A homogenization theorem for Langevin systems with an application to Hamiltonian dynamics

This paper studies homogenization of stochastic differential systems. The standard example of this phenomenon is the small mass limit of Hamiltonian systems. We consider this case first from the heuristic point of view, stressing the role of detailed balance and presenting the heuristics based on a multiscale expansion. This is used to propose a physical interpretation of recent results by the authors, as well as to motivate a new theorem proven here. Its main content is a sufficient condition, expressed in terms of solvability of an associated partial differential equation ("the cell problem"), under which the homogenization limit of an SDE is calculated explicitly. The general theorem is applied to a class of systems, satisfying a generalized detailed balance condition with a position-dependent temperature.Comment: 32 page

High performance computing for a 3-D optical diffraction tomographic application in fluid velocimetry

Optical Diffraction Tomography has been recently introduced in fluid velocimetry to provide three dimensional information of seeding particle locations. In general, image reconstruction methods at visible wavelengths have to account for diffraction. Linear approximation has been used for three-dimensional image reconstruction, but a non-linear and iterative reconstruction method is required when multiple scattering is not negligible. Non-linear methods require the solution of the Helmholtz equation, computationally highly demanding due to the size of the problem. The present work shows the results of a non-linear method customized for spherical particle location using GPU computing and a made-to-measure storing format

Trigonometry of 'complex Hermitian' type homogeneous symmetric spaces

This paper contains a thorough study of the trigonometry of the homogeneous symmetric spaces in the Cayley-Klein-Dickson family of spaces of 'complex Hermitian' type and rank-one. The complex Hermitian elliptic CP^N and hyperbolic CH^N spaces, their analogues with indefinite Hermitian metric and some non-compact symmetric spaces associated to SL(N+1,R) are the generic members in this family. The method encapsulates trigonometry for this whole family of spaces into a single "basic trigonometric group equation", and has 'universality' and '(self)-duality' as its distinctive traits. All previously known results on the trigonometry of CP^N and CH^N follow as particular cases of our general equations. The physical Quantum Space of States of any quantum system belongs, as the complex Hermitian space member, to this parametrised family; hence its trigonometry appears as a rather particular case of the equations we obtain.Comment: 46 pages, LaTe

Trigonometry of spacetimes: a new self-dual approach to a curvature/signature (in)dependent trigonometry

A new method to obtain trigonometry for the real spaces of constant curvature and metric of any (even degenerate) signature is presented. The method encapsulates trigonometry for all these spaces into a single basic trigonometric group equation. This brings to its logical end the idea of an absolute trigonometry, and provides equations which hold true for the nine two-dimensional spaces of constant curvature and any signature. This family of spaces includes both relativistic and non-relativistic homogeneous spacetimes; therefore a complete discussion of trigonometry in the six de Sitter, minkowskian, Newton--Hooke and galilean spacetimes follow as particular instances of the general approach. Any equation previously known for the three classical riemannian spaces also has a version for the remaining six spacetimes; in most cases these equations are new. Distinctive traits of the method are universality and self-duality: every equation is meaningful for the nine spaces at once, and displays explicitly invariance under a duality transformation relating the nine spaces. The derivation of the single basic trigonometric equation at group level, its translation to a set of equations (cosine, sine and dual cosine laws) and the natural apparition of angular and lateral excesses, area and coarea are explicitly discussed in detail. The exposition also aims to introduce the main ideas of this direct group theoretical way to trigonometry, and may well provide a path to systematically study trigonometry for any homogeneous symmetric space.Comment: 51 pages, LaTe

Carnot, Stirling, Ericsson stochastic heat engines: Efficiency at maximum power

This work obtains the efficiency at maximum power for a stochastic heat engine performing Carnot-like, Stirling-like and Ericsson-like cycles. For the mesoscopic engine a Brownian particle trapped by an optical tweezers is considered. The dynamics of this stochastic engine is described as an overdamped Langevin equation with a harmonic potential, whereas is in contact with two thermal baths at different temperatures, namely, hot ($T_h$) and cold ($T_c$). The harmonic oscillator Langevin equation is transformed into a macroscopic equation associated with the mean value $\langle x^2(t)\rangle$ using the original Langevin approach. At equilibrium stationary state this quantity satisfies a state-like equation from which the thermodynamic properties are calculated. To obtained the efficiency at maximum power it is considered the finite-time cycle processes under the framework of low dissipation approach.Comment: 2 3pages, 5 figure

Physical fitnnes, fat distribution and health in school-age children (7 to 12 years) (Condición física, distribucion grasa y salud en escolares aragoneses (7 a 12 años))

La condición física, adiposidad y distribución grasa observadas en la infancia, han mostrado tener relación con la salud cardiovascular en la edad adulta. Objetivo: evaluar el nivel de condición física en escolares de 7 a 12 años y su relación con niveles saludables de condición aeróbica y distribución grasa. Se valoraron 1068 niños y niñas aragoneses de 7-12 años de edad. Se evaluó la condición física con la batería Eurofit y el grado de adiposidad y distribución grasa mediante antropometría. Se obtienen valores normativos de condición física. Un 9,1% de los chicos y 4,8% de las chicas presenta riesgo fututo de salud sobre la base de su condición aeróbica. Mejor condición aeróbica se asocia con cantidades significativamente menores de grasa subcutánea total y en el tronco. Es importante incorporar la evaluación del nivel de condición física y distribución grasa en la valoración del riesgo de salud desde edades tempranas

Privacy-Preserving Patient Similarity Learning in a Federated Environment: Development and Analysis

Background: There is an urgent need for the development of global analytic frameworks that can perform analyses in a privacy-preserving federated environment across multiple institutions without privacy leakage. A few studies on the topic of federated medical analysis have been conducted recently with the focus on several algorithms. However, none of them have solved similar patient matching, which is useful for applications such as cohort construction for cross-institution observational studies, disease surveillance, and clinical trials recruitment. Objective: The aim of this study was to present a privacy-preserving platform in a federated setting for patient similarity learning across institutions. Without sharing patient-level information, our model can find similar patients from one hospital to another. Methods: We proposed a federated patient hashing framework and developed a novel algorithm to learn context-specific hash codes to represent patients across institutions. The similarities between patients can be efficiently computed using the resulting hash codes of corresponding patients. To avoid security attack from reverse engineering on the model, we applied homomorphic encryption to patient similarity search in a federated setting. Results: We used sequential medical events extracted from the Multiparameter Intelligent Monitoring in Intensive Care-III database to evaluate the proposed algorithm in predicting the incidence of five diseases independently. Our algorithm achieved averaged area under the curves of 0.9154 and 0.8012 with balanced and imbalanced data, respectively, in ??-nearest neighbor with ??=3. We also confirmed privacy preservation in similarity search by using homomorphic encryption. Conclusions: The proposed algorithm can help search similar patients across institutions effectively to support federated data analysis in a privacy-preserving manner

DFT molecular dynamics and free energy analysis of a charge density wave surface system

This Accepted Manuscript will be available for reuse under a CC BY-NC-ND licence after 24 months of embargo periodThe K/Si(111):B 3×3 surface, with one K atom per 3×3 unit cell, is considered a prototypical case of a surface Mott phase at room temperature. Our Density Functional Theory (DFT) Molecular Dynamics (MD) and free energy calculations show, however, a 23×3 Charge Density Wave (CDW) ground state. Our analysis shows that at room temperature the K atoms easily diffuse along the lines of a honeycomb network on the surface and that the 3×3 phase appears as the result of the dynamical fluctuations between degenerate CDW states. DFT-MD free energy calculations also show a 23×3↔3×3 transition temperature below 90 K. The competing electron-electron and electron-phonon interactions at low temperature are also analyzed; using DFT calculations, we find that the electron-phonon negative-U * is larger than the electron-electron Hubbard U, indicating that the CDW survives at very low temperatureThis work was supported by grant nos. MAT2014-59966-R and MAT2017-88258-R from the Ministerio de Economía, Industria y Competitividad (Spain