Making use of the N = 2 Liouville theory and world-sheet techniques, we study the properties of D-branes wrapped around vanishing SUSY cycles of singular Calabi-Yau n-folds (n = 2, 3, 4). After constructing boundary states describing the wrapped branes, we evaluate the disc amplitudes corresponding to the periods of SUSY cycles. We use the old technique of KPZ scaling in Liouville theory and de...

This paper considers the classical Shannon sampling theorem in multiresolution spaceswith scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal. They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar function, which...

Let F be a commutative ring with 1. For every set Σ, denote by F the set of all set functions a : Σ → F . This is an F -algebra under pointwise addition, pointwise scaling, and pointwise multiplication; i.e., for a, b in F and for λ in F , for every σ in Σ we define (a+ b)(σ) := a(σ) + b(σ), (λ · b)(σ) := λ · b(σ), (a · b)(σ) := a(σ) · b(σ). These structures make F into a commutative F -algebra...

Although factor analysis is the most commonly-used method for examining the structure of cognitive variable interrelations, multidimensional scaling (MDS) can provide visual representations highlighting the continuous nature of interrelations among variables. Using data (N = 8,813; ages 17-97 years) aggregated across 38 separate studies, MDS was applied to 16 cognitive variables representative ...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. The link between the scaling function extracted from the analysis of (e, e) cross sections and the spectral functio...

The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x∼t(1/2)) and a subdiffusive (x∼t(γ) with a given γ<1/2) length scale, respectively, (ii) the...