The "plus" side of epilepsy phenotyping

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Weyl calculus and dual pairs

We consider a dual pair $(G,G')$, in the sense of Howe, with $G$ compact acting on $L^2(\mathbb R^n)$ for an appropriate $n$ via the Weil Representation. Let $\widetilde{G}$ be the preimage of $G$ in the metaplectic group. Given a genuine irreducible unitary representation $\Pi$ of $\widetilde{G}$ we compute the Weyl symbol of orthogonal projection onto $L^2(\mathbb R^n)_\Pi$, the $\Pi$-isotypic component. We apply the result to obtain an explicit formula for the character of the corresponding irreducible unitary representation $\Pi'$ of $\widetilde{G'}$ and to compute of the wave front set of $\Pi'$ by elementary means

Semisimple orbital integrals on the symplectic space for a real reductive dual pair

We prove a Weyl Harish-Chandra integration formula for the action of a reductive dual pair on the corresponding symplectic space $W$. As an intermediate step, we introduce a notion of a Cartan subspace and a notion of an almost semisimple element in the symplectic space $W$. We prove that the almost semisimple elements are dense in $W$. Finally, we provide estimates for the orbital integrals associated with the different Cartan subspaces in $W$

A systematic analysis of X-ray afterglows of gamma-ray burst observed by XMM-Newton

This work is part of a systematic re-analysis program of all the data of Gamma-Ray Burst (GRB) X-ray afterglows observed so far, in order to constrain the GRB models. We present here a systematic analysis of those afterglows observed by XMM-Newton between January 2000 and March 2004. This dataset includes GRB 011211 and GRB 030329. We have obtained spectra, light curves and colors for these afterglows. In this paper we focus on the continuum spectral and temporal behavior. We compare these values with the theoretical ones expected from the fireball model. We derive constraints about the burst environment (absorption, density profile) and put constraints on their beaming angle.Comment: 7 pages, 2 figures, COSPAR proceeding accepted for publication in Advances in Space Researc

Fiscal Policy and US-Canadian Trade

A factor-augmented vector autoregressive (FAVAR) model is applied to determine the effects of a rise in US government expenditure on the United States and Canadian economies. The results obtained reasonably characterize the effect of a rise in US government spending to the United States and Canadian economies emphasizing the role of the traded goods sector.Factor Model, Principal Component, Government expenditure, VAR.