Some Weak Specification Properties and Strongly Mixing

In this paper,the authors first construct a dynamical system which is strongly mixing but has no weak specification property.Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper,respectively,and the authors prove the equivalence of quasi-weak specification property,semi-weak specification property and strongly mixing.     

On entropy of dynamical systems with almost specification

We construct a family of shift spaces with almost specification and multiple measures of maximal entropy. This answers a question from Climenhaga and Thompson [Israel J. Math. 192 (2012), 785–817]. Elaborating on our examples we prove that sufficient conditions for every shift factor of a shift space to be intrinsically ergodic given by Climenhaga and Thompson are in some sense best possible; moreover, the weak specification property neither implies intrinsic ergodicity, nor follows from almost specification. We also construct a dynamical system with the weak specification property, which does not have the almost specification property. We prove that the minimal points are dense in the support of any invariant measure of a system with the almost specification property. Furthermore, if a system with almost specification has an invariant measure with non-trivial support, then it also has uniform positive entropy over the support of any invariant measure and cannot be minimal.     

Effects of heterogeneity on bank efficiency scores

Bank efficiency estimates often serve as a proxy of managerial skill since they quantify sub-optimal production choices. But such deviations can also be due to omitted systematic differences among banks. In this study, we examine the effects of heterogeneity on bank efficiency scores. We compare different specifications of a stochastic cost and alternative profit frontier model with a baseline specification. After conducting a specification test, we discuss heterogeneity effects on efficiency levels, ranks and the tails of the efficiency distribution. We find that heterogeneity controls influence both banks’ optimal costs and profits and their ability to be efficient. Differences in efficiency scores are important for more than only methodological reasons. First, different ways of accounting for heterogeneity result in estimates of foregone profits and additional costs that are significantly different from what we infer from our general specification. Second, banks are significantly re-ranked when their efficiency is estimated with a specification other than the preferred, general specification. Third, the general specification gives the most reliable estimates of the probability of distress, although differences to the other specifications are low.     

The weak specification property and distributional chaos

In this paper, we first discuss almost periodic points in a compact dynamical system with the weak specification property. On the basis of this discussion, we draw two conclusions: (i) the weak specification property implies a dense Mycielski uniform distributionally scrambled set; (ii) the weak specification property and a fixed point imply a dense Mycielski uniform invariant distributionally scrambled set. These conclusions improve on some of the latest results concerning the specification property, and give a final positive answer to an open problem posed in [P. Oprocha, Invariant scrambled sets and distributional chaos, Dyn. Syst. 24 (2009), 31–43].     

Developing activity duration specification limits for effective project control

We propose a new structure for guiding project control decisions to ensure that a project is completed on schedule when activity durations are uncertain and modeled by random variables. This structure consists of specifying a specification limit for each activity duration. During the project, if the time to complete an activity is going to exceed its specification limit, actions are taken, at some cost, to bring the time down to that limit. We present an algorithm that selects specification limits to achieve targeted on-time probabilities at minimum cost. The method involves estimating the effect of small changes in specification limits on the probability of completing a project on time and on the cost of control actions. The required simulation-based estimates for all activities are obtained in a single set of simulation runs. Computational results show the algorithm to be efficient to apply and, when compared to a more ad hoc approach of using activity importance measures (specifically, activity criticality), the use of the resulting specification limits to be of significant benefit in guiding project control decisions.     

The base of the intersection of two free submonoids

Given two free submonoids of a free monoid, one wishes to find a specification for the base of the intersection. An algorithm to construct a graph-theoretic specification of the base is presented. From this specification it can easily be determined whether the base is finite. In addition, a a polynomial-time algorithm to determine if a regular set is a circular code is presented.     

Structural time series modeling: a Bayesian approach

Alternative progressive strategies for specification of linear dynamic models are presented. The main theme is that specification is basically concerned with endowing the pure incidental case—i.e., the case of different moment for each observations—with progressively more structure. Linearity and exogeneity are successively introduced in that spirit, first at a global level, then at a sequential level. This latter case is also shown to provide fuller possibilities for specification by means of the concepts of innovation and noncausality. This analysis along with the prior specification is conducted within the limits imposed by the possibility of concluding the analysis with computable posterior distributions on the parameters of interest.     

Solenoidal automorphisms with specifications

The specification property for solenoidal automorphisms is discussed; a solenoidal automorphism satisfies specification iff is expansive, and satisfies weak specification but not specification iff is ergodic and central spin. These are problems set up byK. Sigmund for homeomorphisms with specification. The proofs for toral case are given byD. Lind. For solenoidal case, a key ingredient in our proofs is splitting theorems on solenoidal groups with respect to described in § 2. Moreover, the following is proved: (i) If obeys specification then satisfies weak specification and is densely periodic. But the converse is not necessarily true. (ii) Every solenoidal automorphism with specification admits a Markov partition. (iii) Every ergodic solenoidal automorphism without specification does not admit Markov partitions. (iv) There exists an expansive homeomorphism with specification which has not Markov partitions.     

A note on the paper “characterization of all optimal solutions and parametric maximal flows in networks” of G. Ruhe (optimization 16 (1985) 1, 51-61)

First it is shown that the implementation of the algorithm proposed in the considered paper may cause some problems if no further specification is made as to one of its steps. Secondly, such a specification is suggested.     

The Effect of Iteration Parameters on the Convergence of a Two-Step Method

The article examines the general features of convergence of two-step iterative methods with a linearly convergent outer process. Three specifications of the inner process are considered. In the first specification, the inner process iterations end when the specified accuracy is reached. In the second specification, the inner process iterations end when a specified relative error is reached. In the third specification, the inner process is an iterative method with a superlinear rate of convergence.     

Adaptive testing for specification coverage and refinement in CPS models

Design of correct cyber–physical systems (CPS) is of uttermost importance for safety-critical applications. This crucial yet extremely challenging property is often addressed in practice by simulation-based methods. The simulation activity can be made more systematic and rigorous by using formal specifications to express requirements and guide the testing of the system.In this paper, we develop a procedure for generating tests from formal specifications given in Signal Temporal Logic (STL), a declarative language used to express CPS requirements. The proposed test generation method is adaptive with the aim at achieving specification coverage. We devise to this goal cooperative reachability games, which we enhance with numerical optimization to facilitate exercising various parts of specifications. The resulting approach is effective in finding specification violations, but also in increasing confidence (via coverage) that the specification is satisfied. In the latter case, we also propose a method for automatically refining the specification into its part that is actually implemented, thus gaining additional insight into the system-under-test.     

Grothendieck Inclusion Systems

Inclusion systems have been introduced in algebraic specification theory as a categorical structure supporting the development of a general abstract logic-independent approach to the algebra of specification (or programming) modules. Here we extend the concept of indexed categories and their Grothendieck flattenings to inclusion systems. An important practical significance of the resulting Grothendieck inclusion systems is that they allow the development of module algebras for multi-logic heterogeneous specification frameworks. At another level, we show that several inclusion systems in use in some syntactic (signatures, deductive theories) or semantic contexts (models) appear as Grothendieck inclusion systems too. We also study several general properties of Grothendieck inclusion systems.     

Simulation Model Development and Analysis in UNITY

We evaluate UNITY – a computational model, specification language and proof system defined by Chandy and Misra [5] for the development of parallel and distributed programs – as a platform for simulation model specification and analysis. We describe a UNITY-based methodology for the construction, analysis and execution of simulation models. The methodology starts with a simulation model specification in the form of a set of coupled state transition systems. Mechanical methods for mapping the transition systems first into a set of formal assertions, permitting formal verification of the transition systems, and second into an executable program are described. The methodology provides a means to independently verify the correctness of the transition systems: one can specify properties formally that the model should obey and prove them as theorems using the formal specification. The methodology is illustrated through generation of a simulation program solving the machine interference problem using the Time Warp protocol on a distributed memory parallel architecture.     

AN ENCOMPASSING APPROACH TO MODELING FISHERY DYNAMICS: MODELING DYNAMIC NONLINEAR SYSTEMS

Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data.     

Model checking MASL specification of distributed real-time systems

We present model checking algorithms for MASL specification of distributed real-time systems. The proposed algorithms use symbolic model checking approach by analogy with model checking algorithms for branching-time temporal logic CTL and alternating-time temporal logic ATL. For the fixed environment case, the algorithm is polynomial-time in the specification length and sizes of the sets of system states and actions. For the dynamic environment case, the algorithm is polynomial-time in the model size, but it is exponential-time in the structure of environment specification.     

Propositions and specifications of programs in Martin-Löf's type theory

The constructive meaning of mathematical propositions makes it possible to identify specifications for computer programs with propositions. In Martin-Löf's type theory, constructing a program satisfying a specification corresponds to proving the proposition expressing the specification. These ideas are explained and some examples of specifications are given.     

Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.     

Intelligent Front-End for Solving Nonlinear Systems of Differential and Algebraic Equations

INTENSE (INTElligent Nonlinear Systems of Equations solver) is a problem-solving environment that provides necessary computational facilities for finding numerical solutions of ordinary differential equations and systems of nonlinear algebraic equations. INTENSE offers facilities such as a user-friendly interface for specification of problems, an automatic detection of the properties of a problem, a user-friendly interface for specification of a method, an automatic detection of the properties of methods, a mechanism that matches the properties of problems with the properties of methods, the application of a numerical method and supervision of the errors, some lists or graphics of the values of approximate solutions, and solving the problem without specification of a particular method. Bibliography: 35 titles.     

Global and superlinear convergence of an algorithm for one-dimensional minimization of convex functions

This paper studies an algorithm for minimizing a convex function based upon a combination of polyhedral and quadratic approximation. The method was given earlier, but without a good specification for updating the algorithm's curvature matrix. Here, for the case of onedimensional minimization, we provide a specification that insures convergence even in cases where the curvature scalar tends to zero or infinity. Under mild additional assumptions, we show that the convergence is superlinear.     

Bayesian estimation of a covariance matrix with flexible prior specification

Bayesian analysis for a covariance structure has been in use for decades. The commonly adopted Bayesian setup involves the conjugate inverse Wishart prior specification for the covariance matrix. Here we depart from this approach and adopt a novel prior specification by considering a multivariate normal prior for the elements of the matrix logarithm of the covariance structure. This specification allows for a richer class of prior distributions for the covariance structure with respect to strength of beliefs in prior location hyperparameters and the added ability to model potential correlation amongst the covariance structure. We provide three computational methods for calculating the posterior moment of the covariance matrix. The moments of interest are calculated based upon computational results via Importance sampling, Laplacian approximation and Markov Chain Monte Carlo/Metropolis–Hastings techniques. As a particular application of the proposed technique we investigate educational test score data from the project talent data set.