Specht modules and semisimplicity criteria for Brauer and Birman--Murakami--Wenzl Algebras

A construction of bases for cell modules of the Birman--Murakami--Wenzl (or B--M--W) algebra $B_n(q,r)$ by lifting bases for cell modules of $B_{n-1}(q,r)$ is given. By iterating this procedure, we produce cellular bases for B--M--W algebras on which a large abelian subalgebra, generated by elements which generalise the Jucys--Murphy elements from the representation theory of the Iwahori--Hecke algebra of the symmetric group, acts triangularly. The triangular action of this abelian subalgebra is used to provide explicit criteria, in terms of the defining parameters $q$ and $r$, for B--M--W algebras to be semisimple. The aforementioned constructions provide generalisations, to the algebras under consideration here, of certain results from the Specht module theory of the Iwahori--Hecke algebra of the symmetric group

Link Invariants of Finite Type and Perturbation Theory

The Vassiliev-Gusarov link invariants of finite type are known to be closely related to perturbation theory for Chern-Simons theory. In order to clarify the perturbative nature of such link invariants, we introduce an algebra V_infinity containing elements g_i satisfying the usual braid group relations and elements a_i satisfying g_i - g_i^{-1} = epsilon a_i, where epsilon is a formal variable that may be regarded as measuring the failure of g_i^2 to equal 1. Topologically, the elements a_i signify crossings. We show that a large class of link invariants of finite type are in one-to-one correspondence with homogeneous Markov traces on V_infinity. We sketch a possible application of link invariants of finite type to a manifestly diffeomorphism-invariant perturbation theory for quantum gravity in the loop representation.Comment: 11 page

Exploiting Parallelism in the Design of Peer-to-Peer Overlays

Many peer-to-peer overlay operations are inherently parallel and this parallelism can be exploited by using multi-destination multicast routing, resulting in significant message reduction in the underlying network. We propose criteria for assessing when multicast routing can effectively be used, and compare multi-destination multicast and host group multicast using these criteria. We show that the assumptions underlying the Chuang-Sirbu multicast scaling law are valid in large-scale peer-to-peer overlays, and thus Chuang-Sirbu is suitable for estimating the message reduction when replacing unicast overlay messages with multicast messages. Using simulation, we evaluate message savings in two overlay algorithms when multi-destination multicast routing is used in place of unicast messages. We further describe parallelism in a range of overlay algorithms including multi-hop, variable-hop, load-balancing, random walk, and measurement overlay

Application of piezoelectric actuators to active control of composite spherical caps

Abstract. Dynamics of reinforced shallow spherical caps is considered in this paper. The cap is subjected to a uniform dynamic pressure that results in a globally axisymmetric motion. The reduction of amplitudes and stresses is achieved by using pairs of piezoelectric actuators bonded to the meridional stiffeners (one of the actuators can be bonded to the inner surface of the skin). These pairs of actuators produce dynamic couples that can reduce the amplitude of motion. The analysis is based on the theory of shallow shells (Donnell-Mushtari-Vlasov theory) using a smeared stiffeners technique. The analytical solution is generated for a cap clamped along the boundary using the approximation of the meridional curve suggested by Huang. Numerical results illustrate the feasibility of a significant reduction of deflections and stresses using piezoelectric actuators with weight and energy consumption acceptable in practical design

Tendon-to-bone enthesis as a structured nanomaterial

Tendon attaches to bone through a hierarchical and spatial graded structure called the enthesis. Entheses at the rotator cuff of the humeral head are highly resilient against injury in younger adults, but tears are common in older adults. These heal poorly, even following surgery. A central challenge is that potentially important nanoscale features of the material at these enthesis sites are not regenerated following injury or surgery. Our group aims to identify the nanoscale structures that are most important to the resilience of the enthesis, and to develop strategies for reconstituting these during healing. Here, we will present an overview of our recent results on ways that both structured and stochastic features might contribute to the mechanical functioning of the healthy enthesis

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the (finite and infinite) virtually cyclic subgroups of the pure braid groups $P_{n}(RP^2)$ of the projective plane. The maximal finite subgroups of $P_{n}(RP^2)$ are isomorphic to the quaternion group of order 8 if $n=3$, and to $\Z_{4}$ if $n\geq 4$. Further, for all $n\geq 3$, up to isomorphism, the following groups are the infinite virtually cyclic subgroups of $P_{n}(RP^2)$: $\Z$, $\Z_{2} \times \Z$ and the amalgamated product $\Z_{4} \ast_{\Z_{2}} \Z_{4}$.Comment: 15 page

Atropselective syntheses of (-) and (+) rugulotrosin A utilizing point-to-axial chirality transfer

Chiral, dimeric natural products containing complex structures and interesting biological properties have inspired chemists and biologists for decades. A seven-step total synthesis of the axially chiral, dimeric tetrahydroxanthone natural product rugulotrosin A is described. The synthesis employs a one-pot Suzuki coupling/dimerization to generate the requisite 2,2'-biaryl linkage. Highly selective point-to-axial chirality transfer was achieved using palladium catalysis with achiral phosphine ligands. Single X-ray crystal diffraction data were obtained to confirm both the atropisomeric configuration and absolute stereochemistry of rugulotrosin A. Computational studies are described to rationalize the atropselectivity observed in the key dimerization step. Comparison of the crude fungal extract with synthetic rugulotrosin A and its atropisomer verified that nature generates a single atropisomer of the natural product.P50 GM067041 - NIGMS NIH HHS; R01 GM099920 - NIGMS NIH HHS; GM-067041 - NIGMS NIH HHS; GM-099920 - NIGMS NIH HH

The braid groups of the projective plane and the Fadell-Neuwirth short exact sequence

International audienceWe study the pure braid groups $P_n(RP^2)$ of the real projective plane $RP^2$, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence $1 \to P_m(RP^2 \ {x_1,...,x_n} \to P_{n+m}(RP^2) \stackrel{p_{\ast}}{\to} P_n(RP^2) \to 1$, where $n\geq 2$ and $m\geq 1$, and $p_{\ast}$ is the homomorphism which corresponds geometrically to forgetting the last $m$ strings. This problem is equivalent to that of the existence of a section for the associated fibration $p: F_{n+m}(RP^2) \to F_n(RP^2)$ of configuration spaces. Van Buskirk proved in 1966 that $p$ and $p_{\ast}$ admit a section if $n=2$ and $m=1$. Our main result in this paper is to prove that there is no section if $n\geq 3$. As a corollary, it follows that $n=2$ and $m=1$ are the only values for which a section exists. As part of the proof, we derive a presentation of $P_n(RP^2)$: this appears to be the first time that such a presentation has been given in the literature