Nonmonotone Algorithms for Pattern Search Methods

This work deals with the solution of ill-conditioned unconstrained minimization problems by means of pattern search methods. To this end, the usual requirement of monotonic reduction of the objective function is relaxed and nonmonotone pattern search methods are proposed, which maintain the convergence properties of their monotone counterparts. Numerical experimentation on several well-known ill-conditioned functions is reported. The results highlight a class of pattern search methods which benefit very much by the introduction of nonmonotone strategies.     

Conditioning of the Exponential of a Block Triangular Matrix

We propose a new measure of conditioning for the exponential of a block triangular matrix. We also show that different condition numbers must be used to assess the accuracy of different algorithms which implement diagonal Padé with scaling and squaring.     

Complete sets and completion of sets in Banach spaces

In this paper we study properties of complete sets and of completions of sets in Banach spaces. We consider the family of completions of a given set and its size; we also study in detail the relationships concerning diameters, radii, and centers. The results are illustrated by several examples.     

Quantum neural network

In the neural network theory content-addressable memories are defined by patterns that are attractors of the dynamical rule of the system. This paper develops a quantum neural network starting from a classical neural network Hamiltonian and using a Schrödinger-like equation. It then shows that such a system exhibits probabilistic memory storage characteristics analogous to those of the dynamical attractors of classical systems.     

Synthesis and conformational analysis of a cyclic peptide obtained via i to i+4 intramolecular side-chain to side-chain azide-alkyne 1,3-dipolar cycloaddition

Intramolecular side-chain to side-chain cyclization is an established approach to achieve stabilization of specific conformations and a recognized strategy to improve resistance toward proteolytic degradation. To this end, cyclizations, which are bioisosteric to the lactam-type side-chain to side-chain modification and do not require orthogonal protection schemes, are of great interest. Herein, we report the employment of Cu(I)-catalyzed 1,3-dipolar cycloaddition of side chains modified with azido and alkynyl functions and explore alternative synthetic routes to efficiently generate 1,4-disubstituted [1,2,3]triazolyl-containing cyclopeptides. The solid-phase assembly of the linear precursor including epsilon-azido norleucine and the propargylglycine (Pra) in positions i and i+4, respectively, was accomplished by either subjecting the resin-bound peptide to selective on-resin diazo transformation of a Lys into the Nle(epsilon-N3) or the incorporation of Fmoc-Nle(epsilon-N3)-OH during the stepwise build-up of the resin-bound peptide 1b. Solution-phase Cu(I)-catalyzed 1,3-dipolar cycloaddition converts the linear precursor Ac-Lys-Gly-Nle(epsilon-N3)-Ser-Ile-Gln-Pra-Leu-Arg-NH2 (2) into the 1,4-disubstituted [1,2,3]triazolyl-containing cyclopeptide [Ac-Lys-Gly-Xaa(&(1))-Ser-Ile-Gln-Yaa(&(2))-Leu-Arg-NH2][(&(1)(CH2)4-1,4-[1,2,3]triazolyl-CH2&(2))] (3). The conformational preferences of the model cyclopeptide 3 (III), which is derived from the sequence of a highly helical and potent i to i+4 side-chain to side-chain lactam-containing antagonist of parathyroid hormone-related peptide (PTHrP), are compared to the corresponding lactam analogue Ac[Lys(13)(&(1)),Asp(17)(&(2))]hPTHrP(11-19)NH2 (II). CD and NMR studies of 3 and II in water/hexafluoroacetone (HFA) (50:50, v/v) revealed a high prevalence of turn-helical structures involving in particular the cyclic regions of the molecule. Despite a slight difference of the backbone arrangement, the side-chains of Ser, Gln, and Ile located at the i+1 to i+3 of the ring-forming sequences share the same spatial orientation. Both cyclopeptides differ regarding the location of the turn-helical segment, which in II involves noncyclized residues while in 3 it overlaps with residues involved in the cyclic structure. Therefore, the synthetic accessibility and conformational similarity of i to i+4 side-chain to side-chain cyclopeptide containing the 1,4-disubstituted [1,2,3]triazolyl moiety to the lactam-type one may result in similar bioactivities.     

Extending Removed Sets Revision to partially preordered belief bases

Most of belief revision operations have been proposed for totally preordrered information. However, in case of partial ignorance, pieces of information are partially preordered and few effective approaches of revision have been proposed. The paper presents a new framework for revising partially preordered information, called Partially Preordered Removed Sets Revision (PPRSR). The notion of removed set, initially defined in the context of the revision of non ordered or totally preordered information is extended to partial preorders. The removed sets are efficiently computed thanks to a suitable encoding of the revision problem into logic programming with answer set semantics. This framework captures the possibilistic revision of partially preordered information and allows for implementing it with ASP. Finally, it shows how PPRSR can be applied to a real application of the VENUS european project.     

A simple synthesis of N-perfluoroacylated and N-acylated glycals of neuraminic acid with a cyclic aminic substituent at the 4α position as possible inhibitors of sialidases

A simple protocol for the synthesis of N-perfluoroacylated and N-acylated glycals of neuraminic acid, with a secondary cyclic amine (morpholine or piperidine) at the 4α position, has been set-up, starting from peracetylated N-acetylneuraminic acid methyl ester that undergoes, sequentially to its direct N-transacylation followed by a C-4 amination, a β-elimination, and a selective hydrolysis of the ester functions, without affecting the sensitive perfluorinated amide.     

Generalized Pattern Search methods for a class of nonsmooth optimization problems with structure

We propose a Generalized Pattern Search (GPS) method to solve a class of nonsmooth minimization problems, where the set of nondifferentiability is included in the union of known hyperplanes and, therefore, is highly structured. Both unconstrained and linearly constrained problems are considered. At each iteration the set of poll directions is enforced to conform to the geometry of both the nondifferentiability set and the boundary of the feasible region, near the current iterate. This is the key issue to guarantee the convergence of certain subsequences of iterates to points which satisfy first-order optimality conditions. Numerical experiments on some classical problems validate the method.     

Characterization of fluid flow patterns and heat transfer in horizontal channel mixed convection

Two mechanisms of roll initiation are highlighted in a horizontal channel flow, uniformly heated from below, at constant heat flux (Γ = 10, Pr = 7, 50 ≤ Re ≤ 100, 0 ≤ Ra ≤ 10⁶). The first mechanism is the classical one, it occurs for low Rayleigh numbers and is initiated by the lateral wall effect. The second occurs for higher Rayleigh numbers and combines the previous effect with a supercritical vertical temperature gradient in the lower boundary layer, which simultaneously triggers pairs of rolls in the whole zone in between the two lateral rolls. We have found that in the present configuration, the transition between the two roll initiation mechanisms occurs for Ra/Re ² ≈ 18. Consequently, the heat transfer is significantly enhanced compared to the pure forced convection case owing to the flow pattern responsible of the continuous flooding the heated wall with cold fluid.