Open-closed TQFTs extend Khovanov homology from links to tangles

We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of an oriented tangle, we construct a chain complex whose homology is invariant under Reidemeister moves. The terms of this chain complex are modules of a suitable algebra A such that there is one action of A or A^op for every boundary point of the tangle. We give examples of such algebras A for which our tangle homology theory reduces to the link homology theories of Khovanov, Lee, and Bar-Natan if it is evaluated for links. As a consequence of the Cardy condition, Khovanov's graded theory can only be extended to tangles if the underlying field has finite characteristic. In all cases in which the algebra A is strongly separable, i.e. for Bar-Natan's theory in any characteristic and for Lee's theory in characteristic other than 2, we also provide the required algebraic operation for the composition of oriented tangles. Just as Khovanov's theory for links can be recovered from Lee's or Bar-Natan's by a suitable spectral sequence, we provide a spectral sequence in order to compute our tangle extension of Khovanov's theory from that of Bar-Natan's or Lee's theory. Thus, we provide a tangle homology theory that is locally computable and still strong enough to recover characteristic p Khovanov homology for links.Comment: 56 pages, LaTeX2e with xypic and pstricks macro

Introduction to the computational structural mechanics testbed

The Computational Structural Mechanics (CSM) testbed software system based on the SPAR finite element code and the NICE system is described. This software is denoted NICE/SPAR. NICE was developed at Lockheed Palo Alto Research Laboratory and contains data management utilities, a command language interpreter, and a command language definition for integrating engineering computational modules. SPAR is a system of programs used for finite element structural analysis developed for NASA by Lockheed and Engineering Information Systems, Inc. It includes many complementary structural analysis, thermal analysis, utility functions which communicate through a common database. The work on NICE/SPAR was motivated by requirements for a highly modular and flexible structural analysis system to use as a tool in carrying out research in computational methods and exploring computer hardware. Analysis examples are presented which demonstrate the benefits gained from a combination of the NICE command language with a SPAR computational modules

CSM Testbed Development and Large-Scale Structural Applications

A research activity called Computational Structural Mechanics (CSM) conducted at the NASA Langley Research Center is described. This activity is developing advanced structural analysis and computational methods that exploit high-performance computers. Methods are developed in the framework of the CSM Testbed software system and applied to representative complex structural analysis problems from the aerospace industry. An overview of the CSM Testbed methods development environment is presented and some new numerical methods developed on a CRAY-2 are described. Selected application studies performed on the NAS CRAY-2 are also summarized

Syk tyrosine kinase is critical for B cell antibody responses and memory B cell survival

Signals from the BCR are required for Ag-specific B cell recruitment into the immune response. Binding of Ag to the BCR induces phosphorylation of immune receptor tyrosine-based activation motifs in the cytoplasmic domains of the CD79a and CD79b signaling subunits, which subsequently bind and activate the Syk protein tyrosine kinase. Earlier work with the DT40 chicken B cell leukemia cell line showed that Syk was required to transduce BCR signals to proximal activation events, suggesting that Syk also plays an important role in the activation and differentiation of primary B cells during an immune response. In this study, we show that Syk-deficient primary mouse B cells have a severe defect in BCR-induced activation, proliferation, and survival. Furthermore, we demonstrate that Syk is required for both T-dependent and T-independent Ab responses, and that this requirement is B cell intrinsic. In the absence of Syk, Ag fails to induce differentiation of naive B cells into germinal center B cells and plasma cells. Finally, we show that the survival of existing memory B cells is dependent on Syk. These experiments demonstrate that Syk plays a critical role in multiple aspects of B cell Ab responses

Orbit spaces of free involutions on the product of two projective spaces

Let $X$ be a finitistic space having the mod 2 cohomology algebra of the product of two projective spaces. We study free involutions on $X$ and determine the possible mod 2 cohomology algebra of orbit space of any free involution, using the Leray spectral sequence associated to the Borel fibration $X \hookrightarrow X_{\mathbb{Z}_2} \longrightarrow B_{\mathbb{Z}_2}$. We also give an application of our result to show that if $X$ has the mod 2 cohomology algebra of the product of two real projective spaces (respectively complex projective spaces), then there does not exist any $\mathbb{Z}_2$-equivariant map from $\mathbb{S}^k \to X$ for $k \geq 2$ (respectively $k \geq 3$), where $\mathbb{S}^k$ is equipped with the antipodal involution.Comment: 14 pages, to appear in Results in Mathematic

The chameleon groups of Richard J. Thompson: automorphisms and dynamics

The automorphism groups of several of Thompson's countable groups of piecewise linear homeomorphisms of the line and circle are computed and it is shown that the outer automorphism groups of these groups are relatively small. These results can be interpreted as stability results for certain structures of PL functions on the circle. Machinery is developed to relate the structures on the circle to corresponding structures on the line

Educating professionals to support self-management in people with asthma or diabetes: protocol for a systematic review and scoping exercise

This report is independent research funded by the National Institute for Health Research (Programme Development Grants, Implementing supported asthma self-management in routine clinical care: designing, refining, piloting and evaluating a whole systems implementation within an MRC Phase IV programme of research, RP-DG-1213-10008). The views expressed in this publication are those of the author(s) and not necessarily those of the NHS, the National Institute for Health Research or the Department of Health. This work is sponsored by the University of Edinburgh. The funder and sponsor have not had any role in developing the protocol