Acoustic cues such as pitch height and timing are effective at communicating emotion in both music and speech. Numerous experiments altering musical passages have shown that higher and faster melodies generally sound "happier" than lower and slower melodies, findings consistent with corpus analyses of emotional speech. However, equivalent corpus analyses of complex time-varying cues in music ar...

We describe geometric realizations for various classes of admissible representations of reductive Lie groups. The representations occur on partially holomorphic cohomology spaces corresponding to partially holomorphic homogeneous vector bundles over real group orbits in complex flag manifolds. The representations in question include standard tempered and limits of standard tempered representati...

The presence of nonlocal interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role formulating new generation large-eddy simulation (LES) models higher fidelity. We establish tempered fractional-order modeling framework for developing LES subgrid-scale models, starting from kinetic transport. employ L\'evy-stable distributio...

Svetlozar T. Rachev∗ Chair-Professor, Chair of Statistics, Econometrics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and KIT, and Department of Statistics and Applied Probability, University of California, Santa Barbara, and Chief-Scientist, FinAnalytica INC Kollegium am Schloss, Bau II, 20.12, R210, Postfach 6980, D-76128, Karlsruhe, Germany T...

Let G be a reductive group over a non-Archimedean local field. For two tempered smooth representations, it makes no difference for the Ext-groups whether we work in the category of tempered smooth representations of G or of all smooth representations of G. Similar results hold for certain discrete groups. We explain the basic ideas from functional analysis and geometric group theory that are ne...

We derive general properties of anomalous diffusion and nonexponential relaxation from the theory of tempered -stable processes. The tempering results in the existence of all moments of operational time. The subordination by the inverse tempered -stable process provides diffusion relaxation that occupies an intermediate place between subdiffusion Cole-Cole law and normal diffusion exponential l...

We provide a few natural applications of the analytic newvectors, initiated in \cite{JN} arXiv:1911.01880, to some questions automorphic forms for $\mathrm{PGL}_n(\mathbb{Z})$ with $n\ge 2$, archimedean conductor aspect. prove an orthogonality result Fourier coefficients, density estimate non-tempered forms, equidistribution Satake parameters respect Sato--Tate measure, and second moment centra...

The problem of simulation of multivariate Lévy processes is investigated. A method based on generalized shot noise series representations of Lévy processes combined with Gaussian approximation of the remainder is established in full generality. This method is applied to multivariate stable and tempered stable processes and formulas for their approximate simulation are obtained. Key-words: Lévy ...