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.

Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions

We propose a non-equidistant Q rate matrix formula and an adaptive numerical algorithm for a continuous time Markov chain to approximate jump-diffusions with affine or non-affine functional specifications. Our approach also accommodates state-dependent jump intensity and jump distribution, a flexibility that is very hard to achieve with other numerical methods. The Kolmogorov-Smirnov test shows that the proposed Markov chain transition density converges to the one given by the likelihood expansion formula as in Ait-Sahalia (2008). We provide numerical examples for European stock option pricing in Black and Scholes (1973), Merton (1976) and Kou (2002).

Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

Expression and function of beta1 integrins on human eosinophils

Eosinophils preferentially accumulate at sites of chronic allergic diseases such as bronchial asthma. The mechanisms by which selective eosinophil migration occurs are not fully understood. However, interactions of cell-surface adhesion molecules on the eosinophil with molecular counterligands on endothelial and epithelial cells, and on extracellular matrix proteins, are likely to be critical during the recruitment process. One possible mechanism for selective eosinophil recruitment involves the alpha4beta 1 (VLA-4) integrin which is not expressed on neutrophils. Correlations have been found between infiltration of eosinophils and endothelial expression of VCAM-1, the ligand for VLA-4, in the lungs of asthmatic individuals as well as in late phase reactions in the lungs, nose and skin. Epithelial and endothelial cells respond to the Th2-type cytokines IL-4 and IL-13 with selective de novo expression of VCAM-1, consistent with the possible role of VCAM-1/VLA-4 interactions in eosinophil influx during allergic inflammation. Both beta 1 and beta 2 integrins on eosinophils exist in a state of partial activation. For example, eosinophils can be maximally activated for adhesion to VCAM-1 or fibronectin after exposure to beta 1 integrin-activating antibodies or divalent cations, conditions that do not necessarily affect the total cell surface expression of beta 1 integrins. In contrast, cytokines like IL-5 prevent beta 1 integrin activation while promoting beta 2 integrin function. Furthermore, ligation of integrins can regulate the effector functions of the cell. For example, eosinophil adhesion via beta 1 and/or beta 2 integrins has been shown to alter a variety of functional responses including degranulation and apoptosis. Thus, integrins appear to be important in mediating eosinophil migration and activation in allergic inflammation. Strategies that interfere with these processes may prove to be useful for treatment of allergic diseases.

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.

Early functional differentiation in the chick embryonic disc: interaction between mechanical activity and extracellular matrix

The mechanical behaviour of ectodermal cells in the area opaca and the supracellular organization of fibronectin in the adjacent extracellular matrix were studied in whole chick blastoderms developing in vitro. The pattern of spontaneous mechanical activity and its modification by immunoglobulins against fibronectin were determined using a real-time image-analysis system. The pattern of fibronectin was studied using immunocytochemical techniques. It was found that the ectodermal cells in the area opaca actively develop a radially oriented contraction, which leads to a distension of the area pellucida from which the embryo develops. Abnormally increased tension resulted in perturbations of gastrulation and neurulation. An optimized mechanical equilibrium within the blastoderm seems to be necessary for normal development. Anti-fibronectin antibodies applied to the basal side of the blastoderm led rapidly and reversibly to an increase of tension in the contracted cells. This observation indicates that modifications of the extracellular matrix can be transmitted to cytoskeletal elements within adjacent cells. The extracellular matrix of the area opaca contains fibronectin arranged in radially oriented fibrils. This orientation corresponds to the direction of migration of the mesodermal cells. Interestingly, the radial pattern of fibronectin is found in the regions where the ectodermal cells are contracted and develop radially oriented forces. This observation suggests that the supracellular assembly of the extracellular materials could be influenced by the mechanical activity of adjacent cells. Possible modulations of the supracellular organization of extracellular matrix by other factors, e.g. diffusible metabolites, is also discussed. The presence of characteristically organized extracellular matrix components, of spatially differentiated cell activities and of reciprocal interactions between them makes the young chick blastoderm an excellent system for physiological studies of the coordinated cellular activities that lead to changes in form, complexity and function.

Unraveling the complex network of cuticular structure and function.

A hydrophobic cuticle is deposited at the outermost extracellular matrix of the epidermis in primary tissues of terrestrial plants. Besides forming a protective shield against the environment, the cuticle is potentially involved in several developmental processes during plant growth. A high degree of variation in cuticle composition and structure exists between different plant species and tissues. Lots of progress has been made recently in understanding the different steps of biosynthesis, transport, and deposition of cuticular components. However, the molecular mechanisms that underlie cuticular function remain largely elusive.

The ability of haemolysins expressed by atypical enteropathogenic Escherichia coli to bind to extracellular matrix components

Typical and atypical enteropathogenic Escherichia coli (EPEC) are considered important bacterial causes of diarrhoea. Considering the repertoire of virulence genes, atypical EPEC (aEPEC) is a heterogeneous group, harbouring genes that are found in other diarrheagenic E. coli pathotypes, such as those encoding haemolysins. Haemolysins are cytolytic toxins that lyse host cells disrupting the function of the plasma membrane. In addition, these cytolysins mediate a connection to vascular tissue and/or blood components, such as plasma and cellular fibronectin. Therefore, we investigated the haemolytic activity of 72 aEPEC isolates and determined the correlation of this phenotype with the presence of genes encoding enterohaemolysins (Ehly) and cytolysin A (ClyA). In addition, the correlation between the expression of haemolysins and the ability of these secreted proteins to adhere to extracellular matrix (ECM) components was also assessed in this study. Our findings demonstrate that a subset of aEPEC presents haemolytic activity due to the expression of Ehlys and/or ClyA and that this activity is closely related to the ability of these isolates to bind to ECM components.

The mitochondrial targeting function of randomly generated peptide sequences correlates with predicted helical amphiphilicity.

A pool of oligonucleotides encoding a start methionine and nine random amino acids was inserted at the 5'-end of the gene for the yeast cytochrome oxidase subunit IV lacking its own mitochondrial targeting sequence. Approximately one-quarter of the randomly generated sequences targeted subunit IV to its correct intramitochondrial location in vivo. Sequence analysis of 89 randomly generated sequences showed that their efficiencies as mitochondrial targeting signals correlated with the potential to fold into an amphiphilic alpha-helix. Functional targeting sequences were enriched in arginine and isoleucine residues but contained few aspartate, glutamate, and proline residues. Nonfunctional sequences predicted to have significant helical amphiphilicity often had at least one acidic or multiple helix-breaking residues that would be expected to interfere with targeting functioning. These results support the hypothesis that the signal for targeting a protein into the mitochondrial matrix is usually a positively charged amphiphilic helix.

Performance comparison of an active matrix flat panel imager, computed radiography system, and a screen-film system at four standard radiation qualities.

Four standard radiation qualities (from RQA 3 to RQA 9) were used to compare the imaging performance of a computed radiography (CR) system (general purpose and high resolution phosphor plates of a Kodak CR 9000 system), a selenium-based direct flat panel detector (Kodak Direct View DR 9000), and a conventional screen-film system (Kodak T-MAT L/RA film with a 3M Trimax Regular screen of speed 400) in conventional radiography. Reference exposure levels were chosen according to the manufacturer's recommendations to be representative of clinical practice (exposure index of 1700 for digital systems and a film optical density of 1.4). With the exception of the RQA 3 beam quality, the exposure levels needed to produce a mean digital signal of 1700 were higher than those needed to obtain a mean film optical density of 1.4. In spite of intense developments in the field of digital detectors, screen-film systems are still very efficient detectors for most of the beam qualities used in radiology. An important outcome of this study is the behavior of the detective quantum efficiency of the digital radiography (DR) system as a function of beam energy. The practice of users to increase beam energy when switching from a screen-film system to a CR system, in order to improve the compromise between patient dose and image quality, might not be appropriate when switching from screen-film to selenium-based DR systems.

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.

Identification of an agrin mutation that causes congenital myasthenia and affects synapse function.

We report the case of a congenital myasthenic syndrome due to a mutation in AGRN, the gene encoding agrin, an extracellular matrix molecule released by the nerve and critical for formation of the neuromuscular junction. Gene analysis identified a homozygous missense mutation, c.5125G>C, leading to the p.Gly1709Arg variant. The muscle-biopsy specimen showed a major disorganization of the neuromuscular junction, including changes in the nerve-terminal cytoskeleton and fragmentation of the synaptic gutters. Experiments performed in nonmuscle cells or in cultured C2C12 myotubes and using recombinant mini-agrin for the mutated and the wild-type forms showed that the mutated form did not impair the activation of MuSK or change the total number of induced acetylcholine receptor aggregates. A solid-phase assay using the dystrophin glycoprotein complex showed that the mutation did not affect the binding of agrin to alpha-dystroglycan. Injection of wild-type or mutated agrin into rat soleus muscle induced the formation of nonsynaptic acetylcholine receptor clusters, but the mutant protein specifically destabilized the endogenous neuromuscular junctions. Importantly, the changes observed in rat muscle injected with mutant agrin recapitulated the pre- and post-synaptic modifications observed in the patient. These results indicate that the mutation does not interfere with the ability of agrin to induce postsynaptic structures but that it dramatically perturbs the maintenance of the neuromuscular junction.