Stability of quaternionic linear systems

The main goal of this paper is to characterize stability and bounded-input-bounded-output (BIBO)-stability of quaternionic dynamical systems. After defining the quaternion skew-field, algebraic properties of quaternionic polynomials such as divisibility and coprimeness are investigated. Having established these results, the Smith and the Smith-McMillan forms of quaternionic matrices are introduced and studied. Finally, all the tools that were developed are used to analyze stability of quaternionic linear systems in a behavioral framework

Linear fractional discrete-time systems

Mathematicians have been discussing about the existence (and the meaning) of derivatives and integrals of fractional order since the beginnings of differential calculus. Various concepts of fractional calculus have been developed and some of them were already applied to dynamical systems. In particular, the author already proposed a way to consider systems defined by linear differential equations of fractional order within the so-called behavioral approach. In this paper, it is shown how to generalize, analogously, discrete-time linear systems by defining a certain type of difference equations of fractional order. Some of the ideas and techniques which will be used belong to the theory of dynamical systems on time scales

On the stability of linear fractional difference systems

A fractional linear system is defined by differential or difference equations of non-integer order. A well-known result about the stability of fractional differential systems will be extended to discrete-time systems defined by fractional difference equations. This will be accomplished using time scales, which permit to unify continuous and discrete-time systems

Antisymmetry in Portuguese Ceramic Tile Facades

In this work we explore the presence of antisymmetry in Portuguese ceramic tile facades, showing examples from different styles and different antisymmetry groups. We further present some experi-ments with school children who explored symmetry and antisymmetry in a creative way. Children used a particular tile design, the Truchet tile, to create specific types of symmetry and antisymmetry. Truchet tiles can be found in several Portuguese facades from north to south.publishe

Algebraic tools for the study of quaternionic behavioral systems

In this paper we study behavioral systems whose trajectories are given as solutions of quaternionic difference equations. As happens in the commutative case, it turns out that quaternionic polynomial matrices play an important role in this context. Therefore we pay special attention to such matrices and derive new results concerning their Smith form. Based on these results, we obtain a characterization of system theoretic properties such as controllability and stability of a quaternionic behavior

Rank metric convolutional codes

In this contribution, we propose a first general definition of rank-metric convolutional codes for multi-shot network coding. To this aim, we introduce a suitable concept of distance and we establish a generalized Singleton bound for this class of codes

Faster Decoding of rank metric convolutional codes

A new construction of maximum rank distance systematic rank metric convolutional codes is presented, which permits to reduce the computational complexity of the decoding procedure, i.e., of the underlying Viterbi algorithm. This result is achieved by lowering the number of branch metrics to be calculated and by setting to the highest value the metric of the remaining edges in the trellis.publishe

Automated deployment and scaling of automotive safety services in 5G-Transformer

There is a growing interest of verticals (in this case, the automotive industry) to reap the benefits of 5G networks. At the same time, there is a clear trend of the telco industry to under-stand their needs. These are also some of the main goals of the EU 5G-TRANSFORMER (5GT) project. This demo focuses on the need of verticals to dynamically deploy services at the edge and to adapt the vertical service to network operational conditions. In particular, it is presented the extended virtual sensing (EVS) service, which deployed on demand at the distributed computing infrastructure (i.e. in the network), complements sensing and processing functions running in the car to detect the risk of collisions and take appropriate action, even if there is no direct communication between cars. The stringent latency constraints imposed by the EVS network service leave a limited processing budget at the vertical service level. Since such processing time is correlated with the CPU consumption of a virtual machine running a VNF of the EVS network service, in this demo we also show how the vertical service exploits the automated scaling capabilities offered by the 5GT service orchestrator to deploy a new instance of the EVS VNF upon reception of a CPU consumption alert generated by the available 5GT monitoring platform.Grant numbers : grant TEC2017-88373-R (5G-REFINE) and Generalitat de Catalunya grant 2017 SGR 1195.© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works