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On the Hausdorff dimension of Riemann's non-differentiable function
Get PDFRecent findings show that the classical Riemann's non-differentiable function has a physical and geometric nature as the irregular trajectory of a polygonal vortex filament driven by the binormal flow. In this article, we give an upper estimate of its Hausdorff dimension. We also adapt this result to the multifractal setting. To prove these results, we recalculate the asymptotic behavior of Riemann's function around rationals from a novel perspective, underlining its connections with the Talbot effect and Gauss sums, with the hope that it is useful to give a lower bound of its dimension and to answer further geometric questions
Quantum Dynamics Generated by Long-Range Interactions for Lattice Fermion and Quantum Spins
Get PDFWe study the macroscopic dynamics of fermion and quantum-spin systems with long-range, or mean-field, interactions, which turns out to be equivalent to an intricate combination of classical and short-range quantum dynamics. In this paper we focus on the quantumpart of the long-range macroscopic dynamics. The classical part is studied in a companion paper. Altogether, the results obtained are far beyond previous ones and required the development of a suitable mathematical framework. The entanglement of classical and quantum worlds is noteworthy, opening new theoretical perspectives, and is shown here to be a consequence of the highly non-local character of long-range, or mean-field, interactions.CNPq (308337/2017-4),
FAPESP (2017/22340-9),
Basque Government through the grant IT641-13
MTM2017-82160-C2-2-
Algorithms for Large Orienteering Problems
Get PDFIn this thesis, we have developed algorithms to solve large-scale Orienteering Problems. The Orienteering Problem is a combinatorial optimization problem were given a weighted complete graph with vertex profits and a maximum distance constraint, the goal is to find the simple cycle which maximizes the sum of the profits of the visited vertices. To solve the Orienteering Problem, we have developed an evolutionary algorithm and an Branch-and-Cut algorithm. One of the key characteristics of the evolutionary algorithm is to work with unfeasible solutions. From the point of view of genetic operators, the main contribution has
been the development of the Edge Recombination Crossover for the Orienteering Problem, which in a wider context it is also valid for any cycle problem. Another contribution has been the developed local search to handle large problems. The Branch-and-Cut algorithm includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. At the same time, we have generalized for cycle problems the support graph shrinking techniques and procedures to speed up the exact separation
algorithms for subcycle elimination constraints. The experiments carried out in large-sized instances, up to 7393 nodes, show that both algorithms achieve outstanding results, both in terms of the quality of solutions and in terms of the execution time.BERC.2014-2017
SEV-2013-0323
PID2019-104933GB-I00
MTM2015-65317-
Dynamics and rheology of a suspension of super-paramagnetic chains under the combined effect of a shear flow and a rotating magnetic field
Get PDFThis study presents an analysis of the dynamics of a single and multiple chains of spherical super-paramagnetic beads suspended in a Newtonian fluid under the combined effect of an external rotating magnetic field and a shear flow. Viscosity results depend on two main non-dimensional numbers: the ratio between the shear rate and the magnetic rotation frequency and the ratio between the hydrodynamic and magnetostatic interactions (the Mason number). When the shear rate is smaller than the magnetic frequency, the chain rotation accelerates the surrounding fluid, reducing the value of the measured suspension viscosity even below the solvent one. In this regime, shear-thickening is observed. For values of the shear rates comparable to the rotation magnetic frequency, the viscosity reaches a maximum and non-linear coupling effects come up. If the shear rate is increased to values above the rotation frequency, the viscosity decreases and a mild shear-thinning is observed. In terms of the Mason number, the suspension viscosity reduces in line with literature results reported for fixed magnetic fields, whereas the shear-rate/magnetic-frequency ratio parameters induces a shift of the viscosity curve towards larger values. Results at larger concentrations and multiple chains amplify the observed effects
Study of Wound Healing Dynamics by Single Pseudo-Particle Tracking in Phase Contrast Images Acquired in Time-Lapse
Get PDFCellular contacts modify the way cells migrate in a cohesive group with respect to a free single cell. The resulting motion is persistent and correlated, with cells’ velocities self-aligning in time. The presence of a dense agglomerate of cells makes the application of single particle tracking techniques to define cells dynamics difficult, especially in the case of phase contrast images. Here, we propose an original pipeline for the analysis of phase contrast images of the wound healing scratch assay acquired in time-lapse, with the aim of extracting single particle trajectories describing the dynamics of the wound closure. In such an approach, the membrane of the cells at the border of the wound is taken as a unicum, i.e., the wound edge, and the dynamics is described by the stochastic motion of an ensemble of points on such a membrane, i.e., pseudo-particles. For each single frame, the pipeline of analysis includes: first, a texture classification for separating the background from the cells and for identifying the wound edge; second, the computation of the coordinates of the ensemble of pseudo-particles, chosen to be uniformly distributed along the length of the wound edge. We show the results of this method applied to a glioma cell line (T98G) performing a wound healing scratch assay without external stimuli. We discuss the efficiency of the method to assess cell motility and possible applications to other experimental layouts, such as single cell motion. The pipeline is developed in the Python language and is available upon request.Basque Government BERC 2018– 2021
Spanish Ministry of Economy and Competitiveness MINECO via the BCAM Severo Ochoa SEV-2017-0718 accreditatio
Targeting Impaired Antimicrobial Immunity in the Brain for the Treatment of Alzheimer’s Disease
Get PDFAlzheimer’s disease (AD) is the most common form of dementia and aging is the most common risk factor for developing the disease. The etiology of AD is not known but AD may be considered as a clinical syndrome with multiple causal pathways contributing to it. The amyloid cascade hypothesis, claiming that excess production or reduced clearance of amyloid-beta (Aβ) and its aggregation into amyloid plaques, was accepted for a long time as the main cause of AD. However, many studies showed that Aβ is a frequent consequence of many challenges/pathologic processes occurring in the brain for decades. A key factor, sustained by experimental data, is that low-grade infection leading to production and deposition of Aβ, which has antimicrobial activity, precedes the development of clinically apparent AD. This infection is chronic, low grade, largely clinically silent for decades because of a nearly efficient antimicrobial immune response in the brain. A chronic inflammatory state is induced that results in neurodegeneration. Interventions that appear to prevent, retard or mitigate the devel- opment of AD also appear to modify the disease. In this review, we conceptualize further that the changes in the brain antimicrobial immune response during aging and especially in AD sufferers serve as a foundation that could lead to improved treatment strategies for preventing or decreasing the progression of AD in a disease-modifying treatment
From habitat to management: a simulation framework for improving statistical methods in fisheries science
Get PDFMonte Carlo simulation consists of computer experiments that involve creating data by pseudo-random sampling and has shown to be a powerful tool for studying the performance of statistical methods. In this thesis Monte Carlo simulation was used to improve statistical methodology related to three different fields of fisheries science: 1) Species distribution models (SDM) field, where focusing on regression-based models, we proposed using shape-constrained generalised additive models (SC-GAMs) to build SDMs in agreement with the ecological niche theory imposing concavity constraints in the linear predictor scale and testing their performance trough Monte Carlo simulation, 2) stock assessment models field, where uncertainty estimation methods for statistical catch-at-age models with non-parametric effects on fishing mortality were compared through simulation in addition to the comparison of two available stock assessment models to an ad-hoc Bayesian approach, and 3) management advice field, where a full-feedback management strategy evaluation (MSE) was developed for the sardine in the Bay of Biscay, incorporating the official Stoch Synthesis assessment model within the Monte Carlo simulation, and introducing gradually different sources of uncertainty such as process, parameter and observation error in order to study their effect in management advice. Monte Carlo simulation was an adequate tool to accomplish the objectives of this thesis that definitely could not have been achieved using only available real data or analytical solutions
Modeling dengue immune responses mediated by antibodies: A qualitative study
Get PDFDengue fever is a viral mosquito-borne infection and a major international public health concern. With 2.5 billion people at risk of acquiring the infection around the world, disease severity is influenced by the immunological status of the individual, seronegative or seropositive, prior to natural infection. Caused by four antigenically related but distinct serotypes, DENV-1 to DENV-4, infection by one serotype confers life-long immunity to that serotype and a period of temporary cross-immunity (TCI) to other serotypes. The clinical response on exposure to a second serotype is complex with the so-called antibody-dependent enhancement (ADE) process, a disease augmentation phenomenon when pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection, used to explain the etiology of severe disease. In this paper, we present a minimalistic mathematical model framework developed to describe qualitatively the dengue immunological response mediated by antibodies. Three models are analyzed and compared: (i) primary dengue infection, (ii) secondary dengue infection with the same (homologous) dengue virus and (iii) secondary dengue infection with a different (heterologous) dengue virus. We explore the features of viral replication, antibody production and infection clearance over time. The model is developed based on body cells and free virus interactions resulting in infected cells activating antibody production. Our mathematical results are qualitatively similar to the ones described in the empiric immunology literature, providing insights into the immunopathogenesis of severe disease. Results presented here are of use for future research directions to evaluate the impact of dengue vaccines.A.S, H.F., and E.S. E.S. has received funded from the Indonesian RistekBrin Grant No.
122M/IT1.C02/TA.00/2021, 2021 (previously RistekDikti 2018-2021). M.A. received funding from the
European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie
grant agreement No 792494
AT-MFCGA: An Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm for Evolutionary Multitasking
Get PDFTransfer Optimization is an incipient research area dedicated to solving multiple optimization tasks simultaneously. Among the different approaches that can address this problem effectively, Evolutionary Multitasking resorts to concepts from Evolutionary Computation to solve multiple problems within a single search process. In this paper we introduce a novel adaptive metaheuristic algorithm to deal with Evolutionary Multitasking environments coined as Adaptive Transfer-guided Multifactorial Cellular Genetic Algorithm (AT-MFCGA). AT-MFCGA relies on cellular automata to implement mechanisms in order to exchange knowledge among the optimization problems under consideration. Furthermore, our approach is able to explain by itself the synergies among tasks that were encountered and exploited during the search, which helps us to understand interactions between related optimization tasks. A comprehensive experimental setup is designed to assess and compare the performance of AT-MFCGA to that of other renowned Evolutionary Multitasking alternatives (MFEA and MFEA-II). Experiments comprise 11 multitasking scenarios composed of 20 instances of 4 combinatorial optimization problems, yielding the largest discrete multitasking environment solved to date. Results are conclusive in regard to the superior quality of solutions provided by AT-MFCGA with respect to the rest of the methods, which are complemented by a quantitative examination of the genetic transferability among tasks throughout the search process
Discrete Carleman estimates and three balls inequalities
Get PDFWe prove logarithmic convexity estimates and three balls inequalities for discrete magnetic Schrödinger operators. These quantitatively connect the discrete setting in which the unique continuation property fails and the continuum setting in which the unique continuation property is known to hold under suitable regularity assumptions. As a key auxiliary result which might be of independent interest we present a Carleman estimate for these discrete operators.RYC2018-025477-I
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