ï»¿The formalism presented here suggests a way in which the dynamics of perturbations in reasonably complicated scalar field theories can be implemented in software such as CAMB. There are a number of benefits to this approach, as well as some drawb…

We present a formalism for the numerical implementation of general theories of dark energy, combining the computational simplicity of the equation of…

In this section, we construct the odd Khovanov Burnside functor, and the odd Khovanov homotopy type as its realization. We also construct a reduced odd Khovanov homotopy type and the unified Khovanov homotopy type. We establish various properties su…

For each link L in S^3 and every quantum grading j, we construct a stable homotopy type X^j_o(L) whose cohomology recovers Ozsvath-Rasmussen-Szabo's …

In this paper, we studied the problem of finding an (ϵ,γ)-second order stationary point (SOSP) of a generic smooth constrained nonconvex minimization problem. We proposed a procedure that obtains an (ϵ,γ)-SOSP after at most O(max{ϵ−2,ρ−3γ−3}) iterat…

In this paper, we focus on escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a …

This research was supervised by Ken Ono at the Emory University Mathematics REU and was supported by the National Science Foundation (grant number DMS-1250467). We would like to thank Ken Ono and Jesse Thorner for offering their advice and guidance …

Let $E/\mathbb{Q}$ be an elliptic curve with complex multiplication (CM), and for each prime $p$ of good reduction, let $a_E(p) = p + 1 - \#E(\mathbb…

We thank Matt Coudron and Matt Hastings for helpful discussions.

We ask, and answer, the question of what's computable by Turing machines equipped with time travel into the past: that is, closed timelike curves or …

The authors would like to thank Willem Fouché, Yonatan Gutman, Alexander Kechris, André Nies, Arno Pauly, Jan Reimann, and Carol Wood for helpful conversations.

We consider the space of countable structures with fixed underlying set in a given countable language. We show that the number of ergodic probability…

S.A. was supported in part by an Alan T. Waterman Award. A.B. was supported in part by the National Science Foundation Graduate Research Fellowship under Grant No. 1122374 and by the Center for Science of Information (CSoI), an NSF Science and Techn…

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but do…

In this section we extend the notion of stably integral points to higher dimensions. First we need to construct models that play the role of stable models, since the latter are not known to exist for dim≥2. The main idea behind our construction is t…

We prove that the Lang-Vojta conjecture implies the number of stably integral points on curves of log general type, and surfaces of log general type …

To solve canonical problems in the setting of Lemma 2, when an a priori bound on C is known or when f is bounded on R+, it suffices to construct a sequence of probability measures ~Pn that weakly converges to P for almost every sample sequence. Sinc…

We propose a general methodology for performing statistical inference within a `rare-events regime' that was recently suggested by Wagner, Viswanath …

We would like to thank Chinmoy Dutta, Gopal Pandurangan, Rajmohan Rajaraman, and Zhifeng Sun for helpful discussions and for sharing their work at an early stage.

We study lower bounds on information dissemination in adversarial dynamic networks. Initially, k pieces of information (henceforth called tokens) are…

Quantum money is an exciting and open area of research. Wiesner’s original scheme is information-theoretically secure, but is not public-key. In this paper, we proved that the stabilizer construction for public-key quantum money [1] is insecure for …

Public-key quantum money is a cryptographic protocol in which a bank can create quantum states which anyone can verify but no one except possibly the…

In this paper, we have studied the minimum cost flow problem in a time-varying network to capture temporal features of many real-world problems. In this problem, arc and node costs, arc and node capacities, and supplies and demands can change over t…

There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the…

Obviously, the main open problem we would like to see resolved is Conjecture 4. One appealing way to prove the conjecture would be to proceed as we have but to obtain a stronger notion of pseudorandomness in the regularity lemma. The notion of ϵ-uni…

The study of the interplay between the testability of properties of Boolean functions and the invariances acting on their domain which preserve the p…

With the preliminaries out of the way, we are now ready to prove Theorem 1.

In 1989, Thomassen asked whether there is an integer-valued function f(k) such that every f(k)-connected graph admits a spanning, bipartite $k$-conne…

The human brain comprises about one hundred billion neurons and one trillion supporting glial cells. These cells are specialized into a surprising diversity of cell types. The retina alone boasts well over 50 cell types, and it is an active area of …

Cataloging the neuronal cell types that comprise circuitry of individual brain regions is a major goal of modern neuroscience and the BRAIN initiativ…

In designing and improving algorithms for Gröbner basis computation, it is natural to hope that incorporating the generators in some clever order, or inputting generators one at a time to develop the ideal, can lead to efficient methods for restrict…

We introduce a new problem in the approximate computation of Gr\"obner bases that allows the algorithm to ignore a constant fraction of the generator…

In this section, we study lower-bounds on the approximation ratio and size of the composable core-sets for the k-determinant maximization and the experimental design problem. In particular, we prove Theorem 1.2.We also prove the bound given by 6.7 i…

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we s…

In this section, we study two special instances of Problem 3, namely variational inequalities and minimization problems. Moreover, for variational inequalities, we prove an additional result, showing that a suitably defined merit function [2] goes t…

We propose and analyze the convergence of a novel stochastic forward-backward splitting algorithm for solving monotone inclusions given by the sum of…

The authors would like to thank Alexander Rakhlin for his valuable input, and in particular, for bringing to our attention the possibility of having o(√T) bounds on regret in the linear setting.

In the convex optimization approach to online regret minimization, many methods have been developed to guarantee a $O(\sqrt{T})$ bound on regret for …

We propose a method for the emulation of artificial spin orbit coupling in a system of ultracold, neutral atoms trapped in a tight-binding lattice. T…

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