Local inverse scattering at fixed energy in spherically symmetric asymptotically hyperbolic manifolds

In this paper, we adapt the well-known \emph{local} uniqueness results of Borg-Marchenko type in the inverse problems for one dimensional Schr{\"o}dinger equation to prove \emph{local} uniqueness results in the setting of inverse \emph{metric} problems. More specifically, we consider a class of spherically symmetric manifolds having two asymptotically hyperbolic ends and study the scattering properties of massless Dirac waves evolving on such manifolds. Using the spherical symmetry of the model, the stationary scattering is encoded by a countable family of one-dimensional Dirac equations. This allows us to define the corresponding transmission coefficients $T(\lambda,n)$ and reflection coefficients $L(\lambda,n)$ and $R(\lambda,n)$ of a Dirac wave having a fixed energy $\lambda$ and angular momentum $n$. For instance, the reflection coefficients $L(\lambda,n)$ correspond to the scattering experiment in which a wave is sent from the \emph{left} end in the remote past and measured in the same left end in the future. The main result of this paper is an inverse uniqueness result local in nature. Namely, we prove that for a fixed $\lambda \not=0$, the knowledge of the reflection coefficients $L(\lambda,n)$ (resp. $R(\lambda,n)$) - up to a precise error term of the form $O(e^{-2nB})$ with B\textgreater{}0 - determines the manifold in a neighbourhood of the left (resp. right) end, the size of this neighbourhood depending on the magnitude $B$ of the error term. The crucial ingredients in the proof of this result are the Complex Angular Momentum method as well as some useful uniqueness results for Laplace transforms.Comment: 24 page

Cryptanalysis of Server-Aided RSA Protocols with Private-Key Splitting

International audienceWe analyze the security and the efficiency of interactive protocols where a client wants to delegate the computation of an RSA signature given a public key, a public message and the secret signing exponent. We consider several protocols where the secret exponent is splitted using some algebraic decomposition. We first provide an exhaustive analysis of the delegation protocols in which the client outsources a single RSA exponentiation to the server. We then revisit the security of the protocols RSA-S1 and RSA-S2 that were proposed by Matsumoto, Kato and Imai in 1988. We present an improved lattice-based attack on RSA-S1 and we propose a simple variant of this protocol that provides better efficiency for the same security level. Eventually, we present the first attacks on the protocol RSA-S2 that employs the Chinese Remainder Theorem to speed up the client's computation. The efficiency of our (heuristic) attacks has been validated experimentally

A study of stochastic 2D Minority CA : would wearing stripes be a fatality for snob people ?

Cellular automata are usually associated with synchronous deterministic dynamics, and their asynchronous or stochastic versions have been far less studied although relevant for modeling purposes. The study of their asynchronous dynamics is all the more needed that their asynchronous behaviors are drastically different from their synchronous ones. This paper analyzes the dynamics of a two-dimensional cellular automaton, 2D Minority, under fully asynchronous dynamics, where only one random cell updates at each time step. This cellular automaton is of particular interest in computer science, biology or social science for instance, and already presents a rich variety of behaviors although the apparent simplicity of its transition rule. In particular, it captures some important features, like the emergence of striped patterns, which are common, according to experiments, to other important automata, such as Game of Life. In this paper, we present a mathematical analysis of the first steps and the last steps of the asynchronous dynamics of 2D Minority. Our results are based on the definition of an interaction energy and rely on the analysis of the dynamics of the borders between competing regions. Our results are a first step towards a complete analysis of this stochastic cellular automaton. Many questions remain open: in particular describing mathematically the middle part of the evolution of 2D Minority where many regions compete with each other, or defining similar parameters (energy, borders,...) for other automata (such as Game of Life) that present similarities with 2D Minority in their asynchronous behaviors

Polyandry as a Signal of Phase Shift in Female Desert Locust Schistocerca gregaria

The multiple mating by female (polyandry) is a widespread behavior in insect species. This behavior is known to be a kind of fitness maximization, but some case of sexual selection factors can explain the evolution of this behavior in relation with the phenotype plasticity model. In this paper, we analyze the role of polyandry in the reproductive success and in the phase shift process in the gregarious desert locust. In an applied perspective, knowledge on the reproductive success and in the phase shift process is essential to perform mass rearing for human food production. Our results suggest that multiple mating is not associated with fitness benefits. Polyandry acts as a signal of phase shift through offspring. We showed that hatchlings of gregarious females mated only once are smaller and green at 87.2% in first egg pods and produced the solitary form of the desert locust. The coloration of offspring in females mated with two males reaches only 15.2% of green forms versus 84.8% of mostly blacks. In this study, we showed that females mated more than two times with different males produce larger eggs, heavier, and black hatchlings characteristic of gregarious phase known in S. gregaria

Stochastic Minority on Graphs

Cellular automata have been mainly studied on very regular graphs carrying the cells (like lines or grids) and under synchronous dynamics (all cells update simultaneously). In this paper we study how the asynchronism and the topology of cells act upon the dynamics of the classical Minority rule. Beyond its apparent simplicity, this rule yields complex behaviors which are clearly linked to the structure of the graph carrying the cells

Comparison of the photoluminescence properties of semiconductor quantum dots and non-blinking diamond nanoparticles. Observation of the diffusion of diamond nanoparticles in living cells

Long-term observations of photoluminescence at the single-molecule level were until recently very diffcult, due to the photobleaching of organic ?uorophore molecules. Although inorganic semiconductor nanocrystals can overcome this diffculty showing very low photobleaching yield, they suffer from photoblinking. A new marker has been recently introduced, relying on diamond nanoparticles containing photoluminescent color centers. In this work we compare the photoluminescence of single quantum dots (QDs) to the one of nanodiamonds containing a single-color center. Contrary to other markers, photoluminescent nanodiamonds present a perfect photostability and no photoblinking. At saturation of their excitation, nanodiamonds photoluminescence intensity is only three times smaller than the one of QDs. Moreover, the bright and stable photoluminescence of nanodiamonds allows wide field observations of single nanoparticles motion. We demonstrate the possibility of recording the tra jectory of such single particle in culture cells

Efficient caching in content-centric networks using OpenFlow

International audienceContent-Centric Networking (CCN) is designed for efficient content dissemination and supports caching contents on the path from content providers to content consumers to improve user experience and reduce costs. However, this strategy is not optimal inside a domain. In this paper, we propose a solution to improve caching in CCN using a Software-Defined Networking approach

Accurate and efficient linear scaling DFT calculations with universal applicability

Density Functional Theory calculations traditionally suffer from an inherent cubic scaling with respect to the size of the system, making big calculations extremely expensive. This cubic scaling can be avoided by the use of so-called linear scaling algorithms, which have been developed during the last few decades. In this way it becomes possible to perform ab-initio calculations for several tens of thousands of atoms or even more within a reasonable time frame. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis -- which offers ideal properties for accurate linear scaling calculations -- we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large systems with only a moderate demand of computing resources