Byzantine Agreement Given Partial Broadcast

This paper considers unconditionally secure protocols for reliable broadcast among a set of n players, where up to t of the players can be corrupted by a (Byzantine) adversary but the remaining h = n - t players remain honest. In the standard model with a complete, synchronous network of bilateral authenticated communication channels among the players, broadcast is achievable if and only if 2n/h < 3. We show that, by extending this model by the existence of partial broadcast channels among subsets of b players, global broadcast can be achieved if and only if the number h of honest players satisfies 2n/h < b + 1. Achievability is demonstrated by protocols with communication and computation complexities polynomial in the size of the network, i.e., in the number of partial broadcast channels. A respective characterization for the related consensus problem is also given.     

The distribution of class groups of function fields

For any sufficiently general family of curves over a finite field F_q and any elementary abelian ?-group H with ? relatively prime to q, we give an explicit formula for the proportion of curves C for which Jac(C)[?](F_q)≅H. In doing so, we prove a conjecture of Friedman and Washington.     

The Segal-Bargmann transform for noncompact symmetric spaces of the complex type

We consider the generalized Segal-Bargmann transform, defined in terms of the heat operator, for a noncompact symmetric space of the complex type. For radial functions, we show that the Segal-Bargmann transform is a unitary map onto a certain L² space of meromorphic functions. For general functions, we give an inversion formula for the Segal-Bargmann transform, involving integration against an “unwrapped” version of the heat kernel for the dual compact symmetric space. Both results involve delicate cancellations of singularities.     

Rat pups and random robots generate similar self‐organized and intentional behavior

Biorobotic research continually demonstrates that behavior and cognition can be the emergent products of (1) embodied agents that are (2) dynamically embedded within an environment and (3) equipped with simple sensorimotor rules. Thigmotaxis is an orientation response to contact manifested in infant rats by wall following, corner burrowing, and group aggregation. Orientation responses have been long thought to be mediated only by sensory or central processes. Here we show that a random control architecture in a morphologically similar robot embedded in a scaled environment can reproduce thigmotaxic behaviors seen in infant rats. We conclude that (1) and (2) may play a larger role than previously thought in the generation of complex behaviors. © 2006 Wiley Periodicals, Inc. Complexity 12: 53–66, 2006     

Radical aromatic substitution with benzene chromiumtricarbonyl

Radical aromatic substitution of tert-butyl groups for hydrogen on simple arene chromiumtricarbonyl complexes was accomplished. Preexisting tert-butyl groups and methoxy groups directed incoming radicals primarily to the meta-position, and methoxy groups diminished the rate of substitution by roughly tenfold.     

Regiochemistry of addition of aminoheterocycles to α-cyanocinnamonitriles: formation of aza-bridged bi- and tricycles

The additions of various five-membered ring aminoheterocycles to α-cyanocinnamonitriles were studied. Regiochemistry of product formation can in most cases be controlled by choosing the appropriate electrophile. An α-cyanocinnamonitrile with an additional β-leaving group normally provides products arising from initial attack of the ring amino group, while exo attack predominates in the case of the parent α-cyanocinnamonitrile. Aminopyrazole and aminoindazole provide only exo products with either electrophile. Product assignments were made via X-ray and 2D NMR methods; these assignments serve as a benchmark to several literature references and to future investigations of conjugate additions of these nucleophiles.     

Axis alternation for signal propagation over polarization-maintaining fibers

When a signal is split over both axes of polarization-maintaining fibers (PMFs), alternation of axes is well known to cancel the impact of the differential group delay, e.g., in filtering functions such as modulators based on Kerr effect and a Sagnac loop. This solution seems not of concern if the signal remains on one axis as is the case for polarization-maintained signal transportation. As opposed to the common belief, we show experimentally and numerically that alternating the slow and the fast axes is also important to avoid signal distortions in that case. As a matter of fact, strong distortions of polarized signals are observed when the signals are transported with PMF because of the finite extinction ratio of connectors.