On the numerical solution of non-linear equation characterizing minimal cubature formulae

A cubature formula with degree of exactness ≦2k?2 has at leastk(k+1)/2 knots. The existence of such minimal formulae is equivalent to the existence of solutions of a system of quadratic equations. Each solution of such a system generates in a uniquely determined way a minimal formula. For the square [?1, 1]² as domain of integration and for some weight-functions these systems have a simple form, but they seem to be hard to solve. In this note attention is drawn to these systems and to experiences made in order to obtain numerical solutions.     

The construction of cubature formulae for a family of integrals: A bifurcation problem

Cubature formulae of degree 11 with minimal numbers of knots for the integral $$\int\limits_{ - 1}^1 { \int\limits_{ - 1}^1 {(1 - x^2 )^\alpha } } (1 - y^2 )^\alpha f(x,y) dxdy \alpha > - 1$$ which are invariant under rotation over an angle π/2 are determined by a system of 18 nonlinear equations in 18 unknowns. We start with a known solution for this system for α=0. By varying α smoothly, the knots and weights of the cubature formula vary smoothly except in the singular solutions such as turning points and bifurcation points where new solutions branches arise. We use for this purpose the program AUTO. We obtain surprisingly many branches of cubature formulae.     

Minimal cubature formulae of degree 3 for integrals over the surface of the torus

In this note a minimal cubature formula of degree 3 will be determined for integrals over the surface of the torus with arbitrary radii. The construction is based on a normalization of the problem, ideal theory, and computer algebra.     

The construction of symmetric cubature formulas for the square and the triangle

The weights and nodes of a symmetric cubature formula are determined by solving a system of nonlinear equations. The number of equations and their structure are investigated for symmetric cubature formulas for the square and the triangle. A new cubature formula of degree 7 with 12 nodes is given for the triangle.     

Minimal cubature formulae of degree 2k−1 for two classical functionals

Cubature formulae with the number of nodes equal to Möller's lower bound are rare. In this paper, the relation between real polynomial ideals and cubature formulae is used to construct such minimal formulae of arbitrary odd degree for two classical integrals. We found general expressions for bases of these ideals and closed formulae for almost all nodes. We proved that all nodes are inside the domain of integration.     

From pressure fluctuations to dynamic loads on axisymmetric step flows with minimal number of kulites

The present study focuses on two kinds of reconstruction methods designed to capture the dynamic loads acting on the reattaching part of an axisymmetric step flow. The pressure signals on discrete points of the geometry constitute the starting point of this study. Data are taken from a validated numerical simulation in order to maximize the number of sensors at the wall. First, an a priori methodology for the load reconstruction without any hypothesis on the flow behaviour is exposed. The influence of the number of sensors and their spatial distribution over the geometry is investigated. It is shown that azimuthal and longitudinal resolution have different effects on the reconstructed power spectral density of the load. Then, it is found that an experimental process with few unsteady sensors cannot provide an accurate prediction of the load. Then a second kind of reconstruction method based on the physical knowledge of the flow is presented. The original Nguyen approach initially developed for internal side loads is optimized with a spatial analysis and gives a satisfactory prediction of the load with only a minimal number of sensors.     

Testing using a minimal number of instructions

A new technique to test microprocessor chips is presented in this article. The basic test philosophy adopted is to partition a microprocessor's instructions into several sets. Instructions which affect the identical modules inside the processor are grouped into the same set. The appropriate subset of each instruction set is exercised and if the results are satisfactory, then the microprocessor is assumed to be functioning correctly. The instruction subsets form a test sequence for the microprocessor. Stuck-at faults at the address lines, the data lines and at the output of some of the internal modules are also detected by the test sequence.     

View integration: a step forward in solving structural conflicts

Thanks to the development of the federated systems approach on the one hand and the emphasis on user involvement in database design on the other, the interest in schema integration techniques is significantly increasing. Theories, methods and tools have been proposed. Conflict resolution is the key issue. Different perceptions by schema designers may lead to different representations. A way must be found to support these different representations within a single system. Most current integration methodologies rely on modification of initial schemas to solve the conflicts. This approach needs a strong interaction with the database administrator, who has authority to modify the initial schemas. This paper presents an approach to view integration specifically intended to support the coexistence of different representations of the same real-world objects. The main characteristics of this approach are the following: automatic resolution of structural conflicts, conflict resolution performed without modification of initial views, use of a formal declarative approach for user definition of inter-view correspondences, applicability to a variety of data models, and automatic generation of structural and operational mappings between the views and the integrated schema. Allowing users' views to be kept unchanged should result in improved user satisfaction. Each user is able to define his own view of the database, without having to conform to some other user's view. Moreover, such a feature is essential in database integration if existing programs are to be preserved     

TMS 320—a step forward in digital signal processing

Despite the numerous advantages of digital signal processing (DSP), and the existence of a wealth of sophisticated algorithms, the widespread application of DSP has been hindered by a shortage of cost-effective digital hardware for volume use. Now, with the availability of low-cost high-speed VLSI circuits, such as the Texas Instruments TMS320, the virtues and power of DSP are ready for realtime signal processing applications.Development of the single-chip TMS320 DSP computer began in the late 1970s. The architecture, key novel features, instruction set and capabilities of this device are examined. Support software and hardware development tools for the TMS320 are also included with some of its applications. Typical areas of application of the TMS320 include speech signal processing, telecommunications, robotics, radar signal and sonar signal processing, seismology, image processing, audio recording and reproduction, biomedical instrumentation, acoustic noise measurements and automatic test equipment.     

Associating targets with SentiUnits: a step forward in sentiment analysis of Urdu text

This paper presents, a grammatically motivated, sentiment classification model, applied on a morphologically rich language: Urdu. The morphological complexity and flexibility in grammatical rules of this language require an improved or altogether different approach. We emphasize on the identification of the SentiUnits, rather than, the subjective words in the given text. SentiUnits are the sentiment carrier expressions, which reveal the inherent sentiments of the sentence for a specific target. The targets are the noun phrases for which an opinion is made. The system extracts SentiUnits and the target expressions through the shallow parsing based chunking. The dependency parsing algorithm creates associations between these extracted expressions. For our system, we develop sentiment-annotated lexicon of Urdu words. Each entry of the lexicon is marked with its orientation (positive or negative) and the intensity (force of orientation) score. For the evaluation of the system, two corpora of reviews, from the domains of movies and electronic appliances are collected. The results of the experimentation show that, we achieve the state of the art performance in the sentiment analysis of the Urdu text.     

On the minimal number of trajectories determining a multidimensional system

The minimal number(S) of generators of a multidimensional systemS is constructively determined. Such anS is the solution space of a linear system of partial differential or difference equations with constant coefficients. The main theorem generalizes recent results of Heij and Zampieri who calculated the number(S) in the one- (resp. two-) dimensional discrete case. There is also a direct connection with Macaulay's inverse systems in the multidimensional discrete situation, in particular with his principal systems characterized by the relation(S)1. It is surprising that, for dimensions greater than one, very many large systems are principal in this sense.     

A step forward in studying the compact genetic algorithm

The compact Genetic Algorithm (cGA) is an Estimation of Distribution Algorithm that generates offspring population according to the estimated probabilistic model of the parent population instead of using traditional recombination and mutation operators. The cGA only needs a small amount of memory; therefore, it may be quite useful in memory-constrained applications. This paper introduces a theoretical framework for studying the cGA from the convergence point of view in which, we model the cGA by a Markov process and approximate its behavior using an Ordinary Differential Equation (ODE). Then, we prove that the corresponding ODE converges to local optima and stays there. Consequently, we conclude that the cGA will converge to the local optima of the function to be optimized.     

A step forward for Topic Detection in Twitter: An FCA-based approach

The Topic Detection Task in Twitter represents an indispensable step in the analysis of text corpora and their later application in Online Reputation Management. Classification, clustering and probabilistic techniques have been traditionally applied, but they have some well-known drawbacks such as the need to fix the number of topics to be detected or the problem of how to integrate the prior knowledge of topics with the detection of new ones. This motivates the current work, where we present a novel approach based on Formal Concept Analysis (FCA), a fully unsupervised methodology to group similar content together in thematically-based topics (i.e., the FCA formal concepts) and to organize them in the form of a concept lattice. Formal concepts are conceptual representations based on the relationships between tweet terms and the tweets that have given rise to them. It allows, in contrast to other approaches in the literature, their clear interpretability. In addition, the concept lattice represents a formalism that describes the data, explores correlations, similarities, anomalies and inconsistencies better than other representations such as clustering models or graph-based representations. Our rationale is that these theoretical advantages may improve the Topic Detection process, making them able to tackle the problems related to the task. To prove this point, our FCA-based proposal is evaluated in the context of a real-life Topic Detection task provided by the Replab 2013 CLEF Campaign. To demonstrate the efficiency of the proposal, we have carried out several experiments focused on testing: (a) the impact of terminology selection as an input to our algorithm, (b) the impact of concept selection as the outcome of our algorithm, and; (c) the efficiency of the proposal to detect new and previously unseen topics (i.e., topic adaptation). An extensive analysis of the results has been carried out, proving the suitability of our proposal to integrate previous knowledge of prior topics without losing the ability to detect novel and unseen topics as well as improving the best Replab 2013 results.     

A cellular automata rule placing a maximal number of dominoes in the square and diamond

The Journal of Supercomputing - The objective is to demonstrate that a probabilistic cellular automata rule can place reliably a maximal number of dominoes in different active area shapes,...     

Simple algorithms for searching a polygon with flashlights

The k-searcher is a mobile guard whose visibility is limited to k rays emanating from her position, where the direction of each ray can be changed continuously with bounded angular rotation speed. Given a polygonal region P, is it possible for the k-searcher to eventually see a mobile intruder that is arbitrarily faster than the searcher within P? We present O(n²)-time algorithms for constructing a search schedule of the 1-searcher and the 2-searcher, respectively. Our framework for the 1-searcher can be viewed as a modification of that of LaValle et al. [Proc. 16th ACM Symp. on Computational Geometry, 2000, pp. 260-269] and is naturally extended for the 2-searcher.     

Discrete noiseless duel with a skewsymmetric payoff function on the unit square for models of socioeconomic competitive processes with a finite number of pure strategies

A discrete noiseless duel is defined on the unit square; each player in the duel has a finite number of pure strategies uniformly distributed on the unit segment. The theorem on the existence of individual solutions of the discrete noiseless duel in pure strategies is proved. The construction of a program procedure for solving the discrete noiseless duel is presented.     

Covering a convex 3D polytope by a minimal number of congruent spheres

The problem of covering a convex 3D polytope by the minimal number of congruent spheres is reduced to a sequence of problems of minimising sphere radius when fixing the number of the spheres. We form a mathematical model of the problem using the Voronoi polytopes. Characteristics of the model are investigated. Extrema are attained at the vertices of the Voronoi polytopes constructed for sphere centres. To search for local minima, a modification of the Zoutendijk feasible directions method in a combination with random search is developed. Some numerical results for a cube and a non-regular octahedron are obtained.