Delay approximation of fractional integrals

This paper explores the calculation of fractional integrals by means of the time delay operator. The study starts by reviewing the memory properties of fractional operators and their relationship with time delay. Based on the time response of the Mittag-Leffler function an approximation of fractional integrals consisting of time delayed samples is proposed. The tuning of the approximation is optimized by means of a genetic algorithm. The results demonstrate the feasibility of the new perspective and the limits of their application.

The Role of the Humoral Immune Response in the Molecular Evolution of the Envelope C2, V3 and C3 Regions in Chronically HIV-2 Infected Patients

BACKGROUND: This study was designed to investigate, for the first time, the short-term molecular evolution of the HIV-2 C2, V3 and C3 envelope regions and its association with the immune response. Clonal sequences of the env C2V3C3 region were obtained from a cohort of eighteen HIV-2 chronically infected patients followed prospectively during 2-4 years. Genetic diversity, divergence, positive selection and glycosylation in the C2V3C3 region were analysed as a function of the number of CD4+ T cells and the anti-C2V3C3 IgG and IgA antibody reactivity RESULTS: The mean intra-host nucleotide diversity was 2.1% (SD, 1.1%), increasing along the course of infection in most patients. Diversity at the amino acid level was significantly lower for the V3 region and higher for the C2 region. The average divergence rate was 0.014 substitutions/site/year, which is similar to that reported in chronic HIV-1 infection. The number and position of positively selected sites was highly variable, except for codons 267 and 270 in C2 that were under strong and persistent positive selection in most patients. N-glycosylation sites located in C2 and V3 were conserved in all patients along the course of infection. Intra-host variation of C2V3C3-specific IgG response over time was inversely associated with the variation in nucleotide and amino acid diversity of the C2V3C3 region. Variation of the C2V3C3-specific IgA response was inversely associated with variation in the number of N-glycosylation sites. CONCLUSION: The evolutionary dynamics of HIV-2 envelope during chronic aviremic infection is similar to HIV-1 implying that the virus should be actively replicating in cellular compartments. Convergent evolution of N-glycosylation in C2 and V3, and the limited diversification of V3, indicates that there are important functional constraints to the potential diversity of the HIV-2 envelope. C2V3C3-specific IgG antibodies are effective at reducing viral population size limiting the number of virus escape mutants. The C3 region seems to be a target for IgA antibodies and increasing N-linked glycosylation may prevent HIV-2 envelope recognition by these antibodies. Our results provide new insights into the biology of HIV-2 and its relation with the human host and may have important implications for vaccine design.

Regulation and function of the cell wall polymer lipoteichoic acid in staphylococcus aureus

A thesis submitted for the Degree of Master in Medical microbiology

Comparative Analysis of Signals Restoration by Different Kinds of Approximation

The comparative analysis of continuous signals restoration by different kinds of approximation is performed. The software product, allowing to define optimal method of different original signals restoration by Lagrange polynomial, Kotelnikov interpolation series, linear and cubic splines, Haar wavelet and Kotelnikov-Shannon wavelet based on criterion of minimum value of mean-square deviation is proposed. Practical recommendations on the selection of approximation function for different class of signals are obtained.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

Chebyshev polynomial approximation to approximate partial differential equations

This paper suggests a simple method based on Chebyshev approximation at Chebyshev nodes to approximate partial differential equations. The methodology simply consists in determining the value function by using a set of nodes and basis functions. We provide two examples. Pricing an European option and determining the best policy for chatting down a machinery. The suggested method is flexible, easy to program and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of partial differential equations.

Second-Order Approximation to the Rotemberg Model around a Distorted Steady State

Less is known about social welfare objectives when it is costly to change prices, as in Rotemberg (1982), compared with Calvo-type models. We derive a quadratic approximate welfare function around a distorted steady state for the costly price adjustment model. We highlight the similarities and differences to the Calvo setup. Both models imply inflation and output stabilization goals. It is explained why the degree of distortion in the economy influences inflation aversion in the Rotemberg framework in a way that differs from the Calvo setup.

A General and Intuitive Envelope Theorem

We present an envelope theorem for establishing first-order conditions in decision problems involving continuous and discrete choices. Our theorem accommodates general dynamic programming problems, even with unbounded marginal utilities. And, unlike classical envelope theorems that focus only on differentiating value functions, we accommodate other endogenous functions such as default probabilities and interest rates. Our main technical ingredient is how we establish the differentiability of a function at a point: we sandwich the function between two differentiable functions from above and below. Our theory is widely applicable. In unsecured credit models, neither interest rates nor continuation values are globally differentiable. Nevertheless, we establish an Euler equation involving marginal prices and values. In adjustment cost models, we show that first-order conditions apply universally, even if optimal policies are not (S,s). Finally, we incorporate indivisible choices into a classic dynamic insurance analysis.

Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs

In a seminal paper [10], Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the innite d-regular tree. ore recently Sly [8] (see also [1]) showed that this is optimal in the sense that if here is an FPRAS for the hard-core partition function on graphs of maximum egree d for activities larger than the critical activity on the innite d-regular ree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagnetic spin systems on the d-regular tree, weak spatial mixing implies strong spatial mixing. his in turn uses a message-decay argument which extends a similar approach proposed recently for the hard-core model by Restrepo et al [7] to the case of general two-state anti-ferromagnetic spin systems.

Hepatitis C virus proteins: from structure to function.

Great progress has been made over the past years in elucidating the structure and function of the hepatitis C virus (HCV) proteins, most of which are now actively being pursued as antiviral targets. The structural proteins, which form the viral particle, include the core protein and the envelope glycoproteins E1 and E2. The nonstructural proteins include the p7 viroporin, the NS2 protease, the NS3-4A complex harboring protease and NTPase/RNA helicase activities, the NS4B and NS5A proteins, and the NS5B RNA-dependent RNA polymerase. NS4B is a master organizer of replication complex formation while NS5A is a zinc-containing phosphoprotein involved in the regulation of HCV RNA replication versus particle production. Core to NS2 make up the assembly module while NS3 to NS5B represent the replication module (replicase). However, HCV proteins exert multiple functions during the viral life cycle, and these may be governed by different structural conformations and/or interactions with viral and/or cellular partners. Remarkably, each viral protein is anchored to intracellular membranes via specific determinants that are essential to protein function in the cell. This review summarizes current knowledge of the structure and function of the HCV proteins and highlights recent advances in the field.

FtsZ-independent septal recruitment and function of cell wall remodelling enzymes in chlamydial pathogens.

The nature and assembly of the chlamydial division septum is poorly defined due to the paucity of a detectable peptidoglycan (PG)-based cell wall, the inhibition of constriction by penicillin and the presence of coding sequences for cell wall precursor and remodelling enzymes in the reduced chlamydial (pan-)genome. Here we show that the chlamydial amidase (AmiA) is active and remodels PG in Escherichia coli. Moreover, forward genetics using an E. coli amidase mutant as entry point reveals that the chlamydial LysM-domain protein NlpD is active in an E. coli reporter strain for PG endopeptidase activity (ΔnlpI). Immunolocalization unveils NlpD as the first septal (cell-wall-binding) protein in Chlamydiae and we show that its septal sequestration depends on prior cell wall synthesis. Since AmiA assembles into peripheral clusters, trimming of a PG-like polymer or precursors occurs throughout the chlamydial envelope, while NlpD targets PG-like peptide crosslinks at the chlamydial septum during constriction.

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Differential Recognition of Old World and New World Arenavirus Envelope Glycoproteins by Subtilisin Kexin Isozyme 1 (SKI-1)/Site 1 Protease (S1P).

The arenaviruses are an important family of emerging viruses that includes several causative agents of severe hemorrhagic fevers in humans that represent serious public health problems. A crucial step of the arenavirus life cycle is maturation of the envelope glycoprotein precursor (GPC) by the cellular subtilisin kexin isozyme 1 (SKI-1)/site 1 protease (S1P). Comparison of the currently known sequences of arenavirus GPCs revealed the presence of a highly conserved aromatic residue at position P7 relative to the SKI-1/S1P cleavage side in Old World and clade C New World arenaviruses but not in New World viruses of clades A and B or cellular substrates of SKI-1/S1P. Using a combination of molecular modeling and structure-function analysis, we found that residueY285 of SKI-1/S1P, distal from the catalytic triad, is implicated in the molecular recognition of the aromatic "signature residue" at P7 in the GPC of Old World Lassa virus. Using a quantitative biochemical approach, we show that Y285 of SKI-1/S1P is crucial for the efficient processing of peptides derived from Old World and clade C New World arenavirus GPCs but not of those from clade A and B New World arenavirus GPCs. The data suggest that during coevolution with their mammalian hosts, GPCs of Old World and clade C New World viruses expanded the molecular contacts with SKI-1/S1P beyond the classical four-amino-acid recognition sequences and currently occupy an extended binding pocket.

Nrf2 links epidermal barrier function with antioxidant defense.

The skin provides an efficient permeability barrier and protects from microbial invasion and oxidative stress. Here, we show that these essential functions are linked through the Nrf2 transcription factor. To test the hypothesis that activation of Nrf2 provides skin protection under stress conditions, we determined the consequences of pharmacological or genetic activation of Nrf2 in keratinocytes. Surprisingly, mice with enhanced Nrf2 activity in keratinocytes developed epidermal thickening, hyperkeratosis and inflammation resembling lamellar ichthyosis. This resulted from upregulation of the cornified envelope proteins small proline-rich proteins (Sprr) 2d and 2h and of secretory leukocyte peptidase inhibitor (Slpi), which we identified as novel Nrf2 targets in keratinocytes. Since Sprrs are potent scavengers of reactive oxygen species and since Slpi has antimicrobial activities, their upregulation contributes to Nrf2's protective function. However, it also caused corneocyte fragility and impaired desquamation, followed by alterations in the epidermal lipid barrier, inflammation and overexpression of mitogens that induced keratinocyte hyperproliferation. These results identify an unexpected role of Nrf2 in epidermal barrier function, which needs to be considered for pharmacological use of Nrf2 activators.