Discriminants and Functional Equations for Polynomials Orthogonal on the Unit Circle

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate the zeros of the orthogonal polynomials to the stationary values of an explicit quasi-energy and implies recurrences on the orthogonal polynomial coefficients. We also evaluate the discriminants and quantized discriminants of polynomials orthogonal on the unit circle.Comment: 27 pages, Latex2e plus AMS packages Fix to Eqs. (2.72) and (2.74

Prediction of heat transfer from laminar boundary layers, with emphasis on large free- stream velocity gradients and highly cooled walls

Prediction of heat transfer and shear stress from laminar boundary laye

Semantic Image Retrieval via Active Grounding of Visual Situations

We describe a novel architecture for semantic image retrieval---in particular, retrieval of instances of visual situations. Visual situations are concepts such as "a boxing match," "walking the dog," "a crowd waiting for a bus," or "a game of ping-pong," whose instantiations in images are linked more by their common spatial and semantic structure than by low-level visual similarity. Given a query situation description, our architecture---called Situate---learns models capturing the visual features of expected objects as well the expected spatial configuration of relationships among objects. Given a new image, Situate uses these models in an attempt to ground (i.e., to create a bounding box locating) each expected component of the situation in the image via an active search procedure. Situate uses the resulting grounding to compute a score indicating the degree to which the new image is judged to contain an instance of the situation. Such scores can be used to rank images in a collection as part of a retrieval system. In the preliminary study described here, we demonstrate the promise of this system by comparing Situate's performance with that of two baseline methods, as well as with a related semantic image-retrieval system based on "scene graphs.

Vesicular stomatitis virus glycoprotein is necessary for H-2-restricted lysis of infected cells by cytotoxic T lymphocytes

Vesicular stomatitis virus (VSV) elicited cytotoxic thymus-derived lymphocytes (CTLs) in mice of the BALB/c and three congenic strains (BALB.b, BALB.k, BALB.HTG). CTL lysis of VSV-infected fibroblasts from the four strains was restricted by the target cells' major histocompatibility complex (H-2). Target cells were also infected with two temperature-sensitive mutants of VSV, tsM and tsG in which, respectively, the viral matrix protein and glycoprotein are not expressed at 39 degrees (restrictive temperature) on the infected cell's surface membrane. At the restrictive temperature, cells infected with wild-type VSV or tsM were lysed by CTLs, but cells infected with tsG were not. The requirement for the glycoprotein on the target cell was also evident from the ability of antisera to the glycoprotein to block completely CTL lysis of VSV-infected cells

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desirable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to first order in the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.Comment: 18 Pages, 4 Figures. This updated version has a slightly more detailed introduction. In the current form, the paper will appear in SIAM Journal on Numerical Analysi