The glassy phase of Gallager codes

Gallager codes are the best error-correcting codes to date. In this paper we study them by using the tools of statistical mechanics. The corresponding statistical mechanics model is a spin model on a sparse random graph. The model can be solved by elementary methods (i.e. without replicas) in a large connectivity limit. For low enough temperatures it presents a completely frozen glassy phase (q _EA = 1). The same scenario is shown to hold for finite connectivities. In this case we adopt the replica approach and exhibit a one-step replica symmetry breaking order parameter. We argue that our ansatz yields the exact solution of the model. This allows us to determine the whole phase diagram and to understand the performances of Gallager codes. Received 9 April 2001     

Synthesis and characterization of Si/Ga Eni Carbon Silicates

Phenylene-gallosilicates were prepared with the same crystalline structure as their aluminum ana-logues. The new Ga-Eni Carbon Silicates (Ga-ECS) phases were investigated by X-ray diffraction, scanning electron microscopy, nuclear magnetic resonance and thermogravimetric analysis, which demonstrated that gallium isomorphously replaced aluminum in the framework of the organ-ic-inorganic hybrids similar to the case of classical zeolites. Hybrid ECS materials were obtained with different types of bridged silsesquioxane precursors that maintained the aluminum-silicate nature of the inorganic moiety. This work confirms a new level of crystal chemistry versatility for this class of materials, and demonstrates the possibility to tailor also the inorganic part of the framework by changing the nature of the trivalent heteroatom.     

Lipschitz Continuous Viscosity Solutions for a Class of Fully Nonlinear Equations on Lie Groups

In this paper, we prove existence and uniqueness of Lipschitz continuous viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular, we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields.     

On the concentration of the number of solutions of random satisfiability formulas

Let Z(F) be the number of solutions of a random k‐satisfiability formula F with n variables and clause density α. Assume that the probability that F is unsatisfiable is for some . We show that (possibly excluding a countable set of “exceptional” α's) the number of solutions concentrates, i.e., there exists a non‐random function such that, for any , we have with high probability. In particular, the assumption holds for all , which proves the above concentration claim in the whole satisfiability regime of random 2‐SAT. We also extend these results to a broad class of constraint satisfaction problems. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 45, 362–382, 2014     

Ligand efficiency metrics considered harmful

Ligand efficiency metrics are used in drug discovery to normalize biological activity or affinity with respect to physicochemical properties such as lipophilicity and molecular size. This Perspective provides an overview of ligand efficiency metrics and summarizes thermodynamics of protein–ligand binding. Different classes of ligand efficiency metric are critically examined and the study concludes with suggestions for alternative ways to account for physicochemical properties when prioritizing and optimizing leads.     

Synthesis of Mesoionic 4‐(para‐substituted Phenyl‐5‐2,4‐dichlorophenyl)‐1,3‐4‐thiadiazolium‐2‐aminides by Direct Cyclization via Acylation of Thiosemicarbazides

The synthesis of ten novel mesoionic 4‐[para‐substituted (H, CH₃, OCH₃, NO₂, Cl, Br, OH, t‐C₄H₉, C₆H₅, C₄H₉) phenyl‐5‐2,4‐dichlorophenyl]‐1,3‐4‐thiadiazolium‐2‐aminides, as hydrochlorides, are described. The synthesis strategy utilized the corresponding para‐substituted isothiocyanates as starting materials to obtain the thiosemicarbazides through reaction with phenylhydrazine (61–98%), which were then submitted to acylation with 2,4‐dichloro benzoyl chloride and direct cyclization to generate the desired substituted mesoionic compounds in good yields (ca. 80%).     

Dislocation emission in A1 during recrystallization

Summary The dislocation structure evolution during isothermal recrystallization of Al has been followed by means of internal friction, modulus defect and X-ray diffraction analyses accompanying the microscopical observations. Many peaks ofQ ⁻¹ and of modulus defect and X-ray diffraction line width have been found, both in nucleation and grain growth, all referable to dislocations. The first of these peaks, at the beginning of recrystallization, presents recovery characteristics, different from those shown by the subsequent, secondary peaks. Secondary peaks are interpreted in terms of dislocation emission from grain boundaries, whereas the first peak appears connected with subboundaries, walls present in the initial stages of recrystallization. To speed up publication, the authors of this paper have agreed to not receive the proofs for correction.     

Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields

We consider a family ${\mathcal{H}}:= \{X_1, \dots, X_m\}$ of C ¹ vector fields in ? ⁿ and we discuss the associated ${\mathcal{H}}$ -orbits. Namely, we assume that our vector fields belong to a horizontal regularity class and we require that a suitable s-involutivity assumption holds. Then we show that any ${\mathcal{H}}$ -orbit ${\mathcal{O}}$ is a C ¹ immersed submanifold and it is an integral submanifold of the distribution generated by the family of all commutators up to length s. Our main tool is a class of almost exponential maps of which we discuss carefully some precise first order expansions.