These notes are a considerably revised and expanded version of expository lectures given at the Fields Institute Workshop on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" in August 2017. We give a complete and self-cont...
his war elephants had died of injuries or the cold that winter, and none took part in the succeeding battles.[citation needed] Hannibal quartered his
We ask whether it is possible to anonymously communicate a large amount of data using only public (non-anonymous) communication together with a small anonymous channel. We think this is a central question in the theory of anonymous communication and...
We analytically study the effect of a uniform shear flow on the persistence properties of coarsening systems. The study is carried out within the anisotropic Ohta-Jasnow-Kawasaki (OJK) approximation for a system with nonconserved scalar order param...
A perturbation expansion is considered about the Ohta-Jasnow-Kawasaki theory of phase-ordering dynamics; the non-linear terms neglected in the OJK calculation are reinstated and treated as a perturbation to the linearised equation. The first order...
The perturbation theory expansion presented earlier to describe the phase-ordering kinetics in the case of a nonconserved scalar order parameter is generalized to the case of the $n$-vector model. At lowest order in this expansion, as in the scalar...
A consistent perturbation theory expansion is presented for phase-ordering kinetics in the case of a nonconserved scalar order parameter. At zeroth order in this expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At the next n...
A consistent perturbation theory expansion is presented for phase ordering kinetics in the case of a nonconserved scalar order parameter. At lowest order in this formal expansion one obtains the theory due to Ohta, Jasnow and Kawasaki (OJK). At nex...
Numerous security metrics have been proposed in the past for protecting computer networks. However we still lack effective techniques to accurately measure the predictive security risk of an enterprise taking into account the dynamic attributes assoc...
An $R$-algebra $S$ is $R$-solid if there exists a nonzero $R$-linear map $S \rightarrow R$. In characteristic $p$, the study of $F$-singularities such as Frobenius splittings implicitly rely on the $R$-solidity of $R^{1/p}$. Following recent results...
Maryland is one of the most multicultural states in the country; it is one of the nine states where non-Whites compose a majority of the population, with the fifth-highest percentage of African Americans, …
The Gemini theorem asserts that, given certain reasonable assumptions, no physical system can be certainly aware of its own existence. The theorem can be proved algorithmically, but the proof of this theorem is somewhat obscure, and there exists very...
The problem of f-divergence estimation is important in the fields of machine learning, information theory, and statistics. While several nonparametric divergence estimators exist, relatively few have known convergence properties. In particular, even...
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Sponsor has a verb form to describe the action of supporting or leading something. You can sponsor a nonprofit arts organization by donating and participating on the board.
The XXX Gaudin model with generic integrable boundaries specified by the most general non-diagonal K-matrices is studied by the off-diagonal Bethe ansatz method. The eigenvalues of the associated Gaudin operators and the corresponding Bethe ansatz eq...
We study the thermodynamics of the isotropic Heisenberg XXX spin chain with negative spin, focusing on the case $s=-1$. The model is equivalent to the quantum lattice nonlinear Schrödinger (NLS) model and appears as an effective theory in deep inela...
We study the continuous resonant (CR) equation which was derived by Faou-Germain-Hani as the large-box limit of the cubic nonlinear Schrödinger equation in the small nonlinearity (or small data) regime. We first show that the system arises in anothe...
Multi-channel acoustic signal processing is a well-established and powerful tool to exploit the spatial diversity between a target signal and non-target or noise sources for signal enhancement. However, the textbook solutions for optimal data-depende...
We present a technique for simultaneous power-combining and wavelength-conversion of multiple fiber lasers into a single, lower wavelength in a different band through Raman-based, nonlinear power combining. We illustrate this by power combining of tw...