2063 research outputs found
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An inverse problem for data-driven prediction in quantum mechanics
No full textData-driven prediction in quantum mechanics consists in providing an approximative description of the motion of any particles at any given time, from data that have been previously collected for a certain number of particles under the influence of the same Hamiltonian. The difficulty of this problem comes from the ignorance of the exact Hamiltonian ruling the dynamic. In order to address this problem, we formulate an inverse problem consisting in determining the Hamiltonian of a quantum system from the knowledge of the state at some fixed finite time for each initial state. We focus on the simplest case where the Hamiltonian is given by −Δ+V, where the potential V=V(t,x) is non-compactly supported. Our main result is a uniqueness theorem, which establishes that the Hamiltonian ruling the dynamic of all quantum particles is determined by the prescription of the initial and final states of each particle. As a consequence, one expects to be able to know the state of any particle at any given time, without an a priori knowledge of the Hamiltonian just from the data consisting of the initial and final state of each particle
THE HYDROSTATIC LIMIT OF THE BERIS-EDWARDS SYSTEM IN DIMENSION TWO
No full textWe study the scaled anisotropic co-rotational Beris-Edwards system modeling the hydro-
dynamic motion of nematic liquid crystals in dimension two. We prove the global well-posedness with
small analytic data in a thin strip domain. Moreover, we justify the limit to a system involving the
hydrostatic Navier-Stokes system with analytic data and prove the convergence
On the utilization of pair-potential energy functions in multi-objective optimization
Get PDFIn evolutionary multi-objective optimization (EMO), the pair-potential energy functions (PPFs) have been used to construct diversity-preserving mechanisms to improve Pareto front approximations. Despite PPFs have shown promising results when dealing with different Pareto front geometries, there are still some open research questions to improve the way we employ them. In this paper, we answer three important questions: (1) what is the effect of a crucial parameter of some PPFs?, (2) how do we set the optimal parameter value?, and (3) what is the best PPF in EMO? To solve these questions, we designed a brand-new fast algorithm to generate an approximate solution to a PPF-based subset selection problem and, then, we conducted a comprehensive parametrical study to predict the optimal parameter values using a deep neural network. To show the effectiveness of the PPF-based diversity-preserving mechanisms, we selected two application cases: the generation of reference point sets of benchmark problems (DTLZ, WFG, IDTLZ, IWFG, IMOP, and Viennet) with different Pareto front shapes, and the definition of a PPF-based archive that can be coupled to any multi-objective evolutionary algorithm to construct well-diversified Pareto front approximations. Using several diversity indicators, it is shown that the utilization of PPF-based mechanisms lead to good Pareto front approximations regardless of the Pareto front shape
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
Get PDFIn this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations.
We employ some techniques from the blow-up study of nonlinear wave equations. The novelty consists in the introduction of tools from the Orlicz spaces theory to handle the nonlinear term emerging from the pressure , which admits different asymptotic behavior for large and small values of , being the density.
Hence we can establish, in dimensions , unified upper bounds of the lifespan estimate depending only on the dimension and on the damping strength, and independent of the adiabatic index . We conjecture our results to be optimal.
The method employed here not only improves the known upper bounds of the lifespan for , but has potential application in the study of related problems.FJC2021-046835-I;
JSPS Fellowshi
A High-Quality Genome-Scale Model for Rhodococcus opacus Metabolism
Get PDFRhodococcus opacus is a bacterium that has a high tolerance to aromatic compounds and can produce significant amounts of triacylglycerol (TAG). Here, we present iGR1773, the first genome-scale model (GSM) of R. opacus PD630 metabolism based on its genomic sequence and associated data. The model includes 1773 genes, 3025 reactions, and 1956 metabolites, was developed in a reproducible manner using CarveMe, and was evaluated through Metabolic Model tests (MEMOTE). We combine the model with two Constraint-Based Reconstruction and Analysis (COBRA) methods that use transcriptomics data to predict growth rates and fluxes: E-Flux2 and SPOT (Simplified Pearson Correlation with Transcriptomic data). Growth rates are best predicted by E-Flux2. Flux profiles are more accurately predicted by E-Flux2 than flux balance analysis (FBA) and parsimonious FBA (pFBA), when compared to 44 central carbon fluxes measured by 13C-Metabolic Flux Analysis (13C-MFA). Under glucose-fed conditions, E-Flux2 presents an R2 value of 0.54, while predictions based on pFBA had an inferior R2 of 0.28. We attribute this improved performance to the extra activity information provided by the transcriptomics data. For phenol-fed metabolism, in which the substrate first enters the TCA cycle, E-Flux2’s flux predictions display a high R2 of 0.96 while pFBA showed an R2 of 0.93. We also show that glucose metabolism and phenol metabolism function with similar relative ATP maintenance costs. These findings demonstrate that iGR1773 can help the metabolic engineering community predict aromatic substrate utilization patterns and perform computational strain design
Cost-effectiveness analysis of vaccines for COVID-19 according to sex, comorbidity and socioeconomics status: a population study
Get PDFBackground and Objective
Coronavirus disease 2019 (COVID-19) vaccines are extremely effective in preventing severe disease, but their real-world cost-effectiveness is still an open question. We present an analysis of the cost-effectiveness and economic impact of the initial phase of the COVID-19 vaccination rollout in the Basque Country, Spain.
Methods
To calculate costs and quality-adjusted life years for the entire population of the Basque Country, dynamic modelling and a real-world data analysis were combined. Data on COVID-19 infection outcomes (cases, hospitalisations, intensive care unit admissions and deaths) and population characteristics (age, sex, socioeconomic status and comorbidity) during the initial phase of the vaccination rollout, from January to June of 2021, were retrieved from the Basque Health Service database. The outcomes in the alternative scenario (without vaccination) were estimated with the dynamic model used to guide public health authority policies, from February to December 2020. Individual comorbidity-adjusted life expectancy and costs were estimated.
Results
By averting severe disease-related outcomes, COVID-19 vaccination resulted in monetary savings of €26.44 million for the first semester of 2021. The incremental cost-effectiveness ratio was €707/quality-adjusted life year considering official vaccine prices and dominant real prices. While the analysis by comorbidity showed that vaccines were considerably more cost effective in individuals with pre-existing health conditions, this benefit was lower in the low socioeconomic status group.
Conclusions
The incremental cost-effectiveness ratio of the vaccination programme justified the policy of prioritising high-comorbidity patients. The initial phase of COVID-19 vaccination was dominant from the perspective of the healthcare payer
A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks
Get PDFResidual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min–max) problem over the so-called trial and test spaces. In the context of neural networks, we can address this min–max approach by employing one network to seek the trial minimum, while another network seeks the test maximizers. However, the resulting method is numerically unstable as we approach the trial solution. To overcome this, we reformulate the residual minimization as an equivalent minimization of a Ritz functional fed by optimal test functions computed from another Ritz functional minimization. We call the resulting scheme the Deep Double Ritz Method (DRM), which combines two neural networks for approximating trial functions and optimal test functions along a nested double Ritz minimization strategy. Numerical results on different diffusion and convection problems support the robustness of our method, up to the approximation properties of the networks and the training capacity of the optimizers
Swimming Efficiently by Wrapping
No full textSingle flagellated bacteria are ubiquitous in nature. They exhibit various swimming
modes using their flagella to explore complex surroundings such as soil and porous
polymer networks. Some single-flagellated bacteria swim with two distinct modes, one
with its flagellum extended away from its body and another with its flagellum wrapped
around it. The wrapped mode has been observed when the bacteria swim under tight
confinements or in highly viscous polymeric melts. In this study we investigate the
hydrodynamics of these two modes inside a circular pipe. We find that the wrap mode is
slower than the extended mode in bulk but more efficient under strong confinement due
to a hydrodynamic increased of its flagellum translation-rotation coupling
ON THE WEIGHTED INEQUALITY BETWEEN THE GAGLIARDO AND SOBOLEV SEMINORMS
Get PDFWe prove weighted inequalities between the Gagliardo and Sobolev seminorms. With A1 weights we improve earlier results of Bourgain, Brezis, and Mironescu
Implicit Functionally Graded Conforming Microstructures
Get PDFThe tensor product parametric representations are the most commonly used representation in geometric modeling. Yet,
other representations have advantages in certain aspects, and in this work, we focus on employing implicit representations
in the construction of microstructures. An implicit function, either functionally precise, or spline trivariate-based, is
used to populate a macro-shape trivariate parametric form, and construct a conforming microstructure. Either the
implicit tile or the macro-shape can be functionally graded or be heterogeneous, carrying graded properties such as
material, translucency, or color alongside the geometry. Further, the implicit tiles can be parametrized and hence their
geometry can vary across the macro-shape. The representation is locally precise and we demonstrate that in a slicing
process that employs no (piecewise-linear) approximation. Finally, we demonstrate this framework on several 3D printed
heterogeneous models