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We obtain new Poisson type summation formulas with nodes $\pm \sqrt{n}$ and with weights involving the function $r_k(n)$ that gives the number of representations of a positive integer $n$ as the sum of $k$ squares. Our results extend summation formulas due to Guinand an...

A new \emph{spanner} construction algorithm is presented, working under the \emph{LOCAL} model with unique edge IDs. Given an $n$-node communication graph, a spanner with a constant stretch and $O (n^{1 + \varepsilon})$ edges (for an arbitrarily small constant $\varepsi...

Photoluminescence (PL) is a light matter quantum interaction associated with the chemical potential of light formulated by the Generalized Planck's law. Without knowing the inherent temperature dependence of chemical potential, the Generalized Planck's law is insufficie...

We propose a novel approach for microwave and optical fields entanglement using an electrical capacitor loaded with graphene plasmonic waveguide. In the proposed scheme, a quantum microwave signal of frequency ωm drives the electrical capacitor, while an intensiv...

A graph $H$ is {\em $p$-edge colorable} if there is a coloring $\psi: E(H) \rightarrow \{1,2,\dots,p\}$, such that for distinct $uv, vw \in E(H)$, we have $\psi(uv) \neq \psi(vw)$. The {\sc Maximum Edge-Colorable Subgraph} problem takes as input a graph $G$ and integers...

We present a large-scale study on unsupervised spatiotemporal representation learning from videos. With a unified perspective on four recent image-based frameworks, we study a simple objective that can easily generalize all these methods to space-time. Our objective enc...

We theoretically present a design of self-starting operation of microcombs based on laser-cavity solitons in a system composed of a micro-resonator nested in and coupled to an amplifying laser cavity. We demonstrate that it is possible to engineer the modulational-insta...

We study the number of real roots of a Kostlan random polynomial of degree $d$ in one variable. More generally, we are interested in the distribution of the counting measure of the set of real roots of such a polynomial. We compute the asymptotics of the central moments...

The Massively Parallel Computation (MPC) model is an emerging model which distills core aspects of distributed and parallel computation. It has been developed as a tool to solve (typically graph) problems in systems where the input is distributed over many machines with...

To-date, despite remarkable applications in optoelectronics and tremendous amount of theoretical, computational and experimental efforts, there is no technological pathway enabling the fabrication of 3D photonic band gaps in the visible range. The resolution of advanced...