Sim(2) and SUSY

The proposal of hep-ph/0601236, that the laws of physics in flat spacetime need be invariant only under a SIM(2) subgroup of the Lorentz group, is extended to include supersymmetry. $\mathcal{N}=1$ SUSY gauge theories which include SIM(2) couplings for the fermions in chiral multiplets are formulated. These theories contain two conserved supercharges rather than the usual four.Comment: 10 pages, revtex4. Note added and sign correcte

The Regulation of Biological Pollution: Preventing Exotic Species Invasions from Ballast Water Discharged into California Coastal Waters

In Part I of this article, we describe ballast water\u27s use, its contribution to biological invasions, and the technical approaches that could be used to combat the problem. In Part II, we describe opportunities for employing existing laws and regulations to manage ballast discharges in California. We first discuss the limitations of international, federal and state laws that have tried to address ballast discharges of exotic organisms as a shipping issue. We then consider the potential for regulating ballast discharges under federal and state laws aimed at controlling water pollution, protecting wildlife, ensuring the assessment, disclosure and mitigation of environmental impacts, and providing for the planning and management of coastal zone development. While we evaluate these laws in terms of their potential application in California, the federal laws and, in many cases, corresponding state laws could be applied in other coastal regions. We conclude by summarizing how existing regulations may provide a comprehensive overall framework for achieving effective regulation of ballast water discharges

Parameter Uncertainty in the Kalman--Bucy Filter

In standard treatments of stochastic filtering one first has to estimate the parameters of the model. Simply running the filter without considering the reliability of this estimate does not take into account this additional source of statistical uncertainty. We propose an approach to address this problem when working with the continuous time Kalman--Bucy filter, by making evaluations via a nonlinear expectation. We show how our approach may be reformulated as an optimal control problem, and proceed to analyze the corresponding value function. In particular we present a novel uniqueness result for the associated Hamilton--Jacobi--Bellman equation

Ergodic backward stochastic difference equations

We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain this result, we use a Nummelin splitting argument to obtain ergodicity estimates for a discrete time Markov chain which hold uniformly under suitable perturbations of its transition matrix. We conclude with an application of this theory to a treatment of an ergodic control problem

Pathwise stochastic control with applications to robust filtering

We study the problem of pathwise stochastic optimal control, where the optimization is performed for each fixed realisation of the driving noise, by phrasing the problem in terms of the optimal control of rough differential equations. We investigate the degeneracy phenomenon induced by directly controlling the coefficient of the noise term, and propose a simple procedure to resolve this degeneracy whilst retaining dynamic programming. As an application, we use pathwise stochastic control in the context of stochastic filtering to construct filters which are robust to parameter uncertainty, demonstrating an original application of rough path theory to statistics

(De)Constructing Dimensions

We construct renormalizable, asymptotically free, four dimensional gauge theories that dynamically generate a fifth dimension.Comment: 10 pages, late

Electric Scooter Injuries and Hospital Admissions in the United States, 2014-2018.

This study investigates trends of injury and hospital admission associated with electric scooter use

Phenomenology of Electroweak Symmetry Breaking from Theory Space

Recently, a new class of realistic models for electroweak symmetry breaking have been constructed, without supersymmetry. These theories have naturally light Higgs bosons and perturbative new physics at the TeV scale. We describe these models in detail, and show that electroweak symmetry breaking can be triggered by a large top quark Yukawa coupling. A rich spectrum of particles is predicted, with a pair of light Higgs doublets accompanied by new light weak triplet and singlet scalars. The lightest of these new scalars is charged under a geometric discrete symmetry and is therefore stable, providing a new candidate for WIMP dark matter. At TeV energies, a plethora of new heavy scalars, gauge bosons and fermions are revealed, with distinctive quantum numbers and decay modes.Comment: 22 pages, latex, 6 figures. Numerical results corrected, clarifications added, conclusions unchange