Related papers: Hypercontractivity on High Dimensional Expanders: …
We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the…
Optimization techniques are at the core of many scientific and engineering disciplines. The steepest descent methods play a foundational role in this area. In this paper we studied a generalized steepest descent method on Riemannian…
The effect of concentration on coil-stretch hysteresis in extensional flows of polymer solutions is examined with insights from Brownian dynamics simulations of isolated chains and scaling theory for non-dilute solutions. In the hysteresis…
Distributionally robust optimization (DRO) is a worst-case framework for stochastic optimization under uncertainty that has drawn fast-growing studies in recent years. When the underlying probability distribution is unknown and observed…
We introduce a systematic expansion tailored to systems with strong local interactions and capable of computing response functions, including finite DC transport, analytically. The expansion is controlled by a small parameter $s^2$ that…
We study the dynamics of local bond orientation in regular hyperbranched polymers modeled by Vicsek fractals. The local dynamics is investigated through the temporal autocorrelation functions of single bonds and the corresponding relaxation…
Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. We present here an efficient Fourier-space based…
We show local and cocycle rigidity for $\R^k \times \Z^l$ partially hyperbolic translation actions on homogeneous spaces $\mc G/ \Lambda$. We consider a large class of actions whose geometric properties are more complicated than previously…
We prove some extension theorems for quaternionic holomorphic functions in the sense of Fueter. Starting from the existence theorem for the nonhomogeneous Cauchy-Riemann-Fueter Problem, we prove that an $\mathbb{H}$-valued function $f$ on a…
We show the existence of length-constrained expander decomposition in directed graphs and undirected vertex-capacitated graphs. Previously, its existence was shown only in undirected edge-capacitated graphs [Haeupler-R\"acke-Ghaffari, STOC…
Deep-learning models have enabled performance leaps in analysis of high-dimensional functional MRI (fMRI) data. Yet, many previous methods are suboptimally sensitive for contextual representations across diverse time scales. Here, we…
We strengthen the notion of "double samplers", first introduced by Dinur and Kaufman [Proc. 58th FOCS, 2017], which are samplers with additional combinatorial properties, and whose existence we prove using high dimensional expanders. The…
We generalize the recently introduced TRILEX approach (TRiply Irreducible Local EXpansion) to superconducting phases. The method treats simultaneously Mott and spin-fluctuation physics using an Eliashberg theory supplemented by local vertex…
We derive an exact contrast-expansion formalism for the effective conductivity of heterogeneous materials (media) with local properties described by arbitrary continuous random fields, significantly generalizing the widely used binary-field…
Hyperdimensional computing (HDC) is an increasingly popular computing paradigm with immense potential for future intelligent applications. Although the main ideas already took form in the 1990s, HDC recently gained significant attention,…
In this paper some concepts of convex analysis on hyperbolic space are studied. We first study properties of the intrinsic distance, for instance, we present the spectral decomposition of its Hessian. Next, we study the concept of convex…
This work consists in applying the analysis of integrable models to study the problem of Hyper-Kahler metrics building. In this context, we use the harmonic superspace language applied to D=2 N=4 SU(2) Liouville self interacting model and…
We find a class of four dimensional deformed conformal field theories which appear extra dimensional when their gauge symmetries are spontaneously broken. The theories are supersymmetric moose models which flow to interacting conformal…
Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point -- a stationary point of the hyper-objective function obtained by minimizing or maximizing…
Learning effective multi-modal 3D representations of objects is essential for numerous applications, such as augmented reality and robotics. Existing methods often rely on task-specific embeddings that are tailored either for semantic…