Name: Raquel Pinto
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: Minimal realizations of convolutional codes
Abstract: In this talk the minimal realizations of a convolutional code are studied. Moreover, a procedure to obtain a minimal realization of a convolutional code from a minimal realization of an encoder is presented.
Name: Ricardo Pereira
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: Decoding of periodic convolutional codes
Abstract: Periodic convolutional codes seem to have better error correction capabilities than time-invariant convolutional codes. However there are not efficient decoding algorithms for these codes. In this talk we will present a decoding algorithm for error correction of periodic convolutional codes, which is an adaptation of the Viterbi algorithm, using the switched output state-space realizations of these codes. The efficiency of the Viterbi algorithm depends on the size of the associated state-transition diagram which is directly connected with a statespace realization of the code. State-space realizations with minimal dimension allows to define a more efficient decoding algorithm. Thus the minimality of the dimension of switched output state-space realizations of periodic codes is an important topic of research and will be analysed in this talk.
Name: Zita Abreu
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: mD Convolutional Codes
Abstract: In this talk, we explore the theory and construction of multidimensional (mD) convolutional codes with finite support. These codes are characterized by codewords that have compact support indexed in \(\mathbb{N}^{m}\) and values in \(\mathbb{F}^{n}\), where \(\mathbb{F}\) is a finite field. We first establish a natural upper bound on the distance of an mD convolutional code with rate \(k/n\) and degree \(\delta\). This bound extends the classical Singleton bound for block codes and the generalized Singleton bound for one-dimensional convolutional codes to the multidimensional case. We then introduce a specific construction of 3D convolutional codes with finite support, having a rate of \(1/n\) and a degree \(\delta \leq 2\), that meets this bound.
Name: Paolo Vettori
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: Behaviors of difference and differential equations with constant quaternion coefficients
Abstract: Determining the solution set of difference or differential equations is a first fundamental step within the behavioral approach to dynamical systems. This problem is completely solved for linear equations with constant real and complex coefficients, depending only on the roots of the associated characteristic polynomial. This is no longer true for quaternion coefficients: in fact, it will be shown that (and how), in some cases, the solutions also depend on the conjugates of the roots.
Name: Cristiana J. Silva
Affiliation: Iscte - Instituto Universitário de Lisboa & CIDMA, UA
Title: Optimal control near-synchronization of a complex network of Lotka-Volterra systems
Abstract: In this talk, we propose a controlled complex network of Lotka-Volterra systems, where the strength of the migrations of biological individuals is replaced by control functions, reproducing the implementation of ecological corridors. We prove that a solution of the controlled complex network can reach a near-synchronization state, under sufficient conditions which highlight the importance to consider a positive lower bound on the controls functions. After, we study optimal control problems where the main goal is the minimization of the default of synchronization in the complex network. The solutions of the optimal control problems lead to a restoration of the biodiversity of life species in a heterogeneous habitat by reaching at least a global coexistence equilibrium, or in a better scenario, a global limit cycle which would guarantee biological oscillations, which means rich life dynamics.
This is a joint work with Guillaume Cantin from the University of Nantes in France.
References
[1] Cantin G. and Silva C. J. Complex network near-synchronization for non-identical predator-prey systems. AIMS Mathematics, 7 (11), 19975-19997, 2022.
[2] Silva C. J. and Cantin G. Optimal Control Synchronization of a Complex Network of Predator-Prey Systems. In: Bernard Bonnard, Monique Chyba, David Holcman and Emmanuel Trelat (Eds.), IVAN KUPKA LEGACY: A Tour Through Controlled Dynamics, AIMS on Applied Mathematics, 2024
Name: Ana Pedro Paião
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: Parameter sensitivity analysis of an optimal linear-control problem applied to agricultural irrigation
Abstract: We propose an optimal linear-control problem applied to agricultural irrigation, denoted by OC($\beta$), whose aim is to minimize the amount of irrigation water, while ensuring the healthy crop growth, through a state inequality constraint.
A crucial parameter of OC($\beta$) problem is the percentage of water loss due to deep percolation, $\beta$, a parameter hard to estimate and subject to perturbations.
As consequence, OC($\beta$) is a parametric state-constrained optimal linear-control problem for which we conduct a parameter sensitivity analysis.
It consists in determining how perturbations of $\beta$ affect the optimal solutions, as well as the optimal cost, of OC($\beta$).
Since the theory for parametric optimal linear-control problems is not as well developed, particularly in what concerns to second order sufficient conditions, then we prove that OC($\beta$) problem can be transcribed into a finite-dimensional non-linear optimization problem, under some assumptions.
For such transcribed problem a parameter sensitivity analysis can be designed and the corresponding conclusions are translated in terms of OC($\beta$) problem.
To illustrate our findings, some numerical simulations are carried out.
Name: Hugo Alonso
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: A parameter estimation process for improved drug infusion
Abstract: We consider a reduced parameter (RP) model for the effect of the drug atracurium on the neuromuscular blockade (NMB) level of patients undergoing general anesthesia. We propose a generalization of a previously introduced parameter estimation process to obtain the patient dependent parameters of the RP model. Furthermore, we consider a reference tracking problem, where the objective is to force the NMB level of the patients to follow a constant reference, and suggest an open-loop control law based on the estimated RP model. It turns out that the application of the identification process requires choosing two values. In this context, we present an experimental study whose goal is to clarify how these choices impact on the results of the reference tracking problem.
Name: Sofia Rodrigues
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: Assessing Logistics Efficiency Across EU countries
Abstract: The Logistics Performance Index (LPI) serves as a comprehensive metric, assigning a numerical score to each country based on multiple factors, including infrastructure quality, customs efficiency, logistics competence, tracking and tracing capabilities, and shipment timeliness. This study seeks to enhance the understanding of logistics performance intricacies within Europe, aiming to support informed decision-making and promote continuous improvement in the region's logistics sector. Employing the CRITIC (CRiteria Importance Through Intercriteria Correlation) and MARCOS (Measurement of Alternatives and Ranking according to COmpromise Solution) methodologies, the study ranks EU countries using the 2023 LPI indicators provided by the World Bank. Furthermore, a cluster analysis of the LPI indicators is conducted to identify patterns and trends, revealing groups of countries with similar strengths or weaknesses in logistics infrastructure and performance.
Name: Cristina Januário
Affiliation: CIDMA, ISEL - Instituto Superior de Engenharia de Lisboa
Title: A three-species trophic model under the effect of habitat loss
Abstract: Changes in ecosystems progress at a rapid pace mainly due to the climate crisis and human-induced perturbations such as habitat loss, deforestation, or defaunation. Understanding how habitat loss interacts with biotic processes is crucial to anticipate catastrophic tipping points and biodiversity loss. We study the effect of habitat loss in a model that considers a resource species, a consumer, and predators that hunt in cooperation. We identify species coexistence at low fractions of habitat loss and low hutting cooperation between the predators via chaos, periodic oscillations, or static equilibria. Our work highlights the fragility of predators hunting cooperatively under the loss of habitat.
Name: Delfim F. M. Torres
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: On the Inverse Problem of the Fractional Calculus of Variations
Abstract: Given a fractional-order linear equation, we define an appropriate symmetric bilinear form so that the fractional operator is symmetric with respect to that bilinear form. Using the bilinear form, we then use the results of [01] to define a functional of the fractional calculus of variations, proving that the solutions of the given fractional-order equation are critical points of the fractional variational functional. In the case of fractional integral equations, the provided bilinear form is non-degenerate, and all critical points are solutions of the given equation. In the case of fractional differential equations, a relation with the least-squares method is obtained.
Reference
[01] D. F. M. Torres, The duality theory of fractional calculus and a new fractional calculus of variations involving left operators only, Mediterr. J. Math. 21 (2024), no. 3, Paper No. 106, 16pp. https://doi.org/10.1007/s00009-024-02652-x
Name: Natália Martins
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: A Pontryagin Maximum Principle for optimal control problems involving distributed-order fractional derivatives with arbitrary kernels
Abstract: In this talk, we extend fractional optimal control theory by proving a version of Pontryagin's Maximum Principle and establishing a sufficient optimality condition for an optimal control problem. The dynamical system constraint in this problem is governed by a generalized form of a fractional derivative: the left-sided Caputo distributed-order fractional derivative with an arbitrary kernel. This approach provides a more versatile representation of dynamic processes, accommodating a broader range of memory effects and hereditary properties inherent in diverse physical, biological, and engineering systems.
This is a joint work with Fátima Cruz and Ricardo Almeida.
Name: Ricardo Almeida
Affiliation: CIDMA, Department of Mathematics, University of Aveiro
Title: On the variable-order generalized fractional derivatives: concepts and properties
Abstract: In this presentation, we discuss various properties of the Caputo fractional derivative with respect to another function. This operator introduces a new arbitrary function, and through specific concrete instances of this function, we rediscover well-known classical fractional operators. Additionally, we extend some of the previous results by exploring variable order fractional operators. Finally, we provide a numerical method to handle these fractional operators effectively.
Name: Lígia Abrunheiro
Affiliation: ISCA & CIDMA, UA
Title: Geometric approach of a second-order Herglotz Problem
Abstract: In this talk, we provide an overview of recent advancements in Herglotz problems on manifolds. We explore the generalization of the second-order Herglotz problem to particular Lie groups using advanced geometric tools. Our study has significant potential applications, particularly in the control of robotic and thermodynamic systems. We present an illustrative example. This work is a joint work with Alexandre Anahory Simões, Leonardo Colombo, and Luís Machado.