FCT: DM - Artigos em revista internacional com arbitragem científica
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- Direct Reduction of Bias of the Classical Hill EstimatorPublication . Caeiro, Frederico Almeida Gião Gonçalves; Gomes, M. Ivette; Pestana, Dinis; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; INE - Instituto Nacional de EstatísticaIn this paper we are interested in an adequate estimation of the dominant component of the bias of Hill’s estimator of a positive tail index γ, in order to remove it from the classical Hill estimator in different asymptotically equivalent ways. If the second order parameters in the bias are computed at an adequate level k1 of a larger order than that of the level k at which the Hill estimator is computed, there may be no change in the asymptotic variances of these reduced bias tail index estimators, which are kept equal to the asymptotic variance of the Hill estimator, i.e., equal to γ 2 . The asymptotic distributional properties of the proposed estimators of γ are derived and the estimators are compared not only asymptotically, but also for finite samples through Monte Carlo techniques.
- A necessary condition for the boundedness of the maximal operator on Lp(·) over reverse doubling spaces of homogeneous typePublication . Karlovych, O.; Shalukhina, A.; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Springer NatureLet (X,d,μ) be a space of homogeneous type and p(·):X→[1,∞] be a variable exponent. We show that if the measure μ is Borel-semiregular and reverse doubling, then the condition essinfx∈Xp(x)>1 is necessary for the boundedness of the Hardy–Littlewood maximal operator M on the variable Lebesgue space Lp(·)(X,d,μ).
- The two alternative NADH: quinone oxidoreductases from Staphylococcus aureusPublication . Sena, Filipa V.; Sousa, Filipe M.; Pereira, Ana R.; Catarino, Teresa; Cabrita, Eurico J.; Pinho, Mariana G.; Pinto, Francisco R.; Pereira, Manuela M.; Instituto de Tecnologia Química e Biológica António Xavier (ITQB); DQ - Departamento de Química; UCIBIO - Applied Molecular Biosciences Unit; American Society for MicrobiologyStaphylococcus aureus is an opportunistic pathogen that has emerged as a major public health threat due to the increased incidence of its drug resistance. S. aureus presents a remarkable capacity to adapt to differentniches due to the plasticity of its energy metabolism. In this work, we investigated the energy metabolism of S. aureus, focusing on the alternative NADH:quinone oxidoreductases, NDH-2s. S. aureus presents two genes encoding NDH-2s (NDH-2A and NDH-2B) and lacks genes coding for Complex I, the canonical respiratory NADH:quinone oxidoreductase. This observation makes the action of NDH-2s crucial for the regeneration of NAD+ and, consequently, for the progression of metabolism. Our study involved the comprehensive biochemical characterization of NDH-2B and the exploration of the cellular roles of NDH-2A and NDH-2B, utilizing knockout mutants (Δndh-2a and Δndh-2b). We show that NDH-2B uses NADPH instead of NADH, does not establish a charge-transfer complex in the presence of NADPH, and its reduction by this substrate is the catalytic rate-limiting step. In the case of NDH-2B, the reduction of the flavinis inherently slow, and we suggest the establishment of a charge transfer complex between NADP+ and FADH2, as previously observed for NDH-2A, to slow down quinone reduction and, consequently, prevent the overproduction of reactive oxygen species, which is potentially unnecessary. Furthermore, we observed that the lack of NDH-2A or NDH-2B impacts cell growth, volume, and division differently.The absence of these enzymes results in distinct metabolic phenotypes, emphasizing the unique cellular roles of each NDH-2 in energy metabolism.
- Ein Lob der HabilitationPublication . Kahle, Reinhard; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Birkhäuser Verlag | SpringerWenn man den deutschen Universitäten das Urteil ausstellt, im Hinblick auf die Situation des Mittelbaus in einer Krise zu stecken, dürfte man sich zurecht den Vorwurf einer Untertreibung einhandeln. (...)
- Coupled Price–Volume Equity Models with Auto-Induced Regime SwitchingPublication . Esquível, Manuel L.; Krasii, Nadezhda P.; Mota, Pedro P.; Shamraeva, Victoria V.; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; MDPI - Multidisciplinary Digital Publishing InstituteIn this work, we present a rigorous development of a model for the Price–Volume relationship of transactions introduced in 2009. For this development, we rely on the precise formulation of diffusion auto-induced regime-switching models presented in our previous work of 2020. The auto-induced regime-switching models referred to may be based on a finite set of stochastic differential equations (SDE)—all defined on the same bounded time interval—and a sequence of interlacing stopping times defined by the hitting threshold times of the trajectories of the solutions of the SDE. The coupling between price and volume—which we take as a proxy of liquidity—is assumed to be the following: the regime switching in the price variable occurs at the stopping times for which there is a change of region—in the product state space of price and liquidity—for the liquidity variable (and vice versa). The regimes may be defined parametrically—that is, the SDE coefficients keep the same functional form but with varying parameters—or the functional form of the SDE coefficients may change with each regime. By using the same noise source for both the price and the liquidity regime-switching models—volume (liquidity), which, in general, is not a tradable asset—we ensure that despite incorporating information on liquidity, the price part of the coupled model can be assumed to be arbitrage free and complete, allowing the pricing and hedging of derivatives in a simple way.
- Jacques Tits motivic measurePublication . Tabuada, Gonçalo; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; Springer New YorkIn this article we construct a new motivic measure called the Jacques Tits motivic measure. As a first main application, we prove that two Severi-Brauer varieties (or, more generally, two twisted Grassmannian varieties), associated to 2-torsion central simple algebras, have the same class in the Grothendieck ring of varieties if and only if they are isomorphic. In addition, we prove that if two Severi-Brauer varieties, associated to central simple algebras of period { 3 , 4 , 5 , 6 } , have the same class in the Grothendieck ring of varieties, then they are necessarily birational to each other. As a second main application, we prove that two quadric hypersurfaces (or, more generally, two involution varieties), associated to quadratic forms of dimension 6 or to quadratic forms of arbitrary dimension defined over a base field k with I3(k) = 0 , have the same class in the Grothendieck ring of varieties if and only if they are isomorphic. In addition, we prove that the latter main application also holds for products of quadric hypersurfaces.
- Home care routing and scheduling problem with teams’ synchronizationPublication . de Aguiar, Ana Raquel Pena; Ramos, Tânia Rodrigues Pereira; Gomes, Maria Isabel; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; ElsevierThe demand for home care (HC) services has steadily been growing for two main types of services: healthcare and social care. If, for the former, caregivers' skills are of utter importance, in the latter caregivers are not distinguishable in terms of skills. This work focuses social care and models caregivers' synchronization as a means of improving human resources management. Moreover, in social care services, several visits need to be performed in the same day since patients are frequently alone and need assistance throughout the day. Depending on the patient's autonomy, some tasks have to be performed by two caregivers (e.g. assist bedridden patients). Therefore, adequate decision support tools are crucial for assisting managers (often social workers) when designing operational plans and to efficiently assign caregivers to tasks. This paper advances the literature by 1) considering teams of one caregiver that can synchronize to perform tasks requiring two caregivers (instead of having teams of two caregivers), 2) simultaneously modelling daily continuity of care and teams' synchronization, and 3) associating dynamic time windows to teams' synchronizations introducing scheduling flexibility while minimize service and travel times. These concepts are embedded into a daily routing and scheduling MIP model, deciding on the number of caregivers and on the number and type of teams to serve all patient tasks. The main HC features of the problem, synchronization and continuity of care, are evaluated by comparing the proposed planning with the current situation of a home social care service provider in Portugal. The results show that synchronization is the feature that most increases efficiency with respect to the current situation. It evidences a surplus in working time capacity by proposing plans where all requests can be served with a smaller number of caregivers. Consequently, new patients from long waiting lists can now be served by the “available” caregivers.
- Gradient Flow Formulations of Discrete and Continuous Evolutionary ModelsPublication . Chalub, Fabio A. C. C.; Monsaingeon, Léonard; Ribeiro, Ana Margarida; Souza, Max O.; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Springer Science Business MediaWe consider three classical models of biological evolution: (i) the Moran process, an example of a reducible Markov Chain; (ii) the Kimura Equation, a particular case of a degenerated Fokker-Planck Diffusion; (iii) the Replicator Equation, a paradigm in Evolutionary Game Theory. While these approaches are not completely equivalent, they are intimately connected, since (ii) is the diffusion approximation of (i), and (iii) is obtained from (ii) in an appropriate limit. It is well known that the Replicator Dynamics for two strategies is a gradient flow with respect to the celebrated Shahshahani distance. We reformulate the Moran process and the Kimura Equation as gradient flows and in the sequel we discuss conditions such that the associated gradient structures converge: (i) to (ii), and (ii) to (iii). This provides a geometric characterisation of these evolutionary processes and provides a reformulation of the above examples as time minimisation of free energy functionals.
- On Structured Random Matrices Defined by Matrix SubstitutionsPublication . Esquível, Manuel L.; Krasii, Nadezhda P.; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; MDPI - Multidisciplinary Digital Publishing InstituteThe structure of the random matrices introduced in this work is given by deterministic matrices—the skeletons of the random matrices—built with an algorithm of matrix substitutions with entries in a finite field of integers modulo some prime number, akin to the algorithm of one dimensional automatic sequences. A random matrix has the structure of a given skeleton if to the same number of an entry of the skeleton, in the finite field, it corresponds a random variable having, at least, as its expected value the correspondent value of the number in the finite field. Affine matrix substitutions are introduced and fixed point theorems are proven that allow the consideration of steady states of the structure which are essential for an efficient observation. For some more restricted classes of structured random matrices the parameter estimation of the entries is addressed, as well as the convergence in law and also some aspects of the spectral analysis of the random operators associated with the random matrix. Finally, aiming at possible applications, it is shown that there is a procedure to associate a canonical random surface to every random structured matrix of a certain class.
- Spectral Analysis for Comparing Bitcoin to Currencies and AssetsPublication . Pocelli, Maria Chiara; Esquível, Manuel L.; Krasii, Nadezhda P.; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações; MDPI - Multidisciplinary Digital Publishing InstituteWe present an analysis on variability Bitcoin characteristics that help to quantitatively differentiate Bitcoin from the state-owned traditional currencies and the asset Gold. We provide a detailed study on returns of exchange rates—against the Swiss Franc—of several traditional currencies together with Bitcoin and Gold; for that purpose, we define a distance between currencies by means of the spectral densities of the ARMA models of the returns of the exchange rates, and we present the computed matrix of the distances between the chosen currencies. A statistical analysis of these matrix distances is further proposed, which shows that the distance between Bitcoin and any other currency or Gold is not comparable to any of the distances between currencies or between currencies and Gold and not involving Bitcoin. This result shows that Bitcoin is essentially different from the traditional currencies and from Gold, at least in what concerns the structure of its variance and auto-covariances.