New results on the peak algebra

The peak algebra is a unital subalgebra of the symmetric group algebra, linearly spanned by sums of permutations with a common set of peaks. By exploiting the combinatorics of sparse subsets of [n−1] (and of certain classes of compositions of n called almost-odd and thin), we construct three new linear bases of . We discuss two peak analogs of the first Eulerian idempotent and construct a basis of semi-idempotent elements for the peak algebra. We use these bases to describe the Jacobson radical of and to characterize the elements of in terms of the canonical action of the symmetric groups on the tensor algebra of a vector space. We define a chain of ideals of , j = 0,..., , such that is the linear span of sums of permutations with a common set of interior peaks and is the peak algebra. We extend the above results to , generalizing results of Schocker (the case j = 0). Aguiar supported in part by NSF grant DMS-0302423 Orellana supported in part by the Wilson Foundation     

Exotic axion cosmology in theories with phase transitions below the QCD scale

We show that axion phenomenology may be significantly different than conventionally assumed in theories which exhibit late phase transitions (below the QCD scale). In such theories, one can find multiple pseudoscalars with axionlike couplings to matter, including a string scale axion, whose decay constant far exceeds the conventional cosmological bound. Such theories have several dark matter candidates.     

Multisegmented one-dimensional nanorods prepared by hard-template synthetic methods

In the science and engineering communities, the nanoscience revolution is intensifying. As many types of nanomaterials are becoming more reliably synthesized, they are being used for novel applications in all branches of nanoscience and nanotechnology. Since it is sometimes desirable for single nanomaterials to perform multiple functions simultaneously, multicomponent nanomaterials, such as core-shell, alloyed, and striped nanoparticles, are being more extensively researched. Nanoscientists hope to design multicomponent nanostructures and exploit their inherent multiple functionalities for use in many novel applications. This review highlights recent advances in the synthesis of multisegmented one-dimensional nanorods and nanowires with metal, semiconductor, polymer, molecular, and even gapped components. It also discusses the applications of these multicomponent nanomaterials in magnetism, self-assembly, electronics, biology, catalysis, and optics. Particular emphasis is placed on the new materials and devices achievable using these multicomponent, rather than single-component, nanowire structures.     

Smoothness of convolution powers of orbital measures on the symmetric space SU(n)/SO(n)

We prove that if m_a = m_K*d_a*m_K{\mu _{a}\,{=}\,m_{K}*\delta _{a}*m_{K}} is the K-bi-invariant measure supported on the double coset KaK í SU(n){KaK\subseteq SU(n)} , for K = SO(n), then m_a^k{\mu _{a}^{k}} is absolutely continuous with respect to the Haar measure on SU(n) for all a not in the normalizer of K if and only if k ≥ n. The measure, μ _a , supported on the minimal dimension double coset has the property that m_a^n-1{\mu _{a}^{n-1}} is singular to the Haar measure.     

Envisioning uncertainty in geospatial information

Geospatial reasoning has been an essential aspect of military planning since the invention of cartography. Although maps have always been a focal point for developing situational awareness, the dawning era of network-centric operations brings the promise of unprecedented battlefield advantage due to improved geospatial situational awareness. Geographic information systems (GIS) and GIS-based decision support systems are ubiquitous within current military forces, as well as civil and humanitarian organizations. Understanding the quality of geospatial data is essential to using it intelligently. A systematic approach to data quality requires: estimating and describing the quality of data as they are collected; recording the data quality as metadata; propagating uncertainty through models for data processing; exploiting uncertainty appropriately in decision support tools; and communicating to the user the uncertainty in the final product. There are shortcomings in the state-of-the-practice in GIS applications in dealing with uncertainty. No single point solution can fully address the problem. Rather, a system-wide approach is necessary. Bayesian reasoning provides a principled and coherent framework for representing knowledge about data quality, drawing inferences from data of varying quality, and assessing the impact of data quality on modeled effects. Use of a Bayesian approach also drives a requirement for appropriate probabilistic information in geospatial data quality metadata. This paper describes our research on data quality for military applications of geospatial reasoning, and describes model views appropriate for model builders, analysts, and end users.     

Deflected mirage mediation: a phenomenological framework for generalized supersymmetry breaking

We present a general phenomenological framework for dialing between gravity mediation, gauge mediation, and anomaly mediation. The approach is motivated from recent developments in moduli stabilization, which suggest that gravity mediated terms can be effectively loop suppressed and thus comparable to gauge and anomaly mediated terms. The gauginos exhibit a mirage unification behavior at a "deflected" scale, and gluinos are often the lightest colored sparticles. The approach provides a rich setting in which to explore generalized supersymmetry breaking at the CERN Large Hadron Collider.