Abstract: We will discuss certain improvements on recent results on
generalized inverses with the aim of generalizing them to the most general
setting possible by eliminating superfluous assumptions and by simplifying
some of the conditions in statements. In our talk, we will consider Hartwig's
well-known triple reverse order law as an example for showing how this can
be done using a recent framework for algebraic proofs and the software
package OperatorGB. Our improvements of Hartwig's result are proven in
rings with involution and we will be discussing computer-assisted proofs of
these results in other settings based on the mentioned framework and a
single computation with noncommutative polynomials. Also, we will show
how some of the results on generalized inverses we have improved will lead
to solving certain operator equations without having to make assumptions
as was previously required.
The talk is based on a joint work with J. Milošević, G. Regensburger and
C. Hofstadler.
References:
[1] D.S. Cvetković-Ilić, C. Hofstadler, J.H. Poor, J. Milošević, C.G. Raab,
G. Regensburger, Algebraic proof methods for identities of matrices and
operators: improvements of Hartwig’s triple reverse order law, Appl.
Math. Comp., 409, (2021), 126357.
Lunch
14:30 - 14:55 Eurica Henriques [CMAT-ANAP]
Results towards regularity to doubly nonlinear parabolic equations
Abstract: In the last few years many progresses were made in understanding the behaviour of the solutions of doubly
nonlinear evolutionary equations given by
ut-div(|u|m-1|Du|p-2Du)=0, p>1, (1)
or considered written in the form
¶t(uq)-div(|Du|p-2Du)= 0, p>1 and q>0. (2)
In this talk we'll focus on the second doubly nonlinear pde (2) and we'll present the Expansion
of Positivity for its nonnegative bounded weak solutions: we will see how the information on
the measure of the positivity set of u, at a certain time level s over a cuber Kr(y), can be
expanded to the measure of the positivity set of u both in space (say from Kr(y) to Kr(2y)
and in time (from the time level s to all further time levels s+qrp).
15:00 - 15:25 Natalia Cadavid Aguilar [CMAT-GTA]
Immersions and topological complexity
Abstract: This is a self-contained talk where we
will begin by defining what is a manifold, what is an immersion,
what is topological complexity, until we get to the point of
asking if there is a relationship between immersions and
topological complexity.
15:30 - 15:45 Fernanda Pereira [CMAT-SAPOR]
Development of Time Series Forecasting Models: a contribution in the context of dynamic modeling
Abstract: This project aims to develop and evaluate the performance of dynamic models to model and more
accurately predict time series in the context of state space models (SSM), associated with appropriate versions of the Kalman filter, in a mixed-effects
approach that incorporates fixed effects and stochastic components. These models have in their structure a latent process, the state, and it is
usually predicted by the Kalman filter algorithm. When the errors are Gaussian, the estimation of the unknown parameters is, in general, performed
using the maximum likelihood method. However, in many applications (environmental, economic, etc.) the normality of the errors is not always guaranteed.
Therefore, distribution-free estimators will be proposed for these SSM, whose inferential properties do not depend on error distribution. On the other hand,
when the unknown parameter vector is replaced by its estimate, the mean square error of the estimators is underestimated. From this perspective,
the choice falls on estimation through Bootstrap-based resampling methodologies. Another important issue is the identification of changing
trends and patterns of evolution of the series over the observed time. The identification of outliers is also an important step in the
context of time series since they can interfere with the inference process, as well as the presence of missing values, which must be treated using the most appropriate methods.
15:50 - 16:05 Angelos Bampounis [CMAT-ALC]
Matchgate circuits with magic resources for universal quantum computation
Abstract: It is believed that quantum computers are more powerful and offer the possibility of dramatic speed-up
relative to their classical counterparts. A promising approach to understand their power is to study restricted classes of computation
which can be efficiently simulated by classical devices but become quantum-universal by the addition of an extra resource.
Such a resource may then be regarded as the source of the quantum advantage. A way to explain the power of this recourse is to
look for some non-classical features that might display. Two characteristic signs of non-classicality are the notions of quantum contextuality
and negativity of Wigner function. One of the most prominent examples is stabilizer circuits, the class of circuits built out of Clifford gates,
which according to the Gottesmann-Knill theorem can be classically efficiently simulatable, and can be promoted to quantum universality via
the so called magic state injection. In the framework of stabilizer sub-theory, it was shown that the physical property that magic states
exhibit to serve as universal resources is that of quantum contextuality in the case of qudits (d-dimensional quantum systems) with d an odd prime power.
In this talk, I will be talking about the main subject of my research project which is another interesting restricted class of circuits,
which can be classically efficiently simulated, made out of a special set of unitary two-qubit gates restricted to act on nearest-neighbour (n.n.)
qubits, the so-called matchgates. We will also see an interesting aspect of which is their correspondence to quantum evolutions of non-interacting ("free")
fermionic quantum computation via the so called Jordan-Wigner transformation which gives a map between fermions and qubits. In addition,
we will see the ways with which matchgate circuits can be promoted to quantum universality. Finally, I will discuss about my work in progress and future research plans.
Coffee Break
16:40 - 17:05 José Carlos Costa [CMAT-ALC]
Orders of elements in finite quotients of a free group
Abstract: A positive integer n is said to be a finitistic order for an element u of a group F if there exist a
finite group G and a homomorphism h from F into G such that h(u) has order n in G. Let u be a non-identity element of a free group F.
It is well known that u has infinite order. In this talk we describe an algorithm which shows that any positive integer is a finitistic order for u.
This is a joint work with Conceição Nogueira and M. Lurdes Teixeira.
17:10 - 17:55 João Gama [FEP - Universidade do Porto]
Data Science in Our Lives
Abstract: We are living in a digital society. The economic, social, business, and scientific impacts are immense.
Every day, we interact with machines and systems that explore artificial intelligence tools and data science algorithms.
In this talk, we discuss the desirable properties of machine learning and data mining algorithms.
We discuss the fundamental issues in learning in dynamic environments like continuously maintain learning
models that evolve over time, learning and forgetting, concept drift, and change detection.
We present illustrative AI projects, related to our daily life, that explores data science.
End
Posters
Mouse over the titles shows poster abstracts.
Bessa, V.
CMAT (GTA)
Global dynamics of interacting monomial scalar field potentials and perfect fluids
Abstract: Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations
with a minimally coupled scalar field with monomial potentials V(f)~f2n,
nÎIN, interacting with a perfect fluid with linear equation of state in flat Robertson-Walker spacetimes. The friction-like interaction term
is of the form G(f)~f2p ,
pÎIN0. We perform a global dynamical analysis of the model and provide a detailed description of the future and past asymptotics.
The analysis rely on the introduction of a new regular dynamical systems formulation of the Einstein equations on a compact state space and the use of dynamical systems tools
such as averaging methods involving a time-dependent perturbation parameter.
Chimpanzo, J.A.L., Catarino, P., Borges, A., Vasco, P.
Bolseiro da Fundação Calouste Gulbenkian, (CMAT - ALC, ALC, ALC)
Bidimensional extensions of Balancing and Lucas-Balancing Numbers
Abstract: Numerical sequences have been the subject of several research studies in recent decades. In this work we incorporated
the background of the Balancing and Lucas-Balancing Numbers, and we define the bidimensional versions of these two sequences. We also study some identities that are
satisfied by these two new sequences.
Coelho, C., Costa, M.F.P., Ferrás, L.L.
(CMAT - SAPOR, SAPOR, ANAP)
Neural Networks and Fractional Differential Equations
Abstract: The impact of the optimization algorithms Adam, RMSprop, L-BFGS, and SGD with
momentum on the solution of the Fractional Laplacian Equation (FLE) by physics-informed neural networks is investigated considering
two different analytical solutions, one smooth and the other non-smooth. The influence of the optimization approach, the smoothness
of the analytical solution, and the network configuration on the predicted solution, is thoroughly discussed.
Coelho, C., Costa, M.F.P., Ferrás, L.L., Soares, A.J.
(CMAT - SAPOR, SAPOR, ANAP, ANAP)
Implementation of a Deep Learning model capable of detecting objects from satellite images
Abstract: This study involves a review of existing object detection methods as well as the development of a
Deep Learning model that can detect swimming pools from satellite pictures.
The model was trained on a Kaggle-customized dataset and then evaluated on a newly created dataset containing aerial images.
Several metrics are used to evaluate the trained model's performance.
Costa, M.F.P., Coelho,C., Ferrás, L.L.
(CMAT - SAPOR, SAPOR, ANAP)
Parameter Estimation for Constitutive Differential Equations: An Optimization Approach
Abstract: When studying complex viscoelastic fluids, the exponential form of the original Phan-Thien and Tanner (PTT)
model is frequently used. A generalized version of the PTT model was recently proposed, which employs the Mittag-Leffler function to generate a new
function of the trace of the stress tensor. We propose two optimization problems for predicting the model parameters, while fitting experimental
data in shear flows (storage modulus, loss modulus, shear viscosity). The model can almost exactly replicate the experimental data with
the optimal values of the parameters generated by the optimization approach.
Falcão, M.I., Miranda, F., Ferreira, V.
CMAT (ANAP, ANAP, ANAP)
quatPol: a Matlab toolbox
Abstract: Hamilton's quaternions are inextricably linked to rotations and their use has become indispensable in all
high technologies with need of calculations in real time. In this context, several software packages to perform computations in the algebra of the real quaternions have emerged.
In more recent years, quaternions have found a wealth of applications in a number of different areas which motivated the design of efficient methods for numerically
approximating the zeros of quaternionic polynomials. This work presents a Matlab toolbox for manipulating such polynomials and discuss a root-finding
method entirely based on quaternionic arithmetic.
Faustino, C.
CMAT (GTA)
Directed homology
Abstract: In the framework of his research on directed algebraic topology, M. Grandis developed a theory of
directed homology for cubical sets. In this work, we adapt Grandis' theory to precubical sets, which are more suitable than cubical sets for
applications in concurrency theory.
Filipe, V., Teixeira, P., Teixeira, A.P.
NESC TEC, Universidade de Trás-os-Montes e Alto Douro, CMAT (SAPOR)
On Using Clustering and Thermography to Predict Diabetic Foot
Summary:
Diabetes Mellitus (DM) is a chronic disease characterized by the inability of our body to use its main source of energy, glucose,
resulting in increased blood glucose levels [1]. Diabetic patients have between 12% and 25% of risk of developing foot ulcers during life [2,3].
As the risk of ulceration is directly linked to an increase of the temperature in the plantar region, several studies use thermography as a method
for automatic identification of problems in diabetic foot. The main objective of this work is to develop a methodology, that uses thermographic
photos of the plant of the feet, to analyze the diversity of thermal changes in the plantar region of diabetic and healthy individuals,
classifying each foot as belonging to a DM or to a healthy individual. Thus, helping to early detection of injury risk and helping to prevent ulceration.
To accomplish this task, a binary classifier, based on the concept of clustering, is presented; additionally, a quantitative indicator and a
classification thresholder are proposed.
Gonçalves, B.
CMAT (GTA)
A model of immunotherapy for recurrent autoimmune diseases
Many autoimmune diseases are chronic in nature, so that in general patients experience periods of recurrence and
remission of the symptoms. Recently, a mathematical model of kinetic type describing the immune system cellular interactions, in the context of autoimmunity,
exhibiting recurrent dynamics, was constructed. This model describes the interactions between self-antigen presenting cells, self-reactive T cells and
immunosuppressive cells. A constant input of self-antigen presenting cells is considered in the problem and is interpreted as being due to external environmental
factors that are believed to trigger autoimmunity in people with predisposition for this condition.
In this project, we add a fourth population of Interleukin-2 cytokines in the macroscopic system of the previous model and a term representing a drug therapy
consisting of an intake of Interleukin-2 cytokines which boosts the effect of immunosuppressive cells on the autoimmune reaction. We then study the equilibria
of the dynamical system and their stability properties. By applying dynamical system theory, we prove that steady oscillations may arise due to the
occurrence of a Hopf bifurcation. We perform some numerical simulations for our system, and we observe the effect of the drug therapy on the recurrent pattern of the model.
Guimarães, P.1,2, Ferreira, F.1, Wojtak, W.1,2, Barbosa, P.1,2,
Erlhagen, W.1, Bicho, E.2, Monteiro, S.2
1 CMAT (ANAP) - 2 Centre Algoritmi
In-car cognitive recommendation engine for assisting users daily routines: a dynamic neural fields approach
Abstract: Many private cars have their routine activity that includes moving to the same locations at about the same
time on a certain day of the week, carrying the same objects and passengers, and, in some cases, being driven by different drivers. We present the first steps on the
development of an embedded solution, based on Dynamic Neural Fields (DNF), with cognitive abilities of learning, adaptation, and recall of different aspects of daily
driving routines. For such, we employ instances of a generic DNF model capable of learning spatial and temporal information. Learning takes place continuously and implicitly.
The final goal is to endow a vehicle with cognition to predict: (1) where and when to arrive/depart; (2) the driver, passengers, and objects that enter/leave the vehicle;
and (3) the preferred comfort settings. This concept comes in handy with the future of mobility in which, with the rise of intelligent vehicles, they may be capable
of supporting their users in a personalised and individualised way
Oliveira, J.
CMAT (GTA)
On the sheaf of smooth forms on Lie algebroids over triangulated spaces
Abstratct: A sheaf of differential forms on a compatible family of Lie algebroids defined over regular open subsets
of a simplicial complex is constructed and is proved that sheaf is fine.
Silva, D., Menezes, R., Garrido, S., Moreno, A.
CMAT( SAPOR, SAPOR), IPMA (DivRP, DivRP)
Spatio-temporal variability of distribution and abundance of sardine in Portuguese continental coast:
environmental effects
Abstract: In the last decades, the challenge of sustainability has become a popular concern due to resource depletion
and adverse impacts of environmental degradationm such as the loss of biodiversity. Therefore, improving knowledge about biodiversity and species dynamics represents a
essential step for its conservation. Although the fishing dynamics depends on the human decision-making process, the changes in the abundance and distribution of fishery
resources are also strongly related to the variability of environment conditions. The study of the relationship between the spatial distribution of marine species and the
environmental changes makes it possibe to know the processes of change in abundance indicators, identify potential habitats and improve the ability to predict trends in the
dynamics of these species. This study aims the estimation of spatial distribution of sardine (Sardina pilchardus), relating the spatio-temporal variability of biomass with
environmental conditions. The hurdle model, adopted in this work, allows to incorporate the specificities of the data: complex spatio-temporal dynamics, excess of zeros and
the difference between the occurrence and abundance under occurrence processes. In addition to considering environmental covariates and the spatio-temporal structure in the
model, the impact of environmental conditions with time lag on biomass indicator is evaluated. West coast data and south coast data are studied separately due to the shape of
the coast and the different oceanographic conditions. The application of this approach will allow to understand spatio-temporal dynamic of sardine in Portuguese continental
coast and in Gulf of Cádiz as well as relate the biomass indicator with environmental conditions, being able to contribute to a better management of this species.
Sousa, A.C.
CMAT
Minimal Quantum Logic: a brief comparison with Classical Logic
Abstract: Semantically, Classical Logic (CL) is associated with Boolean algebras, while Minimal Quantum Logic (MQL)
is associated with ortholattices, which are lattices where, notably, the distributivity laws are not necessarily true. Deductively, when employing the sequent calculus,
one has to impose restrictions on the inferences rules of QML, notably on the cut rule, in order to prove less theorems. Examples will be given.
Soutinho, G., Machado, L.M.
Instituto de Saúde Pública da Universidade do Porto, CMAT (SAPOR)
markovMSM: An R package for checking the Markov condition in multi-state survival data
Multi-state models can be successfully used to describe processes in which an individual move through a finite number of states
in continuous time. These models allow a detailed view of the evolution or recovery of the process, and can be used to study the effect of a vector of explanatory
variables on the transition intensities or to obtain prediction probabilities of future events, after a given event history. In both cases, before using these models,
we have to evaluate whether the Markov assumption is tenable. This paper introduces the markovMSM package, a software application for R, which considers tests of the
Markov assumption that are applicable to general multi-state models. Three approaches using existing methodology are considered: a simple method based on including
covariates depending on the history in Cox models for the transition intensities; methods based on measuring the discrepancy of the non-Markov estimators of the
transition probabilities to the Markovian Aalen-Johansen estimators; and, finally, methods that were developed by considering summaries from families of log-rank
statistics where patients are grouped by the state occupied of the process at a particular time point. The main functionalities of the markovMSM package are illustrated
using real data examples.
This event is supported by
Portuguese funds through the CIDMA - Center for Research and
Development in Mathematics and Applications - and the Portuguese
Foundation for Science and Technology ("FCT-Fundação para a
Ciência e a Tecnologia"), within project UID/MAT/04106/2013.
This event is supported by
Portuguese funds through the CMAT - Research Centre of
Mathematics of the University of Minho - and the Portuguese
Foundation for Science and Technology ("FCT-Fundação para a
Ciência e a Tecnologia"), projects UIDB/00013/2020 and UIDP/00013/2020.
