range 5.9-7.7. PMID:17405366
Nonparametric checks for count data models: an application to demand for health care in Spain
Álvarez, Begoña; Delgado, Miguel A.
1997-01-01
This paper presents model specification checking procedures for count data regression models which are consistent in the direction of nonparametric alternatives. The discussion is motivated in the context of a model of demand for health care in Spain. The parameters of the regression model are estimated by maximum likelihood based on Poisson and Negative Binomial specifications as well as by ordinary least squares and semiparametric generalized least squares. However, our interest is not only...
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'…
International Nuclear Information System (INIS)
The reflection equation algebra of Sklyanin is extended to the supersymmetric case. A graded reflection equation algebra is proposed and the corresponding graded (supersymmetric) boundary quantum inverse scattering method (QISM) is formulated. As an application, integrable open-boundary conditions for the doped spin-1 chain of the supersymmetric t-J model are studied in the framework of the boundary QISM. Diagonal boundary K-matrices are found and four classes of integrable boundary terms are determined. (author)
The classical origin of quantum affine algebra in squashed sigma models
Kawaguchi, Io; Matsumoto, Takuya; Yoshida, Kentaroh
2012-01-01
We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassic...
Incremental checking of Master Data Management model based on contextual graphs
Lamolle, Myriam; Menet, Ludovic; Le Duc, Chan
2015-10-01
The validation of models is a crucial step in distributed heterogeneous systems. In this paper, an incremental validation method is proposed in the scope of a Model Driven Engineering (MDE) approach, which is used to develop a Master Data Management (MDM) field represented by XML Schema models. The MDE approach presented in this paper is based on the definition of an abstraction layer using UML class diagrams. The validation method aims to minimise the model errors and to optimisethe process of model checking. Therefore, the notion of validation contexts is introduced allowing the verification of data model views. Description logics specify constraints that the models have to check. An experimentation of the approach is presented through an application developed in ArgoUML IDE.
Specification and Generation of Environment for Model Checking of Software Components
Czech Academy of Sciences Publication Activity Database
Pařízek, P.; Plášil, František
2007-01-01
Roč. 176, - (2007), s. 143-154. ISSN 1571-0661 R&D Projects: GA AV ČR 1ET400300504 Institutional research plan: CEZ:AV0Z10300504 Keywords : software components * behavior protocols * model checking * automated generation of environment Subject RIV: JC - Computer Hardware ; Software
Three Notes on the Complexity of Model Checking Fixpoint Logic with Chop
DEFF Research Database (Denmark)
Lange, Martin
2007-01-01
This paper provides lower complexity bounds of deterministic exponential time for the combined, data and expression complexity of Fixpoint Logic with Chop. This matches the previously known upper bound showing that its model checking problem is EXPTIME-complete, even when the transition system or...
On Derivations Of Genetic Algebras
International Nuclear Information System (INIS)
A genetic algebra is a (possibly non-associative) algebra used to model inheritance in genetics. In application of genetics this algebra often has a basis corresponding to genetically different gametes, and the structure constant of the algebra encode the probabilities of producing offspring of various types. In this paper, we find the connection between the genetic algebras and evolution algebras. Moreover, we prove the existence of nontrivial derivations of genetic algebras in dimension two
Symmetric structure of field algebra of G-spin models determined by a normal subgroup
International Nuclear Information System (INIS)
Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra FH of the field algebra F of G-spin models, so that FH is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A(H,G) is obtained as the D(H; G)-invariant subalgebra of FH, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A(H,G) are commutants with each other
On Robustness Analysis of Stochastic Biochemical Systems by Probabilistic Model Checking
Brim, Lubos; Ceska, Milan; Drazan, Sven; Safranek, David
2013-01-01
This report proposes a novel framework for a rigorous robustness analysis of stochastic biochemical systems. The technique is based on probabilistic model checking. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluat...
Machine Learning Methods in Statistical Model Checking and System Design – Tutorial
Bortolussi, Luca; Milios, Dimitrios; Sanguinetti, Guido
2015-01-01
Recent research has seen an increasingly fertile convergence of ideas from machine learning and formal modelling. Here we review some recently introduced methodologies for model checking and system design/parameter synthesis for logical properties against stochastic dynamical models. The crucial insight is a regularity result which states that the satisfaction probability of a logical formula is a smooth function of the parameters of a CTMC. This enables us to select an appropriate class of f...
An algebraic stress model analysis of fully developed turbulent flow in a square duct
International Nuclear Information System (INIS)
A numerical experiment has been carried out on a fully developed turbulent flow in a square duct. Special attention is given to clarify the effectiveness of the algebraic stress models treated by Launder-Reece-Rodi (LRR) and Gibson-Launder (GL) in explaining the secondary flow of the second kind. The results favor the LRR model over the GL model in comparison with the experiment. The computational time for an algebraic stress model is not much greater than that of the kε model. (author)
Investigating modularity in the analysis of process algebra models of biochemical systems
Ciocchetta, Federica; Hillston, Jane; 10.4204/EPTCS.19.4
2010-01-01
Compositionality is a key feature of process algebras which is often cited as one of their advantages as a modelling technique. It is certainly true that in biochemical systems, as in many other systems, model construction is made easier in a formalism which allows the problem to be tackled compositionally. In this paper we consider the extent to which the compositional structure which is inherent in process algebra models of biochemical systems can be exploited during model solution. In essence this means using the compositional structure to guide decomposed solution and analysis. Unfortunately the dynamic behaviour of biochemical systems exhibits strong interdependencies between the components of the model making decomposed solution a difficult task. Nevertheless we believe that if such decomposition based on process algebras could be established it would demonstrate substantial benefits for systems biology modelling. In this paper we present our preliminary investigations based on a case study of the phero...
Directory of Open Access Journals (Sweden)
Ravie c. Muniyandi
2010-01-01
Full Text Available Problem statement: Membrane computing formalism has provided better modeling capabilities for biological systems in comparison to conventional mathematical models. Model checking could be used to reason about the biological system in detail and with precision by verifying formally whether membrane computing model meets the properties of the system. Approach: This study was carried to investigate the preservation of properties of two biological systems that had been modeled and simulated in membrane computing by a method of model checking using PRISM. The two biological systems were prey-predator population and signal processing in the legend-receptor networks of protein TGF-ß. Results: The model checking of membrane computing model of the biological systems with five different properties showed that the properties of the biological systems could be preserved in the membrane computing model. Conclusion: Membrane computing model not only provides a better approach in representing and simulating a biological system but also able to sustain the basic properties of the system.
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
Galois Correspondence in Field Algebra of G-spin Model
Institute of Scientific and Technical Information of China (English)
蒋立宁; 郭懋正
2003-01-01
@@ A C*-system is a pair (B, G) consisting of a unital C*-algebra B and a continuous group homomorphism α: G → Aut(B) where G is a compact group and Aut(B) the group of automor-phisms of B. If K is a normal subgroup of G and BK = {B∈ B: k(B) = B, k ∈ K}, then BK is a G-invariant C*-subalgebra of B. On the other hand, if A is a G-invariant C*-algebra with BG A B, set G (A) = {g ∈ G: g(A) = A, A ∈ A}, G (A) is a normal subgroup of G. Clearly K G(BK) and we call K Galois closed ifK = G(BK). Similarly, A BG(A) and we call A Galois closed if A = BG(A).
Dual algebraic structures for the two-level pairing model
International Nuclear Information System (INIS)
Duality relations are explicitly established relating the Hamiltonians and basis classification schemes associated with the number-conserving unitary and number-nonconserving quasispin algebras for the two-level system with pairing interactions. These relations are obtained in a unified formulation for both bosonic and fermionic systems, with arbitrary and, in general, unequal degeneracies for the two levels. Illustrative calculations are carried out comparing the bosonic and fermionic quantum phase transitions.
Towards Support for Software Model Checking: Improving the Efficiency of Formal Specifications
Directory of Open Access Journals (Sweden)
Salamah Salamah
2011-01-01
presented in this paper provides improved LTL specifications for patterns and scopes over those originally provided by Prospec. This improvement comes in the efficiency of the LTL formulas as measured in terms of the number of states in the Büchi automaton generated for the formula. Minimizing the size of the Büchi automata for an LTL specification provides a significant improvement for model checking software systems using such tools as the highly acclaimed Spin model checker.
SMT-Based Bounded Model Checking for Embedded ANSI-C Software
Cordeiro, Lucas; Marques-Silva, Joao
2009-01-01
Propositional bounded model checking has been applied successfully to verify embedded software but is limited by the increasing propositional formula size and the loss of structure during the translation. These limitations can be reduced by encoding word-level information in theories richer than propositional logic and using SMT solvers for the generated verification conditions. Here, we investigate the application of different SMT solvers to the verification of embedded software written in ANSI-C. We have extended the encodings from previous SMT-based bounded model checkers to provide more accurate support for finite variables, bit-vector operations, arrays, structures, unions and pointers. We have integrated the CVC3, Boolector, and Z3 solvers with the CBMC front-end and evaluated them using both standard software model checking benchmarks and typical embedded applications from telecommunications, control systems and medical devices. The experiments show that our approach can analyze larger problems and sub...
Universal Algebras of Hurwitz Numbers
A. Mironov; Morozov, A; Natanzon, S.
2009-01-01
Infinite-dimensional universal Cardy-Frobenius algebra is constructed, which unifies all particular algebras of closed and open Hurwitz numbers and is closely related to the algebra of differential operators, familiar from the theory of Generalized Kontsevich Model.
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.
Max-plus algebra models of queueing networks
Krivulin, Nikolai K.
2012-01-01
A class of queueing networks which may have an arbitrary topology, and consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. It is shown how the matrices inherent in particular ne...
The Algebraic Cluster Model: Structure of 16O
Bijker, R
2016-01-01
We discuss an algebraic treatment of four-body clusters which includes both continuous and discrete symmetries. In particular, tetrahedral configurations with T(d) symmetry are analyzed with respect to the energy spectrum, transition form factors and B(EL) values. It is concluded that the low-lying spectrum of 16O can be described by four alpha-particles at the vertices of a regular tetrahedron, not as a rigid structure but rather a more floppy structure with relatively large rotation-vibration interactions and Coriolis forces.
Mathematical modelling in engineering: A proposal to introduce linear algebra concepts
Directory of Open Access Journals (Sweden)
Andrea Dorila Cárcamo
2016-03-01
Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
Model checking Branching-Time Properties of Multi-Pushdown Systems is Hard
Atig, Mohamed Faouzi; Kumar, K Narayan; Saivasan, Prakash
2012-01-01
We address the model checking problem for shared memory concurrent programs modeled as multi-pushdown systems. We consider here boolean programs with a finite number of threads and recursive procedures. It is well-known that the model checking problem is undecidable for this class of programs. In this paper, we investigate the decidability and the complexity of this problem under the assumption of bounded context-switching defined by Qadeer and Rehof, and of phase-boundedness proposed by La Torre et al. On the model checking of such systems against temporal logics and in particular branching time logics such as the modal $\\mu$-calculus or CTL has received little attention. It is known that parity games, which are closely related to the modal $\\mu$-calculus, are decidable for the class of bounded-phase systems (and hence for bounded-context switching as well), but with non-elementary complexity (Seth). A natural question is whether this high complexity is inevitable and what are the ways to get around it. This...
Checking the Adequacy of Fit of Models from Split-Plot Designs
DEFF Research Database (Denmark)
Almini, A. A.; Kulahci, Murat; Montgomery, D. C.
2009-01-01
-plot models. In this article, we propose the computation of two R-2, R-2-adjusted, prediction error sums of squares (PRESS), and R-2-prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types...... of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have...
Stochastic Semantics and Statistical Model Checking for Networks of Priced Timed Automata
David, Alexandre; Legay, Axel; Mikučionis, Marius; Poulsen, Danny Bøgsted; van Vliet, Jonas; Wang, Zheng
2011-01-01
This paper offers a natural stochastic semantics of Networks of Priced Timed Automata (NPTA) based on races between components. The semantics provides the basis for satisfaction of probabilistic Weighted CTL properties (PWCTL), conservatively extending the classical satisfaction of timed automata with respect to TCTL. In particular the extension allows for hard real-time properties of timed automata expressible in TCTL to be refined by performance properties, e.g. in terms of probabilistic guarantees of time- and cost-bounded properties. A second contribution of the paper is the application of Statistical Model Checking (SMC) to efficiently estimate the correctness of non-nested PWCTL model checking problems with a desired level of confidence, based on a number of independent runs of the NPTA. In addition to applying classical SMC algorithms, we also offer an extension that allows to efficiently compare performance properties of NPTAs in a parametric setting. The third contribution is an efficient tool implem...
HyLTL: a temporal logic for model checking hybrid systems
Directory of Open Access Journals (Sweden)
Davide Bresolin
2013-08-01
Full Text Available The model-checking problem for hybrid systems is a well known challenge in the scientific community. Most of the existing approaches and tools are limited to safety properties only, or operates by transforming the hybrid system to be verified into a discrete one, thus loosing information on the continuous dynamics of the system. In this paper we present a logic for specifying complex properties of hybrid systems called HyLTL, and we show how it is possible to solve the model checking problem by translating the formula into an equivalent hybrid automaton. In this way the problem is reduced to a reachability problem on hybrid automata that can be solved by using existing tools.
Hopf Algebra Structure of a Model Quantum Field Theory
Solomon, A I; Blasiak, P; Horzela, A; Penson, K A
2006-01-01
Recent elegant work on the structure of Perturbative Quantum Field Theory (PQFT) has revealed an astonishing interplay between analysis(Riemann Zeta functions), topology (Knot theory), combinatorial graph theory (Feynman Diagrams) and algebra (Hopf structure). The difficulty inherent in the complexities of a fully-fledged field theory such as PQFT means that the essential beauty of the relationships between these areas can be somewhat obscured. Our intention is to display some, although not all, of these structures in the context of a simple zero-dimensional field theory; i.e. a quantum theory of non-commuting operators which do not depend on spacetime. The combinatorial properties of these boson creation and annihilation operators, which is our chosen example, may be described by graphs, analogous to the Feynman diagrams of PQFT, which we show possess a Hopf algebra structure. Our approach is based on the partition function for a boson gas. In a subsequent note in these Proceedings we sketch the relationship...
On the 2D zero modes' algebra of the SU(n) WZNW model
Hadjiivanov, Ludmil
2014-01-01
A quantum group covariant extension of the chiral parts of the Wess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to two matrix algebras with non-commutative entries. These are generated by "chiral zero modes" which combine in the 2D model into "Q-operators" which encode information about the internal symmetry and the fusion ring. We review earlier results about the SU(n) WZNW Q-algebra and its Fock representation for n=2 and display the first steps towards their generalization to higher n.
U(2) algebraic model applied to stretching vibrational spectra of tetrahedral molecules
Hou, X W; Hou, Xi-Wen; Ma, Zhong-Qi
1998-01-01
The highly excited stretching vibrational energy levels and the intensities of infrared transitions in tetrahedral molecules are studied in a U(2) algebraic model. Its applications to silane and silicon tetrafluoride are presented with smaller standard deviations than those of other models.
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…
Construction of the Model of the Lambda Calculus System with Algebraic Operators
Institute of Scientific and Technical Information of China (English)
陆汝占; 张政; 等
1991-01-01
A lambda system with algebraic operators,Lambda-plus system,is introduced.After giving the definitions of the system,we present a sufficient condition for formulating a model of the system.Finally,a model of such system is constructed.
Permutation invariant algebras, a Fock space realization and the Calogero model
International Nuclear Information System (INIS)
We study permutation invariant oscillator algebras and their Fock space representations using three equivalent techniques, i.e. (i) a normally ordered expansion in creation and annihilation operators, (ii) the action of annihilation operators on monomial states in Fock space and (iii) Gram matrices of inner products in Fock space. We separately discuss permutation invariant algebras which possess hermitean number operators and permutation invariant algebras which possess non-hermitean number operators. The results of a general analysis are applied to the SM-extended Heisenberg algebra, underlying the M-body Calogero model. Particular attention is devoted to the analysis of Gram matrices for the Calogero model. We discuss their structure, eigenvalues and eigenstates. We obtain a general condition for positivity of eigenvalues, meaning that all norms of states in Fock space are positive if this condition is satisfied. We find a universal critical point at which the reduction of the physical degrees of freedom occurs. We construct dual operators, leading to the ordinary Heisenberg algebra of free Bose oscillators. From the Fock-space point of view, we briefly discuss the existence of a mapping from the Calogero oscillators to the free Bose oscillators and vice versa. (orig.)
Combination of Model Checking and Theorem Proving to Verify Embedded Software
Institute of Scientific and Technical Information of China (English)
XIAO Jian-yu; ZHANG De-yun; DONG Hao; CHEN Hai-quan
2005-01-01
In this paper, a scheme of combining model checking and theorem proving techniques to verify high trustworthy embedded software is proposed. The software model described in state machine of unified model language is transformed into the input modeling language of a model checker in which the model is analyzed with associated property specifications expressed in temporal logic. The software model which has been verified by model checker is then transformed into abstract specifications of a theorem prover , in which the model will be refined, verified and translated into source C code. The transformation rules from state machine to input language of model checker and abstract specifications of theorem prover are given. The experiment shows that the proposed scheme can effectively improve the development and verification of high trustworthy embedded software.
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. PMID:24135792
Algebraic formulation of duality
International Nuclear Information System (INIS)
Two dimensional lattice spin (chiral) models over (possibly non-abelian) compact groups are formulated in terms of a generalized Pauli algebra. Such models over cyclic groups are written in terms of the generalized Clifford algebra. An automorphism of this algebra is shown to exist and to lead to the duality transformation
Visual Predictive Check in Models with Time-Varying Input Function.
Largajolli, Anna; Bertoldo, Alessandra; Campioni, Marco; Cobelli, Claudio
2015-11-01
The nonlinear mixed effects models are commonly used modeling techniques in the pharmaceutical research as they enable the characterization of the individual profiles together with the population to which the individuals belong. To ensure a correct use of them is fundamental to provide powerful diagnostic tools that are able to evaluate the predictive performance of the models. The visual predictive check (VPC) is a commonly used tool that helps the user to check by visual inspection if the model is able to reproduce the variability and the main trend of the observed data. However, the simulation from the model is not always trivial, for example, when using models with time-varying input function (IF). In this class of models, there is a potential mismatch between each set of simulated parameters and the associated individual IF which can cause an incorrect profile simulation. We introduce a refinement of the VPC by taking in consideration a correlation term (the Mahalanobis or normalized Euclidean distance) that helps the association of the correct IF with the individual set of simulated parameters. We investigate and compare its performance with the standard VPC in models of the glucose and insulin system applied on real and simulated data and in a simulated pharmacokinetic/pharmacodynamic (PK/PD) example. The newly proposed VPC performance appears to be better with respect to the standard VPC especially for the models with big variability in the IF where the probability of simulating incorrect profiles is higher. PMID:26265094
Model-Checking Real-Time Properties of an Aircraft Landing Gear System Using Fiacre
Berthomieu, Bernard; Dal Zilio, Silvano; Fronc, Lukasz
2014-01-01
International audience We describe our experience with modeling the landing gear system of an aircraft using the formal specification language Fiacre. Our model takes into account the behavior and timing properties of both the physical parts and the control software of this system. We use this formal model to check safety and real-time properties on the system but also to find a safe bound on the maximal time needed for all gears to be down and locked (assuming the absence of failures). Ou...
Model-Checking the Higher-Dimensional Modal mu-Calculus
Lange, Martin; 10.4204/EPTCS.77.6
2012-01-01
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in polynomial time, and conversely every polynomial-time decidable problem that has a bisimulation-invariant encoding into labeled transition systems can also be defined in the higher-dimensional modal mu-calculus. We exemplify the latter connection by giving several examples of decision problems which reduce to model checking of the higher-dimensional modal mu-calculus for some fixed formulas. This way generic model checking algorithms for the logic can then be used via partial evaluation in order to obtain algorithms for theses problems which may benefit from improvements that are well-established in the field of program verification, namely on-the-fly and symbolic techniques. The aim of this work is to extend such techniques to other fields as well, here exemplarily done for process...
Malekpour, Mahyar R.
2007-01-01
This report presents the mechanical verification of a simplified model of a rapid Byzantine-fault-tolerant self-stabilizing protocol for distributed clock synchronization systems. This protocol does not rely on any assumptions about the initial state of the system. This protocol tolerates bursts of transient failures, and deterministically converges within a time bound that is a linear function of the self-stabilization period. A simplified model of the protocol is verified using the Symbolic Model Verifier (SMV) [SMV]. The system under study consists of 4 nodes, where at most one of the nodes is assumed to be Byzantine faulty. The model checking effort is focused on verifying correctness of the simplified model of the protocol in the presence of a permanent Byzantine fault as well as confirmation of claims of determinism and linear convergence with respect to the self-stabilization period. Although model checking results of the simplified model of the protocol confirm the theoretical predictions, these results do not necessarily confirm that the protocol solves the general case of this problem. Modeling challenges of the protocol and the system are addressed. A number of abstractions are utilized in order to reduce the state space. Also, additional innovative state space reduction techniques are introduced that can be used in future verification efforts applied to this and other protocols.
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).
Graded Poisson-Sigma models and dilaton-deformed 2D supergravity algebra
International Nuclear Information System (INIS)
Supergravity extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. On the other hand, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to supergravity algebras (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them - like the one linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint without deformation - we are able not only to remove the ambiguities but, at the same time, the singularities referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well. (author)
An Efficient Explicit-time Description Method for Timed Model Checking
Wang, Hao; 10.4204/EPTCS.14.6
2009-01-01
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 p...
A stochastic extension of the explicit algebraic subgrid-scale models
International Nuclear Information System (INIS)
The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data
Left Artinian Algebraic Algebras
Institute of Scientific and Technical Information of China (English)
S. Akbari; M. Arian-Nejad
2001-01-01
Let R be a left artinian central F-algebra, T(R) = J(R) + [R, R],and U(R) the group of units of R. As one of our results, we show that, if R is algebraic and char F = 0, then the number of simple components of -R = R/J(R)is greater than or equal to dimF R/T(R). We show that, when char F = 0 or F is uncountable, R is algebraic over F if and only if [R, R] is algebraic over F. As another approach, we prove that R is algebraic over F if and only if the derived subgroup of U(R) is algebraic over F. Also, we present an elementary proof for a special case of an old question due to Jacobson.
Algebraic Bethe ansatz for the gl(1|2) generalized model: II. the three gradings
International Nuclear Information System (INIS)
The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same R-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe ansatz for all models with 9 x 9, rational, gl(1|2) invariant R-matrix and all three possibilities of choosing the grading. Our Bethe ansatz solution applies, for instance, to the supersymmetric t-J model, the supersymmetric U model and a number of interesting impurity models. It may be extended to obtain the quantum transfer matrix spectrum for this class of models. The properties of a specific model enter the Bethe ansatz solution (i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz equations) through the three pseudo vacuum eigenvalues of the diagonal elements of the monodromy matrix which in this context are called the parameters of the model
CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra
Au-Yang, Helen; Perk, Jacques H. H.
2016-04-01
Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.
Construction of linear models: A framework based on commutative Jordan algebras
Covas, R.; Carvalho, F.
2016-06-01
We show how to obtain the necessary structures for statistical analysis of the folllowing orthogonal models Y˜(1 μ +∑i Xiβi ,∑j σj2Mj+σ2I ) . These structures rely on the existence of Jordan algebras, in the sequence of [24], [8], [12], [9], [5] and [10].
Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis
Czech Academy of Sciences Publication Activity Database
Bulíček, M.; Haslinger, J.; Málek, J.; Stebel, Jan
2009-01-01
Roč. 60, č. 2 (2009), s. 185-212. ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model * outflow boundary condition Subject RIV: BA - General Mathematics Impact factor: 0.757, year: 2009
Algebraic Bethe ansatz for 19-vertex models with upper triangular K-matrices
International Nuclear Information System (INIS)
By means of an algebraic Bethe ansatz approach, we study the Zamolodchikov–Fateev and Izergin–Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors are used to diagonalize the associated transfer matrix. The eigenvalues as well as the Bethe equations are presented. (paper)
Algebraic Bethe ansatz for scalar products in SU(3)-invariant integrable models
Belliard, S; Ragoucy, E; Slavnov, N A
2012-01-01
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of form factors and correlation functions of XXX SU(3)-invariant Heisenberg chain.
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
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…
Reduced Chern-Simons Quiver Theories and Cohomological 3-Algebra Models
DeBellis, Joshua
2013-01-01
We study the BPS spectrum and vacuum moduli spaces in dimensional reductions of Chern-Simons-matter theories with N>=2 supersymmetry to zero dimensions. Our main example is a matrix model version of the ABJM theory which we relate explicitly to certain reduced 3-algebra models. We find the explicit maps from Chern-Simons quiver matrix models to dual IKKT matrix models. We address the problem of topologically twisting the ABJM matrix model, and along the way construct a new twist of the IKKT model. We construct a cohomological matrix model whose partition function localizes onto a moduli space specified by 3-algebra relations which live in the double of the conifold quiver. It computes an equivariant index enumerating framed BPS states with specified R-charges which can be expressed as a combinatorial sum over certain filtered pyramid partitions.
Kink states in P(φ)2-models. (An algebraic approach)
International Nuclear Information System (INIS)
Several two-dimensional quantum field theory models have more than one vacuum state. Familiar examples are the Sine-Gordon and the φ24-model. It is known that in these models there are also states, called kink states, which interpolate different vacua. A general construction scheme for kink states in the framework of algebraic quantum field theory is developed in a previous paper. However, for the application of this method, the crucial condition is the split property for wedge algebras in the vacuum representations of the considered models. It is believed that the vacuum representations of P(φ)2-models fulfill this condition, but a rigorous proof is only known for the massive free scalar field. Therefore, we investigate in a construction of kink states which can directly be applied to P(φ)2-model, by making use of the properties of the dynamic of a P(φ)2-model. (orig.)
Model Checking and Code Generation for UML Diagrams Using Graph Transformation
Directory of Open Access Journals (Sweden)
Wafa Chama
2012-12-01
Full Text Available UML is considered as the standard for object-oriented modelling language adopted by the ObjectManagement Group. However, UML has been criticized due to the lack of formal semantics and theambiguity of its models. In other hands, UML models can be mathematically verified and checked by usingits equivalent formal representation. So, in this paper, we propose an approach and a tool based on graphtransformation to perform an automatic mapping for verification purposes. This transformation aims tobridge the gap between informal and formal notations and allows a formal verification of concurrent UMLmodels using Maude language. We consider both static (Class Diagram and dynamic (StateChart andCommunication Diagrams features of concurrent object-oriented system. Then, we use Maude LTL ModelChecker to verify the formal model obtained (Automatic Code Generation Maude. The meta-modellingAToM3 tool is used. A case study is presented to illustrate our approach.
International Nuclear Information System (INIS)
We construct a special type of quantum soliton solutions for quantized affine Toda models. The elements of the principal Heisenberg subalgebra in the affinised quantum Lie algebra are found. Their eigenoperators inside the quantized universal enveloping algebra for an affine Lie algebra are constructed to generate quantum soliton solutions
Khovanova, Tanya
2008-01-01
I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simply-laced compact Lie groups.
Combinatorics of solvable lattice models, and modular representations of Hecke algebras
Foda, O E; Okado, M; Thibon, J Y; Welsh, Trevor A; Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
We review and motivate recently-observed relationships between exactly solvable lattice models and modular representations of Hecke algebras. Firstly, we describe how the set of $n$-regular partitions label both of the following classes of objects: 1. The spectrum of unrestricted solid-on-solid lattice models based on level-1 representations of the affine algebras $\\sl_n$, 2. The irreducible representations of type-A Hecke algebras at roots of unity: $H_m(\\sqrt[n]{1})$. Secondly, we show that a certain subset of the $n$-regular partitions label both of the following classes of objects: 1. The spectrum of restricted solid-on-solid lattice models based on cosets of affine algebras $(sl(n)^_1 \\times sl(n)^_1)/ sl(n)^_2$. 2. Jantzen-Seitz (JS) representations of $H_m(\\sqrt[n]{1})$: irreducible representations that remain irreducible under restriction to $H_{m-1}(\\sqrt[n]{1})$. Using the above relationships, we characterise the JS representations of $H_m(\\sqrt[n]{1})$ and show that the generating series that count...
Deskins, W E
1996-01-01
This excellent textbook provides undergraduates with an accessible introduction to the basic concepts of abstract algebra and to the analysis of abstract algebraic systems. These systems, which consist of sets of elements, operations, and relations among the elements, and prescriptive axioms, are abstractions and generalizations of various models which evolved from efforts to explain or discuss physical phenomena.In Chapter 1, the author discusses the essential ingredients of a mathematical system, and in the next four chapters covers the basic number systems, decompositions of integers, diop
Directory of Open Access Journals (Sweden)
Christian Krause
2011-11-01
Full Text Available The assurance of quality of service properties is an important aspect of service-oriented software engineering. Notations for so-called service level agreements (SLAs, such as the Web Service Level Agreement (WSLA language, provide a formal syntax to specify such assurances in terms of (legally binding contracts between a service provider and a customer. On the other hand, formal methods for veriﬁcation of probabilistic real-time behavior have reached a level of expressiveness and efﬁciency which allows to apply them in real-world scenarios. In this paper, we suggest to employ the recently introduced model of Interval Probabilistic Timed Automata (IPTA for formal veriﬁcation of QoS properties of service-oriented systems. Speciﬁcally, we show that IPTA in contrast to Probabilistic Timed Automata (PTA are able to capture the guarantees speciﬁed in SLAs directly. A particular challenge in the analysis of IPTA is the fact that their naive semantics usually yields an inﬁnite set of states and inﬁnitely-branching transitions. However, using symbolic representations, IPTA can be analyzed rather efﬁciently. We have developed the ﬁrst implementation of an IPTA model checker by extending the PRISM tool and show that model checking IPTA is only slightly more expensive than model checking comparable PTA.
Directory of Open Access Journals (Sweden)
Marcus Völp
2012-11-01
Full Text Available Reliability in terms of functional properties from the safety-liveness spectrum is an indispensable requirement of low-level operating-system (OS code. However, with evermore complex and thus less predictable hardware, quantitative and probabilistic guarantees become more and more important. Probabilistic model checking is one technique to automatically obtain these guarantees. First experiences with the automated quantitative analysis of low-level operating-system code confirm the expectation that the naive probabilistic model checking approach rapidly reaches its limits when increasing the numbers of processes. This paper reports on our work-in-progress to tackle the state explosion problem for low-level OS-code caused by the exponential blow-up of the model size when the number of processes grows. We studied the symmetry reduction approach and carried out our experiments with a simple test-and-test-and-set lock case study as a representative example for a wide range of protocols with natural inter-process dependencies and long-run properties. We quickly see a state-space explosion for scenarios where inter-process dependencies are insignificant. However, once inter-process dependencies dominate the picture models with hundred and more processes can be constructed and analysed.
Model checking of safety-critical software in the nuclear engineering domain
International Nuclear Information System (INIS)
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.
Development of an explicit algebraic turbulence model for buoyant flows – Part 1: DNS analysis
International Nuclear Information System (INIS)
Highlights: • DNS analysis of channel flow for forced, mixed and natural convection regime. • Examination of algebraic turbulenc model main features with buoyancy. • Investigation of the weak equilibrium assumption for buoyant flows. • Assessment of the redistribution term model for EARSM with buoyancy effect. • Assessment of the pressure scrambling term model for EAHFM. -- Abstract: An analysis of DNS databases of vertical plane channel flow for forced, mixed and natural convection is proposed. This analysis aims to assess the main features needed to develop an algebraic model for buoyant flows. First, the weak equilibrium assumption, at the root of algebraic models, is investigated. This hypothesis is shown to fail near the velocity maximum and close to the walls but remains valid otherwise, whatever the convection regime. The models for the redistribution term and the pressure scrambling term are then analyzed on the same configurations. A linear form of the Speziale et al. (1991) model is retained for the redistribution term. No model for the pressure scrambling term is fully satisfactory; nevertheless some models are recommended. The buoyant contributions to the pressure term are investigated. Finally, the generalized gradient diffusion hypothesis, which could be used to model the turbulent heat fluxes in order to avoid the coupling with the Reynolds stresses, is shown to be inaccurate
A new class of Matrix Models arising from the W-infinity Algebra
Herce, Henry D.; Zemba, Guillermo R.
2002-01-01
We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a class of random hermitian matrix models. The corresponding potentials are given, and the thermodynamic limit interpreted in terms of a simple plasma picture. The new matrix models can be successfully applied to the full bosonization of interesting one-dimensi...
Lochbihler, Andreas
2012-01-01
The Java programming language provides safety and security guarantees such as type safety and its security architecture. They distinguish it from other mainstream programming languages like C and C++. In this work, we develop a machine-checked model of concurrent Java and the Java memory model and investigate the impact of concurrency on these guarantees. From the formal model, we automatically obtain an executable verified compiler to bytecode and a validated virtual machine.
Monitor-Based Statistical Model Checking for Weighted Metric Temporal Logic
DEFF Research Database (Denmark)
Bulychev, Petr; David, Alexandre; Larsen, Kim Guldstrand;
2012-01-01
We present a novel approach and implementation for ana- lysing weighted timed automata (WTA) with respect to the weighted metric temporal logic (WMTL≤ ). Based on a stochastic semantics of WTAs, we apply statistical model checking (SMC) to estimate and test probabilities of satisfaction with...... desired levels of confidence. Our ap- proach consists in generation of deterministic monitors for formulas in WMTL≤ , allowing for efficient SMC by run-time evaluation of a given formula. By necessity, the deterministic observers are in general approx- imate (over- or under-approximations), but are most...
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, ...
Algebraic approach to electro-optic modulation of light: Exactly solvable multimode quantum model
Miroshnichenko, George P; Trifanov, Alexander I; Gleim, Artur V
2016-01-01
We theoretically study electro-optic light modulation based on the quantum model where the linear electro-optic effect and the externally applied microwave field result in the interaction between optical cavity modes. The model assumes that the number of interacting modes is finite and effects of the mode overlapping coefficient on the strength of the intermode interaction can be taken into account through dependence of the coupling coefficient on the mode characteristics. We show that, under certain conditions, the model is exactly solvable and, in the semiclassical approximation where the microwave field is treated as a classical mode, can be analyzed using the technique of the Jordan mappings for the su(2) Lie algebra. Analytical results are applied to study effects of light modulation on the frequency dependence of the photon counting rate. We also establish the conditions of validity of the semiclassical approximation by applying the methods of polynomially deformed Lie algebras for analysis of the model...
Directory of Open Access Journals (Sweden)
G. Bussi
2013-08-01
Full Text Available Soil loss and sediment transport in Mediterranean areas are driven by complex non-linear processes which have been only partially understood. Distributed models can be very helpful tools for understanding the catchment-scale phenomena which lead to soil erosion and sediment transport. In this study, a modelling approach is proposed to reproduce and evaluate erosion and sediment yield processes in a Mediterranean catchment (Rambla del Poyo, Valencia, Spain. Due to the lack of sediment transport records for model calibration and validation, a detailed description of the alluvial stratigraphy infilling a check dam that drains a 12.9 km2 sub-catchment was used as indirect information of sediment yield data. These dam infill sediments showed evidences of at least 15 depositional events (floods over the time period 1990–2009. The TETIS model, a distributed conceptual hydrological and sediment model, was coupled to the Sediment Trap Efficiency for Small Ponds (STEP model for reproducing reservoir retention, and it was calibrated and validated using the sedimentation volume estimated for the depositional units associated with discrete runoff events. The results show relatively low net erosion rates compared to other Mediterranean catchments (0.136 Mg ha−1 yr−1, probably due to the extensive outcrops of limestone bedrock, thin soils and rather homogeneous vegetation cover. The simulated sediment production and transport rates offer model satisfactory results, further supported by in-site palaeohydrological evidences and spatial validation using additional check dams, showing the great potential of the presented data assimilation methodology for the quantitative analysis of sediment dynamics in ungauged Mediterranean basins.
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.
An algebraic stress/flux model for two-phase turbulent flow
International Nuclear Information System (INIS)
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 Cμ, 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
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.
Lefschetz, Solomon
2012-01-01
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.
Surfaces immersed in su(N+1) Lie algebras obtained from the CPN sigma models
International Nuclear Information System (INIS)
We study some geometrical aspects of two-dimensional orientable surfaces arising from the study of CPN sigma models. To this aim we employ an identification of RN(N+2) with the Lie algebra su(N+1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CPN model defining it. Further, the first and second fundamental forms, the Gaussian curvature, the mean curvature vector, the Willmore functional and the topological charge of surfaces are expressed in terms of this solution. We present detailed implementation of these results for surfaces immersed in su(2) and su(3) Lie algebras
International Nuclear Information System (INIS)
Recent developments and applications of an algebraic version of Bohr's collective model, known as the algebraic collective model (ACM), have shown that fully converged calculations can be performed for a large range of Hamiltonians. Examining the algebraic structure underlying the Bohr model (BM) has also clarified its relationship with the interacting boson model (IBM), with which it has related solvable limits and corresponding dynamical symmetries. In particular, the algebraic structure of the IBM is obtained as a compactification of the BM and conversely the BM is regained in various contraction limits of the IBM. In a previous paper, corresponding contractions were identified and confirmed numerically for axially-symmetric states of relatively small deformation. In this paper, we extend the comparisons to realistic deformations and compare results of the two models in the rotor-vibrator limit. These models describe rotations and vibrations about an axially symmetric prolate or oblate rotor, and rotations and vibrations of a triaxial rotor. It is determined that most of the standard results of the BM can be obtained as contraction limits of the IBM in its U(5)-SO(6) dynamical symmetries.
Czech Academy of Sciences Publication Activity Database
Haslinger, J.; Stebel, Jan
2011-01-01
Roč. 63, č. 2 (2011), s. 277-308. ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2011 http://link.springer.com/article/10.1007%2Fs00245-010-9121-x
Another algebraic variational principle for the spectral curve of matrix models
Eynard, B
2014-01-01
We propose an alternative variational principle whose critical point is the algebraic plane curve associated to a matrix model (the spectral curve, i.e. the large $N$ limit of the resolvent). More generally, we consider a variational principle that is equivalent to the problem of finding a plane curve with given asymptotics and given cycle integrals. This variational principle is not given by extremization of the energy, but by the extremization of an "entropy".
Mohammad Shahzad
2016-01-01
This study deals with the control of chaotic dynamics of tumor cells, healthy host cells, and effector immune cells in a chaotic Three Dimensional Cancer Model (TDCM) by State Space Exact Linearization (SSEL) technique based on Lie algebra. A non-linear feedback control law is designed which induces a coordinate transformation thereby changing the original chaotic TDCM system into a controlled one linear system. Numerical simulation has been carried using Mathematica that witness the robustne...
RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity
Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
A special family of partitions occurs in two apparently unrelated contexts: the evaluation of 1-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras $H_m$. We provide an explanation of this coincidence by showing how the irreducible $H_m$-modules which remain irreducible under restriction to $H_{m-1}$ (Jantzen-Seitz modules) can be determined from the decomposition of a tensor product of representations of aff...
Algebraic and relational models for a system based on a poset of two elements
Iturrioz, Luisa
2014-01-01
The aim of this paper is to present a very simple set of conditions, necessary for the management of knowledge of a poset $T$ of two agents, which are partially ordered by the capabilities available in the system. We build up a formal system and we elaborate suitable semantic models in order to derive information from the poset. The system is related to three-valued Heyting algebras with Boolean operators.
On the algebraic structure of self-dual gauge fields and sigma models
International Nuclear Information System (INIS)
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 nonlinear 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. (author)
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...
Svetoslav Markov
2005-01-01
This survey paper aims to promote certain novel mathematical tools, such as computer algebra systems, enclosure methods and interval analysis, to the mathematical modelling and optimization of biotechnological processes.
Vibrational spectrum of CF4 isotopes in an algebraic model
Indian Academy of Sciences (India)
Joydeep Choudhury; Srinivasa Rao Karumuri; Nirmal Kumar Sarkar; Ramendu Bhattacharjee
2009-11-01
n this paper the stretching vibrational modes of CF4 isotopes are calculated up to first overtone using the one-dimensional vibron model for the first time. The model Hamiltonian so constructed seems to describe the C–F stretching modes accurately using a relatively small set of well-defined parameters.
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Directory of Open Access Journals (Sweden)
Blekherman Grigoriy
2011-07-01
Full Text Available Abstract Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM, which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides
Algebraic Watchdog: Mitigating Misbehavior in Wireless Network Coding
Kim, MinJi; Barros, Joao
2010-01-01
We propose a secure scheme for wireless network coding, called the algebraic watchdog. By enabling nodes to detect malicious behaviors probabilistically and use overheard messages to police their downstream neighbors locally, the algebraic watchdog delivers a secure global self-checking network. Unlike traditional Byzantine detection protocols which are receiver-based, this protocol gives the senders an active role in checking the node downstream. The key idea is inspired by Marti et al.'s watchdog-pathrater, which attempts to detect and mitigate the effects of routing misbehavior. As an initial building block of a such system, we first focus on a two-hop network. We present a graphical model to understand the inference process nodes execute to police their downstream neighbors; as well as to compute, analyze, and approximate the probabilities of misdetection and false detection. In addition, we present an algebraic analysis of the performance using an hypothesis testing framework that provides exact formulae...
Application of a hazard-based visual predictive check to evaluate parametric hazard models.
Huh, Yeamin; Hutmacher, Matthew M
2016-02-01
Parametric models used in time to event analyses are evaluated typically by survival-based visual predictive checks (VPC). Kaplan-Meier survival curves for the observed data are compared with those estimated using model-simulated data. Because the derivative of the log of the survival curve is related to the hazard--the typical quantity modeled in parametric analysis--isolation, interpretation and correction of deficiencies in the hazard model determined by inspection of survival-based VPC's is indirect and thus more difficult. The purpose of this study is to assess the performance of nonparametric hazard estimators of hazard functions to evaluate their viability as VPC diagnostics. Histogram-based and kernel-smoothing estimators were evaluated in terms of bias of estimating the hazard for Weibull and bathtub-shape hazard scenarios. After the evaluation of bias, these nonparametric estimators were assessed as a method for VPC evaluation of the hazard model. The results showed that nonparametric hazard estimators performed reasonably at the sample sizes studied with greater bias near the boundaries (time equal to 0 and last observation) as expected. Flexible bandwidth and boundary correction methods reduced these biases. All the nonparametric estimators indicated a misfit of the Weibull model when the true hazard was a bathtub shape. Overall, hazard-based VPC plots enabled more direct interpretation of the VPC results compared to survival-based VPC plots. PMID:26563504
Continuous Verification of Large Embedded Software using SMT-Based Bounded Model Checking
Cordeiro, Lucas; Marques-Silva, Joao
2009-01-01
The complexity of software in embedded systems has increased significantly over the last years so that software verification now plays an important role in ensuring the overall product quality. In this context, SAT-based bounded model checking has been successfully applied to discover subtle errors, but for larger applications, it often suffers from the state space explosion problem. This paper describes a new approach called continuous verification to detect design errors as quickly as possible by looking at the Software Configuration Management (SCM) system and by combining dynamic and static verification to reduce the state space to be explored. We also give a set of encodings that provide accurate support for program verification and use different background theories in order to improve scalability and precision in a completely automatic way. A case study from the telecommunications domain shows that the proposed approach improves the error-detection capability and reduces the overall verification time by...
Taming Numbers and Durations in the Model Checking Integrated Planning System
Edelkamp, S
2011-01-01
The Model Checking Integrated Planning System (MIPS) is a temporal least commitment heuristic search planner based on a flexible object-oriented workbench architecture. Its design clearly separates explicit and symbolic directed exploration algorithms from the set of on-line and off-line computed estimates and associated data structures. MIPS has shown distinguished performance in the last two international planning competitions. In the last event the description language was extended from pure propositional planning to include numerical state variables, action durations, and plan quality objective functions. Plans were no longer sequences of actions but time-stamped schedules. As a participant of the fully automated track of the competition, MIPS has proven to be a general system; in each track and every benchmark domain it efficiently computed plans of remarkable quality. This article introduces and analyzes the most important algorithmic novelties that were necessary to tackle the new layers of expressiven...
Meadow enriched ACP process algebras
J.A. Bergstra; Middelburg, C.A.
2009-01-01
We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization of the notion of an ACP process algebra to processes in which data are involved. In meadow enriched ACP process algebras, the mathematical structure for data is a meadow.
A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models
International Nuclear Information System (INIS)
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)L × U(1)R. It is known that SU(2)L is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1)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
From Clifford Algebra of Nonrelativistic Phase Space to Quarks and Leptons of the Standard Model
Żenczykowski, Piotr
2015-01-01
We review a recently proposed Clifford-algebra approach to elementary particles. We start with: (1) a philosophical background that motivates a maximally symmetric treatment of position and momentum variables, and: (2) an analysis of the minimal conceptual assumptions needed in quark mass extraction procedures. With these points in mind, a variation on Born's reciprocity argument provides us with an unorthodox view on the problem of mass. The idea of space quantization suggests then the linearization of the nonrelativistic quadratic form ${\\bf p}^2 +{\\bf x}^2$ with position and momentum satisfying standard commutation relations. This leads to the 64-dimensional Clifford algebra ${Cl}_{6,0}$ of nonrelativistic phase space within which one identifies the internal quantum numbers of a single Standard Model generation of elementary particles (i.e. weak isospin, hypercharge, and color). The relevant quantum numbers are naturally linked to the symmetries of macroscopic phase space. It is shown that the obtained pha...
International Nuclear Information System (INIS)
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)
Conformal Field Theory, Vertex Operator Algebra and Stochastic Loewner Evolution in Ising Model
Zahabi, Ali
2015-01-01
We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model. We obtain the scaling limit of the correlation functions of Ising free fermions on an arbitrary simply connected two-dimensional domain $D$. Then, we study the analytic and algebraic aspects of the fermionic CFT on $D$, using the Fock space formalism of fields, and the Clifford vertex operator algebra (VOA). These constructions lead to the conformal field theory of the Fock space fields and the fermionic Fock space of states and their relations in case of the Ising free fermions. Furthermore, we investigate the conformal structure of the fermionic Fock space fields and the Clifford VOA, namely the operator product expansions, correlation functions and differential equations. Finally, by using the Clifford VOA and the fermionic CFT, we investigate a rigorous realization of the CFT/SLE correspondence in the Ising model. First, by studying t...
A new algebraic structure in the standard model of particle physics
Boyle, Latham
2016-01-01
We introduce a new formulation of non-commutative geometry (NCG): we explain its mathematical advantages and its success in capturing the structure of the standard model of particle physics. The idea, in brief, is to represent $A$ (the algebra of differential forms on some possibly-noncommutative space) on $H$ (the Hilbert space of spinors on that space); and to reinterpret this representation as a simple super-algebra $B=A\\oplus H$ with even part $A$ and odd part $H$. $B$ is the fundamental object in our approach: we show that (nearly) all of the basic axioms and assumptions of the traditional ("spectral triple") formulation of NCG are elegantly recovered from the simple requirement that $B$ should be a differential graded $\\ast$-algebra (or "$\\ast$-DGA"). But this requirement also yields other, new, geometrical constraints. When we apply our formalism to the NCG traditionally used to describe the standard model of particle physics, we find that these new constraints are physically meaningful and phenomenolo...
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
International Nuclear Information System (INIS)
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 Am 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 Am(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; Am(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 j1 and j2 take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra Am into a ribbon Hopf algebra, and we show that this is 'Morita equivalent' to the quantum group Uq(sl2) for m=q+q-1. The open-chain results are extended to the cases vertical bar m vertical barm or Uq(sl2
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
Teaching Algebra and Geometry Concepts by Modeling Telescope Optics
Siegel, Lauren M.; Dickinson, Gail; Hooper, Eric J.; Daniels, Mark
2008-01-01
This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…
Moments, Model Reduction and Nonlinearity in Solving linear Algebraic Problems
Czech Academy of Sciences Publication Activity Database
Strakoš, Z.; Hnětynková, I.; O'Leary, D.P.; Plešinger, M.; Tichý, Petr
Prague : ICS AS CR, 2012. [Joint French-Czech Workshop on Krylov Methods for Inverse Problem s. 19.07.2012-20.07.2012, Prague] Institutional support: RVO:67985807 Keywords : problem of moments * model reduction * Krylov subspace Subject RIV: BA - General Mathematics
Algebraic nonlinear collective motion
Troupe, J.; Rosensteel, G.
1999-01-01
Finite-dimensional Lie algebras of vector fields determine geometrical collective models in quantum and classical physics. Every set of vector fields on Euclidean space that generates the Lie algebra sl(3, R) and contains the angular momentum algebra so(3) is determined. The subset of divergence-free sl(3, R) vector fields is proven to be indexed by a real number $\\Lambda$. The $\\Lambda=0$ solution is the linear representation that corresponds to the Riemann ellipsoidal model. The nonlinear g...
Algebraic statistics computational commutative algebra in statistics
Pistone, Giovanni; Wynn, Henry P
2000-01-01
Written by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science.
A branch-and-bound methodology within algebraic modelling systems
Bisschop, J.J.; Heerink, J.B.J.; Kloosterman, G.
1998-01-01
Through the use of application-specific branch-and-bound directives it is possible to find solutions to combinatorial models that would otherwise be difficult or impossible to find by just using generic branch-and-bound techniques within the framework of mathematical programming. {\\sc Minto} is an example of a system which offers the possibility to incorporate user-provided directives (written in {\\sc C}) to guide the branch-and-bound search. Its main focus, however, remains on mathematical p...
The standard model of quantum physics in Clifford algebra
Daviau, Claude
2016-01-01
We extend to gravitation our previous study of a quantum wave for all particles and antiparticles of each generation (electron + neutrino + u and d quarks for instance). This wave equation is form invariant under Cl3*, then relativistic invariant. It is gauge invariant under the gauge group of the standard model, with a mass term: this was impossible before, and the consequence was an impossibility to link gauge interactions and gravitation.
Safety properties test data selection from an algebraic model of Lustre programs
International Nuclear Information System (INIS)
In the context to validate an industrial software, which is a set of reactive programs, we are confronted with the safety properties verification problem. This thesis reports an experience in which our goal is to generate the test data satisfying a safety property. The software to be validated is designed with the SAGA tool, in which a view can be regarded as a program of a programming language called LUSTRE. We adapt a test data generation tool called LOFT to this kind of programs. In this way, we consider the functional testing method on which the LOFT tool is based. Given any LUSTRE program, we try to give it an algebraic model because LOFT treats algebraic specifications. So, our task consists In defining a formal framework in which any LUSTRE program can be translated into a LOFT module: based on an operational semantics of the LUSTRE language, the flow types 'T-flow' are specified with the constructive algebraic formalism, then implemented in a LOFT modules base. Next, in a test selection process assisted by LOFT, a safety property Is expressed by an equation to join other control hypotheses, and to guide the test data selection. Some concrete test data set are generated in this way on some significant examples. This experience confirm the feasibility of formal method on test data selection for the reactive programs. (author)
Jaynes-Cummings model and the deformed-oscillator algebra
International Nuclear Information System (INIS)
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.))
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.
Algebraic equations for the exceptional eigenspectrum of the generalized Rabi model
International Nuclear Information System (INIS)
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)
International Nuclear Information System (INIS)
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)
Extended FRAM by Integrating with Model Checking to Effectively Explore Hazard Evolution
Directory of Open Access Journals (Sweden)
Guihuan Duan
2015-01-01
Full Text Available Functional Resonance Analysis Method (FRAM, which defines a systemic framework to model complex systems from the perspective of function and views accidents as emergent phenomenon of function’s variability, is playing an increasingly significant role in the development of systemic accident theory. However, as FRAM is typically taken as a theoretic method, there is a lack of specific approaches or supportive tools to bridge the theory and practice. To fill the gap and contribute to the development of FRAM, (1 function’s variability was described further, with the rules of interaction among variability of different functions being determined and (2 the technology of model checking (MC was used for the analysis of function’s variability to automatically search the potential paths that could lead to hazards. By means of MC, system’s behaviors (normal or abnormal are simulated and the counter example(s that violates the safety constraints and requirements can be provided, if there is any, to improve the system design. The extended FRAM approach was applied to a typical air accident analysis, with more details drawn than the conclusions in the accident report issued officially by Agenzia Nazionale per la Sicurezza del Volo (ANSV.
Enlarged symmetry algebras of spin chains, loop models, and S-matrices
Energy Technology Data Exchange (ETDEWEB)
Read, N. [Department of Physics, Yale University, PO Box 208120, New Haven, CT 06520-8120 (United States)]. E-mail: nicholas.read@yale.edu; Saleur, H. [Service de Physique Theorique, CEA Saclay, 91191 Gif-sur-Yvette (France) and Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089 (United States)]. E-mail: hubert.saleur@cea.fr
2007-08-20
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{sub 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{sub 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{sub 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{sub 1} and j{sub 2} take the same form as the Clebsch-Gordan series for SU(2). This and other structures turn the symmetry algebra A{sub m} into a ribbon Hopf algebra, and we show that this is 'Morita equivalent' to the quantum group U{sub q}(sl{sub 2}) for m=q+q{sup -1}. The open-chain results
Institute of Scientific and Technical Information of China (English)
HUA ZuLin; GU Li; XING LingHang; DAI WenHong
2009-01-01
On the numerical simulation of active scalar, a new explicit algebraic expression on active scalar flux was derived based on Wikstrom, Wallin and Johansson model (aWWJ model). Reynolds stress algebraic expressions were added by a term to account for the buoyancy effect. The new explicit Reynolds stress and active scalar flux model was then established. Governing equations of this model were solved by finite volume method with unstructured grids. The thermal shear stratified cylinder wake flow was computed by this new model. The computational results are in good agreement with Laboratorial measurements. This work is the development on modeling of explicit algebraic Reynolds stress and scalar flux, and is also a further modification of the aWWJ model for complex situations such as a shear stratified flow.
International Nuclear Information System (INIS)
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
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
Phantom energy from graded algebras
Chaves, Max; Singleton, Douglas
2006-01-01
We construct a model of phantom energy using the graded Lie algebra SU(2/1). The negative kinetic energy of the phantom field emerges naturally from the graded Lie algebra, resulting in an equation of state with w
Algebraic Bethe ansatz for the six vertex model with upper triangular K-matrices
International Nuclear Information System (INIS)
We consider a formulation of the algebraic Bethe ansatz for the six vertex model with non-diagonal open boundaries. Specifically, we study the case where both left and right K-matrices have an upper triangular form. We show that the main difficulty entailed by those forms of the K-matrices is the construction of the excited states. However, it is possible to treat this problem with the aid of an auxiliary transfer matrix and by means of a generalized creation operator. (paper)
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.
RSOS models and Jantzen-Seitz representations of Hecke algebras at roots of unity
Foda, O E; Okado, M; Thibon, J Y; Welsh, Trevor A; Foda, Omar; Leclerc, Bernard; Okado, Masato; Thibon, Jean-Yves; Welsh, Trevor A.
1997-01-01
A special family of partitions occurs in two apparently unrelated contexts: the evaluation of 1-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras $H_m$. We provide an explanation of this coincidence by showing how the irreducible $H_m$-modules which remain irreducible under restriction to $H_{m-1}$ (Jantzen-Seitz modules) can be determined from the decomposition of a tensor product of representations of affine $\\sl_n$.
Modeling boyciana-fish-human interaction with partial differential algebraic equations.
Jiang, Yushan; Zhang, Qingling; Wang, Haiyan
2016-07-01
Under the influence of human population distribution, the boyciana-fish ecological system is considered. First, the system can be described as a nonlinear partial differential algebraic equations system (PDAEs) with Neumann boundary conditions and ratio-dependent functional response. Second, we examine the system's persistence properties: the loacl stabilities of positive steady states, the absorbtion region and the global stability. And the proposed approach is illustrated by numerical simulation. Finally, by using the realistic data collected in the past fourteen years, the PDAEs parameter optimization model is built to predict the boyciana population. PMID:27155570
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.
Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
Energy Technology Data Exchange (ETDEWEB)
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
International Nuclear Information System (INIS)
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
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 ...
DEFF Research Database (Denmark)
Vester, Steen
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...
Hidden Q-structure and Lie 3-algebra for non-abelian superconformal models in six dimensions
Lavau, Sylvain; Strobl, Thomas
2014-01-01
We disclose the mathematical structure underlying the gauge field sector of the recently constructed non-abelian superconformal models in six spacetime dimensions. This is a coupled system of 1-form, 2-form, and 3-form gauge fields. We show that the algebraic consistency constraints governing this system permit to define a Lie 3-algebra, generalizing the structural Lie algebra of a standard Yang-Mills theory to the setting of a higher bundle. Reformulating the Lie 3-algebra in terms of a nilpotent degree 1 BRST-type operator Q, this higher bundle can be compactly described by means of a Q-bundle; its fiber is the shifted tangent of the Q-manifold corresponding to the Lie 3-algebra and its base the odd tangent bundle of spacetime equipped with the de Rham differential. The generalized Bianchi identities can then be retrieved concisely from Q^2=0, which encode all the essence of the structural identities. Gauge transformations are identified as vertical inner automorphisms of such a bundle, their algebra being ...
An Algebraic Graphical Model for Decision with Uncertainties, Feasibilities, and Utilities
Pralet, C; Verfaillie, G; 10.1613/jair.2151
2011-01-01
Numerous formalisms and dedicated algorithms have been designed in the last decades to model and solve decision making problems. Some formalisms, such as constraint networks, can express "simple" decision problems, while others are designed to take into account uncertainties, unfeasible decisions, and utilities. Even in a single formalism, several variants are often proposed to model different types of uncertainty (probability, possibility...) or utility (additive or not). In this article, we introduce an algebraic graphical model that encompasses a large number of such formalisms: (1) we first adapt previous structures from Friedman, Chu and Halpern for representing uncertainty, utility, and expected utility in order to deal with generic forms of sequential decision making; (2) on these structures, we then introduce composite graphical models that express information via variables linked by "local" functions, thanks to conditional independence; (3) on these graphical models, we finally define a simple class ...
The quantum Rabi model and Lie algebra representations of sl2
International Nuclear Information System (INIS)
The aim of the present paper is to understand the spectral problem of the quantum Rabi model in terms of Lie algebra representations of sl2(R). We define a second order element of the universal enveloping algebra U(sl2) of sl2(R), which, through the image of a principal series representation of sl2(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 sl2(R). (paper)
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
Background 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 mode...
Algebraic model for bubble tracking in horizontal gas-liquid flow
Energy Technology Data Exchange (ETDEWEB)
Freitas, Felipe G.C. de; Tisserant, Hendy R. [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil); Morales, Rigoberto E.M. [Universidade Tecnologica Federal do Parana (UTFPR), Curitiba, PR (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica e de Materiais; Mazza, Ricardo A.; Rosa, Eugenio S. [Universidade Estadual de Campinas (UNICAMP), SP (Brazil). Fac. de Engenharia Mecanica
2008-07-01
The current work extends the concept of unit-cell applied in gas-liquid slug flow models to predict the evolution of the gas and liquid flow properties along a horizontal pipe. The motivation of this model is its simplicity, easiness of application and low computational cost. It is a useful tool of reference data generation in order to check the consistency of numerical slug tracking models. The potential of the model is accessed by comparing the gas bubbles and liquid slug sizes, the translational bubble velocity and the pressure drop against experimental data. (author)
Entanglement in a model for Hawking radiation: An Application of Quadratic Algebras
Bambah, Bindu A; Shreecharan, T; Prasad, K Siva
2012-01-01
Quadratic polynomially deformed $su(1,1)$ and $su(2)$ algebras are utilised 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. Lastly, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance.
Izhakian, Zur; Rowen, Louis
2008-01-01
We develop the algebraic polynomial theory for "supertropical algebra," as initiated earlier over the real numbers by the first author. The main innovation there was the introduction of "ghost elements," which also play the key role in our structure theory. Here, we work somewhat more generally over an ordered monoid, and develop a theory which contains the analogs of several basic theorems of classical commutative algebra. This structure enables one to develop a Zariski-type algebraic geomet...
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
International Nuclear Information System (INIS)
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)
Lorentz invariant noncommutative algebra for cosmological models coupled to a perfect fluid
Energy Technology Data Exchange (ETDEWEB)
Abreu, Everton M.C.; Marcial, Mateus V.; Mendes, Albert C.R.; Oliveira, Wilson [Universidade Federal Rural do Rio de Janeiro (UFRRJ), Seropedica, RJ (Brazil); Universidade Federal de Juiz de Fora, MG (Brazil)
2013-07-01
Full text: In current theoretical physics there is a relevant number of theoretical investigations that lead to believe that at the first moments of our Universe, the geometry was not commutative and the dominating physics at that time was ruled by the laws of noncommutative (NC) geometry. Therefore, the idea is that the physics of the early moments can be constructed based on these concepts. The first published work using the idea of a NC spacetime were carried out by Snyder who believed that NC principles could make the quantum field theory infinities disappear. However, it did not occur and Snyder's ideas were put to sleep for a long time. The main modern motivations that rekindle the investigation about NC field theories came from string theory and quantum gravity. In the context of quantum mechanics for example, R. Banerjee discussed how NC structures appear in planar quantum mechanics providing a useful way for obtaining them. The analysis was based on the NC algebra used in planar quantum mechanics that was originated from 't Hooft's analysis on dissipation and quantization. In this work we carry out a NC algebra analysis of the Friedmann-Robert-Walker model, coupled to a perfect fluid and in the presence of a cosmological constant. The classical field equations are modified, by the introduction of a shift operator, in order to introduce noncommutativity in these models. (author)
New solutions from algebraic equations for the Skyrme model coupled to a scalar meson
Energy Technology Data Exchange (ETDEWEB)
Braghin, Fabio L. [Universidade Federal do Rio Grande do Norte (IIF/UFRN), Natal, RN (Brazil). Inst. Internacional de Fisica
2010-07-01
Full text: In this work a modified Skyrme model is considered such as to incorporate the interaction of the hedgehog with a scalar field, based on a previous work. The Skyrme model is a model of the nucleon in which the baryon emerges as a topological soliton and its coupling to a scalar field can either correspond to the coupling to the lightest scalar isoscalar meson sigma and also to implement the spontaneous breakdown of chiral symmetry in a consistent way. Therefore it can be related to modifications of a dense interacting medium and it becomes suitable for investigating the role of the symmetry breaking and its restoration. A transcendental algebraic equation is found to be enough to extract a new class of profile solutions of the skyrmion in a constant background. The mass of the corresponding topological soliton was found to decrease considerably in the case small masses are associated to the scalar field. (author)
Algebraic turbulent heat flux model for prediction of thermal stratification in piping system
International Nuclear Information System (INIS)
The effect of stratification on the flow in bounded geometries is studied through computational fluid dynamics (CFD) and two different modeling of the turbulent heat flux, namely constant turbulent Prandtl number and Algebraic Heat Flux Model (AHFM). The main feature of the work is the evaluation of the effect of buoyancy on the thermal quantities, velocity field and related pressure drop. It has been stated the superiority of the AHFM for the evaluation of turbulent heat flux and temperature field together with a correct evaluation of the thickness of the thermal layer (i.e stratification persistence), in comparison with the simple eddy diffusivity approach. However the adopted model shows over-prediction of the momentum transport in the vertical direction in comparison with the experimental data introducing higher uncertainties for the obtained pressure drop and related Fanning friction factor. (author)
A new class of Matrix Models arising from the W-infinity Algebra
Herce, H D; Herce, Henry D.; Zemba, Guillermo R.
2002-01-01
We present a new class of hermitian one-matrix models originated in the W-infinity algebra: more precisely, the polynomials defining the W-infinity generators in their fermionic bilinear form are shown to expand the orthogonal basis of a class of random hermitian matrix models. The corresponding potentials are given, and the thermodynamic limit interpreted in terms of a simple plasma picture. The new matrix models can be successfully applied to the full bosonization of interesting one-dimensional systems, including all the perturbative orders in the inverse size of the system. As a simple application, we present the all-order bosonization of the free fermionic field on the one-dimensional lattice.
A note on the "logarithmic-W_3" octuplet algebra and its Nichols algebra
Semikhatov, A M
2013-01-01
We describe a Nichols-algebra-motivated construction of an octuplet chiral algebra that is a "W_3-counterpart" of the triplet algebra of (p,1) logarithmic models of two-dimensional conformal field theory.
Meadow enriched ACP process algebras
J.A. Bergstra; C.A. Middelburg
2009-01-01
We introduce the notion of an ACP process algebra. The models of the axiom system ACP are the origin of this notion. ACP process algebras have to do with processes in which no data are involved. We also introduce the notion of a meadow enriched ACP process algebra, which is a simple generalization o
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…
International Nuclear Information System (INIS)
In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system is obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 108 unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.
On various avatars of the Pasquier algebra
International Nuclear Information System (INIS)
A Pasquier algebra is a commutative associative algebra of normal matrices attached to a graph. I review various appearances of such algebras in different contexts: operator product algebras and structure constants in conformal theories and lattice models, integrable N = 2 supersymmetric models and their topological partners. (author)
Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model
Chamseddine, Ali H.; Connes, Alain
2007-11-01
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.
Two types of loop algebras and their expanding Lax integrable models
Institute of Scientific and Technical Information of China (English)
Yue Chao; Zhang Yu-Feng; Wei Yuan
2007-01-01
Though various integrable hierarchies of evolution equations were obtained by choosing proper U in zero-curvature equation Ut-Vx+[U,V]=0,but in this paper,a new integrable hierarchy possessing bi-Hamiltonian structure is worked out by selecting V with spectral potentials.Then its expanding Lax integrable model of the hierarchy possessing a simple Hamiltonian operator (J) is presented by constructing a subalgebra (G) of the loop algebra (A)2.As linear expansions of the above-mentioned integrable hierarchy and its expanding Lax integrable model with respect to their dimensional numbers,their (2+1)-dimensional forms are derived from a (2+1)-dimensional zero-curvature equation.
Structure of $^{23}$Al from a multi-channel algebraic scattering model based on mirror symmetry
Fraser, P R; Massen-Hane, K; Amos, K; Canton, L; Karataglidis, S; van der Knijff, D; Bray, I
2016-01-01
The proton-rich nucleus $^{23}$Al has a ground state just 123 keV below the proton drip-line, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering (MCAS) method to describe states as resonances of a valence proton coupled to a $^{22}$Mg rotor core. Six states with low-excitation energies and defined $J^\\pi$ are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.
Sensitivity analysis of groundwater flow model using the differential algebra method
International Nuclear Information System (INIS)
The techniques of sensitivity and uncertainty analyses are necessary for the performance assessment of the waste repositories and validations of mathematical and numerical models to determine key parameters in the models. An automated procedure is developed for performing large-scale sensitivity studies based on the use of computer tools. The procedure is composed of a FORTRAN precompiler called SANA and a preprocessor called PRESANA. The computer code SANA translates a FORTRAN code into its sensitivity analysis code using the Differential Algebra method, and the PRESANA is the computer tool to help the translation of the FORTRAN code. In this presentation, the automated procedure of sensitivity analysis and its application to the 3D-SEEP code which simulates 3-dimensional groundwater flow in the porous media are described. The sensitivity calculations for a sample problem are performed, and the applicability of SANA and PRESANA codes is discussed. 7 figs., 7 refs
Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry
Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.
2016-09-01
The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.
International Nuclear Information System (INIS)
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
W-algebras, new rational models and completeness of the c=1 classification
International Nuclear Information System (INIS)
Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If c=1-24k, there exists a W(2,3k) algebra for k element of Z+/2 and a W(2,8k) algebra for k element of Z+/4. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these theories are rational. It is shown, that these non-unitary theories complete the classification of all rational theories with effective central charge ceff=1. The results are generalized to the case of extended supersymmetric conformal algebras. (orig.)
W-algebras, new rational models and completeness of the c=1 classification
International Nuclear Information System (INIS)
Two series of W-algebras with two generators are constructed from chiral vertex operators of a free field representation. If c = 1 - 24 k, there exists a W(2,3k) algebra for kelement of Z+/2 and a W (2,8k) algebra for k element of Z+/4. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these therories are rational. It is shown, that these non-unitary theories complete the classification of all rational therories with effective central charge ceff = 1. The results are generalized to the case of extended supersymmetric conformal algebras. (orig.)
Jorgensen, PET
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
ALGEBRAIC ANOSOV ACTIONS OF NILPOTENT LIE GROUPS
Barbot, Thierry; Maquera, Carlos
2013-01-01
40 pages International audience In this paper we classify algebraic Anosov actions of nilpotent Lie groups on closed manifolds, extending the previous results by P. Tomter. We show that they are all nil-suspensions over either suspensions of Anosov actions of Z^k on nilmanifolds, or (modified) Weyl chamber actions. We check the validity of the generalized Verjovsky conjecture in this algebraic context. We also point out an intimate relation between algebraic Anosov actions and Cartan su...
International Nuclear Information System (INIS)
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 φ42-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 Yukawa2-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.)
Poisson bracket algebra for chiral group elements in the WZNW model
Bimonte, G; Simoni, A; Stern, A
1992-01-01
We examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left and right moving chiral group elements. Our computations apply for arbitrary groups and boundary conditions, the latter being characterized by the monodromy matrix. Unlike in previous treatments, they do not require specifying a particular parametrization of the group valued fields in terms of angles spanning the group. We do however find it necessary to make a gauge choice, as the chiral group elements are not gauge invariant observables. (On the other hand, the quadratic form of the Poisson brackets may be defined independent of a gauge fixing.) Gauge invariant observables can be formed from the monodromy matrix and these observables are seen to commute in the quantum theory.
Approach method of the solutions of algebraic models of the N body problem
International Nuclear Information System (INIS)
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
Algebraic geometry methods associated to the one-dimensional Hubbard model
Martins, M. J.
2016-06-01
In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.
Poisson bracket algebra for chiral group elements in the WZNW model
International Nuclear Information System (INIS)
In this paper, the authors examine the Wess-Zumino-Novikov-Witten (WZNW) model on a circle and compute the Poisson bracket algebra for left- and right-moving chiral group elements. The authors' computations apply for arbitrary groups and arbitrary boundary conditions, the latter being characterized by the monodromy matrix. Unlike previous treatments, the Poisson brackets do not require specifying a particular parametrization of the group valued fields in terms of angles spanning the group. The authors do however find it necessary to make a gauge choice, as the chiral group elements are not gauge invariant observables. (On the other hand, the quadratic form of the Poisson brackets may be defined independently of a gauge fixing.) Gauge invariant observables can be formed from the monodromy matrix and these observbles are seen to commute in the quantum theory
Particle-hole symmetry in algebraic Bethe Ansatz for the XXX model
International Nuclear Information System (INIS)
It is well known that the space of all quantum states of the XXX model for a magnetic ring of N nodes, each with the spin 1/2, decomposes into sectors with r spin deviations, r = 0,1, 2,..., N [1, 2, 3, 4]. The sectors r and N - r are related mutually by the particle-hole transformation which exchanges the signs + and - on each node. We discuss here effects of this transformation on the formalism of algebraic Bethe Ansatz, in particular on the form of the monodromy matrix, the main tool of this formalism. We derive explicitly appropriate transformation rules for CN- orbits of magnetic configurations and the corresponding Fourier transformations within the bases of wavelets. In particular, we point out some important phase relations between orbits on both sides of the equator.
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…
Algebraic Signal Processing Theory
Pueschel, Markus; Moura, Jose M. F.
2006-01-01
This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and phi generalizes the concept of the z-transform to bijective linear mappings from a vector space of, e.g., signal samples, into the module M. A signal model provides the structure for a p...
Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models
Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.
2016-08-01
We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.
An algebraic pairing model with Sp(4) symmetry and its deformation
International Nuclear Information System (INIS)
A fermion realization of the compact symplectic sp(4) algebra provides a natural framework for studying isovector-pairing correlations in nuclei. While these correlations manifest themselves most clearly in the binding energies of 0+ ground states, they also have a large effect on the energies of excited states, including especially excited 0+ states. In this paper, we consider non-deformed as well as deformed algebraic descriptions of pairing through the reductions of sp(q)(4) to different realizations of u(q)(2) for single-j and multi-j orbitals. The model yields a classification scheme for completely paired 0+ states of even-even and odd-odd nuclei in the 1d3/2, 1f7/2 and 1f5/2 2p1/2 2p3/2 1g9/2 shells. Phenomenological non-deformed and deformed isospin-breaking Hamiltonians are expressed in terms of the generators of the dynamical symmetry groups Sp(4) and Spq(4). These Hamiltonians are related to the most general microscopic pairing problem, including isovector pairing and isoscalar proton-neutron interaction along with nonlinear interaction in the deformed extension. In both the non-deformed and deformed cases the eigenvalues of the Hamiltonian are fit to the relevant Coulomb corrected experimental 0+ energies and this, in turn, allows us to estimate the interaction strength parameters, to investigate isovector-pairing properties and symmetries breaking and to predict the corresponding energies. While the non-deformed theory yields results that are comparable to other theories for light nuclei, the deformed extension, which takes into account higher order interactions between the particles, gives a better fit to the data. The multi-shell applications of the model provide for reasonable predictions of energies of exotic nuclei
Killing scalar of non-linear σ-model on G/H realizing the classical exchange algebra
International Nuclear Information System (INIS)
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
International Nuclear Information System (INIS)
The construction of an invariant action of the σ-model based on relative Lie algebra cohomology is discussed and compared with the conventional topological interpretation. An example of the Wess-Zumino term for a topologically trivial target space is given. (orig.)
Multiple model updating using the finite element method over a polynomial algebra
International Nuclear Information System (INIS)
Vibration control is an important issue when it comes to preserving the structural integrity of mechanical structures, particularly in the case of lightweight structures found aboard flying vehicles, such as printed circuit boards. In order for a simulation to be effective, a suitable numerical model of the structure must be used. Such a model can be obtained using a model updating method, such as that which is presented in this work, based on the modified constitutive relation error principle. However, like many other model updating strategies, this method can be very expensive. When the structural parameters change over time, it would be too time consuming to perform another full calculation. In order to circumvent this problem, we introduce a new technique called the 'finite element method over a polynomial algebra', which involves modules defined over a ring of truncated polynomials in multiple variables. In this paper, we illustrate the method with the updating and reduction of a model of a beam instrumented with piezoelectric sensors and actuators, which are all taken into account in the numerical model. This is a simple problem, yet it is representative of the updating of printed circuit boards
DEFF Research Database (Denmark)
2007-01-01
The workshop continued a series of Oberwolfach meetings on algebraic groups, started in 1971 by Tonny Springer and Jacques Tits who both attended the present conference. This time, the organizers were Michel Brion, Jens Carsten Jantzen, and Raphaël Rouquier. During the last years, the subject of...... algebraic groups (in a broad sense) has seen important developments in several directions, also related to representation theory and algebraic geometry. The workshop aimed at presenting some of these developments in order to make them accessible to a "general audience" of algebraic group-theorists, and to...
Model checking of time Petri nets using the state class timed automaton
DEFF Research Database (Denmark)
Lime, Didier; Roux, Olivier H.
2006-01-01
behavioral semantics of the TPN (the initial TPN and the obtained TA are proved timed-bisimilar). It allows us to check real-time properties on TPN by using the state class TA. This can be done efficiently thanks to a reduction of the number of clocks. We have implemented the method, and give some...... experimental results illustrating the efficiency of the translation algorithm in terms of number of clocks. Using the state class TA, we also give a framework for expressing and efficiently verifying TCTL properties on the initial TPN....
Karassiov, V. P.; A. A. Gusev; Vinitsky, S. I.
2001-01-01
We compare exact and SU(2)-cluster approximate calculation schemes to determine dynamics of the second-harmonic generation model using its reformulation in terms of a polynomial Lie algebra $su_{pd}(2)$ and related spectral representations of the model evolution operator realized in algorithmic forms. It enabled us to implement computer experiments exhibiting a satisfactory accuracy of the cluster approximations in a large range of characteristic model parameters.
Directory of Open Access Journals (Sweden)
Katie Ovens
2012-01-01
Full Text Available Introduction: Delta checks use two specimen test results taken in succession in order to detect test result changes greater than expected physiological variation. One of the most common and serious errors detected by delta checks is specimen mix-up errors. The positive and negative predictive values of delta checks for detecting specimen mix-up errors, however, are largely unknown. Materials and Methods: We addressed this question by first constructing a stochastic dynamic model using repeat test values for five analytes from approximately 8000 inpatients in Calgary, Alberta, Canada. The analytes examined were sodium, potassium, chloride, bicarbonate, and creatinine. The model simulated specimen mix-up errors by randomly switching a set number of pairs of second test results. Sensitivities and specificities were then calculated for each analyte for six combinations of delta check equations and cut-off values from the published literature. Results: Delta check specificities obtained from this model ranged from 50% to 99%; however the sensitivities were generally below 20% with the exception of creatinine for which the best performing delta check had a sensitivity of 82.8%. Within a plausible incidence range of specimen mix-ups the positive predictive values of even the best performing delta check equation and analyte became negligible. Conclusion: This finding casts doubt on the ongoing clinical utility of delta checks in the setting of low rates of specimen mix-ups.
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
International Nuclear Information System (INIS)
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
Energy Technology Data Exchange (ETDEWEB)
Okuda, Satoshi [Department of Physics, Rikkyo University,Toshima, Tokyo 171-8501 (Japan); Yoshida, Yutaka [High Energy Accelerator Research Organization (KEK),Tsukuba, Ibaraki 305-0801 (Japan)
2014-03-03
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.
G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra
Okuda, Satoshi
2013-01-01
We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from a viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.
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 ve...
Sensitivity analysis of radionuclide transport model using the Differential Algebra method
International Nuclear Information System (INIS)
The technique of sensitivity analysis is necessary for the performance assessment of the waste repositories and validation of models to determine key parameters in the models. Because, the parameters of the models describe physical and chemical processes in geologic conditions are generally not well known. An automated procedure is developed for performing large-scale sensitivity studies based on the use of computer tools. The procedure is composed of a FORTRAN precompilar called SANA and a preprocessor called PRESANA. The SANA code translates a FORTRAN code into its sensitivity analysis code using the Differential Algebra method, and the PRESANA is the computer tool to help the translation of FORTRAN code. In this presentation, we describe the automated procedure of sensitivity analysis and its application to the radionuclide transport codes, and discuss the applicability of SANA and PRESANA codes. The UCB-NE-10.3 and Finite Element codes developed to simulate the migration of radionuclides in groundwater were chosen as the targets of this procedure. (author)
Algebraic stress model for axial flow in a bare rod-bundle
International Nuclear Information System (INIS)
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
Segal algebras in commutative Banach algebras
INOUE, Jyunji; TAKAHASI, Sin-Ei
2014-01-01
The notion of Reiter's Segal algebra in commutative group algebras is generalized to a notion of Segal algebra in more general classes of commutative Banach algebras. Then we introduce a family of Segal algebras in commutative Banach algebras under considerations and study some properties of them.
Algebra-Geometry of Piecewise Algebraic Varieties
Institute of Scientific and Technical Information of China (English)
Chun Gang ZHU; Ren Hong WANG
2012-01-01
Algebraic variety is the most important subject in classical algebraic geometry.As the zero set of multivariate splines,the piecewise algebraic variety is a kind generalization of the classical algebraic variety.This paper studies the correspondence between spline ideals and piecewise algebraic varieties based on the knowledge of algebraic geometry and multivariate splines.
The algebraic structure of the Onsager algebra
DATE, ETSURO; Roan, Shi-shyr
2000-01-01
We study the Lie algebra structure of the Onsager algebra from the ideal theoretic point of view. A structure theorem of ideals in the Onsager algebra is obtained with the connection to the finite-dimensional representations. We also discuss the solvable algebra aspect of the Onsager algebra through the formal Lie algebra theory.
Energy Technology Data Exchange (ETDEWEB)
Choudhury, A.G.; Chowdhury, A.R. [Jadavpur Univ., Calcutta (India)
1996-08-01
Intertwining relations for the quantum R-matrix of the SU{sub p,q}(2) invariant spin chain are obtained and the corresponding face model is deduced. An important difference is seen to arise due to the asymmetry generated by the parameters p and q, which leads to a asymmetric face model. An algebraic Bethe ansatz is set up and solved with the help of these intertwining vectors.
Directory of Open Access Journals (Sweden)
Cătălin Dima
2010-06-01
Full Text Available We present a variant of ATL with distributed knowledge operators based on a synchronous and perfect recall semantics. The coalition modalities in this logic are based on partial observation of the full history, and incorporate a form of cooperation between members of the coalition in which agents issue their actions based on the distributed knowledge, for that coalition, of the system history. We show that model-checking is decidable for this logic. The technique utilizes two variants of games with imperfect information and partially observable objectives, as well as a subset construction for identifying states whose histories are indistinguishable to the considered coalition.
W-algebras in conformal field theory
International Nuclear Information System (INIS)
Quantum W-algebras are defined and their relevance for conformal field theories is outlined. We describe direct constructions of W-algebras using associativity requirements. With this approach one explicitly obtains the first members of series of W-algebras, including in particular 'Casimir algebras' (related to simple Lie algebras) and extended symmetry algebras corresponding to special Virasoro-minimal models. We also describe methods for the study of highest weight representations of W-algebras. In some cases consistency of the corresponding quantum field theory already imposes severe restrictions on the admitted representations, i.e. allows to determine the field content. We conclude by reviewing known results on W-algebras and RCFTs and show that most known rational conformal fields theories can be described in terms of Casimir algebras although on the level of W-algebras exotic phenomena occur. (author). 40 refs
Coherent States and Schwinger Models for Pseudo Generalization of the Heisenberg Algebra
Fakhri, H.; Mojaveri, B.; Dehghani, A.
We show that the non-Hermitian Hamiltonians of the simple harmonic oscillator with {PT} and {C} symmetries involve a pseudo generalization of the Heisenberg algebra via two pairs of creation and annihilation operators which are {T}-pseudo-Hermiticity and {P}-anti-pseudo-Hermiticity of each other. The non-unitary Heisenberg algebra is represented by each of the pair of the operators in two different ways. Consequently, the coherent and the squeezed coherent states are calculated in two different approaches. Moreover, it is shown that the approach of Schwinger to construct the su(2), su(1, 1) and sp(4, ℝ) unitary algebras is promoted so that unitary algebras with more linearly dependent number of generators are made.
C*-index of observable algebras in G-spin model
Institute of Scientific and Technical Information of China (English)
JIANG; Lining
2005-01-01
In two-dimensional lattice spin systems in which the spins take values in a finite group G,one can define a field algebra F which carries an action of a Hopf algebra D(G),the double algebra of G and moreover,an action of D(G; H),which is a subalgebra of D(G) determined by a subgroup H of G,so that F becomes a modular algebra.The concrete construction of D(G; H)-invariant subspace AH in F is given.By constructing the quasi-basis of conditional expectation γG of AH onto AG,the C*-index of γG is exactly the index of H in G.
Stabilizer quantum codes over the Clifford algebra
International Nuclear Information System (INIS)
The key problem for constructing a stabilizer quantum code is how to create a set of generators for the stabilizer of the stabilizer quantum code, i.e. check matrix. In this paper, we suggest an approach based on the Clifford algebra to create the check matrix for the stabilizer quantum codes. In the proposed approach, the recursive relation of the matrix transform over the Clifford algebra is employed to generate the check matrix. With the proposed approach, a quantum code with any length can be constructed easily. Especially some new codes, which are impossible via previous approaches, are constructed
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
Song, Yunquan; Lin, Lu; Jian, Ling
2016-07-01
Single-index varying-coefficient model is an important mathematical modeling method to model nonlinear phenomena in science and engineering. In this paper, we develop a variable selection method for high-dimensional single-index varying-coefficient models using a shrinkage idea. The proposed procedure can simultaneously select significant nonparametric components and parametric components. Under defined regularity conditions, with appropriate selection of tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Moreover, due to the robustness of the check loss function to outliers in the finite samples, our proposed variable selection method is more robust than the ones based on the least squares criterion. Finally, the method is illustrated with numerical simulations.
Mokler, Claus
2009-01-01
The face monoid described in [M1] acts on the integrable highest weight modules of a symmetrizable Kac-Moody algebra. It has similar structural properties as a reductive algebraic monoid whose unit group is a Kac-Moody group. We found in [M5] two natural extensions of the action of the Kac-Moody group on its building to actions of the face monoid on the building. Now we give an algebraic geometric model of one of these actions of the face monoid. The building is obtained as a part of the spectrum of homogeneous prime ideals of the Cartan algebra of the Kac-Moody group. We describe the full spectrum of homogeneous prime ideals of the Cartan algebra.
Holtz, Olga; Ron, Amos
2007-01-01
A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\\cal H}(X)$. This well-known line of study is particularly interesting in case $n\\eqbd\\rank X \\ll N$. We enhance this study to an algebraic level, and associate $X$ with three algebraic structures, referred herein as {\\it external, central, and internal.} Each algebraic structure is ...
International Nuclear Information System (INIS)
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.)
Issa, A. Nourou
2010-01-01
Hom-Akivis algebras are introduced. The commutator-Hom-associator algebra of a non-Hom-associative algebra (i.e. a Hom-nonassociative algebra) is a Hom-Akivis algebra. It is shown that non-Hom-associative algebras can be obtained from nonassociative algebras by twisting along algebra automorphisms while Hom-Akivis algebras can be obtained from Akivis algebras by twisting along algebra endomorphisms. It is pointed out that a Hom-Akivis algebra associated to a Hom-alternative algebra is a Hom-M...
Super Lie n-algebra extensions, higher WZW models, and super p-branes with tensor multiplet fields
Fiorenza, Domenico; Schreiber, Urs
2013-01-01
We formalize higher dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type sigma-model branes (open brane ending on background brane) are encoded precisely in (super-) L-infinity-extension theory and how the resulting "extended (super-)spacetimes" formalize spacetimes containing sigma model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super p-brane spectrum of superstring/M-theory is realized this way, including the pure sigma-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional spacetime with an M2-brane condensate turns out to be the ...
Directory of Open Access Journals (Sweden)
Murali Bosukonda
2011-01-01
Full Text Available This paper reveals mathematical models of the simplest Mamdani PI/PD controllers which employ two fuzzy sets (N: negative and P: positive on the universe of discourse (UoD of each of two input variables (displacement and velocity and three fuzzy sets (N: negative, Z: zero, and P: positive on the UoD of output variable (control output in the case of PD, and incremental control output in the case of PI. The basic constituents of these models are algebraic product/minimum AND, bounded sum/algebraic sum/maximum OR, algebraic product inference, three linear fuzzy control rules, and Center of Sums (CoS defuzzification. Properties of all these models are investigated. It is shown that all these controllers are different nonlinear PI/PD controllers with their proportional and derivative gains changing with the inputs. The proposed models are significant and useful to control community as they are completely new and qualitatively different from those reported in the literature.
Institute of Scientific and Technical Information of China (English)
ZHAO xiao-Song; L(U) Jian-Qin
2009-01-01
Both the PIC(Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams.The PIC model is to calculate the space charge field,which is blended into the external field,and then simulate the trajectories of particles in the total field;the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes.Two simulation codes based on the two methods are developed respectively,and the simulated results of transport in a set of electrostatic lenses are compared.It is found that the results from the two codes are in agreement with each other.and both approaches have their own merits.
Surfaces immersed in su(N+1) Lie algebras obtained from the CP{sup N} sigma models
Energy Technology Data Exchange (ETDEWEB)
Grundland, A M [Centre de Recherches Mathematiques, Universite de Montreal, CP 6128, Succ. Centre-ville, Montreal (Ciheam) H3C 3J7 (Canada) Universite du Quebec, Trois-Rivieres CP500 (QC) G9A 5H7 (Canada); Strasburger, A [Department of Mathematical Economics, Warsaw Agricultural University, ul. Nowoursynowska 166, 02-787 Warsaw (Poland); Zakrzewski, W J [Department of Mathematical Sciences, University of Durham, Durham DH1 3LE (United Kingdom)
2006-07-21
We study some geometrical aspects of two-dimensional orientable surfaces arising from the study of CP{sup N} sigma models. To this aim we employ an identification of R{sup N(N+2)} with the Lie algebra su(N+1) by means of which we construct a generalized Weierstrass formula for immersion of such surfaces. The structural elements of the surface like its moving frame, the Gauss-Weingarten and the Gauss-Codazzi-Ricci equations are expressed in terms of the solution of the CP{sup N} model defining it. Further, the first and second fundamental forms, the Gaussian curvature, the mean curvature vector, the Willmore functional and the topological charge of surfaces are expressed in terms of this solution. We present detailed implementation of these results for surfaces immersed in su(2) and su(3) Lie algebras.
Institute of Scientific and Technical Information of China (English)
XIEBing_Hao; ZHANGHong－Biao; 等
2002-01-01
An algebraic diagonalization method is proposed.As two examples,the Hamiltonians of BCS ground state under mean-field approximation and XXZ antiferromagnetic model in linear spin-wave frame have been diagonalized by using SU(2),SU(1,1) Lie algebraic method,respectively.Meanwhile,the eignenstates of the above two models are revealed to be SU(2),SU(1,1) coherent states,respectively,The relation between the usual Bogoliubov-Valatin transformation and the algebraic method in a special case is also discussed.
$\\eta_{c}$ Elastic and Transition Form Factors: Contact Interaction and Algebraic Model
Bedolla, Marco A; Cobos-Martínez, J J; Bashir, Adnan
2016-01-01
For the flavor-singlet heavy quark system of charmonia in the pseudoscalar ($\\eta_c(1S)$) channel, we calculate the elastic (EFF) and transition form factors (TFF) ($\\eta_c(1S) \\rightarrow \\gamma \\gamma^*$) for a wide range of photon momentum transfer squared ($Q^2$). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation (SDE) and Bethe-Salpeter equation (BSE) treatment of a vector$\\times$vector contact interaction (CI). We also employ an algebraic model (AM), developed earlier to describe the light quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The CI results agree with the lattice data for low $Q^2$. For $Q^2 \\geqslant Q_0^2$, the results start deviating from the lattice results by more than $20 \\%$. $Q_0^2 \\thickapprox 2.5 {\\rm GeV}^2$ for the EFF and $\\thickapprox 25 {\\rm GeV}^2$ for the TFF. We also present the results for the EFF, TFF as well as $\\eta_c(1S)$ parton distribution amplitude for the AM. Wherev...
Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; José M. Cela
2014-01-01
We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element solvers for three-dimensional electromagnetic numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation and Gauss-Seidel, as smoothers and the wav...
International Nuclear Information System (INIS)
Since the works of Gelfand, Harish-Chandra, Kostant and Duflo, a new theory has earned its place in the field of mathematics, due to the abundance of its results and the coherence of its methods: the theory of enveloping algebras. This study is the first to present the whole subject in textbook form. The most recent results are included, as well as complete proofs, starting from the elementary theory of Lie algebras. (Auth.)
Introduction to Clifford's Geometric Algebra
Hitzer, Eckhard
2013-01-01
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing, tracking, geographic information systems and neural computing. This tutorial explains the basics of geometric algebra, with concrete examples of the plane, of 3D space, of spacetime, and the popular conformal model. Geometric algebras are ideal to represen...
A new model for algebraic Rossby solitary waves in rotation fluid and its solution
Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru
2015-09-01
A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.
Which multiplier algebras are $W^*$-algebras?
Akemann, Charles A.; Amini, Massoud; Asadi, Mohammad B.
2013-01-01
We consider the question of when the multiplier algebra $M(\\mathcal{A})$ of a $C^*$-algebra $\\mathcal{A}$ is a $ W^*$-algebra, and show that it holds for a stable $C^*$-algebra exactly when it is a $C^*$-algebra of compact operators. This implies that if for every Hilbert $C^*$-module $E$ over a $C^*$-algebra $\\mathcal{A}$, the algebra $B(E)$ of adjointable operators on $E$ is a $ W^*$-algebra, then $\\mathcal{A}$ is a $C^*$-algebra of compact operators. Also we show that a unital $C^*$-algebr...
Directory of Open Access Journals (Sweden)
Yuan-Shyi Peter Chiu
2013-02-01
Full Text Available 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 each cycle. The objective is to determine the optimal replenishment lot size and optimal number of shipments that minimizes total expected costs for such a specific supply chains system. Conventional method is by the use of differential calculus on system cost function to derive the optimal policy (Chiu et al al., 2012c, whereas the proposed algebraic approach is a straightforward method that enables practitioners who may not have sufficient knowledge of calculus to understand and manage more effectively the real-life systems.
THE EXPERIMENTAL CHECK OF RELIABILITY OF MATHEMATICAL MODELS OF FRICTION JOINTS
Directory of Open Access Journals (Sweden)
A. Yu. Klyukin
2011-07-01
Full Text Available Problem statement. Up to now, there has been no model describing work of friction joints on high-strength bolts in elastic stage. All previous models describe the structure after macrodis-placement when bolt was subjected to shearing and crushing. There also has been no model of complex joint with gusset and linings.Results and conclusions. The bolted joint model involving substitution of the friction rigidity for elastic links is presented. Stresses in complex joints of metal bridge are determined experimentally. The results obtained with the use of the model are compared with experimental results. Stresses at the points of joint beyond the reach of experiment are calculated. Experimental results supported the validity of the model.
Algebraic entropy for algebraic maps
International Nuclear Information System (INIS)
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)
Homotopy DG algebras induce homotopy BV algebras
Terilla, John; Tradler, Thomas; Wilson, Scott O.
2011-01-01
Let TA denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then TA is a differential Batalin-Vilkovisky algebra. Moreover, if A is an A-infinity algebra, then TA is a commutative BV-infinity algebra.
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.
Sato, Kimiko; ODA, MEGUMI
2011-01-01
A questionnaire survey was administered to 317 parents who attended infant health check-ups in City B, Okayama Prefecture between October, 2008 and March, 2009. The questionnaire survey studied 7 factors based on the PRECEDE-PROCEED Model. We analysed factors that affected oral health behaviour and attendance at scheduled dental health check-ups. The survey containing 22 items concerning matters such as 'QOL' and 'health problems' was posted to parents and guardians in advance, and then colle...
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\\geq2), 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 \\bar{m}. We find that these spin chains, even with {\\em arbitrary} coefficients of these interactions, have a symmetry algebra A_m much larger than U(m), which implies that the en...
Lazeroms, W. M.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.; Svensson, G.
2014-12-01
Turbulent flows with buoyancy effects occur in many situations, both in industry and in the atmosphere. It is challenging to correctly model such flows, especially in the case of stably stratified turbulence, where vertical motions are damped by buoyancy forces. For this purpose, we have derived a so-called explicit algebraic model for the Reynolds stresses and turbulent heat flux that gives accurate predictions in flows with buoyancy effects. Although inspired by turbulence models from engineering, the main aim of our work is to improve the parametrization of turbulence in the atmospheric boundary layer (ABL). Explicit algebraic turbulence models are a class of parametrizations that, on the one hand, are more advanced than standard eddy-diffusivity relations. On the other hand, they are signficantly easier to handle numerically than models that require the solution of the full flux-budget equations. To derive the algebraic model, we apply the assumption that transport terms of dimensionless fluxes can be neglected. Careful considerations of the algebra lead to a consistent formulation of the Reynolds stresses and turbulent heat flux, which is more general and robust than previous models of a similar kind. The model is shown to give good results compared to direct numerical simulations of engineering test cases, such as turbulent channel flow. Recent work has been aimed at testing the model in an atmospheric context. The first of these tests makes use of the GABLS1 case, in which a stable atmospheric boundary layer develops through a constant surface cooling rate. The model is able to give good predictions of this case compared to LES (see attached figure). Interestingly, the results are very close to the outcome of the recently developed Energy-Flux-Budget (EFB) closure by Zilitinkevich et al. (2013). A detailed discussion of the similarities and differences between these models will be given, which can give insight in the more general gap between engineering and
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. PMID:27186457
Checking Fine and Gray subdistribution hazards model with cumulative sums of residuals
DEFF Research Database (Denmark)
Li, Jianing; Scheike, Thomas; Zhang, Mei Jie
2015-01-01
of residuals, which validate the model in three aspects: (1) proportionality of hazard ratio, (2) the linear functional form and (3) the link function. For each assumption testing, we provide a p-values and a visualized plot against the null hypothesis using a simulation-based approach. We also consider......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...
A Framework for Relating Timed Transition Systems and Preserving TCTL Model Checking
DEFF Research Database (Denmark)
Jacobsen, Lasse; Jacobsen, Morten; Møller, Mikael Harkjær; Srba, Jiri
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...
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Hansen, Zaza Nadja Lee
2016-01-01
This article presents a framework for the automated restructuring of stochastic workflows to reduce the impact of faults. The framework allows for the modelling of workflows by means of a formalised subset of the BPMN workflow language. We extend this modelling formalism to describe faults and...... 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....
Automated evolutionary restructuring of workflows to minimise errors via stochastic model checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Hansen, Zaza Nadja Lee; Jacobsen, Peter
2014-01-01
This paper presents a framework for the automated restructuring of workflows that allows one to minimise the impact of errors on a production workflow. The framework allows for the modelling of workflows by means of a formalised subset of the Business Process Modelling and Notation (BPMN) language......, a well-established visual language for modelling workflows in a business context. The framework’s modelling language is extended to include the tracking of real-valued quantities associated with the process (such as time, cost, temperature). In addition, this language also allows for an intention...... by means of a case study from the food industry. Through this case study we explore the extent to which the risk of production faults can be reduced and the impact of these can be minimised, primarily through restructuring of the production workflows. This approach is fully automated and only the...
Kick, Alexander
2007-01-01
We present a reduction algorithm which reduces Kripke structures by eliminating transitions from the model which do not affect the visible components of the model. These are exactly the variables contained in the specification formula. The reduction algorithm preserves the truth of special CTL formulae. In contrast to formula-dependent reduction algorithms presented so far, which are mostly computationally expensive, our algorithm needs only one pass through the reachable ...
Providência, C; Tsue, Y; Yamamura, M
2005-01-01
Following the Schwinger boson representation for the su(M+1)- and the su(N,1)-algebra presented by two of the present authors (J. da P. and M. Y.) and Kuriyama, a possible counterpart of the Lipkin model in the su(M+1)-algebra formulated in the fermion space is presented. The free vacuum, which plays a fundamental role in the conventional treatment of the Lipkin model, is generalized in a quite natural way, and further, the excited state generating operators such as the particle-hole pairs are also given in a natural scheme. As concrete examples, the cases of the su(2)-, su(3)- and the su(4)-algebra are discussed. Especially, the case of the su(4)-algebra is investigated in detail in relation to the nucleon pairing correlations and the high temperature superconductivity.
Kumar, Rajendra; Grubmüller, Helmut
2016-01-19
During replication of the ϕ29 bacteriophage inside a bacterial host cell, a DNA packaging motor transports the viral DNA into the procapsid against a pressure difference of up to 40 ± 20 atm. Several models have been proposed for the underlying molecular mechanism. Here we have used molecular dynamics simulations to examine the role of the connector part of the motor, and specifically the one-way revolution and the push-roll model. We have focused at the structure and intermolecular interactions between the DNA and the connector, for which a near-complete structure is available. The connector is found to induce considerable DNA deformations with respect to its canonical B-form. We further assessed by force-probe simulations to which extent the connector is able to prevent DNA leakage and found that the connector can act as a partial one-way valve by a check-valve mechanism via its mobile loops. Analysis of the geometry, flexibility, and energetics of channel lysine residues suggested that this arrangement of residues is incompatible with the observed DNA packaging step-size of ∼2.5 bp, such that the step-size is probably determined by the other components of the motor. Previously proposed DNA revolution and rolling motions inside the connector channel are both found implausible due to structural entanglement between the DNA and connector loops that have not been resolved in the crystal structure. Rather, in the simulations, the connector facilitates minor DNA rotation during the packaging process compatible with recent optical-tweezers experiments. Combined with the available experimental data, our simulation results suggest that the connector acts as a check-valve that prevents DNA leakage and induces DNA compression and rotation during DNA packaging. PMID:26789768
Brat, Guillaume P.; Martinie, Celia; Palanque, Philippe
2013-01-01
During early phases of the development of an interactive system, future system properties are identified (through interaction with end users in the brainstorming and prototyping phase of the application, or by other stakehold-ers) imposing requirements on the final system. They can be specific to the application under development or generic to all applications such as usability principles. Instances of specific properties include visibility of the aircraft altitude, speed… in the cockpit and the continuous possibility of disengaging the autopilot in whatever state the aircraft is. Instances of generic properties include availability of undo (for undoable functions) and availability of a progression bar for functions lasting more than four seconds. While behavioral models of interactive systems using formal description techniques provide complete and unambiguous descriptions of states and state changes, it does not provide explicit representation of the absence or presence of properties. Assessing that the system that has been built is the right system remains a challenge usually met through extensive use and acceptance tests. By the explicit representation of properties and the availability of tools to support checking these properties, it becomes possible to provide developers with means for systematic exploration of the behavioral models and assessment of the presence or absence of these properties. This paper proposes the synergistic use two tools for checking both generic and specific properties of interactive applications: Petshop and Java PathFinder. Petshop is dedicated to the description of interactive system behavior. Java PathFinder is dedicated to the runtime verification of Java applications and as an extension dedicated to User Interfaces. This approach is exemplified on a safety critical application in the area of interactive cockpits for large civil aircrafts.
Institute of Scientific and Technical Information of China (English)
WANG Renhong; ZHU Chungang
2004-01-01
The piecewise algebraic variety is a generalization of the classical algebraic variety. This paper discusses some properties of piecewise algebraic varieties and their coordinate rings based on the knowledge of algebraic geometry.
Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations
Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie
2015-01-01
The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…
Caglayan, Günhan
2013-01-01
This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…
Algebraic modelling and performance evaluation of acyclic fork-join queueing networks
Krivulin, Nikolai K.
2012-01-01
Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)-algebra based representation of network dynamics. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented.
Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context
Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.
2015-01-01
An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…
Algebraic Bethe Ansatz for Open XXX Model with Triangular Boundary Matrices
Belliard, Samuel; Crampé, Nicolas; Ragoucy, Eric
2013-05-01
We consider an open XXX spin chain with two general boundary matrices whose entries obey a relation, which is equivalent to the possibility to put simultaneously the two matrices in a upper-triangular form. We construct Bethe vectors by means of a generalized algebraic Bethe ansatz. As usual, the method uses Bethe equations and provides transfer matrix eigenvalues.
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…
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
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...
Model checking a cache coherence protocol for a Java DSM implementation
Pang, J.; Fokkink, W.J.; Hofman, R.; Veldema, R.
2007-01-01
Jackal is a fine-grained distributed shared memory implementation of the Java programming language. It aims to implement Java's memory model and allows multithreaded Java programs to run unmodified on a distributed memory system. It employs a multiple-writer cache coherence protocol. In this paper,
Lee, Young-Sun; Wollack, James A.; Douglas, Jeffrey
2009-01-01
The purpose of this study was to assess the model fit of a 2PL through comparison with the nonparametric item characteristic curve (ICC) estimation procedures. Results indicate that three nonparametric procedures implemented produced ICCs that are similar to that of the 2PL for items simulated to fit the 2PL. However for misfitting items,…
Model based feasibility study on bidirectional check valves in wave energy converters
DEFF Research Database (Denmark)
Hansen, Anders Hedegaard; Pedersen, Henrik C.; Andersen, Torben Ole
2014-01-01
valves in wave energy converters to improve the system efficiency. A single float arm of the Wavestar wave energy converter is modelled including the power take-off (PTO) system. The primary stage of the utilised PTO-system is a discrete fluid power force system consisting of a multi-chamber cylinder and...
Fluid-structure interaction model to check up discharging pipe system
International Nuclear Information System (INIS)
Within phenomena group that occur in a pipelines system that lead some fluid in stationary state, the loss of lateral stability is which one of the more common and important of them since it is showed in periodic vibrations or aleatories, way against whose effects it will have to be designed the piping to avoid catastrophic failures. The present work is a part of the realized effort for incorporating to the programs of digital computers used for the structural analysis of piping systems based in the finite element method. It is a model that includes the lateral effect that induces the fluid on the pipes. For this effect was planted and obtained a model or element for straight pipes segments. It was through the use of analytical variational methods and polynomial approximations (typical techniques using in finite elements). When were effected the calculations of characteristic frequencies in straight pipe sections configurations. It was obtained concordance with the analytical predictions. There fore it was demonstrated that the model is correct. A continuation of this work will be to obtain the models for curved segments of piping. (Author)
Clifford algebra, geometric algebra, and applications
Lundholm, Douglas; Svensson, Lars
2009-01-01
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra construction (then called geometric algebra) with geometric applications in mind, as well as in an algebraically more general form which is well suited for combinatorics, and for defining and understanding the numerous products and operations of the algebra. The v...
Cofree Hopf algebras on Hopf bimodule algebras
Fang, Xin; Jian, Run-Qiang
2013-01-01
We investigate a Hopf algebra structure on the cotensor coalgebra associated to a Hopf bimodule algebra which contains universal version of Clifford algebras and quantum groups as examples. It is shown to be the bosonization of the quantum quasi-shuffle algebra built on the space of its right coinvariants. The universal property and a Rota-Baxter algebra structure are established on this new algebra.
International Nuclear Information System (INIS)
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
Energy Technology Data Exchange (ETDEWEB)
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
On uniform topological algebras
Azhari, M. El
2013-01-01
The uniform norm on a uniform normed Q-algebra is the only uniform Q-algebra norm on it. The uniform norm on a regular uniform normed Q-algebra with unit is the only uniform norm on it. Let A be a uniform topological algebra whose spectrum M (A) is equicontinuous, then A is a uniform normed algebra. Let A be a regular semisimple commutative Banach algebra, then every algebra norm on A is a Q-algebra norm on A.
Marchuk, Nikolay
2011-01-01
Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this paper we define a notion of $N$-metric exterior algebra, which depends on $N$ matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as 0-metric exterior algebra. Clifford algebra can be considered as 1-metric exterior algebra. $N$-metric exterior algebras for $N\\geq2$ can be considered as generalizations of the Grassmann alg...
Hazewinkel, Michiel
2004-01-01
Two important generalizations of the Hopf algebra of symmetric functions are the Hopf algebra of noncommutative symmetric functions and its graded dual the Hopf algebra of quasisymmetric functions. A common generalization of the latter is the selfdual Hopf algebra of permutations (MPR Hopf algebra). This latter Hopf algebra can be seen as a Hopf algebra of endomorphisms of a Hopf algebra. That turns out to be a fruitful way of looking at things and gives rise to wide ranging further generaliz...
Allenby, Reg
1995-01-01
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.Solutions to the exercises are available onlin
Jacobson, Nathan
1979-01-01
Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints
Kothari, Sunil; 10.4204/EPTCS.42.3
2010-01-01
We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU), which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.
A Machine Checked Model of Idempotent MGU Axioms For Lists of Equational Constraints
Directory of Open Access Journals (Sweden)
Sunil Kothari
2010-12-01
Full Text Available We present formalized proofs verifying that the first-order unification algorithm defined over lists of satisfiable constraints generates a most general unifier (MGU, which also happens to be idempotent. All of our proofs have been formalized in the Coq theorem prover. Our proofs show that finite maps produced by the unification algorithm provide a model of the axioms characterizing idempotent MGUs of lists of constraints. The axioms that serve as the basis for our verification are derived from a standard set by extending them to lists of constraints. For us, constraints are equalities between terms in the language of simple types. Substitutions are formally modeled as finite maps using the Coq library Coq.FSets.FMapInterface. Coq's method of functional induction is the main proof technique used in proving many of the axioms.
A Deductive Approach towards Reasoning about Algebraic Transition Systems
Jun Fu; Jinzhao Wu; Hongyan Tan
2015-01-01
Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semanti...
Sparse Representations of Clifford and Tensor algebras in Maxima
Prodanov, Dimiter; Toth, Viktor T.
2016-01-01
Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an extensive demonstration of the applications of Clifford algebras in electromagnetism using the geometric algebra G3 = Cl(3,0) as a computational model in the Maxima computer algebra system. We compare the geometric algebra-based approach with conventional symboli...
GOLDMAN ALGEBRA, OPERS AND THE SWAPPING ALGEBRA
Labourie, François
2012-01-01
We define a Poisson Algebra called the {\\em swapping algebra} using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra -- called the {\\em algebra of multifractions} -- as an algebra of functions on the space of cross ratios and thus as an algebra of functions on the Hitchin component as well as on the space of $\\mathsf{SL}_n(\\mathbb R)$-opers with trivial holonomy. We relate this Poisson algebra to the Atiyah--Bott--Goldman symple...
Algebraic Squares: Complete and Incomplete.
Gardella, Francis J.
2000-01-01
Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)
Algebraic Thinking in Adult Education
Manly, Myrna; Ginsburg, Lynda
2010-01-01
In adult education, algebraic thinking can be a sense-making tool that introduces coherence among mathematical concepts for those who previously have had trouble learning math. Further, a modeling approach to algebra connects mathematics and the real world, demonstrating the usefulness of math to those who have seen it as just an academic…
Smarandache Jordan Algebras - abstract
Vasantha Kandasamy, W. B.; Christopher, S.; A. Victor Devadoss
2004-01-01
We prove a S-commutative Jordan Algebra is a S-weakly commutative Jordan algebra. We define a S-Jordan algebra to be S-simple Jordan algebras if the S-Jordan algebra has no S-Jordan ideals. We obtain several other interesting notions and results on S-Jordan algebras.
Directory of Open Access Journals (Sweden)
Jörg Becker
2012-11-01
Full Text Available With a steady increase of regulatory requirements for business processes, automation support of compliance management is a field garnering increasing attention in Information Systems research. Several approaches have been developed to support compliance checking of process models. One major challenge for such approaches is their ability to handle different modeling techniques and compliance rules in order to enable widespread adoption and application. Applying a structured literature search strategy, we reflect and discuss compliance-checking approaches in order to provide an insight into their generalizability and evaluation. The results imply that current approaches mainly focus on special modeling techniques and/or a restricted set of types of compliance rules. Most approaches abstain from real-world evaluation which raises the question of their practical applicability. Referring to the search results, we propose a roadmap for further research in model-based business process compliance checking.
Kang, Soo Hoon; Lim, Yaeji; Lee, Hyuk; Kim, Joungyoun; Chi, Sangah; Min, Yang Won; Min, Byung-Hoon; Lee, Jun Haeng; Son, Hee Jung; Ryu, Seungho; Rhee, Poong-Lyul; Kim, Jae J
2016-01-01
Erosive esophagitis is a major risk factor for Barrett esophagus and esophageal adenocarcinoma. Information regarding the putative risk factors for developing erosive esophagitis is considerably heterogeneous; thus, a risk model is required to clinically predict the incidence of erosive esophagitis. This study was to derive and validate a predictive model for the incidence of developing erosive esophagitis after negative index endoscopy in a population subjected to routine health check-ups. This retrospective cohort study of health check-ups included 11,535 patients who underwent repeated screening endoscopy after >3 years from a negative index endoscopy. We used logistic regression analysis to predict the incidence of erosive esophagitis, and a Simple Prediction of Erosive Esophagitis Development score for risk assessment was developed and internally validated using the split-sample approach. The development and validation cohorts included 5765 patients (675 with erosive esophagitis [11.7%]) and 5770 patients (670 with erosive esophagitis [11.6%]), respectively. The final model included sex, smoking behavior, body mass index, hypertension, and the triglyceride level as variables. This model predicted 667 cases of erosive esophagitis, yielding an expected-to-observed ratio of 1.00 (95% confidence interval [CI], 0.92-1.07). A simplified 5-item risk scoring system based on coefficients was developed, with a risk of erosive esophagitis of 6.2% (95% CI, 5.2-7.1) for the low-risk group (score ≤2), 15.1% (95% CI, 13.5-16.6) for the intermediate-risk group (score ≤3, 4), and 18.2% (95% CI, 15.2-21.3) for the high-risk group (score ≥5). The discriminative performance of the risk-prediction score was consistent in the derivation cohort and validation cohort (c-statistics 0.68 and 0.64, respectively); the calibration was good (Brier score 0.099 and 0.1, respectively). In conclusion, a simple risk-scoring model using putative risk factors can predict the future
Faria, J. M.; Mahomad, S.; Silva, N.
2009-05-01
The deployment of complex safety-critical applications requires rigorous techniques and powerful tools both for the development and V&V stages. Model-based technologies are increasingly being used to develop safety-critical software, and arguably, turning to them can bring significant benefits to such processes, however, along with new challenges. This paper presents the results of a research project where we tried to extend current V&V methodologies to be applied on UML/SysML models and aiming at answering the demands related to validation issues. Two quite different but complementary approaches were investigated: (i) model checking and the (ii) extraction of robustness test-cases from the same models. These two approaches don't overlap and when combined provide a wider reaching model/design validation ability than each one alone thus offering improved safety assurance. Results are very encouraging, even though they either fell short of the desired outcome as shown for model checking, or still appear as not fully matured as shown for robustness test case extraction. In the case of model checking, it was verified that the automatic model validation process can become fully operational and even expanded in scope once tool vendors help (inevitably) to improve the XMI standard interoperability situation. For the robustness test case extraction methodology, the early approach produced interesting results but need further systematisation and consolidation effort in order to produce results in a more predictable fashion and reduce reliance on expert's heuristics. Finally, further improvements and innovation research projects were immediately apparent for both investigated approaches, which point to either circumventing current limitations in XMI interoperability on one hand and bringing test case specification onto the same graphical level as the models themselves and then attempting to automate the generation of executable test cases from its standard UML notation.
Directory of Open Access Journals (Sweden)
Bonura Carlo A
2001-04-01
Full Text Available Abstract Background A previous report showed that the open field behavior of rats sensitized to the dopamine agonist quinpirole satisfies 5 performance criteria for compulsive checking behavior. In an effort to extend the parallel between the drug-induced phenomenon and human obsessive-compulsive disorder (OCD, the present study investigated whether the checking behavior of quinpirole rats is subject to interruption, which is an attribute characteristic of OCD compulsions. For this purpose, the rat's home-cage was placed into the open field at the beginning or the middle of a 2-hr test. Results Introduction of the home-cage reduced checking behavior, as rats stayed inside the cage. After 40 min, checking resurfaced, as quinpirole rats exited the home-cage often. An unfamiliar cage had no such effects on quinpirole rats or saline controls. Conclusions Checking behavior induced by quinpirole is not irrepressible but can be suspended. Results strengthen the quinpirole preparation as an animal model of OCD compulsive checking.
Indian Academy of Sciences (India)
Tomás L Gómez
2001-02-01
This is an expository article on the theory of algebraic stacks. After introducing the general theory, we concentrate in the example of the moduli stack of vector bundles, giving a detailed comparison with the moduli scheme obtained via geometric invariant theory.
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.