The goal of this section is to prove the following mild generalization of Theorem 1.4.

For a prime $\ell$ and an abelian variety $A$ over a global field $K$, the $\ell$-parity conjecture predicts that, in accordance with the ideas of Bi…

We propose a new dataset for evaluating question answering models with respect to their capacity to reason about beliefs. Our tasks are inspired by t…

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is deterministic, state-specific, applies a variational principle to a minimally correlated ansatz, prod…

We present a mean field theory for excited states that is broadly analogous to ground state Hartree-Fock theory. Like Hartree-Fock, our approach is d…

We would like to thank Mark Bun and Justin Thaler for helpful discussions and feedback on an early draft of this work. We would also like to thank Harry Buhrman for bringing reference [BdW98] to our attention. R.K. would like to thank Jeongwan Haah …

We prove lower bounds on complexity measures, such as the approximate degree of a Boolean function and the approximate rank of a Boolean matrix, usin…

We have analyzed algorithms for optimization problems that use only random function values—as opposed to gradient computations—to minimize an objective function. The algorithms we present are optimal: their convergence rates cannot be improved (in a…

We consider derivative-free algorithms for stochastic and non-stochastic convex optimization problems that use only function values rather than gradi…

Under Assumption 5, Assumption 1 is satisfied for d1∈N, Gd1:[Δ×{0,1}]d1→D. Then, there exists md1({δi}mi=1)∈Id1 such that Hmd1=Gd1({(δi,\mathbbm1T(δi))}i∈md1) is consistent with {(δi,\mathbbm1T(δi))}mi=1. Since Hmd1={δ∈Δ: g(xd1({δi}i∈md1),δ)≤0},

We investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistenc…

Gravitational non-linear evolution induces a shift in the position of the baryon acoustic oscillations (BAO) peak together with a damping and broaden…

We present a variational function that targets excited states directly based on their position in the energy spectrum, along with a Monte Carlo metho…

We report an evaluation of a semi-empirical quantum chemical method PM7 from the perspective of uncertainty quantification. Specifically, we apply Bo…

In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general e…

Cross-correlations between biased tracers and the dark matter field encode information about the physical variables which characterize these tracers.…

This paper presents a new teleoperated spherical tensegrity robot capable of performing locomotion on steep inclined surfaces. With a novel control s…

Inference algorithms in probabilistic programming languages (PPLs) can be thought of as interpreters, since an inference algorithm traverses a model …

We considered the problem of inducing efficient equilibria in traffic networks with mixed vehicle autonomy via pricing. We showed that minimum social delay may not be attained by imposing undifferentiated link prices, in which human–driven and auton…

In a traffic network, vehicles normally select their routes selfishly. Consequently, traffic networks normally operate at an equilibrium characterize…

In this paper, we establish lower bounds on the ratio of posterior probabilities R(s|{xi}ni=1) for the number of clusters under several settings of prior distributions on the parameter space. The aim of our study is to increase our understanding of …

Dirichlet process mixture models (DPMM) play a central role in Bayesian nonparametrics, with applications throughout statistics and machine learning.…

It is common to implicitly assume access to intelligently captured inputs (e.g., photos from a human photographer), yet autonomously capturing good o…

Traditional Markov chain Monte Carlo (MCMC) sampling of hidden Markov models (HMMs) involves latent states underlying an imperfect observation proces…

Robot design is often a slow and difficult process requiring the iterative construction and testing of prototypes, with the goal of sequentially opti…

A star approaching a supermassive black hole (SMBH) can be torn apart in a tidal disruption event (TDE). We examine ultra-deep TDEs, a new regime in …

We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with…

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