This paper introduces a new method for analyzing scaling phenomena in natural images, and draws some consequences as to whether natural images belong to the space of functions with bounded variation. In some sense, our analysis computes the size distribution of objects in an image. By using the dead leaves model, we study the innuence of occlusion on size distribution, and prove compatibility w...

We prove that each perfect Frobenius field is algebraically bounded and hence has a dimension function in the sense of v.d. Dries on the collection of all definable sets. Given a definable set S over Q (resp. Fp) we can effectively determine for each k ∈ {−∞, 0, 1, . . .} whether there exists a perfect Frobenius fieldM of characteristic 0 (resp., of characteristic p) such that the dimension of ...

The goal of this article is to show that the notion of generalized graphs is able to represent the limit points of the sequence {g(un) dun} in the weak-⋆ topology of measures when {un} is a sequence of continuous functions of uniformly bounded variation. The representation theorem induces a natural definition for the nonconservative product g(u) du in a BV context. Several existing definitions ...

the control problem and dynamic programming is a powerful tool in economics and management. we review the dynamic programming problem from its beginning up to its present stages. a problem which was involved in physics and mathematics in i 7” century led to a branch of mathematics called calculus of variation which was used in economic, and management at the end of the first quarter of the 20” ...

This paper presents a numerical method for finding the solution of Plateau’s problem in parametric form. Using the properties of minimal surfaces we succeded in transfering the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is pro...

with a well defined notion of trace at x = 0. We allow the boundary x = 0 to have the same speed of one of the characteristic speed of the limiting hyperbolic system. This result is achieved by a new decomposition of the solution into travelling profiles and the non characteristic part of boundary profile, the analysis of the interaction of travelling profiles with the boundary profile, the con...

Hierarchical predictive coding suggests that attention in humans emerges from increased precision in probabilistic inference, whereas expectation biases attention in favor of contextually anticipated stimuli. We test these notions within auditory perception by independently manipulating top-down expectation and attentional precision alongside bottom-up stimulus predictability. Our findings supp...

In this work we wish to recover an unknown image from a blurry, or noisy-blurry version. We solve this inverse problem by energy minimization and regularization. We seek a solution of the form u + v, where u is a function of bounded variation (cartoon component), while v is an oscillatory component (texture), modeled by a Sobolev function with negative degree of differentiability. We give sever...

Female choice for male ornamental traits is widely accepted as a mechanism by which females maximize their reproductive success and/or offspring quality. However, there is an increasing empirical literature that shows a fitness benefit of genetic diversity and a tendency for females to use genetic dissimilarity as a criterion for mate choice. This genetic compatibility hypothesis for female mat...

one of the most important fuel cells (fcs) is proton exchange membrane fuel cells (pemfcs). the outputvoltage of this fc depends on current loads. this paper tries to introduce, implement and control the voltage ofpemfc, during load variations. the output voltage of fuel cell should be constant during load variation. toachieve this goal, a controller should be designed. here, the lead-lag contr...