Real-time tomographic reconstructor based on convolutional neural networks for solar observation

Solar observation is the branch of astronomy devoted to the study of the Sun. When the light wavefront that comes from the Sun penetrates the atmosphere, it suffers some distortions caused by optically turbulent layers that change the wavefront's shape and morphology. Therefore, in order to obtain a good-quality image, it is necessary to correct the induced error. This is done by applying adaptive optics (AO) techniques. In the case of the present research, it is performed with the help of a Single Conjugate Adaptive Optics System (SCAO). The reconstruction technique proposed in this research is a SCAO based on convolutional neural networks (CNNs). This research develops and assesses a real-time tomographic reconstructor based on CNN, able to correct the error introduced by the atmosphere in the light wavefront received from the Sun. The CNN was trained and validated using data from the Durham AO Simulation Platform as input information. This platform incorporates certain solar functionalities that have been employed in the present research, allowing us to simulate a solar telescope. The normalized errors obtained for both ReLu and Leaky ReLu kernels were promising, without showing statistically significant differences among kernels in the value of RMSE volts of the deformable mirror commands. When different kernel dimensions are compared, statistically significant differences are found, showing that RMSE volts of the deformable mirror commands are lower for 3 × 3 kernels when compared with those of dimensions 5 × 5 and 7 × 7. As far as the authors know, this is the first time that an AO system based on CNN has been developed for solar telescopes.     

Using Zernike moments for analysis of images

A method for analyzing AFM images of the cell nuclei of higher organisms by expanding these images by Zernike moments is proposed. This method allows for expanding the pilot image by Zernike moments whose spatial harmonics are Zernike polynomials. It is shown that the reverse procedure of image reconstruction using Zernike polynomials converges to the experimental image and the expansion amplitude is a quantitative spectral characteristic in comparing the morphological features of different images. It is shown that expansion amplitudes can be used as input vectors for cluster analysis of images by PCA.     

Existence for dynamic contact of a stochastic viscoelastic Gao Beam

This work presents and analyzes a model for the vibrations of a viscoelastic Gao Beam, which may come in contact with a deformable random foundation and allows for stochastic inputs. The body force involves a stochastic integral that includes Brownian motion. In addition, the gap between the beam and the foundation is a stochastic process, which is one of the novelties in the paper, and contact is described with the normal compliance condition. The existence and uniqueness of strong solutions to the model is established and it is shown that the solutions are adapted to the filtration determined by a given Wiener process for the stochastic force noise term.     

基于双指数跳扩散过程的公司债券定价

研究基于公司资产价值服从双指敷跳扩散过程,公司负债服从连续扩散过程的公司债券定价问题.首先用计价单位方法给出简单情况下以零息票债券为基础的公司债券定价问题的解析解;其次给出一般情况下公司债券定价问题的违约概率,并讨论信用价差的期限结构.实证分析表明该模型能较好地拟合实际情况.     

Stochastic mirror descent method for distributed multi-agent optimization

This paper considers a distributed optimization problem encountered in a time-varying multi-agent network, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on the mirror descent method, we develop a distributed algorithm by utilizing the subgradient information with stochastic errors. We firstly analyze the effects of stochastic errors on the convergence of the algorithm and then provide an explicit bound on the convergence rate as a function of the error bound and number of iterations. Our results show that the algorithm asymptotically converges to the optimal value of the problem within an error level, when there are stochastic errors in the subgradient evaluations. The proposed algorithm can be viewed as a generalization of the distributed subgradient projection methods since it utilizes more general Bregman divergence instead of the Euclidean squared distance. Finally, some simulation results on a regularized hinge regression problem are presented to illustrate the effectiveness of the algorithm.     

Minimal surfaces: a geometric three dimensional segmentation approach

Summary. A novel geometric approach for three dimensional object segmentation is presented. The scheme is based on geometric deformable surfaces moving towards the objects to be detected. We show that this model is related to the computation of surfaces of minimal area (local minimal surfaces). The space where these surfaces are computed is induced from the three dimensional image in which the objects are to be detected. The general approach also shows the relation between classical deformable surfaces obtained via energy minimization and geometric ones derived from curvature flows in the surface evolution framework. The scheme is stable, robust, and automatically handles changes in the surface topology during the deformation. Results related to existence, uniqueness, stability, and correctness of the solution to this geometric deformable model are presented as well. Based on an efficient numerical algorithm for surface evolution, we present a number of examples of object detection in real and synthetic images. Received January 4, 1996 / Revised version received August 2, 1996     

Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows

Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration’s “Global Drifter Program”, this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from Holm (Proc R Soc A 471:20140963, 2015) is reviewed, in which the spatial correlations are time independent. Two new models, called Model 2 and Model 3, introduce two different symmetry breaking mechanisms by which the spatial correlations may be advected by the flow. These models are derived using reduction by symmetry of stochastic variational principles, leading to stochastic Hamiltonian systems, whose momentum maps, conservation laws and Lie–Poisson bracket structures are used in developing the new stochastic Hamiltonian models of GFD.     

On Tries, Contention Trees and Their Analysis

In this paper a survey on tries, a contention resolution algorithm, their similarities, dissimilarities, and their mathematical treatment, will be given. It has already been mentioned in some papers that tries and contention trees follow one common stochastic model, but still they are frequently treated as separate objects in the literature. Hence the aim of the current work is to contribute to the unification of the various results in that area and to exhibit the employed methods, which involve, among others, analytic poissonization/depoissonization and the Mellin transform. For the sake of the example, a new parameter in contention trees, the number of terminal frames, will be studied.      

Analysis of survivorship life insurance portfolios with stochastic rates of return

A general portfolio of survivorship life insurance contracts is studied in a stochastic rate of return environment with a dependent mortality model. Two methods are used to derive the first two moments of the prospective loss random variable. The first one is based on the individual loss random variables while the second one studies annual stochastic cash flows. The distribution function of the present value of future losses at a given valuation time is derived. For illustrative purposes, an AR(1) process is used to model the stochastic rates of return, and the future lifetimes of a couple are assumed to follow a copula model. The effects of the mortality dependence, the portfolio size and the policy type, as well as the impact of investment strategies on the riskiness of portfolios of survivorship life insurance policies are analyzed by means of moments and probability distributions.     

Algorithms for a Facility Location Problem with Stochastic Customer Demand and Immobile Servers

This paper studies a facility location problem with stochastic customer demand and immobile servers. Motivated by applications to locating bank automated teller machines (ATMs) or Internet mirror sites, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. Customers are assumed to visit the closest open facility. The objective of this problem is to minimize customers' total traveling cost and waiting cost. In addition, there is a restriction on the number of facilities that may be opened and an upper bound on the allowable expected waiting time at a facility. Three heuristic algorithms are developed, including a greedy-dropping procedure, a tabu search approach and an -optimal branch-and-bound method. These methods are compared computationally on a bank location data set from Amherst, New York.     

Numerical investigation of nanoindentation of viscoelastic polymer layers and parameters re-identification

In the present contribution, we focus on the numerical investigation of nanoindentation of viscoelastic polymer layers using the finite element code ABAQUS®. The time-dependent behaviour of the viscoelastic layer is modeled with Boltzman hereditary integration based on Prony series. The normal contact between the rigid indenter and the deformable layer are treated numerically as a unilateral non-penetration constraint problem. The computer-based numerical optimisation routine is treated by employing the Matrix Laboratory MATLAB® combined with ABAQUS®. The stochastic strategy is used based on principles of biological evolution, i. e. an evolution strategy. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

平面不可压缩的Navier-Stokes方程的一个新七模截断(英文)

A new seven-modes truncation of Fourier series of Navier-Stokes equations for a two-dimensional incompressible fluid on a torus is obtained.And its stationary solutions,the existence of attractor and the global stability of the equations are firmly proved.At the same time,several issues such as some basic dynamical behaviors and routs to chaos are shown numerically by changing Reynolds number.The system exhibits a stochastic behavior approached through an involved sequence of bifurcations.     

Stabilization of a platform under wind loads

The Steward platform is employed in dynamic simulation of a number of controlled mechanical systems, in control of the active surface of a telescope mirror, and other constructions. Position and orientation of this platform is regulated by changing the lengths of its supporting bars, and corresponding change of their angles relative to the base. Viable motions of the platform depend on how the bars are hinged to the base and to the platform. This paper studies dynamics and stabilization of a platform leaning on three bars of controlled length under wind loads. This problem is of interest for design of active mirror surfaces of radio telescopes. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 97–115, 2005.     

INVESTIGATING TAX DISTORTIONS: AN APPLIED MODEL OF PETROLEUM EXPLORATION AND EXTRACTION DECISIONS

Abstract A numerical model is proposed for the testing of distortions caused by petroleum fiscal systems on the exploration and extraction activities of a profit‐maximizing firm. Traditional models have not been capable of testing for the distortions caused by the complex tax structures most often used by governments. Two tax combinations, as well as certain other taxes, are analyzed for distortions in the model. The model is parameterized using generic data because specific jurisdictions are not considered. The distortions due to rentals and royalties are as expected by theory. Property taxes show a new distortion result where production tilting is ambiguous.     

Numerical solution of stochastic differential equations with random structure on supercomputers

In this paper, the accuracy of estimating the expectation of solutions to stochastic differential equations with random structure is investigated. This accuracy is shown as a function of the integration step in the generalized Euler method and the number of simulated trajectories. A drastic decrease in the accuracy at deterministic or random times of changing the SDE structure is shown by a simple equation as an example. This could be improved by the use of supercomputers for statistical modeling. The results of some numerical experiments carried out at the Siberian Supercomputer Center are presented.     

Kinetic Monte Carlo models for the study of chemical reactions in the Earth’s upper atmosphere

A stochastic approach to study the non-equilibrium chemistry in the Earth’s upper atmosphere is presented, which has been developed over a number of years. Kinetic Monte Carlo models based on this approach are an effective tool for investigating the role of suprathermal particles both in local variations of the atmospheric chemical composition and in the formation of the hot planetary corona.     

The efficient solution of the (quietly constrained) noisy, linear regulator problem

In a previous paper we gave a new, natural extension of the calculus of variations/optimal control theory to a (strong) stochastic setting. We now extend the theory of this most fundamental chapter of optimal control in several directions. Most importantly we present a new method of stochastic control, adding Brownian motion which makes the problem “noisy.” Secondly, we show how to obtain efficient solutions: direct stochastic integration for simpler problems and/or efficient and accurate numerical methods with a global a priori error of O(h3/2) for more complex problems. Finally, we include “quiet” constraints, i.e. deterministic relationships between the state and control variables. Our theory and results can be immediately restricted to the non “noisy” (deterministic) case yielding efficient, numerical solution techniques and an a priori error of O(h²). In this event we obtain the most efficient method of solving the (constrained) classical Linear Regulator Problem. Our methods are different from the standard theory of stochastic control. In some cases the solutions coincide or at least are closely related. However, our methods have many advantages including those mentioned above. In addition, our methods more directly follow the motivation and theory of classical (deterministic) optimization which is perhaps the most important area of physical and engineering science. Our results follow from related ideas in the deterministic theory. Thus, our approximation methods follow by guessing at an algorithm, but the proof of global convergence uses stochastic techniques because our trajectories are not differentiable. Along these lines, a general drift term in the trajectory equation is properly viewed as an added constraint and extends ideas given in the deterministic case by the first author.     

Grain rotations and distortions in the asymptotic variance of vacancy of the Boolean model

We consider the asymptotic variance of vacancy (AVV) in the high intensity small-grain Boolean model. Subjecting the grains to rotations or, more generally, linear distortions gives rise to a function which maps distortion distributions to the AVV of the corresponding Boolean model. We mainly study continuity properties of this function, where we use the L¹ Wasserstein metric on distortion distributions. An important role in the formulation and derivation of our results is played by notions of symmetry commonly used in multivariate analysis and stochastic simulation, such as conjugation-invariance and group models.     

Switching diffusion logistic models involving singularly perturbed Markov chains: Weak convergence and stochastic permanence

Focusing on stochastic dynamics involve continuous states as well as discrete events, this article investigates stochastic logistic model with regime switching modulated by a singular Markov chain involving a small parameter. This Markov chain undergoes weak and strong interactions, where the small parameter is used to reflect rapid rate of regime switching among each state class. Two-time-scale formulation is used to reduce the complexity. We obtain weak convergence of the underlying system so that the limit has much simpler structure. Then we utilize the structure of limit system as a bridge, to invest stochastic permanence of original system driving by a singular Markov chain with a large number of states. Sufficient conditions for stochastic permanence are obtained. A couple of examples and numerical simulations are given to illustrate our results.     

On some measures and distances for positive random variables

A number of conventional measures of risk as real‐valued functions on the space of positive random variables are considered: the expected shortfall, the mean excess over the threshold, the stop‐loss and some others. Ordering of risks, based on these measures and the distances between corresponding distribution functions, are described. The perturbed measures, describing the effect of changing environment, are discussed. These measures are defined by the accelerated life and proportional hazards models widely used in reliability and survival analysis. The case of a random environment is of a prime interest in the paper. The main result states that if, for instance, the stochastic environment is ‘neutral in expectation’ with respect to the baseline one, the distance between the corresponding distribution functions can be still sufficiently large. Copyright © 2003 John Wiley & Sons, Ltd.