Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

A public key cryptosystem based on block upper triangular matrices

We propose a public key cryptosystem based on block upper triangular matrices. This system is a variant of the Discrete Logarithm Problem with elements in a finite group, capable of increasing the difficulty of the problem while maintaining the key size. We also propose a key exchange protocol that guarantees that both parties share a secret element of this group and a digital signature scheme that provides data authenticity and integrity.

Comparison of Lattice-Fluid Binary Parameters For Mixtures and Block Copolymers

The aim of this report is to discuss the method of determination of lattice-fluid binary interaction parameters by comparing well characterized immiscible blends and block copolymers of poly(methyl methacrylate) (PMMA) and poly(ϵ−caprolactone) (PCL). Experimental pressure-volume-temperature (PVT) data in the liquid state were correlated with the Sanchez—Lacombe (SL) equation of state with the scaling parameters for mixtures and copolymers obtained through combination rules of the characteristic parameters for the pure homopolymers. The lattice-fluid binary parameters for energy and volume were higher than those of block copolymers implying that the copolymers were more compatible due to the chemical links between the blocks. Therefore, a common parameter cannot account for both homopolymer blend and block copolymer phase behaviors based on current theory. As we were able to adjust all data of the mixtures with a single set of lattice-binary parameters and all data of the block copolymers with another single set we can conclude that both parameters did not depend on the composition for this system. This characteristic, plus the fact that the additivity law of specific volumes can be suitably applied for this system, allowed us to model the behavior of the immiscible blend with the SL equation of state. In addition, a discussion on the relationship between lattice-fluid binary parameters and the Flory–Huggins interaction parameter obtained from Leibler's theory is presented.

Muscle-Type Nicotinic Receptor Blockade by Diethylamine, the Hydrophilic Moiety of Lidocaine

Lidocaine bears in its structure both an aromatic ring and a terminal amine, which can be protonated at physiological pH, linked by an amide group. Since lidocaine causes multiple inhibitory actions on nicotinic acetylcholine receptors (nAChRs), this work was aimed to determine the inhibitory effects of diethylamine (DEA), a small molecule resembling the hydrophilic moiety of lidocaine, on Torpedo marmorata nAChRs microtransplanted to Xenopus oocytes. Similarly to lidocaine, DEA reversibly blocked acetylcholine-elicited currents (IACh) in a dose-dependent manner (IC50 close to 70 μM), but unlike lidocaine, DEA did not affect IACh desensitization. IACh inhibition by DEA was more pronounced at negative potentials, suggesting an open-channel blockade of nAChRs, although roughly 30% inhibition persisted at positive potentials, indicating additional binding sites outside the pore. DEA block of nAChRs in the resting state (closed channel) was confirmed by the enhanced IACh inhibition when pre-applying DEA before its co-application with ACh, as compared with solely DEA and ACh co-application. Virtual docking assays provide a plausible explanation to the experimental observations in terms of the involvement of different sets of drug binding sites. So, at the nAChR transmembrane (TM) domain, DEA and lidocaine shared binding sites within the channel pore, giving support to their open-channel blockade; besides, lidocaine, but not DEA, interacted with residues at cavities among the M1, M2, M3, and M4 segments of each subunit and also at intersubunit crevices. At the extracellular (EC) domain, DEA and lidocaine binding sites were broadly distributed, which aids to explain the closed channel blockade observed. Interestingly, some DEA clusters were located at the α-γ interphase of the EC domain, in a cavity near the orthosteric binding site pocket; by contrast, lidocaine contacted with all α-subunit loops conforming the ACh binding site, both in α-γ and α-δ and interphases, likely because of its larger size. Together, these results indicate that DEA mimics some, but not all, inhibitory actions of lidocaine on nAChRs and that even this small polar molecule acts by different mechanisms on this receptor. The presented results contribute to a better understanding of the structural determinants of nAChR modulation.