The frontal method in hydrodynamics simulations

The frontal solution method has proven to be an effective means of solving the matrix equations resulting from the application of the finite element method to a variety of problems. In this study, several versions of the frontal method were compared in efficiency for several hydrodynamics problems. Three basic modifications were shown to be of value: 1. Elimination of equations with boundary conditions beforehand, 2. Modification of the pivoting procedures to allow dynamic management of the equation size, and 3. Storage of the eliminated equations in a vector. These modifications are sufficiently general to be applied to other classes of problems.     

An improved feature transformation method using mutual information

The feature transformation is a very important step in pattern recognition systems. A feature transformation matrix can be obtained using different criteria such as discrimination between classes or feature independence or mutual information between features and classes. The obtained matrix can also be used for feature reduction. In this paper, we propose a new method for finding a feature transformation-based on Mutual Information (MI). For this purpose, we suppose that the Probability Density Function (PDF) of features in classes is Gaussian, and then we use the gradient ascent to maximize the mutual information between features and classes. Experimental results show that the proposed MI projection consistently outperforms other methods for a variety of cases. In the UCI Glass database we improve the classification accuracy up to 7.95 %. Besides, the improvement of phoneme recognition rate is 3.55 % on TIMIT.     

Finite semigroup varieties defined by programs

We study the regular languages recognized by polynomial-length programs over finite semigroups belonging to product varieties V * LI, where V is a variety of finite monoids, and LI is the variety of finite locally trivial semigroups. In the case where the semigroup variety has a particular closure property with respect to programs, we are able to give precise characterizations of these regular languages. As a corollary we obtain new proofs of the results of Barrington, Compton, Straubing and Therien characterizing the regular languages in certain circuit complexity classes.     

Generating the variety of BL-algebras

This paper collects some results from [AFM] and from [AM]. Our purpose is to illustrate some interesting classes of algebras which generate the whole variety of BL-algebras. In particular, we prove that such variety is generated by its finite members and by the class of finite ordinal sums of Lukasiewicz t-norm algebras. Finally, we characterize the BL-chains which generate the whole variety of BL-algebras.     

On the state complexity of reversals of regular languages

We compare the number of states between minimal deterministic finite automata accepting a regular language and its reversal (mirror image). In the worst case the state complexity of the reversal is 2ⁿ for an n-state language. We present several classes of languages where this maximal blow-up is actually achieved and study the conditions for it. In the case of finite languages the maximal blow-up is not possible but still a surprising variety of different growth types can be exhibited.     

Stochastic approximation and realization of Hankel matrices

Dynamic systems are considered whose outputs can be represented either by a deterministic series of the input variables or by a stochastic series of brownian motion processes. Approximate representations of such series are proposed. The representations are based on the Hankel matrix representation of the series. First, it is shown that any Hankel matrix, belonging to suitable classes, can be approximated in the deterministic and stochastic sense by finite rank Hankel matrices. Then, a method is proposed to design bilinear realizations of finite rank Hankel matrices, effective in the deterministic and stochastic sense.     

A partitioning scheme and iterative solution for sparse bordered systems

Sparse bordered matrix systems arise in certain classes of problems. An example is the Jacobian system for the finite difference or finite element approximation and continuation solution of nonlinear PDE's. We develop a partitioning scheme that can be exploited in residual-based iterative methods and permits easy implementation in existing software. The scheme has been examined for several iterative methods, and particularly the Lanczos algorithms which proves very effective for the representative nonlinear test problems examined. The scheme vectorizes well and performance studies on vectorized supercomputers are given.     

Analysis of stiffness and elastic deformation of a 2(SP+SPR+SPU) serial–parallel manipulator

A 2(SP+SPR+SPU) manipulator is a serial–parallel manipulator, which includes an upper manipulator and a lower manipulator. Its stiffness and elastic deformation are studied systematically in this paper. Firstly, a 2(SP+SPR+SPU) manipulator is constructed and its characteristics are analyzed. Secondly, the formulae for solving the elastic deformation and the compliance matrix of the active legs are derived and the elastic deformation and the total stiffness matrix of this manipulator are solved and analyzed. Finally, a finite element model of this manipulator is constructed and its elastic deformations are solved. The analytic solutions of elastic deformations of this manipulator are coincident with that of its finite element model.     

Probabilistic Type-2 Operators and “Almost”-Classes

We define and examine several probabilistic operators ranging over sets (i.e., operators of type 2), among them the formerly studied ALMOST-operator. We compare their power and prove that they all coincide for a wide variety of classes. As a consequence, we characterize the ALMOST-operator which ranges over infinite objects (sets) by a bounded-error probabilistic operator which ranges over strings, i.e., finite objects. This leads to a number of consequences about complexity classes of current interest. As applications, we obtain (a) a criterion for measure 1 inclusions of complexity classes, (b) a criterion for inclusions of complexity classes relative to a random oracle, (c) a new upper time bound for ALMOST-PSPACE, and (d) a characterization of ALMOST-PSPACE in terms of checking stack automata. Finally, a connection between the power of ALMOST-PSPACE and that of probabilistic circuits is given. Received: 16 April 1996     

Comments analysis and programming errors

Software validation is treated as the problem of detecting errors that programmers make during the software development process. This includes fault detection, in which the focus is on techniques for detecting the occurrence of local errors that result in well-defined classes of program statement faults. It also includes detecting other kinds of errors, such as decomposition errors. The main focus of the work is on a decomposition-error analysis technique called comments analysis. In this technique, errors are detected by analyzing special classes of program comments. Comments analysis has been applied to a variety of systems, including a data-processing program and an avionics real-time program. The use of comments analysis for sequential and concurrent systems is discussed, and the basic features of comments analysis tools are summarized. The relationship of comments analysis to other techniques, such as event sequence analysis, is discussed, and the differences between it and earlier work are explained     

Matrix and finite element stack machines for structural engineering computations with units

Despite the well known benefits of physical units, matrices, and matrix algebra in engineering computations, most engineering analysis packages are essentially dimensionless. This paper describes the design and implementation of matrix and finite element stack machines for Aladdin, a new computational environment that embeds units inside matrix and finite element calculations. Functionality of the Aladdin stack machine is illustrated by working step by step through the setup and execution of three examples: (1) Parsing and stack machine execution for x = 2 in; (2) Deflection analysis of a cantilever beam, and (3) Rollup maneuver for a long cantilever beam.     

Variations of the matrix models

The matrix models of [6] are parallel sequential generative models generating two dimensional rectangular arrays. Here we change the definition of matrix models a-little and define extended matrix models which generate arrays not necessarily rectangular. The effect of placing a control on these models is studied. The corresponding automata are defined by combining a finite number of FSA which can be live or dead, active or idle, with a FSA, PDA, LBA or TM. Several other variations of the matrix models are also introduced and Shown to generate interesting classes of pictures with suitable control.     

Convergence of powers for a fuzzy matrix with convex combination of max-min and max-arithmetic mean operations

Fuzzy matrices have been proposed to represent fuzzy relations on finite universes. Since Thomason’s paper in 1977 showing that powers of a max-min fuzzy matrix either converge or oscillate with a finite period, conditions for limiting behavior of powers of a fuzzy matrix have been studied. It turns out that the limiting behavior depends on the algebraic operations employed, which usually in the literature includes max-min/max-product/max-Archimedean t-norm/max t-norm/max-arithmetic mean operations, respectively. In this paper, we consider the powers of a fuzzy matrix with convex combination of max-min and max-arithmetic mean operations. We show that the powers of such a fuzzy matrix are always convergent.     

Solution of linear equations with skyline-stored symmetric matrix

Fortran IV subroutines for the in-core solution of linear algebraic systems with a sparse, symmetric, skyline-stored coefficient matrix are presented. Such systems arise in a variety of applications, notably the numerical discretization of conservative physical systems by finite differences or finite element techniques. The routines can be used for processing constrained systems without need for prearranging equations. The application to ‘superelement’ condensation of large-scale systems is discussed.     

Some new maximum VC classes

Set systems of finite VC dimension are frequently used in applications relating to machine learning theory and statistics. Two simple types of VC classes which have been widely studied are the maximum classes (those which are extremal with respect to Sauer's lemma) and so-called Dudley classes, which arise as sets of positivity for linearly parameterized functions. These two types of VC class were related by Floyd, who gave sufficient conditions for when a Dudley class is maximum. It is widely known that Floyd's condition applies to positive Euclidean half-spaces and certain other classes, such as sets of positivity for univariate polynomials.In this paper we show that Floyd's lemma applies to a wider class of linearly parameterized functions than has been formally recognized to date. In particular we show that, modulo some minor technicalities, the sets of positivity for any linear combination of real analytic functions is maximum on points in general position. This includes sets of positivity for multivariate polynomials as a special case.     

Quadratic stabilization of a collection of linear systems

The paper considers the problem of simultaneous quadratic (SQ) stablizability of a finite collection linear time-invariant (LTI) system by a static state feedback controller. At first, the solvability conditions for SQ stablization are derived in terms of the solution of certain reduced order matrix inequalities. The existence conditions for the solution of such matrix inequalities are then investigated. Based on that, two new classes of systems are characterized for which a SQ stabilization problem is solvable. These class of systems are (1) partially commutative systems and (2) partially normal systems. These systems are shown to be different from matched uncertain systems and also do not possess any generalised antisymmetric configurations. Both existence and computational algorithm for designing a state feedback controller are given.     

Unsupervised classification of SAR images using normalized gamma process mixtures

We propose an image prior for the model-based nonparametric classification of synthetic aperture radar (SAR) images that allows working with infinite number of mixture components. In order to enclose the spatial interactions of the pixel labels, the prior is derived by incorporating a conditional multinomial auto-logistic random field into the Normalized Gamma Process prior. In this way, we obtain an image classification prior that is free from the limitation on the number of classes and includes the smoothing constraint into classification problem. In this model, we introduced a hyper-parameter that can control the preservation of the important classes and the extinction of the weak ones. The recall rates reported on the synthetic and the real TerraSAR-X images show that the proposed model is capable of accurately classifying the pixels. Unlike the existing methods, it applies a simple iterative update scheme without performing a hierarchical clustering strategy. We demonstrate that the estimation accuracy of the proposed method in number of classes outperforms the conventional finite mixture models.     

On Uniform Stabilization of Discrete-Time Linear Parameter-Varying Control Systems

For discrete-time polytopic linear parameter-varying systems, the uniform exponential stability, which is equivalent to the asymptotic stability and includes the quadratic stability as a special case, is characterized by the union of an increasing family of linear matrix inequality conditions. On the other hand, in certain cases, nonconservative synthesis of uniformly stabilizing controllers is achieved via a system of finite number of linear matrix inequalities if the controller is allowed to have finite memory of past parameters. Two such cases are robust state feedback (in a relaxed sense) against polytopic parameter variations, and multiple output injections under polytopic fusion rules.     

A new notion of equivalence for discrete time AR representations

We present a new equivalence transformation termed divisor equivalence, that has the property of preserving both the finite and the infinite elementary divisor structures of a square non-singular polynomial matrix. This equivalence relation extends the known notion of strict equivalence, which dealt only with matrix pencils, to the general polynomial matrix case. It is proved that divisor equivalence characterizes in a closed form relation the equivalence classes of polynomial matrices that give rise to fundamentally equivalent discrete time auto-regressive representations.     

A conical shell finite element

In the analysis of rocket and missiles structures one frequently encounters cylindrical and cornica' shells. A simple finite element which fits the above configuration is obviously a conical shell finite element. In this paper stiffness matrix for a conical shell finite element is derived using Novozhilov's strain-displacement relations for a conical shell. Numerical integration is carried out to ge. the stiffness matrix. The element has 28 degrees-of-freedom and is nonconforming. An eigenvalue analysis of the stiffness matrix showed that it contains all the rigid body modes (six in this case) adequately, which is one of the convergence criteria. An advantage of this element is that a cylindrical shell, an annular segment flat plate, a rectangular flat plate elements can easily be obtained as degenerate cases. The effectiveness of this element is shown through a variety of numerical examples pertaining to annular plate, cylindrical shell and conical shell problems. Comparison of the present solution is made with the existing ones wherever possible. The comparison shows that the present element is superior in some respects to the existing elements