The Dualizing Spectrum, II

To an inclusion topological groups H->G, we associate a naive G-spectrum. The special case when H=G gives the dualizing spectrum D_G introduced by the author in the first paper of this series. The main application will be to give a purely homotopy theoretic construction of Poincare embeddings in stable codimension.Comment: Fixed an array of typo

Poincare submersions

We prove two kinds of fibering theorems for maps X --> P, where X and P are Poincare spaces. The special case of P = S^1 yields a Poincare duality analogue of the fibering theorem of Browder and Levine.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-2.abs.html Version 5: Statement of Theorem B corrected, see footnote p2

Solvable and/or integrable and/or linearizable N-body problems in ordinary (three-dimensional) space. I

Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact treatment (``solvable'' and/or ``integrable'' and/or ``linearizable''). These equations of motion are always rotation-invariant, and sometimes translation-invariant as well. In many cases they are Hamiltonian, but the discussion of this aspect is postponed to a subsequent paper. We consider ``few-body problems'' (with, say, \textit{N}=1,2,3,4,6,8,12,16,...) as well as ``many-body problems'' (N an arbitrary positive integer). The main focus of this paper is on various techniques to uncover such N-body problems. We do not discuss the detailed behavior of the solutions of all these problems, but we do identify several models whose motions are completely periodic or multiply periodic, and we exhibit in rather explicit form the solutions in some cases

Muon Production in Relativistic Cosmic-Ray Interactions

Cosmic-rays with energies up to $3\times10^{20}$ eV have been observed. The nuclear composition of these cosmic rays is unknown but if the incident nuclei are protons then the corresponding center of mass energy is $\sqrt{s_{nn}} = 700$ TeV. High energy muons can be used to probe the composition of these incident nuclei. The energy spectra of high-energy ($>$ 1 TeV) cosmic ray induced muons have been measured with deep underground or under-ice detectors. These muons come from pion and kaon decays and from charm production in the atmosphere. Terrestrial experiments are most sensitive to far-forward muons so the production rates are sensitive to high-$x$ partons in the incident nucleus and low-$x$ partons in the nitrogen/oxygen targets. Muon measurements can complement the central-particle data collected at colliders. This paper will review muon production data and discuss some non-perturbative (soft) models that have been used to interpret the data. I will show measurements of TeV muon transverse momentum ($p_T$) spectra in cosmic-ray air showers from MACRO, and describe how the IceCube neutrino observatory and the proposed Km3Net detector will extend these measurements to a higher $p_T$ region where perturbative QCD should apply. With a 1 km$^2$ surface area, the full IceCube detector should observe hundreds of muons/year with $p_T$ in the pQCD regime.Comment: 4 pages, 2 figures - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennessee. Tweaked formatting at organizers reques

The Veterans Health Administration: Implementing Patient-Centered Medical Homes in the Nation's Largest Integrated Delivery System

Describes the implementation of a model that organizes care around an interdisciplinary team of providers who work to identify and remove barriers to access and clinical effectiveness in primary care clinics. Outlines two case studies and lessons learned

Hamiltonian spectral invariants, symplectic spinors and Frobenius structures II

In this article, we continue our study of 'Frobenius structures' and symplectic spectral invariants in the context of symplectic spinors. By studying the case of $C^1$-small Hamiltonian mappings on symplectic manifolds $M$ admitting a metaplectic structure and a parallel $\hat O(n)$-reduction of its metaplectic frame bundle we derive how the construction of 'singularly rigid' resp. 'self-dual' pairs of irreducible Frobenius structures associated to this Hamiltonian mapping $\Phi$ leads to a Hopf-algebra-type structure on the set of irreducible Frobenius structures. We then generalize this construction and define abstractly conditions under which 'dual pairs' associated to a given $C^1$-small Hamiltonian mapping emerge, these dual pairs are esssentially pairs $(s_1, J_1), (s_2, J_2)$ of closed sections of the cotangent bundle $T^*M$ and (in general singular) comptaible almost complex structures on $M$ satisfying certain integrability conditions involving a Koszul bracket. In the second part of this paper, we translate these characterizing conditions for general 'dual pairs' of Frobenius structures associated to a $C^1$-small Hamiltonian system into the notion of matrix factorization. We propose an algebraic setting involving modules over certain fractional ideals of function rings on $M$ so that the set of 'dual pairs' in the above sense and the set of matrix factorizations associated to these modules stand in bijective relation. We prove, in the real-analytic case, a Riemann Roch-type theorem relating a certain Euler characteristic arising from a given matrix factorization in the above sense to (integral) cohomological data on $M$ using Cheeger-Simons-type differential characters, derived from a given pair $(s_1, J_1), (s_2, J_2)$. We propose extensions of these techniques to the case of 'geodesic convexity-smallness' of $\Phi$ and to the case of general Hamiltonian systems on $M$.Comment: 24 pages, minor corrections in statement and proof of Theorem 1.11, this paper builds in content, notation and referencing on arXiv:1411.423

Remembering with and without Memory: A Theory of Memory and Aspects of Mind that Enable its Experience

This article builds on ideas presented in Klein (2015a) concerning the importance of a more nuanced, conceptually rigorous approach to the scientific understanding and use of the construct “memory”. I first summarize my model, taking care to situate discussion within the terminological practices of contemporary philosophy of mind. I then elucidate the implications of the model for a particular operation of mind – the manner in which content presented to consciousness realizes its particular phenomenological character (i.e., mode of presentation). Finally, I discuss how the model offers a reconceptualization of the technical language used by psychologists and neuroscientists to formulate and test ideas about memory