A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.

Exposure to parabens at the concentration of maximal proliferative response increases migratory and invasive activity of human breast cancer cells in vitro

Alkyl esters of p–hydroxybenzoic acid (parabens) are widely used as preservatives in personal care products, foods and pharmaceuticals. Their oestrogenic activity, their measurement in human breast tissue and their ability to drive proliferation of oestrogen-responsive human breast cancer cells has opened a debate on their potential to influence breast cancer development. Since proliferation is not the only hallmark of cancer cells, we have investigated the effects of exposure to parabens at concentrations of maximal proliferative response on migratory and invasive properties using three oestrogen-responsive human breast cancer cell lines (MCF-7, T-47-D, ZR-75-1). Cells were maintained short-term (1 week) or long-term (20±2 weeks) in phenol-red-free medium containing 5% charcoal-stripped serum with no addition, 10-8M 17-oestradiol, 1-5x10-4M methylparaben, 10-5M n-propylparaben or 10-5M n-butylparaben. Long-term exposure (20±2 weeks) of MCF-7 cells to methylparaben, n-propylparaben or n-butylparaben increased migration as measured using a scratch assay, time-lapse microscopy and xCELLigence technology: invasive properties were found to increase in matrix degradation assays and migration through matrigel on xCELLigence. Western immunoblotting showed an associated downregulation of E-cadherin and -catenin in the long-term paraben-exposed cells which could be consistent with a mechanism involving epithelial to mesenchymal transition. Increased migratory activity was demonstrated also in long-term paraben-exposed T-47-D and ZR-75-1 cells using a scratch assay and time-lapse microscopy. This is the first report that in vitro, parabens can influence not only proliferation but also migratory and invasive properties of human breast cancer cells.

On the spectra and pseudospectra of a class of non-self-adjoint random matrices and operators

In this paper we develop and apply methods for the spectral analysis of non-selfadjoint tridiagonal infinite and finite random matrices, and for the spectral analysis of analogous deterministic matrices which are pseudo-ergodic in the sense of E. B. Davies (Commun. Math. Phys. 216 (2001), 687–704). As a major application to illustrate our methods we focus on the “hopping sign model” introduced by J. Feinberg and A. Zee (Phys. Rev. E 59 (1999), 6433–6443), in which the main objects of study are random tridiagonal matrices which have zeros on the main diagonal and random ±1’s as the other entries. We explore the relationship between spectral sets in the finite and infinite matrix cases, and between the semi-infinite and bi-infinite matrix cases, for example showing that the numerical range and p-norm ε - pseudospectra (ε > 0, p ∈ [1,∞] ) of the random finite matrices converge almost surely to their infinite matrix counterparts, and that the finite matrix spectra are contained in the infinite matrix spectrum Σ. We also propose a sequence of inclusion sets for Σ which we show is convergent to Σ, with the nth element of the sequence computable by calculating smallest singular values of (large numbers of) n×n matrices. We propose similar convergent approximations for the 2-norm ε -pseudospectra of the infinite random matrices, these approximations sandwiching the infinite matrix pseudospectra from above and below.

Toeplitz operators on Dirichlet-Besov spaces

We study Toeplitz operators on the Besov spaces in the case of the open unit disk. We prove that a symbol satisfying a weak Lipschitz type condition induces a bounded Toeplitz operator. Such symbols do not need to be bounded functions or have continuous extensions to the boundary of the open unit disk. We discuss the problem of the existence of nontrivial compact Toeplitz operators, and also consider Fredholm properties and prove an index formula.

Schatten class Toeplitz operators on generalized Fock spaces

In this paper we characterize the Schatten p class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range p>0.

Reduced maximal oxygen consumption and overproduction of proinflammatory cytokines in athletes

Objective: It was the aim of this study to evaluate whether chronic pain in athletes is related to performance, measured by the maximum oxygen consumption and production of hormones and cytokines. Methods: Fifty-five athletes with a mean age of 31.9 +/- 4.2 years engaged in regular competition and showing no symptoms of acute inflammation, particularly fever, were studied. They were divided into 2 subgroups according to the occurrence of pain. Plasma concentrations of adrenaline, noradrenaline, cortisol, prolactin, growth hormone and dopamine were measured by radioimmunoassay, and the production of the cytokines interleukin (IL)-1, IL-2, IL-4, IL-6, tumor necrosis factor-alpha, interferon-alpha and prostaglandin E-2 by whole-blood culture. Maximal oxygen consumption was determined during an incremental treadmill test. Results: There was no change in the concentration of stress hormones, but the athletes with chronic pain showed a reduction in maximum oxygen consumption (22%) and total consumption at the anaerobic threshold (25%), as well as increased cytokine production. Increases of 2.7-, 8.1-, 1.7- and 3.7-fold were observed for IL-1, IL-2, tumor necrosis factor-alpha and interferon-alpha, respectively. Conclusions: Our data show that athletes with chronic pain have enhanced production of proinflammatory cytokines and lipid mediators and reduced performance in the ergospirometric test. Copyright (c) 2008 S. Karger AG, Basel.

Maximal inflammatory response benefits syngeneic skin graft acceptance

Objective: We investigated the influence of acute inflammation in skin isograft acceptance. Methods: Two mouse lines selected for maximal (AIR(MAX)) or minimal inflammatory response (AIR(MIN)) were transplanted with syngeneic skin. Cellular infiltrates and cytokine production were measured 1, 3, 7 or 14 days post-transplantation. The percentage of CD4(+) CD25(+) Foxp3(+) cells in the lymph nodes was also evaluated. Results: Grafts were totally accepted in 100% of AIR(MAX) and in 26% of AIR(MIN) mice. In the latter, partial acceptance was observed in 74% of the animals. Emigrated cells were basically PMN and were enhanced in AIR(MAX) transplants. IL-10 production by graft infiltrating cells showed no interline differences. IFN-gamma was increased in AIR(MIN) grafts at day 14 and lower percentages of CD4(+)CD25(+)Foxp3(+) cells in the lymph nodes were observed in these mice. Conclusions: Our data suggest that differences in graft acceptance might be due to a lack of appropriate regulation of the inflammatory response in AIR(MIN) mice compromising the self/non-self recognition.

Monotone positive solutions for a fourth order equation with nonlinear boundary conditions

This work is concerned with the existence of monotone positive solutions for a class of beam equations with nonlinear boundary conditions. The results are obtained by using the monotone iteration method and they extend early works on beams with null boundary conditions. Numerical simulations are also presented. (C) 2009 Elsevier Ltd. All rights reserved.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

CONSTRUCTING QUANTUM OBSERVABLES AND SELF-ADJOINT EXTENSIONS OF SYMMETRIC OPERATORS. III. SELF-ADJOINT BOUNDARY CONDITIONS

This paper completes the review of the theory of self-adjoint extensions of symmetric operators for physicists as a basis for constructing quantum-mechanical observables. It contains a comparative presentation of the well-known methods and a newly proposed method for constructing ordinary self-adjoint differential operators associated with self-adjoint differential expressions in terms of self-adjoint boundary conditions. The new method has the advantage that it does not require explicitly evaluating deficient subspaces and deficiency indices (these latter are determined in passing) and that boundary conditions are of explicit character irrespective of the singularity of a differential expression. General assertions and constructions are illustrated by examples of well-known quantum-mechanical operators like momentum and Hamiltonian.

Classification of quantum relativistic orientable objects

Extending our previous work `Fields on the Poincare group and quantum description of orientable objects` (Gitman and Shelepin 2009 Eur. Phys. J. C 61 111-39), we consider here a classification of orientable relativistic quantum objects in 3 + 1 dimensions. In such a classification, one uses a maximal set of ten commuting operators (generators of left and right transformations) in the space of functions on the Poincare group. In addition to the usual six quantum numbers related to external symmetries (given by left generators), there appear additional quantum numbers related to internal symmetries (given by right generators). Spectra of internal and external symmetry operators are interrelated, which, however, does not contradict the Coleman-Mandula no-go theorem. We believe that the proposed approach can be useful for the description of elementary spinning particles considered as orientable objects. In particular, it gives a group-theoretical interpretation of some facts of the existing phenomenological classification of spinning particles.

A new proposal for the picture changing operators in the minimal pure spinor formalism

Using a new proposal for the ""picture lowering"" operators, we compute the tree level scattering amplitude in the minimal pure spinor formalism by performing the integration over the pure spinor space as a multidimensional Cauchy-type integral. The amplitude will be written in terms of the projective pure spinor variables, which turns out to be useful to relate rigorously the minimal and non-minimal versions of the pure spinor formalism. The natural language for relating these formalisms is the. Cech-Dolbeault isomorphism. Moreover, the Dolbeault cocycle corresponding to the tree-level scattering amplitude must be evaluated in SO(10)/SU(5) instead of the whole pure spinor space, which means that the origin is removed from this space. Also, the. Cech-Dolbeault language plays a key role for proving the invariance of the scattering amplitude under BRST, Lorentz and supersymmetry transformations, as well as the decoupling of unphysical states. We also relate the Green`s function for the massless scalar field in ten dimensions to the tree-level scattering amplitude and comment about the scattering amplitude at higher orders. In contrast with the traditional picture lowering operators, with our new proposal the tree level scattering amplitude is independent of the constant spinors introduced to define them and the BRST exact terms decouple without integrating over these constant spinors.

PARALLEL ALGORITHMS FOR MAXIMAL CLIQUES IN CIRCLE GRAPHS AND UNRESTRICTED DEPTH SEARCH

We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges. To count the number of all the maximal cliques, without actually generating them, our algorithm requires O(log p) communication rounds with O(nm/p) local computation time. We also present an algorithm to generate the first maximal clique in O(log p) communication rounds with O(nm/p) local computation, and to generate each one of the subsequent maximal cliques this algorithm requires O(log p) communication rounds with O(m/p) local computation. The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with O(m/p) local computation for each maximal path. We also show that the presented algorithms can be extended to the CREW PRAM model.