Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems

[EN] Linear systems over vector spaces and feedback morphisms form an additive category taking into account the parallel gathering of linear systems. This additive category has a minimal exact structure and thus a notion of simple systems as those systems have no subsystems apart from zero and themselves. The so-called single-input systems are proven to be exactly the simple systems in the category of reachable systems over vector spaces. The category is also proven to be semisimple in objects because every reachable linear system is decomposed in a finite parallel gathering of simple systems. Hence, decomposition result is fulfilled for linear systems and feedback morphisms, but category of reachable linear systems is not abelian semisimple because it is not balanced and hence fails to be abelian. Finally, it is conjectured that the category of linear systems and feedback actions is in fact semiabelian; some threads to find the result and consequences are also givenS

Some Categorical Properties of Linear Systems

[EN] Linear control systems are studied by means of a state-space approach. Feedback morphisms are presented as natural generalization of feedback equivalences. The set of feedback morphisms between two linear systems is a vector space. Kernels, cokernels, as well as monomorphisms, epimorphisms, sections, and retracts of feedback morphisms are studied in the category of linear systems over finite dimensional vector spaces. Finally, a classical Kalman's decomposition of linear systems over vector spaces is presented as a split short exact sequence in the category.S

Feedback actions on linear parameter-varying systems

pág. 69-71mLinear parameter-varying systems are studied by means of geometrical translation of some recent results of algebraic nature dealing with the feedback actions on linear control systems.S

Kalman reduced form and pole placement by state feedback for multi‐input linear systems over Hermite rings

[EN] A Kalman reduced form is obtained for linear systems over Hermite rings. This reduced form gives information of the set of assignable polynomials to a given linear system.S

Towards Supercomputing Categorizing the Maliciousness upon Cybersecurity Blacklists with Concept Drift

[EN] In this article, we have carried out a case study to optimize the classification of the maliciousness of cybersecurity events by IP addresses using machine learning techniques. The optimization is studied focusing on time complexity. Firstly, we have used the extreme gradient boosting model, and secondly, we have parallelized the machine learning algorithm to study the effect of using a different number of cores for the problem. We have classified the cybersecurity events' maliciousness in a biclass and a multiclass scenario. All the experiments have been carried out with a well-known optimal set of features: the geolocation information of the IP address. However, the geolocation features of an IP address can change over time. Also, the relation between the IP address and its label of maliciousness can be modified if we test the address several times. Then, the models' performance could degrade because the information acquired from training on past samples may not generalize well to new samples. This situation is known as concept drift. For this reason, it is necessary to study if the optimization proposed works in a concept drift scenario. The results show that the concept drift does not degrade the models. Also, boosting algorithms achieving competitive or better performance compared to similar research works for the biclass scenario and an effective categorization for the multiclass case. The best efficient setting is reached using five nodes regarding high-performance computation resources.SIInstituto Nacional de SeguridadPartial support was received from the Spanish National Cybersecurity Institute (INCIBE) under the contract art (83, 203 key: X54

On the State Approach Representations of Convolutional Codes over Rings of Modular Integers

[EN] In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers.S

Enumeration of locally Brunovsky linear systems over C(S1)-modules. A procedure

pp. 72-76In this paper we describe a procedure to visit all feedback classes of locally Brunovsky linear system over fixed R=C(S1) the ring of real continuos functions defined on the unit circle. Furthermore, we give the exact number of such classes throughout partitions of integers, binary strings and colored Ferrers diagrams.S

Preface

pp. 52Preface of the Special Issue of Cybernetics and Physics Journal (CAP)is entitled “Control And Linear Algebra: Theory And Applications”. It collects highly selected papers which focus on both theoretical and practical system treatment by using time invariant linear systems. This special issue presents extended versions of relevant works presented in the invited minisymposium called “Control and Linear Algebra: Theory And Applications” held at 6th International Scientific Conference on Physics and Control (PhysCon 2013) on August, 26th–29th, 2013, which was organized by the University of San Luis de Potosí (México) and the International Physics and Control Society (IPACS).S

On dynamic network security: A random decentering algorithm on graphs

pp. 656-668Random Decentering Algorithm (RDA) on a undirected unweighted graph is defined and tested over several concrete scale-free networks. RDA introduces ancillary nodes to the given network following basic principles of minimal cost, density preservation, centrality reduction and randomness. First simulations over scale-free networks show that RDA gives a significant decreasing of both betweenness centrality and closeness centrality and hence topological protection of network is improved. On the other hand, the procedure is performed without significant change of the density of connections of the given network. Thus ancillae are not distinguible from real nodes (in a straightforward way) and hence network is obfuscated to potential adversaries by our manipulation.S

Rosenbrock's theorem for systems over von Neumann regular rings

pp. 122-130If is a finite system over a commutative von Neumann regular ring R, the problem of searching for a matrix F such that the pencil has some prescribed Smith normal form is reduced to the case where R is a field, a problem which for controllable systems is described by a well-known theorem of Rosenbrock on pole assignment [12], and was then generalized to noncontrollable pairs [14]. It this paper, von Neumann regular rings are characterized as the class of commutative rings for which the solution of the above problem over the ring is equivalent to its solution in each residue field.S