Identification of protein coding genes in genomes with statistical functions based on the circular code

A new statistical approach using functions based on the circular code classifies correctly more than 93 % of bases in protein (coding) genes and non-coding genes of human sequences. Based on this statistical study, a research software called "Analysis of Coding Genes" (ACG) has been developed for identifying protein genes in the genomes and for determining their frame. Furthermore, the software ACG also allows an evaluation of the length of protein genes, their position in the genome, their relative position between themselves, and the prediction of internal frames in protein genes

Rooted maps on orientable surfaces, Riccati's equation and continued fractions

International audienceWe present a new approach in the study of rooted maps without regard to genus. We prove the existence of a new type of equation for the generating series of these maps enumerated with respect to edges and vertices. This is Riccati's equation. It seems to be the first time that such a differential equation appears in the enumeration of rooted maps. Solving this equation leads to different closed forms of the studied generating series. The most interesting consequence is a development of this generating function in a very nice continued fraction leading to a new equation generalizing the well-known Dyck equation for rooted planar trees. In a second part, we also obtain a differential equation for the generating series of rooted trees regardless of the genus, with respect to edges. This also leads to a continued fraction for the generating series of rooted genus independent trees and to an unexpected relation between both previous generating series of trees and rooted maps

Real Time Rendering of Atmospheric Scattering and Volumetric Shadows

International audienceReal time rendering of atmospheric light scattering is one of the most difficult lighting effect to achieve in computer graphics. This paper presents a new real time method which renders these effects including volumetric shadows, which provides a great performance improvement over previous methods. Using an analytical expression of the light transport equation we are able to render directly the contribution of the participating medium on any surface. The rendering of shadow planes, sorted with a spatial coherence technique, and in the same philosophy than the shadow volume algorithm will add the volumetric shadows. Realistic images can be produced in real time for usual graphic scenes and at a high level framerate for complex scenes, allowing animation of lights, objects or even participating media. The method proposed in this paper use neither precomputation depending on light positions, nor texture memory

A New Mathematical Development for Radiosity Animation with Galerkin

International audienceCombining animation and global illumination constitutes, at present, a true challenge in computer graphics, especially when light sources move in a complex scene because the entire illumination has to be recomputed. This paper introduces a new algorithm, based on the Galerkin method, which can efficiently manage any moving surface -even light source- to compute animation sequences. For each new frame of a sequence, we take into account the continuous property of the moves to determine the necessary energy differences between the previous global illumination solution and the new one. Based on a mathematical development of the form factor, this new approach leads to an efficient and simple algorithm, similar to the classical progressive refinement algorithm, and which computes animated sequence about three times faster

Analysis of Gene Evolution: the software AGE

The software AGE (Analysis of Gene Evolution) has been developed both to study a genetic reality, i. e. the identification of statistical properties in genes (e.g. periodicities), and to simulate this observed genetic reality, by models of molecular evolution. AGE has two types of models: (i) models of sequence creation from oligonucleotides: concatenation model in series of an oligonucleotide, independent (or Markov) mixing model of oligonucleotides according to given probabilities (or a Markov matrix); (ii) models of sequence evolution from created sequences: insertion/deletion process of (mono, di, tri)nucleot-ides, base mutation process. The study of a reality and the development of simulation models are based on several new algorithms: approximated simulation and exact calculus to compute various autocorrelation functions, Fourier transformation of autocorrelation curves, recognition of a curve form, etc. AGE is implemented on IBM or compatible microcomputers and can be used by biologists without any computer knowledge to identify statistical properties in their newly determined DNA sequence and to explain them by models of molecular evolutio

n-colored maps and multilabel n-colored trees

New topological operations are introduced in order to recover in another way the generalized Dyck equation for the generating function of n-colored maps presented in a former paper, by decomposing maps topologically and bijectively. Applying repeatedly the operations which allowed to reveal the generalized Dyck equation to the successive transformed maps, a one-to-one correspondence is obtained between n-colored maps on any surface and n-colored trees whose vertices can be labelled with several labels. This bijection provides us with a coding of these maps

Pentagon partitions of polygons and a special class of planar maps

A geometrical one-to-one correspondence is given between partitions of a rooted polygon into pentagons and a family of rooted planar maps, called planar maps of order one (each edge having at least one extremity incident to the exterior face), with a bridge root edge

Generalized Dyck equations and multilabel trees

New topological operations are introduced in order to recover in another way the generalized Dyck equations presented by D. Arquès and al. for the generating functions of maps and colored maps, by decomposing maps topologically and bijectively. Applying repeatedly the operations which made it possible to reveal the generalized Dyck equations for the successive transformed maps, one-to-one correspondences are obtained between maps (colored or not) of indeterminate genus and trees (colored or not) whose vertices can be labelled with several labels, following rules that we will define. These bijections provide us with a coding of these maps

Improving the zonal method through the use of series developments to approximate volume/volume form factors

This paper introduces a new acceleration technique for the zonal method. We present mathematical developments which improve, in a considerable way, the time due to the form factor calculus. More precisely, we show that, under the assumption of classical modeling conditions, we can: - simplify the mathematical expression of the volume/volume form factor, - approximate this simplification by a series development of orthogonal polynomials with a complete error control. Analog results can be obtained for the other types of form factors