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Uniform profile near the point defect of Landau-de Gennes model
Get PDFFor the Landau-de Gennes functional on 3D domains,
it is well-known that under suitable boundary conditions, the global minimizer converges strongly in to a uniaxial minimizer up to some subsequence \e_n\rightarrow\infty , where is a minimizing harmonic map. In this paper we further investigate the structure of near the core of a point defect which is a singular point of the map . The main strategy is to study the blow-up profile of where are carefully chosen and converge to . We prove that converges in to a tangent map which at infinity behaves like a ``hedgehog" solution that coincides with the asymptotic profile of near . Moreover, such convergence result implies that the minimizer can be well approximated by the Oseen-Frank minimizer outside the neighborhood of the point defect
On the use of the descriptive variable for enhancing the aggregation of crowdsourced labels
Get PDFThe use of crowdsourcing for annotating data has become a popular and cheap alternative to expert labelling. As a consequence, an aggregation task is required to combine the different labels provided and agree on a single one per example. Most aggregation techniques, including the simple and robust majority voting—to select the label with the largest number of votes—disregard the descriptive information provided by the explanatory variable. In this paper, we propose domain-aware voting, an extension of majority voting which incorporates the descriptive variable and the rest of the instances of the dataset for aggregating the label of every instance. The experimental results with simulated and real-world crowdsourced data suggest that domain-aware voting is a competitive alternative to majority voting, especially when a part of the dataset is unlabelled. We elaborate on practical criteria for the use of domain-aware voting
Transitions from P to NP-hardness: the case of the Linear Ordering Problem
Get PDFIn this paper we evaluate how constructive heuristics
degrade when a problem transits from P to NP-hard. This is
done by means of the linear ordering problem. More specifically,
for this problem we prove that the objective function can be
expressed as the sum of two objective functions, one of which is
associated with a P problem (an exact polynomial time algorithm
is proposed to solve it), while the other is associated with an NPhard problem. We study how different constructive algorithms
whose behaviour only depends on univariate information perform
depending on the contribution of the P or NP-hard components
of the problem. A number of experiments are conducted with
reduced dimensions, where the global optimum of the problems
is known, giving different weights to the NP-hard component,
while the weight of the P component is fixed. It is observed how
the performance of the constructive algorithms gets worse as the
weight given to the NP-hard component increases
The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm.
Get PDFBy collecting from literature data the experimental evidences of
anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live E. coli cells, we
get the probability density function of molecules’ displacement and we
derive the corresponding Fokker–Planck equation. Molecules’ distribution emerges to be related to the Kr¨atzel function and its Fokker–
Planck equation be a fractional diffusion equation in the Erd´elyi–Kober
sense. The irreducibility of the derived Fokker–Planck equation to
those of other literature models is also discussed
Solving Boundary Value Problems Via the Nyström Method Using Spline Gauss Rules
Get PDFWe propose to use spline Gauss quadrature rules for solving boundary value problems (BVPs) using the Nyström method. When solving BVPs, one converts the corresponding partial differential equation inside a domain into the Fredholm integral equation of the second kind on the boundary in the sense of boundary integral equation (BIE). The Fredholm integral equation is then solved using the Nyström method, which involves a use of a particular quadrature rule, thus, converting the BIE problem to a linear system. We demonstrate this concept on the 2D Laplace problem over domains with smooth boundary as well as domains containing corners. We validate our approach on benchmark examples and the results indicate that, for a fixed number of quadrature points (i.e., the same computational effort), the spline Gauss quadratures return an approximation that is by one to two orders of magnitude more accurate compared to the solution obtained by traditional polynomial Gauss counterparts
THE EFFECT OF SUPERVISED FEATURE EXTRACTION TECHNIQUES ON THE FACIES CLASSIFICATION USING MACHINE LEARNING
Get PDFThe widely accepted supervised machine learning classification algorithms are used for
the semi-automating of the feature extraction process. In the machine learning facies
classification process, each wireline log is a feature in the feature space. Since features are
important in classification decisions, using suitable features improves the performance of a
classification algorithm.
In this study, three feature sets are compared containing the original conventional features
(well-logs), and the extracted features from the unsupervised PCA and supervised FDA
methods, using two classifier algorithms, namely SVM and RF. The FDA showed an
improvement in the performance of facies classifiers while PCA can even deteriorate the
results. An F1 score of 0.61 averaged over the available 20 folds for the combination of FDA
feature extractor and RF classifier is achieved. This represents a 5% improvement in the
prediction accuracy, compared to the conventional use of wells information as features with an
F1 score of 0.56. Moreover, the conventional method uses all seven well-logs while with the
FDA we only use three features
A numerical method for suspensions of articulated bodies in viscous flows
Get PDFAn articulated body is defined as a finite number of rigid bodies connected by a set of arbitrary constraints that limit the relative motion between pairs of bodies. Such a general definition encompasses a wide variety of situations in the microscopic world, from bacteria to synthetic micro-swimmers, but it is also encountered when discretizing inextensible bodies, such as filaments or membranes. In this work we consider hybrid articulated bodies, i.e. constituted of both linear chains, such as filaments, and closed-loop chains, such as membranes. Simulating suspensions of such articulated bodies requires to solve the hydrodynamic interactions between large collections of objects of arbitrary shape while satisfying the multiple constraints that connect them. Two main challenges arise in this task: limiting the cost of the hydrodynamic solves, and enforcing the constraints within machine precision at each time-step. To address these challenges we propose a formalism that combines the body mobility problem in Stokes flow with a velocity formulation of the constraints, resulting in a mixed mobility-resistance problem. While resistance problems are known to scale poorly with the particle number, our preconditioned iterative solver is not sensitive to the system size, therefore allowing to study large suspensions with quasilinear computational cost. Additionally, constraint violations, e.g. due to discrete time-integration errors, are prevented by correcting the particles' positions and orientations at the end of each time-step. Our correction procedure, based on a nonlinear minimisation algorithm, has negligible computational cost and preserves the accuracy of the time-integration scheme. The versatility of our method allows to study a plethora of articulated systems within a unified framework. We showcase its robustness and scalability by exploring the locomotion modes of a model microswimmer inspired by the diatom colony Bacillaria Paxillifer, and by simulating large suspensions of bacteria interacting near a no-slip boundary. Finally, we provide a Python implementation of our framework in a collaborative publicly available code, where the user can prescribe a set of constraints through a single input file to study a wide spectrum of applications involving suspensions of articulated bodies.“la Caixa” Foundation (ID 100010434), fellowship LCF/BQ/PI20/11760014.
The European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 847648.
The Basque Government through the BERC 2022-2025 program.
The Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718.
The French National Research Agency (ANR), under award ANR-20-CE30-0006.
The NVIDIA Academic Partnership program
COHOMOLOGY OF CONTACT LOCI
Get PDFWe construct a spectral sequence converging to the cohomology with compact support of the m-th contact locus of a complex polynomial. The first page is explicitly described in terms of a log resolution and coincides with the first page of McLean's spectral sequence converging to the Floer cohomology of the m-th iterate of the monodromy, when the polynomial has an isolated singularity. Inspired by this connection, we conjecture that if two germs of holomorphic functions are embedded topologically equivalent, then the Milnor fibers of their tangent cones are homotopy equivalent
Modeling the initial phase of COVID-19 epidemic: The role of age and disease severity in the Basque Country, Spain
Get PDFDeclared a pandemic by the World Health Organization (WHO), COVID-19 has spread rapidly around the globe. With eventually substantial global underestimation of infection, by the end of March 2022, more than 470 million cases were confirmed, counting more than 6.1 million deaths worldwide. COVID-19 symptoms range from mild (or no) symptoms to severe illness, with disease severity and death occurring according to a hierarchy of risks, with age and pre-existing health conditions enhancing risks of disease severity. In order to understand the dynamics of disease severity during the initial phase of the pandemic, we propose a modeling framework stratifying the studied population into two groups, older and younger, assuming different risks for severe disease manifestation. The deterministic and the stochastic models are parametrized using epidemiological data for the Basque Country population referring to confirmed cases, hospitalizations and deaths, from February to the end of March 2020. Using similar parameter values, both models were able to describe well the existing data. A detailed sensitivity analysis was performed to identify the key parameters influencing the transmission dynamics of COVID-19 in the population. We observed that the population younger than 60 years old of age would contribute more to the overall force of infection than the older population, as opposed to the already existing age-structured models, opening new ways to understand the effect of population age on disease
severity during the COVID-19 pandemic. With mild/asymptomatic cases significantly influencing the disease spreading and control, our findings support the vaccination strategy prioritising the most vulnerable individuals to reduce hospitalization and deaths, as well as the non-pharmaceutical intervention measures to reduce disease transmission.BERC 2022-202
A∞ condition for general bases revisited: complete classification of definitions
Get PDFWe refer to the discussion on different characterizations of the
A∞ class of weights, initiated by Duoandikoetxea, Martín-Reyes, and Ombrosi
[Math. Z. 282 (2016), pp. 955–972]. Twelve definitions of the A∞ condition are
considered. For cubes in Rd every two conditions are known to be equivalent,
while for general bases we have a trichotomy: equivalence, one-way implication,
or no dependency may occur. In most cases the relations between different
conditions have already been established. Here all the unsolved cases are
treated and, as a result, a full diagram of the said relations is presented.START Scholarship (the Foundation for Polish Science