MATLAB-Based Applications for Image Processing and Image Quality Assessment – Part I: Software Description

This paper describes several MATLAB-based applications useful for image processing and image quality assessment. The Image Processing Application helps user to easily modify images, the Image Quality Adjustment Application enables to create series of pictures with different quality. The Image Quality Assessment Application contains objective full reference quality metrics that can be used for image quality assessment. The Image Quality Evaluation Applications represent an easy way to compare subjectively the quality of distorted images with reference image. Results of these subjective tests can be processed by using the Results Processing Application. All applications provide Graphical User Interface (GUI) for the intuitive usage

Utility maximization with random horizon: a BSDE approach

International audienceIn this paper we study a utility maximization problem with random horizon and reduce it to the analysis of a specific BSDE, which we call BSDE with singular coefficients, when the support of the default time is assumed to be bounded. We prove existence and uniqueness of the solution for the equation under interest. Our results are illustrated by numerical simulations

On arbitrages arising from honest times

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.Comment: 25 pages, revised versio

Herding model and 1/f noise

We provide evidence that for some values of the parameters a simple agent based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of number of agents and show, that it has the form proposed earlier for modeling of 1/f^beta noise with different exponents beta. The non-linear terms in the transition probabilities, quantifying the herding behavior, are crucial to the appearance of 1/f noise. Thus, the herding dynamics can be seen as a microscopic explanation of the proposed non-linear stochastic differential equations generating signals with 1/f^beta spectrum. We also consider the possible feedback of macroscopic state on microscopic transition probabilities strengthening the non-linearity of equations and providing more opportunities in the modeling of processes exhibiting power-law statistics

Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function. This result is valid for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the Edwards-Wilkinson interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [ S.N. Majumdar and A. Comtet, Phys. Rev. Lett., 92, 225501 (2004)].Comment: 27 pages, 10 .eps figures included. Two figures improved, new discussion and references adde

Functionals of the Brownian motion, localization and metric graphs

We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly disordered metals (weak localization). Two aspects of the physics of the one-dimensional strong localization are reviewed : some properties of the scattering by a random potential (time delay distribution) and a study of the spectrum of a random potential on a bounded domain (the extreme value statistics of the eigenvalues). Then we mention several results concerning the diffusion on graphs, and more generally the spectral properties of the Schr\"odinger operator on graphs. The interest of spectral determinants as generating functions characterizing the diffusion on graphs is illustrated. Finally, we consider a two-dimensional model of a charged particle coupled to the random magnetic field due to magnetic vortices. We recall the connection between spectral properties of this model and winding functionals of the planar Brownian motion.Comment: Review article. 50 pages, 21 eps figures. Version 2: section 5.5 and conclusion added. Several references adde

Optimal entry to an irreversible investment plan with non convex costs

A problem of optimally purchasing electricity at a real-valued spot price (that is, allowing negative prices) has been recently addressed in De Angelis et al. (SIAM J Control Optim 53(3), 1199–1223, 2015). The problem can be considered one of irreversible investment with a cost function which is non convex with respect to the control variable. In this paper we study optimal entry into the investment plan. The optimal entry policy can have an irregular boundary, with a kinked shape

Three SRA-Domain Methylcytosine-Binding Proteins Cooperate to Maintain Global CpG Methylation and Epigenetic Silencing in Arabidopsis

Methylcytosine-binding proteins decipher the epigenetic information encoded by DNA methylation and provide a link between DNA methylation, modification of chromatin structure, and gene silencing. VARIANT IN METHYLATION 1 (VIM1) encodes an SRA (SET- and RING-associated) domain methylcytosine-binding protein in Arabidopsis thaliana, and loss of VIM1 function causes centromere DNA hypomethylation and centromeric heterochromatin decondensation in interphase. In the Arabidopsis genome, there are five VIM genes that share very high sequence similarity and encode proteins containing a PHD domain, two RING domains, and an SRA domain. To gain further insight into the function and potential redundancy among the VIM proteins, we investigated strains combining different vim mutations and transgenic vim knock-down lines that down-regulate multiple VIM family genes. The vim1 vim3 double mutant and the transgenic vim knock-down lines showed decreased DNA methylation primarily at CpG sites in genic regions, as well as repeated sequences in heterochromatic regions. In addition, transcriptional silencing was released in these plants at most heterochromatin regions examined. Interestingly, the vim1 vim3 mutant and vim knock-down lines gained ectopic CpHpH methylation in the 5S rRNA genes against a background of CpG hypomethylation. The vim1 vim2 vim3 triple mutant displayed abnormal morphological phenotypes including late flowering, which is associated with DNA hypomethylation of the 5′ region of FWA and release of FWA gene silencing. Our findings demonstrate that VIM1, VIM2, and VIM3 have overlapping functions in maintenance of global CpG methylation and epigenetic transcriptional silencing

Boolean-controlled systems via receding horizon and linear programing.

We consider dynamic systems controlled by boolean signals or decisions. We show that in a number of cases, the receding horizon formulation of the control problem can be solved via linear programing by relaxing the binary constraints on the control. The idea behind our approach is conceptually easy: a feasible control can be forced by imposing that the boolean signal is set to one at least one time over the horizon. We translate this idea into constraints on the controls and analyze the polyhedron of all feasible controls. We specialize the approach to the stabilizability of switched and impulsively controlled systems