Critical percolation on random regular graphs

The behavior of the random graph G(n,p) around the critical probability p_c = is well understood. When p = (1 + O(n^1/3))p_c the components are roughly of size n^2/3 and converge, when scaled by n^?2/3, to excursion lengths of a Brownian motion with parabolic drift. In particular, in this regime, they are not concentrated. When p = (1 ‐ ?(n))p_c with ?(n)n^1/3 →∞ (the subcritical regime) the largest component is concentrated around 2?^?2 log(?³n). When p = (1 + ?(n))p_c with ?(n)n^1/3 →∞ (the supercritical regime), the largest component is concentrated around 2?n and a duality principle holds: other component sizes are distributed as in the subcritical regime. Itai Benjamini asked whether the same phenomenon occurs in a random d‐regular graph. Some results in this direction were obtained by (Pittel, Ann probab 36 (2008) 1359–1389). In this work, we give a complete affirmative answer, showing that the same limiting behavior (with suitable d dependent factors in the non‐critical regimes) extends to random d‐regular graphs. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Weighted matching with pair restrictions

The weighted matroid parity problems for the matching matroid and gammoids are among the very few cases for which the weighted matroid parity problem is polynomial time solvable. In this work we extend these problems to a general revenue function for each pair, and show that the resulting problem is still solvable in polynomial time via a standard weighted matching algorithm. We show that in many other directions, extending our results further is impossible (unless P = NP). One consequence of the new polynomial time algorithm is that it demonstrates, for the first time, that a prize-collecting assignment problem with “pair restriction” is solved in polynomial time. The prize collecting assignment problem is a relaxation of the prize-collecting traveling salesman problem which requires, for any prescribed pair of nodes, either both nodes of the pair are matched or none of them are. It is shown that the prize collecting assignment problem is equivalent to the prize collecting cycle cover problem which is hence solvable in polynomial time as well.     

A rapid method for the determination of radiostrontium in river water

A rapid analytical method, applicable for the selective separation and determination of⁹⁰Sr and⁸⁹Sr in river water, is described. Strontium is extracted from the water sample at pH 10.5 by TTA/TOPO in cyclohexane in the presence of Tiron as masking agent for interfering ß-emitters. Radiostrontium is measured by liquid scintillation after back-extraction into 1N nitric acid. The distribution coefficient of strontium is over 400 and the separation factors from other radionuclides are higher than 5.0×10³.     

A Raman and dielectric study of ferroelectric ceramics

Dielectric and Raman scattering experiments were performed on various ceramics with composition Ba(Ti_1-xZr_x)O₃. Such lead-free, environmental-friendly materials were shown, from dielectric measurements, to exhibit behaviours extending from conventional to relaxor ferroelectrics on increasing the zirconium concentration. The evolution of the Raman spectra was studied as a function of temperature for various compositions, and the spectroscopic signature of the corresponding phases was determined. In the relaxor state, the variation of the integrated intensity of the Raman lines with temperature showed a plateau at low temperature. This anomaly was also detected as a peak in depolarization current measurements, and attributed to ergodicity breaking which characterizes usual relaxor systems. Raman results hint at locally rhombohedral polar nanoregions resulting from the random fields associated with Zr ions. Received 25 September 1998     

Minorations non triviales du plus petit commun multiple de certaines suites finies d'entiers

We present here a method which allows to derive a nontrivial lower bounds for the least common multiple of some finite sequences of integers. We obtain efficient lower bounds (which in a way are optimal) for the arithmetical progressions and lower bounds less efficient (but nontrivial) for some class of quadratic sequences.In the last part of this Note, we study the integer $\mathrm{lcm}(n,n+1,\dots ,n+k)$ ($k\in \mathbb{N},n\in {\mathbb{N}}^1$). We show that it has a divisor $d_{n,k}$ simple in its dependence on n and k, and a multiple $m_{n,k}$ also simple in its dependence on n. In addition, we prove that both equalities: $\mathrm{lcm}(n,n+1,\dots ,n+k)=d_{n,k}$ and $\mathrm{lcm}(n,n+1,\dots ,n+k)=m_{n,k}$ hold for infinitely many pairs $(n,k)$. To cite this article: B. Farhi, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Standard Gibbs free energy of formation of SnO2 from high-temperature e.m.f. measurements

The thermodynamic equilibrium Sn(l) + O₂(g) = SnO₂(s) has been studied between 773 and 1380 K by e.m.f. measurements on cells involving a solid electrolyte, of the type:

$\text{Pt∥Ni(s), NiO(s)∥ZrO}{}_2\text{+ Y}{}_2\text{O}{}_3\text{∥Sn(1), SnO}{}_2\text{(s)∥Pt}$

     

Observation of a new excitation in bcc 4He by inelastic neutron scattering

We report neutron-scattering measurements of the phonons in bcc solid 4He. In general, only three acoustic phonon branches should exist in a monatomic cubic crystal. In addition to these phonon branches, we found a new "opticlike" mode along the [110] direction. One possible interpretation of this new mode is in terms of localized excitations unique to a quantum solid.     

Self‐Assembled Cyclic d,l‐α‐Peptides as Generic Conformational Inhibitors of the α‐Synuclein Aggregation and Toxicity: In Vitro and Mechanistic Studies

Many peptides and proteins with large sequences and structural differences self‐assemble into disease‐causing amyloids that share very similar biochemical and biophysical characteristics, which may contribute to their cross‐interaction. Here, we demonstrate how the self‐assembled, cyclic d,l ‐α‐peptide CP‐2 , which has similar structural and functional properties to those of amyloids, acts as a generic inhibitor of the Parkinson′s disease associated α‐synuclein (α‐syn) aggregation to toxic oligomers by an ?off‐pathway“ mechanism. We show that CP‐2 interacts with the N‐terminal and the non‐amyloid‐β component region of α‐syn, which are responsible for α‐syn′s membrane intercalation and self‐assembly, thus changing the overall conformation of α‐syn. CP‐2 also remodels α‐syn fibrils to nontoxic amorphous species and permeates cells through endosomes/lysosomes to reduce the accumulation and toxicity of intracellular α‐syn in neuronal cells overexpressing α‐syn. Our studies suggest that targeting the common structural conformation of amyloids may be a promising approach for developing new therapeutics for amyloidogenic diseases.