Natural Density Distribution of Hermite Normal Forms of Integer Matrices

The Hermite Normal Form (HNF) is a canonical representation of matrices over any principal ideal domain. Over the integers, the distribution of the HNFs of randomly looking matrices is far from uniform. The aim of this article is to present an explicit computation of this distribution together with some applications. More precisely, for integer matrices whose entries are upper bounded in absolute value by a large bound, we compute the asymptotic number of such matrices whose HNF has a prescribed diagonal structure. We apply these results to the analysis of some procedures and algorithms whose dynamics depend on the HNF of randomly looking integer matrices

Some Inequalities Related to the Seysen Measure of a Lattice

Given a lattice $L$, a basis $B$ of $L$ together with its dual $B^*$, the orthogonality measure $S(B)=\sum_i ||b_i||^2 ||b_i^*||^2$ of $B$ was introduced by M. Seysen in 1993. This measure is at the heart of the Seysen lattice reduction algorithm and is linked with different geometrical properties of the basis. In this paper, we explicit different expressions for this measure as well as new inequalities.Comment: Typos correcte

Efficient recovering of operation tables of black box groups and rings

People have been studying the following problem: Given a finite set S with a hidden (black box) binary operation * on S which might come from a group law, and suppose you have access to an oracle that you can ask for the operation x*y of single pairs (x,y) you choose. What is the minimal number of queries to the oracle until the whole binary operation is recovered, i.e. you know x*y for all x,y in S? This problem can trivially be solved by using |S|^2 queries to the oracle, so the question arises under which circumstances you can succeed with a significantly smaller number of queries. In this presentation we give a lower bound on the number of queries needed for general binary operations. On the other hand, we present algorithms solving this problem by using |S| queries, provided that * is an abelian group operation. We also investigate black box rings and give lower and upper bounds for the number of queries needed to solve product recovering in this case.Comment: 5 page

Acoustic analysis and Modeling of the Group and phase Velocities of an Acoustic circumferential waves by an Adaptative Neuro-Fuzzy Inference System (ANFIS)

In this work, an Adaptative Neuro-Fuzzy Inference System (ANFIS) is applied to predict the velocity dispersion curves of the antisymmetric (A1) circumferential waves propagating around an elastic cooper cylindrical shell of various radius ratio b/a (a: outer radius and b: inner radius) for an infinite length cylindrical shell excited perpendicularly to its axis. The group and phase velocities, are determined from the values calculated using the eigenmode theory of resonances. These data are used to train and to test the performances of these models. This technique is able to model and to predict the group and phase velocities, of the anti-symmetric circumferential waves, with a high precision, based on different estimation errors such as mean relative error (MRE), mean absolute error (MAE) and standard error (SE). A good agreement is obtained between the output values predicted using ANFIS model and those computed by the eigenmode theory. It is found that the ANFIS networks are good tools for simulation and prediction of some parameters that carry most of the information available from the response of the shell. Such parameters may be found from the velocity dispersion of the circumferential waves, since it is directly related to the geometry and to the physical properties of the target

PREDICTION OF THE GROUP VELOCITY OF ACOUSTIC CIRCUMFERENTIAL WAVES BY ARTIFICIAL NEURAL NETWORK

International audienceThe present study investigates the use an Artificial Neural Network (ANN) to predict the velocity dispersion curve of the antisymmetric (A 1) circumferential waves propagating around an elastic cooper cylindrical shell of various radius ratio b/a (a: outer radius and b: inner radius) for an infinite length cylindrical shell excited perpendicularly to its axis. The group velocity is determined from the values calculated using the eigen mode theory of resonances. These data are used to train and to test the performances of this model. Levenberg-Marquaedt backpropagation training algorithm with tangent sigmoid transfer function and linear transfer function results in best model for prediction of group velocity. The overall regression coefficient, mean relative error (MRE), mean absolute error (MAE) and standard error (SE) are 1, 0.01%, 0.38 and 0.07. It is found that the neural networks are good tools for simulation and prediction of some parameters that carry most of the information available from the response of the shell. Such parameters may be found from the velocity dispersion of the circumferential waves, since it is directly related to the geometry and to the physical properties of the target

Measurement of acoustic stopbands in bubbly water

International audienc