Visual Analysis of Eudora Welty's One Time,One Place

Eudora Welty's One Time,One Place snapped Mississippi featuring Jackson,Hinds County,Yazoo County,Utica and so on.These photographs of daily life stories,most of which were taken without the awareness of the people photographed,show an aesthetic vi-sion that reveals the real life of Mississippi in the 1930 s.They also show that a fiction writer's camera records people's life and citylandscapes that are somewhat different from what we see in newspapers or geography books.The unique angles chosen and the specialmoments captured by Welty make these photographs worth a careful attention.Visual Grammar is used to examine and analyze the innerworld of the people photographed by Welty.By analyzing three photographs through action processes,reactional processes,and symbolicprocesses as well as by studying the systems of Contact and Social Distance of the photographs,representational meaning and interactivemeaning are explored.The system of information value is also studied to find out how the compositional meaning is realized in the photo-graphs.After a thorough study,the lost inner worlds of the people photographed by Welty can be exposed.

Approximating Nash Equilibrium for Optimal Consumption in Stochastic Growth Model with Jumps

In this paper,we study a class of dynamic games consisting of finite agents under a stochastic growth model with jumps.The jump process in the dynamics of the capital stock of each agent models announcements regarding each agent in the game occur at Poisson distributed random times.The aim of each agent is to maximize her objective functional with mean-field interactions by choosing an optimal consumption strategy.We prove the existence of a fixed point related to the so-called consistence condition as the number of agents goes large.Building upon the fixed point,we establish an optimal feedback consumption strategy for all agents which is in fact an approximating Nash equilibrium which describes strategies for each agent such that no agent has any incentive to change her strategy.

Spatial Localization for Nonlinear Dynamical Stochastic Models for Excitable Media

Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.