An Optimal Complexity Algorithm for Computing Topological Degree in Two Dimensions

An algorithm is presented to compute the topological degree for any function from a class F. The class F consists of functions defined on a two dimensional unit square C, f, C → ℝ², which satisfy Lipschitz condition with constant K > 0, and whose infinity norm on the boundary of C is at least d > 0. A worst case lower bound, m* = 4[K/4d], is established on the number of function evaluations necessary to compute the topological degree for any function f from the class F. The parallel information used by our algorithm permits the computation of the degree for every f in F with m* function evaluations necessary. The cost of our algorithm is shown to be almost equal to the complexity of the problem

Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN

The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude

Quasi-Monte Carlo, Monte Carlo, and regularized gradient optimization methods for source characterization of atmospheric releases

An inversion technique based on MC/QMC search and regularized gradient optimization was developed to solve the atmospheric source characterization problem. The Gaussian Plume Model was adopted as the forward operator and QMC/MC search was implemented in order to find good starting points for the gradient optimization. This approach was validated on the Copenhagen Tracer Experiments. The QMC approach with the utilization of clasical and scrambled Halton, Hammersley and Sobol points was shown to be 10-100 times more efficient than the Mersenne Twister Monte Carlo generator. Further experiments are needed for different data sets. Computational complexity analysis needs to be carried out

Fluorescence spectroscopy for characterization and differentiation of beers

Total luminescence and synchronous scanning fluorescence spectroscopic techniques were applied for characterization of the intrinsic fluorescence of eight different beers. Spectra were measured using different geometries to reveal the presence of similar fluorescent components. The total luminescence and synchronous fluorescence spectra exhibit a relatively intense short-wavelength emission ascribed to aromatic amino acids and less intense emission in the long-wavelength region, which may originate from B vitamins. Classification of beers based on their synchronous fluorescence spectra was performed using non-parametrical k nearest neighbours method and linear discriminant analysis. Very good discrimination was obtained in both methods with a low classification error. The results demonstrate the potential of fluorescence techniques to characterize and differentiate beers

Construcción social de la sexualidad en hombres y mujeres, adultos jóvenes, que sostienen una relación de pareja heterosexual, en el Área Metropolitana de Guadalajara

En esta investigación se buscó analizar la construcción social sobre la sexualidad en hombres y mujeres, adultos jóvenes, que sostienen una relación de pareja heterosexual en el Área Metropolitana de Guadalajara (AMG). La población, hombres y mujeres están en un rango de edad de 35-45 años, más-menos 3 años y los mismos forman parte de un estrato socioeconómico medio. En este estudio se trabajó con una metodología cualitativa y específicamente con el método biográfico. Se utilizaron relatos biográficos como recurso principal para la obtención de información sobre las experiencias y significados de los participantes. En dicha investigación se buscó conocer e identificar los elementos que constituyen la construcción social que ha sido instalada a manera de imposición sobre la sexualidad en las parejas heterosexuales y cómo es que se han vivido los participantes en el ejercicio de su sexualidad. En el estudio se ahondó profundamente en recabar información respecto a la forma en que se ha ejercido la sexualidad en pareja de acuerdo con las demandas impuestas socioculturalmente. En los resultados se logra aportar a través del marco teórico del estudio, construcción social, propuesto por Berger & Luckmann, sobre las transformaciones y resistencias que viven hombres y mujeres, en el ejercicio de su sexualidad y la influencia de los mandatos socioculturales de género sobre estas prácticas sexuales. Así mismo, se analizan la conflictividad en las parejas en este campo y que ha producido distanciamientos importantes, rupturas, periodos prolongados de ansiedad, malestares físicos y psicosomáticos, estancamiento en la relación. Por último, se encontró que la sexualidad de los participantes ha sido experimentada con angustia, estrés, culpa, ataques de ansiedad o incluso llegó a desarrollar algún tipo de trastorno de deseo sexual inhibido. Con ello se argumenta que, por medio de la psicoterapia, sean abordadas todas las inquietudes que vayan surgiendo y/o enfrentándose en la vida en parejaITESO, A. C

Can We Approximate Zeros of Functions with Non-zero Topological Degree?

The bisection method provides an affirmative answer for scalar functions. We show that the answer is negative for bivariate functions. This means, in particular, that an arbitrary continuation method cannot approximate a zero of every smooth bivariate function with non-zero topological degree

Oscillation modes of two-dimensional nanostructures within the time-dependent local-spin-density approximation

We apply the time-dependent local-spin-density approximation as general theory to describe ground states and spin-density oscillations in the linear response regime of two-dimensional nanostructures of arbitrary shape. For this purpose, a frequency analysis of the simulated real-time evolution is performed. The effect on the response of the recently proposed spin-density waves in the ground state of certain parabolic quantum dots is considered. They lead to the prediction of a new class of excitations, soft spin-twist modes, with energies well below that of the spin dipole oscillation.Comment: 4 RevTex pages and 4 GIF figures, accepted in PR