University of Marne-la-Vallée

About: University of Marne-la-Vallée is a based out in . It is known for research contribution in the topics: Estimator & Context (language use). The organization has 831 authors who have published 1855 publications receiving 55316 citations.

A code in the protein coding genes.

Abstract: A statistical analysis with 12,288 autocorrelation functions applied in protein (coding) genes of prokaryotes and eukaryotes identifies three subsets of trinucleotides in their three frames: T0 = X0 [symbol: see text] {AAA, TTT} with X0 = {AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC} in frame 0 (the reading frame established by the ATG start trinucleotide), T1 = X1 [symbol: see text] {CCC} in frame 1 and T2 = X2 [symbol: see text] {GGG} in frame 2 (the frames 1 and 2 being the frame 0 shifted by one and two nucleotides, respectively, to the right). These three subsets are identical in these two gene populations and have five important properties: (i) the property of maximal (20 trinucleotides) circular code for X0 (resp. X1, X2) allowing to retrieve automatically the frame 0 (resp. 1, 2) in any region of the gene without start codon; (ii) the DNA complementarity property C (e.g. C(AAC) = GTT): C(T0) = T0, C(T1) = T2 and C(T2) = T1 allowing the two paired reading frames of a DNA double helix simultaneously to code for amino acids; (iii) the circular permutation property P (e.g. P(AAC) = ACA): P(X0) = X1 and P(X1) = X2 implying that the two subsets X1 and X2 can be deduced from X0; (iv) the rarity property with an occurrence probability of X0 = 6 x 10(-8); and (v) the concatenation properties in favour of an evolutionary code: a high frequency (27.5%) of misplaced trinucleotides in the shifted frames, a maximum (13 nucleotides) length of the minimal window to retrieve automatically the frame and an occurrence of the four types of nucleotides in the three trinucleotide sites. In Discussion, a simulation based on an independent mixing of the trinucleotides of T0 allows to retrieve the two subsets T1 and T2. Then, the identified subsets T0, T1 and T2 replaced in the 2-letter genetic alphabet {R, Y} (R = purine = A or G, Y = pyrimidine = C or T) allow to retrieve the RNY model (N = R or Y) and to explain previous works in the alphabet {R, Y}. Then, these three subsets are related to the genetic code. The trinucleotides of T0 code for 13 amino acids: Ala, Asn, Asp, Gln, Glu, Gly, Ile, Leu, Lys, Phe, Thr, Tyr and Val. Finally, a strong correlation between the usage of the trinucleotides of T0 in protein genes and the amino acid frequencies in proteins is observed as six among seven amino acids not coded by T0, have as expected the lowest frequencies in proteins of both prokaryotes and eukaryotes.

Euclidean embeddings in spaces of finite volume ratio via random matrices

Abstract: Let (RN , ‖ · ‖) be the space RN equipped with a norm ‖ · ‖ whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N × n matrix with N > n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space (Rn, | · |) onto its image in (RN , ‖ · ‖), i. e. there exist α, β > 0 such that for all x ∈ Rn, α √ N |x| ≤ ‖Γx‖ ≤ β √ N |x|. This solves a conjecture of Schechtman on random embeddings of `2 into ` N 1 .

A study on the performance of natural neighbour-based Galerkin methods

Abstract: In this paper we address the problem of improving natural element simulations in terms of computational cost. Several problems are discussed, that include an efficient natural neighbour search algorithm and a comparison of different natural neighbour-based interpolation algorithms. In particular, we review the so-called pseudo-NEM, a moving least squares-like approximation scheme that employs natural neighbours, and compare it with traditional Sibson and Laplace interpolation schemes in terms of both accuracy and computational cost. Some examples in linear Elasticity and visco-plasticity are analysed in order to test the proposed schemes in engineering problems.

Dynamics and disintegration of drops of polymeric liquids

Abstract: The deformation and the disintegration of drops of polymer solution upon impact with solid obstacles are investigated both experimentally and theoretically. High molecular polyethylene oxide (PEO) and polyacrylamide (PAM) solutions at concentrations 1–10,000 ppm, as well as pure water and glycerine, are used as tested liquids. A feature of this work is the use of a non-standard hydrodynamic situation, namely the collision of a spherical drop with a small disk-like solid target. In the experiments, a drop of 3 mm diameter collides with a 4 mm disk target with velocity of 3.4 m/s. If water is used, upon impact the drop is transformed into a liquid lamella (i.e. a circular film with a rather thick toroidal rim). The lamella increases in diameter and then it retracts with ejection from the rim of a set of radially directed secondary jets that, in turn, break up into secondary droplets. Typically polymeric additives do not influence much the growth and the retraction rate, but they drastically modify the disintegration process. Depending on the polymer nature and its concentration, four regimes of drop impact are observed: (i) the secondary jets are transformed into capillary thinning filaments partially retarding the detachment of secondary drops, (ii) the elastic stresses in the thinning filaments force all secondary droplets to move back to the target suppressing splashing, (iii) no rim instabilities are developed and lamella with smooth rim is formed and (iv) no lamella formation. Criteria of transition from one to another regime of drop impact are proposed.