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Plactic-like monoids arising from meets and joins of stalactic and taiga congruences
Publication . Aird, Thomas; Ribeiro, Duarte; CMA - Centro de Matemática e Aplicações; Faculdade de Ciências e Tecnologia (FCT); Elsevier
We study the four plactic-like monoids that arise by taking the meets and joins of stalactic and taiga congruences. We obtain the combinatorial objects associated with the meet monoids, establishing Robinson–Schensted-like correspondences and giving extraction and iterative insertion algorithms for these objects. We then obtain results on the sizes of classes of words equal in plactic-like monoids, show that some of these monoids are syntactic, and characterise their equational theories.
Lattices of varieties of plactic-like monoids
Publication . Aird, Thomas; Ribeiro, Duarte; CMA - Centro de Matemática e Aplicações; Springer
We study the equational theories and bases of meets and joins of several varieties of plactic-like monoids. Using those results, we construct sublattices of the lattice of varieties of monoids, generated by said varieties. We calculate the axiomatic ranks of their elements, obtain plactic-like congruences whose corresponding factor monoids generate varieties in the lattice, and determine which varieties are joins of the variety of commutative monoids and a finitely generated variety. We also show that the hyposylvester and metasylvester monoids generate the same variety as the sylvester monoid.
A new algorithm for inference in HMM's with lower span complexity
Publication . Pereira, Diogo; Nunes, Cláudia; Rodrigues, Rui; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Elsevier Science B.V., Inc
The maximum likelihood problem for Hidden Markov Models is usually numerically solved by the Baum-Welch algorithm, which uses the Expectation-Maximization algorithm to find the estimates of the parameters. This algorithm has a recursion depth equal to the data sample size and cannot be computed in parallel, which limits the use of modern GPUs to speed up computation time. A new algorithm is proposed that provides the same estimates as the Baum-Welch algorithm, requiring about the same number of iterations, but is designed in such a way that it can be parallelized. As a consequence, it leads to a significant reduction in the computation time. This reduction is illustrated by means of numerical examples, where we consider simulated data as well as real datasets.
Integrals of groups. II
Publication . Araújo, João; Cameron, Peter J.; Casolo, Carlo; Matucci, Francesco; Quadrelli, Claudio; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Springer New York
An integral of a group G is a group H whose derived group (commutator subgroup) is isomorphic to G. This paper continues the investigation on integrals of groups started in the work [1]. We study: A sufficient condition for a bound on the order of an integral for a finite integrable group (Theorem 2.1) and a necessary condition for a group to be integrable (Theorem 3.2). The existence of integrals that are p-groups for abelian p-groups, and of nilpotent integrals for all abelian groups (Theorem 4.1). Integrals of (finite or infinite) abelian groups, including nilpotent integrals, groups with finite index in some integral, periodic groups, torsion-free groups and finitely generated groups (Section 5). The variety of integrals of groups from a given variety, varieties of integrable groups and classes of groups whose integrals (when they exist) still belong to such a class (Sections 6 and 7). Integrals of profinite groups and a characterization for integrability for finitely generated profinite centreless groups (Section 8.1). Integrals of Cartesian products, which are then used to construct examples of integrable profinite groups without a profinite integral (Section 8.2). We end the paper with a number of open problems.
The effect of asymmetric zeta potentials on the electro-osmotic flow of a generalized Phan–Thien–Tanner fluid
Publication . Ribau, A. M.; Ferrás, L. L.; Morgado, M. L.; Rebelo, M.; Pinho, F. T.; Afonso, A. M.; Faculdade de Ciências e Tecnologia (FCT); Springer
Electrokinetic flows driven by electro-osmotic forces are especially relevant in micro and nano-devices, presenting specific applications in medicine, biochemistry, and miniaturized industrial processes. In this work, we integrate analytical solutions with numerical methodologies to explore the fluid dynamics of viscoelastic electro-osmotic/pressure-driven fluid flows (described by the generalized Phan–Thien–Tanner (gPTT) constitutive equation) in a microchannel under asymmetric zeta potential conditions. The constitutive equation incorporates the Mittag–Leffler function with two parameters (α and β), which regulate the rate of destruction of junctions in a network model. We analyze the impact of the various model parameters on the velocity profile and observe that our newly proposed model provides a more comprehensive depiction of flow behavior compared to traditional models, rendering it suitable for modeling complex viscoelastic flows.
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Fundação para a Ciência e a Tecnologia
Programa de financiamento
Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base
Número da atribuição
UIDB/04621/2020