Isoperimetric functions for graph products

AbstractLet Γ be a finite graph, and for each vertex i let Gi be a finitely presented group. Let G be the graph product of the Gi. That is, G is the group obtained from the free product of the Gi by factoring out by the smallest normal subgroup containing all [g, h] where g EGi and h Gj and there is an edge joining i and j. We show that G has an isoperimetric function of degree k > 1 (or an exponential isoperimetric function) if each vertex group has such an isoperimetric function

Supersymmetric Baryogenesis from Exotic Quark Decays

In a simple extension of the minimal supersymmetric standard model, out-of-equilibrium decays of TeV scale exotic vector-like squarks may generate the baryon asymmetry of the universe. Baryon number and CP violation are present in the superpotential, so this mechanism does not rely on CP violation in supersymmetry breaking parameters. We discuss phenomenological constraints on the model as well as potential signals for the Large Hadron Collider and electronic dipole moment experiments. A variation on the TeV scale model allows the exotic squarks to be the messengers of gauge mediated supersymmetry breaking.Comment: 28 pages, 7 figures, 2 appendices, v2: typos corrected, results unchange

Gait Transitions for Quasi-Static Hexapedal Locomotion on Level Ground

As robot bodies become more capable, the motivation grows to better coordinate them—whether multiple limbs attached to a body or multiple bodies assigned to a task. This paper introduces a new formalism for coordination of periodic tasks, with specific application to gait transitions for legged platforms. Specifically, we make modest use of classical group theory to replace combinatorial search and optimization with a computationally simpler and conceptually more straightforward appeal to elementary algebra. We decompose the space of all periodic legged gaits into a cellular complex indexed using “Young Tableaux”, making transparent the proximity to steady state orbits and the neighborhood structure. We encounter the simple task of transitioning between these gaits while locomoting over level ground. Toward that end, we arrange a family of dynamical reference generators over the “Gait Complex” and construct automated coordination controllers to force the legged system to converge to a specified cell’s gait, while assessing the relative static stability of gaits by approximating their stability margin via transit through a “Stance Complex”. To integrate these two different constructs—the Gait Complex describing possible gaits, the Stance Complex defining safe locomotion—we utilize our compositional lexicon to plan switching policies for a hybrid control approach. Results include automated gait transitions for a variety of useful gaits, shown via tests on a hexapedal robot

Dynamical system representation, generation, and recognition of basic oscillatory motion gestures

We present a system for generation and recognition of oscillatory gestures. Inspired by gestures used in two representative human-to-human control areas, we consider a set of oscillatory motions and refine from them a 24 gesture lexicon. Each gesture is modeled as a dynamical system with added geometric constraints to allow for real time gesture recognition using a small amount of processing time and memory. The gestures are used to control a pan-tilt camera neck. We propose extensions for use in areas such as mobile robot control and telerobotics

Efficient Immunization Strategies for Computer Networks and Populations

We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquaintance immunization, calls for the immunization of random acquaintances of random nodes (individuals). The strategy requires no knowledge of the node degrees or any other global knowledge, as do targeted immunization strategies. We study analytically the critical threshold for complete immunization. We also study the strategy with respect to the susceptible-infected-removed epidemiological model. We show that the immunization threshold is dramatically reduced with the suggested strategy, for all studied cases.Comment: Revtex, 5 pages, 4 ps fig

Semi-Classical Description of Antiproton Capture on Atomic Helium

A semi-classical, many-body atomic model incorporating a momentum-dependent Heisenberg core to stabilize atomic electrons is used to study antiproton capture on Helium. Details of the antiproton collisions leading to eventual capture are presented, including the energy and angular momentum states of incident antiprotons which result in capture via single or double electron ionization, i.e. into [He$^{++}\,\bar p$ or He$^{+}\,\bar p$], and the distribution of energy and angular momentum states following the Auger cascade. These final states are discussed in light of recently reported, anomalously long-lived antiproton states observed in liquid He.Comment: 15 pages, 9 figures may be obtained from authors, Revte

Nucleon-Nucleon Scattering under Spin-Isospin Reversal in Large-N_c QCD

The spin-flavor structure of certain nucleon-nucleon scattering observables derived from the large N_c limit of QCD in the kinematical regime where time-dependent mean-field theory is valid is discussed. In previous work, this regime was taken to be where the external momentum was of order N_c which precluded the study of differential cross sections in elastic scattering. Here it is shown that the regime extends down to order N_c^{1/2} which includes the higher end of the elastic regime. The prediction is that in the large N_c limit, observables describable via mean-field theory are unchanged when the spin and isospin of either nucleon are both flipped. This prediction is tested for proton-proton and neutron-proton elastic scattering data and found to fail badly. We argue that this failure can be traced to a lack of a clear separation of scales between momentum of order N_c^{1/2} and N_c^1 when N_c is as small as three. The situation is compounded by an anomalously low particle production threshold due to approximate chiral symmetry.Comment: 5 pages, 1 figur