Name: Zita Abreu
Affiliation: University of Aveiro & CIDMA
Title: Efficient Algorithms for Computing the Free Distance of Convolutional Codes
Abstract: The free distance of a convolutional code is a key indicator of its performance. However, calculating it is a challenging task. In this talk, we present some efficient algorithms for computing the free distance, applicable to convolutional codes of any rate and over any field. Additionally, we analyze why a certain algorithm, often claimed to be highly efficient, is in fact incorrect.
Name: Ricardo Almeida
Affiliation: University of Aveiro & CIDMA
Title: Optimization conditions for functionals with distributed-order fractional derivatives
Abstract: In this talk, we introduce a novel approach that combines two key concepts: calculus of variations and fractional derivatives dependent on an auxiliary function. For these operators, we develop a comprehensive variational framework by establishing necessary conditions for optimization. We begin by addressing the fundamental variational problem, deriving an Euler-Lagrange equation, and subsequently extend our analysis to more advanced formulations, including the isoperimetric and Herglotz problems. To complement our theoretical results, we propose a numerical method for solving fractional variational problems involving these generalized derivatives. Our approach is based on approximating the fractional derivative through an expansion formula in terms of integer-order derivatives, thereby transforming the fractional optimization problem into a classical one.
Name: Daniel Graça
Affiliation: Universidade do Algarve & CIDMA
Title: The multidimensional generalized shift
Abstract: The generalized shift is a broadening of the well-known shift map that was introduced in 1990, and which models the dynamics of some classes of piecewise linear maps defined on the unit ball. In this talk we introduce multidimensional generalized shifts and analyze their behavior from a dynamical and from a computational perspective. We will see that tools from the theory of computation are especially well-suited to analyze the dynamics of such maps. In particular we show that multidimensional generalized shifts are computationally equivalent to the classical generalized shift and we show that these can also be modeled by some classes of Lebesgue preserving piecewise linear maps defined on higher dimensional unit balls.
Nome: Ana P. Lemos-Paião
Afiliação: University of Aveiro & CIDMA
Título: $L^1$ versus $L^2$ cost in a parametric optimal control problem applied to irrigation
Resumo: Water scarcity is a pressing issue in many countries with significant consequences for agriculture. To give answer to this, we propose irrigation models designed to optimize water use, while ensuring healthy crops. These models are framed as parametric optimal control problems with state constraints, incorporating a $L^1$, or a $L^2$, cost functional. Since such models are often based on a parameter that is hard to estimate, the percentage of water losses due to run off and deep percolation, parameter sensitivity analysis is used to mathematically understand how uncertainties of this parameter can influence the optimal solutios and the corresponding costs. The resulting sensitivity insights for the problems with $L^1$ and the $L^2$ costs are compared.
Name: Natália Martins
Affiliation: University of Aveiro & CIDMA
Title: Existence and stability analysis of anti-periodic boundary value problems with generalized tempered fractional derivatives
Abstract: In this talk, we study implicit fractional differential equations with anti-periodic boundary conditions. The fractional operator incorporates two distinct generalizations: the tempered fractional derivative and the derivative with respect to a smooth function. We investigate the existence and uniqueness of solutions using fixed-point theorems. Stability in the sense of Ulam-Hyers and Ulam-Hyers-Rassias is also considered. Some examples are provided to illustrate the applicability of our results. Several existing results in the literature can be recovered as particular cases of the framework developed in this work. This is a join work with Ricardo Almeida.
Name: Sandra Pinelas
Affiliation: Academia Militar & CIDMA, UA
Title: Mixed type differential equations with non-monotone deviating arguments
Abstract: In this work, we examine the oscillatory and the asymptotic properties of solutions to first-order mixed differential equations with variable coefficients, variable delays, and variable advances.
Name: Raquel Pinto
Affiliation: CIDMA, Universidade de Aveiro
Title: Decoding of a convolutional code over an erasure channel
Abstract: Erasure channels are channels where a transmitted bit is lost or it is received correctly. An example of an erasure channel is the internet. Reliable transmission of information over these channels is an important problem in nowadays. In this context, convolutional codes are very suitable, allowing an efficient correction (decoding) of introduced erasures during transmission. Usually, the decoding is done via a parity-check matrix of the code. In this talk we show how the decoding can be done via an encoder of the code.
Name: Cristiana J. Silva
Affiliation: Iscte - Instituto Universitário de Lisboa & CIDMA, UA
Title: Hybrid mathematical models in epidemiology
Abstract: In this talk, we explore hybrid epidemiological models, which offer a powerful framework for epidemic modeling by combining deterministic and probabilistic approaches. These models provide comprehensive insights into disease dynamics and control strategies. We consider hybrid epidemic models defined by systems of ordinary differential equations (ODEs) and reaction-diffusion equations. These models couple continuous ODE or reaction-diffusion systems, which describe the temporal or spatio-temporal dynamics of the infectious disease, with a discrete probabilistic process that represent potential changes in the transmission rates. This hybrid structure allows for a more accurate representation of real-world epidemic scenarios.