Lower Bounds on the State Complexity of Geometric Goppa Codes

We reinterpret the state space dimension equations for geometric Goppa codes. An easy consequence is that if deg G less than or equal to n-2/2 or deg G greater than or equal to n-2/2 + 2g then the state complexity of C-L(D, G) is equal to the Wolf bound. For deg G is an element of [n-1/2, n-3/2 + 2g], we use Clifford's theorem to give a simple lower bound on the state complexity of C-L(D, G). We then derive two further lower bounds on the state space dimensions of C-L(D, G) in terms of the gonality sequence of F/F-q. (The gonality sequence is known for many of the function fields of interest for defining geometric Goppa codes.) One of the gonality bounds uses previous results on the generalised weight hierarchy of C-L(D, G) and one follows in a straightforward way from first principles; often they are equal. For Hermitian codes both gonality bounds are equal to the DLP lower bound on state space dimensions. We conclude by using these results to calculate the DLP lower bound on state complexity for Hermitian codes.

The role of the Eph-ephrin signalling system in the regulation of developmental patterning

The Eph and ephrin system, consisting of fourteen Eph receptor tyrosine kinase proteins and nine ephrin membrane proteins in vertebrates, has been implicated in the regulation of many critical events during development. Binding of cell surface Eph and ephrin proteins results in bi-directional signals, which regulate the cytoskeletal, adhesive and motile properties of the interacting cells. Through these signals Eph and ephrin proteins are involved in early embryonic cell movements, which establish the germ layers, cell movements involved in formation of tissue boundaries and the pathfinding of axons. This review focuses on two vertebrate models, the zebrafish and mouse, in which experimental perturbation of Eph and/or ephrin expression in vivo have provided important insights into the role and functioning of the Eph/ephrin system.

Model specification tests in nonparametric stochastic regression models

In this paper, we consider testing for additivity in a class of nonparametric stochastic regression models. Two test statistics are constructed and their asymptotic distributions are established. We also conduct a small sample study for one of the test statistics through a simulated example. (C) 2002 Elsevier Science (USA).

Simple operational interpretation of the fidelity of mixed states

This Brief Report presents a corollary to Uhlmann's theorem which provides a simple operational interpretation of the fidelity of mixed states.

Predictor-corrector methods of Runge-Kutta type for stochastic differential equations

In this paper we construct predictor-corrector (PC) methods based on the trivial predictor and stochastic implicit Runge-Kutta (RK) correctors for solving stochastic differential equations. Using the colored rooted tree theory and stochastic B-series, the order condition theorem is derived for constructing stochastic RK methods based on PC implementations. We also present detailed order conditions of the PC methods using stochastic implicit RK correctors with strong global order 1.0 and 1.5. A two-stage implicit RK method with strong global order 1.0 and a four-stage implicit RK method with strong global order 1.5 used as the correctors are constructed in this paper. The mean-square stability properties and numerical results of the PC methods based on these two implicit RK correctors are reported.

A uniform white-noise model for fixed-point roundoff errors in digital systems

Fixed-point roundoff noise in digital implementation of linear systems arises due to overflow, quantization of coefficients and input signals, and arithmetical errors. In uniform white-noise models, the last two types of roundoff errors are regarded as uniformly distributed independent random vectors on cubes of suitable size. For input signal quantization errors, the heuristic model is justified by a quantization theorem, which cannot be directly applied to arithmetical errors due to the complicated input-dependence of errors. The complete uniform white-noise model is shown to be valid in the sense of weak convergence of probabilistic measures as the lattice step tends to zero if the matrices of realization of the system in the state space satisfy certain nonresonance conditions and the finite-dimensional distributions of the input signal are absolutely continuous.

Human peripheral blood V alpha 24(+) V beta 11(+) NKT cells expand following administration of alpha-galactosylceramide-pulsed dendritic cells

Background and Objectives We have undertaken the first clinical trial involving the administration of alpha-GalactosylCeramine (alpha-GalCer)-pulsed dendritic cells (DCs) to human subjects, to determine safety, optimal dose, optimal administration route and immunological effects. Materials and Methods Subjects (n = 4) with metastatic malignancy received two infusions of alpha-GalCer-pulsed DCs intravenously, and two infusions intradermally. The percentages of Valpha24 Vbeta11 NKT cells in peripheral blood (PB) were determined by three-colour flow cytometry and the PB NKT cell numbers were calculated using the total number of PB lymphocytes/ml determined by automated full-blood counts. Results No serious treatment related adverse events were observed during the study period. Administration of alpha-GalCer-pulsed DCs in vivo can significantly (P < 0.03) increase PB Valpha24(+) Vbeta11(+) NKT cell numbers above pretreatment baseline levels after the transient fall in the NKT numbers within 48 h. Conclusions Administration of alpha-GalCer-pulsed DCs is well tolerated, modulates PB Valpha24(+) Vbeta11(+) NKT cells and may have a role in the therapy of malignancies sensitive to activities of Valpha24(+) Vbeta11(+) NKT cells, or for autoimmune diseases.

Single-chain antibodies produced by phage display against the C-terminal 19 kDa region of merozoite surface protein-1of Plasinodium yoelii reduce parasite growth following challenge

Antibodies have the potential to be therapeutic reagents for malaria. Here we describe the production of a novel phage antibody display library against the C-terminal 19 kDa region of the Plasmodium yoelii YM merozoite surface protein-1 (MSP1(19)). In vivo studies against homologous lethal malaria challenge show an anti-parasite effect in a dose dependent manner, and analysis by plasmon resonance indicates binding to the antigen is comparable to the binding of a protective monoclonal antibody. The data support the lack of a need for any antibody Fc-related function and hold great significance for the development of a therapeutic reagent for malaria. (C) 2002 Elsevier Science Ltd. All rights reserved.

Ephrin-A5 induces rounding, blebbing and deadhesion of EphA3-expressing 293T and melanoma cells by CrkII and Rho-mediated signalling

Eph receptor tyrosine kinases and ephrins regulate morphogenesis in the developing embryo where they effect adhesion and motility of interacting cells. Although scarcely expressed in adult tissues, Eph receptors and ephrins are overexpressed in a range of tumours. In malignant melanoma, increased Eph and ephrin expression levels correlate with metastatic progression. We have examined cellular and biochemical responses of EphA3-expressing melanoma cell lines and human epithelial kidney 293T cells to stimulation with polymeric ephrin-A5 in solution and with surfaces of defined ephrin-A5 densities. Within minutes, rapid reorganisation of the actin and myosin cytoskeleton occurs through activation of RhoA, leading to the retraction of cellular protrusions, membrane blebbing and detachment, but not apoptosis. These responses are inhibited by monomeric ephrin-A5, showing that receptor clustering is required for this EphA3 response. Furthermore, the adapter CrkII, which associates with tyrosine-phosphorylated EphA3 in vitro, is recruited in vivo to ephrin-A5-stimulated EphA3. Expression of an SH3-domain mutated CrkII ablates cell rounding, blebbing and detachment. Our results suggest that recruitment of CrkII and activation of Rho signalling are responsible for EphA3-mediated cell rounding, blebbing and de-adhesion, and that ephrin-A5-mediated receptor clustering and EphA3 tyrosine kinase activity are essential for this response.

Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.