Plancherel Inversion as Unified Approach to Wavelet Transforms and Wigner functions

We demonstrate that the Plancherel transform for Type-I groups provides one with a natural, unified perspective for the generalized continuous wavelet transform, on the one hand, and for a class of Wigner functions, on the other. The wavelet transform of a signal is an $L^2$-function on an appropriately chosen group, while the Wigner function is defined on a coadjoint orbit of the group and serves as an alternative characterization of the signal, which is often used in practical applications. The Plancherel transform maps $L^2$-functions on a group unitarily to fields of Hilbert-Schmidt operators, indexed by unitary irreducible representations of the group. The wavelet transform can essentiallly be looked upon as restricted inverse Plancherel transform, while Wigner functions are modified Fourier transforms of inverse Plancherel transforms, usually restricted to a subset of the unitary dual of the group. Some known results both on Wigner functions and wavelet transforms, appearing in the literature from very different perspectives, are naturally unified within our approach. Explicit computations on a number of groups illustrate the theory.Comment: 41 page

Nonlinear Realization of the Local Conform-Affine Symmetry Group for Gravity in the Composite Fiber Bundle Formalism

A gauge theory of gravity based on a nonlinear realization (NLR) of the local Conform-Affine (CA) group of symmetry transformations is presented. The coframe fields and gauge connections of the theory are obtained. The tetrads and Lorentz group metric are used to induce a spacetime metric. The inhomogenously transforming (under the Lorentz group) connection coefficients serve as gravitational gauge potentials used to define covariant derivatives accommodating minimal coupling of matter and gauge fields. On the other hand, the tensor valued connection forms serve as auxillary dynamical fields associated with the dilation, special conformal and deformational (shear) degrees of freedom inherent in the bundle manifold. The bundle curvature of the theory is determined. Boundary topological invariants are constructed. They serve as a prototype (source free) gravitational Lagrangian. The Bianchi identities, covariant field equations and gauge currents are obtained.Comment: 24 pages. to appear in IJGMM

Deformed Complex Hermite Polynomials

We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along the way we also work out some additional properties of the (undeformed) complex Hermite polynomials and their relationships to the standard Hermite polynomials (of a single real variable).Comment: 12 page

Trade Restrictions and Trade Reversal: Lessons from the U.S.-Canada Herring Dispute

This paper analyzes international trade in value added products when free trade and perfect competition in the market for an intermediate product, such as raw fish, are the exception rather than the rule. Current evidence from the General Agreement on Tariffs and Trade (GATT) regarding disputes between countries, such as the V.S.-Canada dispute over trade in raw herring, suggests that bilateral trade in raw fish among major exporters of seafood products may not be completely free of structural and political barriers. The study presents models showing that restrictions on the exportation of raw fish from an exporting country can make possible monopsony behavior by fish processors in a rival exporting country and they outline the market behavior of the players under such circumstances. The analysis illustrates how, under such conditions, economic forces contribute to the creation of trade disputes. It further demonstrates how expansion of the demand for final product may, through trade reversal pressures, dilute the market power of the processor monopsony and make trade restriction policies irrelevant.roe herring, trade reversal, trade restrictions, monopsony, trade dispute, GATT, market imperfection, free trade, fishery management, comparative advantage reversal, Environmental Economics and Policy, International Relations/Trade,

Cosmic Pathways for Compact Groups in the Milli-Millennium Simulation

We detected 10 compact galaxy groups (CGs) at $z=0$ in the semi-analytic galaxy catalog of Guo et al. (2011) for the milli-Millennium Cosmological Simulation (sCGs in mGuo2010a). We aimed to identify potential canonical pathways for compact group evolution and thus illuminate the history of observed nearby compact groups. By constructing merger trees for $z=0$ sCG galaxies, we studied the cosmological evolution of key properties, and compared them with $z=0$ Hickson CGs (HCGs). We found that, once sCG galaxies come within 1 (0.5) Mpc of their most massive galaxy, they remain within that distance until $z=0$, suggesting sCG "birth redshifts". At $z=0$ stellar masses of sCG most-massive galaxies are within $10^{10} \lesssim M_{\ast}/M_{\odot} \lesssim 10^{11}$. In several cases, especially in the two 4- and 5-member systems, the amount of cold gas mass anti-correlates with stellar mass, which in turn correlates with hot gas mass. We define the angular difference between group members' 3D velocity vectors, $\Delta\theta_{\rm vel}$, and note that many of the groups are long-lived because their small values of $\Delta\theta_{\rm vel}$ indicate a significant parallel component. For triplets in particular, $\Delta\theta_{\rm vel}$ values range between $20^{\circ}$ and $40^{\circ}$ so that galaxies are coming together along roughly parallel paths, and pairwise separations do not show large pronounced changes after close encounters. The best agreement between sCG and HCG physical properties is for $M_{\ast}$ galaxy values, but HCG values are higher overall, including for SFRs. Unlike HCGs, due to a tail at low SFR and $M_{\ast}$, and a lack of $M_{\ast}\gtrsim 10^{11}M_{\odot}$ galaxies, only a few sCG galaxies are on the star-forming main sequence.Comment: Style fixes to better match ApJ published version. Uses likeapj1.1 style files: 17 pages, 13 figures, 2 tables. LaTex style files available at https://github.com/qtast/likeapj/releases/lates

White coat hypertension is associated with increased small vessel disease in the brain

Objective: Small vessel disease, as measured by white matter hyperintensity (WMH) in the brain, is known to be associated with increased stroke risk and cognitive impairment. This study explored the relationship between WMH on computerised tomography (CT) and white coat hypertension/effect (WCH/E) in patients with recent transient ischaemic attack (TIA) or lacunar stroke (LS). Design and method: Ninety-six patients recruited for the ASIST trial (Arterial Stiffness in Lacunar Stroke and TIA) underwent measurement of clinic blood pressure (BP) and ambulatory BP monitoring (APBM) within two weeks of TIA or LS. Twenty-three patients had normotension (clinic BP / = 140/90mmHg and day-time ABPM < 135/85mmHg). Arterial stiffness was measured using carotid-femoral pulse wave velocity (PWV) (Complior®, ALAM Medical) and carotid-ankle vascular index (CAVI) (VaSera VS-1500N®, Fukuda Denshi). CT images were scored for WMH using the four-point Fazekas visual rating scale. Patients were grouped into no-mild WMH (scores 0–1) or moderate-severe (scores 2–3) groups. The relationship between BP, vascular stiffness and WMH was explored with t-tests, chi-square and logistic regression accounting for known cardiovascular risk factors. Results: Forty-four percent of patients with WCH/E had moderate-severe WMH compared to 17% of normotensives (p = 0.047). The regression model with WMH as the dependent factor, and WCH/E and cardiovascular risk factors as independent factors showed WCH/E and either CAVI or PWV to be the only independent significant factor contributing to WMH (CAVI:p = 0.038, PWV:p = 0.043)

Coherent States on Hilbert Modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over $C^*$-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert $C^*$-modules which have a natural left action from another $C^*$-algebra say, $\mathcal A$. The coherent states are well defined in this case and they behave well with respect to the left action by $\mathcal A$. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive kernel between two $C^*$-algebras, in complete analogy to the Hilbert space situation. Related to this there is a dilation result for positive operator valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory

Multiple classical limits in relativistic and nonrelativistic quantum mechanics

The existence of a classical limit describing interacting particles in a second-quantized theory of identical particles with bosonic symmetry is proved. This limit exists in addition to a previously established classical limit with a classical field behavior, showing that the limit $\hbar \to 0$ of the theory is not unique. An analogous result is valid for a free massive scalar field: two distinct classical limits are proved to exist, describing a system of particles or a classical field. The introduction of local operators in order to represent kinematical properties of interest is shown to break the permutation symmetry under some localizability conditions, allowing the study of individual particle properties.Comment: 13 page

A complete characterization of phase space measurements

We characterize all the phase space measurements for a non-relativistic particle.Comment: 11 pages, latex, no figures, iopart styl