ON COMPUTING A BUY/COPY POLICY USING THE PITT-KRAFT MODEL

The Pitt-Kraft model of buying versus photocopying results in a small, but complex, nonlinear program. This paper identifies a Kuhn-Tucker point and demonstrates that for certain parameter values it is not optimal. A policy generation procedure is presented; the purpose is to prevent convergence of a primal algorithm to this inferior policy, which satisfies the Kuhn-Tucker optimality conditions

Regional differences in the coupling between resting cerebral blood flow and metabolism may indicate action preparedness as a default state.

Although most functional neuroimaging studies examine task effects, interest intensifies in the "default" resting brain. Resting conditions show consistent regional activity, yet oxygen extraction fraction constancy across regions. We compared resting cerebral metabolic rates of glucose (CMRgl) measured with 18F-labeled 2-fluoro-2-deoxy-D-glucose to cerebral blood flow (CBF) 15O-H2O measures, using the same positron emission tomography scanner in 2 samples (n = 60 and 30) of healthy right-handed adults. Region to whole-brain ratios were calculated for 35 standard regions of interest, and compared between CBF and CMRgl to determine perfusion relative to metabolism. Primary visual and auditory areas showed coupling between CBF and CMRgl, limbic and subcortical regions--basal ganglia, thalamus and posterior fossa structures--were hyperperfused, whereas association cortices were hypoperfused. Hyperperfusion was higher in left than right hemisphere for most cortical and subcallosal limbic regions, but symmetric in cingulate, basal ganglia and somatomotor regions. Hyperperfused regions are perhaps those where activation is anticipated at short notice, whereas downstream cortical modulatory regions have longer "lead times" for deployment. The novel observation of systematic uncoupling of CBF and CMRgl may help elucidate the potential biological significance of the "default" resting state. Whether greater left hemispheric hyperperfusion reflects lateral dominance needs further examination

Superfield Realizations of Lorentz and CPT Violation

Superfield realizations of Lorentz-violating extensions of the Wess-Zumino model are presented. These models retain supersymmetry but include terms that explicitly break the Lorentz symmetry. The models can be understood as arising from superspace transformations that are modifications of the familiar one in the Lorentz-symmetric case.Comment: 10 page

The chameleon groups of Richard J. Thompson: automorphisms and dynamics

The automorphism groups of several of Thompson's countable groups of piecewise linear homeomorphisms of the line and circle are computed and it is shown that the outer automorphism groups of these groups are relatively small. These results can be interpreted as stability results for certain structures of PL functions on the circle. Machinery is developed to relate the structures on the circle to corresponding structures on the line

All-Optical Switching with Transverse Optical Patterns

We demonstrate an all-optical switch that operates at ultra-low-light levels and exhibits several features necessary for use in optical switching networks. An input switching beam, wavelength $\lambda$, with an energy density of $10^{-2}$ photons per optical cross section [$\sigma=\lambda^2/(2\pi)$] changes the orientation of a two-spot pattern generated via parametric instability in warm rubidium vapor. The instability is induced with less than 1 mW of total pump power and generates several $\mu$Ws of output light. The switch is cascadable: the device output is capable of driving multiple inputs, and exhibits transistor-like signal-level restoration with both saturated and intermediate response regimes. Additionally, the system requires an input power proportional to the inverse of the response time, which suggests thermal dissipation does not necessarily limit the practicality of optical logic devices

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields

We study the arithmetic of Eisenstein cohomology classes (in the sense of G. Harder) for symmetric spaces associated to GL_2 over imaginary quadratic fields. We prove in many cases a lower bound on their denominator in terms of a special L-value of a Hecke character providing evidence for a conjecture of Harder that the denominator is given by this L-value. We also prove under some additional assumptions that the restriction of the classes to the boundary of the Borel-Serre compactification of the spaces is integral. Such classes are interesting for their use in congruences with cuspidal classes to prove connections between the special L-value and the size of the Selmer group of the Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected statement of Theorem 3, and revised introductio

Spin-Charge Decoupling and Orthofermi Quantum Statistics

Currently Gutzwiller projection technique and nested Bethe ansatz are two main methods used to handle electronic systems in the $U$ infinity limit. We demonstrate that these two approaches describe two distinct physical systems. In the nested Bethe ansatz solutions, there is a decoupling between the spin and charge degrees of freedom. Such a decoupling is absent in the Gutzwiller projection technique. Whereas in the Gutzwiller approach, the usual antisymmetry of space and spin coordinates is maintained, we show that the Bethe ansatz wave function is compatible with a new form of quantum statistics, viz., orthofermi statistics. In this statistics, the wave function is antisymmetric in spatial coordinates alone. This feature ultimately leads to spin-charge decoupling.Comment: 12 pages, LaTex Journal_ref: A slightly abridged version of this paper has appeared as a brief report in Phys. Rev. B, Vol. 63, 132405 (2001