Miguel V. Carriegos

Canonical forms for single input linear systems

In this paper, we obtain a canonical form for single input n-dimensional linear systems over Z and, in general, over a Bezout domain. We also give an algorithm to obtain that canonical form.

On matrix inverses modulo a subspace

Given a pair of matrices (A,B)∈Rn×n×Rn×m with coefficients in a commutative ring we study the problem of finding a matrix F such that A+BF becomes invertible. We point out some relations between the problem of finding feedback inverses of A modulo B and the pole-shifting problem for the pair (A,B). In fact we give feedback invertibility results over a well known large class of rings related with the pole-shifting: the class of PA rings. On the other hand we also give a pointwise-global characterization. The ring R of rational integers and the coordinate ring of the real unit circle R[x,y]/(x2+y2−1) are studied in some detail. Finally the problem of derivative feedback standardization of generalized linear systems is reviewed as a particular case.

On the local-global decomposition of linear control systems ☆

Abstract This paper deals with the local study of linear (control) systems. Brunovsky and locally Brunovsky linear systems are studied. A complete set of invariants for both classes of linear systems are given. Finally, some examples on the real unit circle and on the real unit sphere are also given.

Pole-shifting for linear systems over commutative rings☆

Abstract This paper deals with the pole-shifting problem for non-necessarily reachable linear systems. The notion of PS ring is introduced in the same way as the notion of pole assignable ring is given for reachable systems. We prove that a bcs ring is a PS ring and that over a Prufer domain these properties are equivalent. Finally, we study when the converse of the pole-shifting theorem is verified.

On Detecting and Removing Superficial Redundancy in Vector Databases

A mathematical model is proposed in order to obtain an automatized tool to remove any unnecessary data, to compute the level of the redundancy, and to recover the original and filtered database, at any time of the process, in a vector database. This type of database can be modeled as an oriented directed graph. Thus, the database is characterized by an adjacency matrix. Therefore, a record is no longer a row but a matrix. Then, the problem of cleaning redundancies is addressed from a theoretical point of view. Superficial redundancy is measured and filtered by using the 1-norm of a matrix. Algorithms are presented by Python and MapReduce, and a case study of a real cybersecurity database is performed.

Assessment of the Recent Postgraduates in Cybersecurity on Barriers and Required Skills for Their Early Career.

Cybersecurity training is one of the relevant priorities for nations around the world in order to ensure a qualified, competitive and plentiful workforce in the years to come. It is necessary to promote the vocations of students towards cybersecurity studies to deal with the excess of uncovered labor demand with special attention to an under-represented group such as the female. To further this goal, our study focuses on a sample from among the group of students who have reached the postgraduate degree of MSc in Cybersecurity. Our methodology included in-person interviews and discussion groups and aims to identify the challenges/barriers that exist in the initial stages of career for young postgraduates as well as the skills and knowledge required for this group of young professionals.

Automatic generation of Moodle questionnaires to assess learning of Descriptive Geometry

Descriptive Geometry is included within the core subjects in the Schools of Engineering and Architecture. More and more centres are using the Moodle virtual platform to help learning and for evaluation. Creating Moodle questionnaires in drawing subjects is challenging, as problems are solved in a graphic manner. With this aim, we propose a Matlab-based tool for the automatic generation of Moodle questionnaires able to assess graphical Descriptive Geometry problem solving by the students.

ON LINEAR MULTI-INPUT SYSTEMS DEPENDING ON CONTINUOUS PARAMETERS. FEEDBACK EQUIVALENCES IN LOW DIMENSION

We survey some recent results relating different notions of feedback equivalence of linear systems in a geometric point of view.

SPECTRA ANALYSIS IN DETECTION OF TRACES OF EXPLOSIVES

We focus the problem of classification of Raman spectra by using different techniques: Statistic models, neural networks and expert systems. We point out some results for the concrete problem of identification of explosive substances.