Related papers: Small circuits and dual weak PHP in the universal …
The late time response of vacuum black holes in General Relativity is notoriously governed by power law tails arising from the wave scattering off the curved spacetime geometry far from the black hole. While it is known that such tails are…
State-of-the-art quantum computers can only reliably execute circuits with limited qubit numbers and computational depth. This severely reduces the scope of algorithms that can be run. While numerous techniques have been invented to exploit…
Myasnikov, Ushakov, and Won introduced power circuits in 2012 to construct a polynomial-time algorithm for the word problem in the Baumslag group, which has a non-elementary Dehn function. Power circuits are computational structures that…
We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima's ergodic theorem for the harmonic functions in the domain of the $ L^{p} $ generator. Secondly we prove analogues of Yau's and Karp's…
A theory T is tight if different deductively closed extensions of T (in the same language) cannot be bi-interpretable. Many well-studied foundational theories are tight, including PA [Visser2006], ZF, Z2, and KM [enayat2017]. In this…
Since the work of Polyanskiy, Poor and Verd\'u on the finite blocklength performance of capacity-achieving codes for discrete memoryless channels, many papers have attempted to find further results for more practically relevant channels.…
We use a variety of computational tools to obtain a degree-$\binom{m + n - 2}{m - 1}$ polynomial equation conjecturally satisfied by the top-left entry of the Sinkhorn limit of a positive $m \times n$ matrix. The degree of this equation has…
We provide polynomial-time reductions between three search problems from three distinct areas: the P-matrix linear complementarity problem (P-LCP), finding the sink of a unique sink orientation (USO), and a variant of the $\alpha$-Ham…
Matchgates are a family of parity-preserving two-qubit gates, nearest-neighbour circuits of which are known to be classically simulable in polynomial time. In this work, we present a simulation method to classically simulate an…
Let $u$ be a maximal plurisubharmonic function in a domain $\Omega\subset\mathbb{C}^n$ ($n\geq 2$). It is classical that, for any $U\Subset\Omega$, there exists a sequence of bounded plurisubharmonic functions $PSH(U)\ni u_j\searrow u$…
Let $\mathsf{TT}^2_k$ denote the combinatorial principle stating that every $k$-coloring of pairs of compatible nodes in the full binary tree has a homogeneous solution, i.e. an isomorphic subtree in which all pairs of compatible nodes have…
Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…
We show that for all $\varepsilon>0$, for sufficiently large $q\in\mathbb{N}$ power of $2$, for all $\delta>0$, it is NP-hard to distinguish whether a given $2$-Prover-$1$-Round projection game with alphabet size $q$ has value at least…
Point particles fall freely along geodesics; strings do not. In string theory all probes of spacetime structure, including photons, are extended objects and therefore always subject to tidal forces. We illustrate how string theory modifies…
The Schwartz-Zippel Lemma states that if a low-degree multivariate polynomial with coefficients in a field is not zero everywhere in the field, then it has few roots on every finite subcube of the field. This fundamental fact about…
We introduce an operation on modules over an $F$-finite ring of characteristic $p$. We call this operation \emph{tight interior}. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight…
It has been often conjectured that the correct theory of quantum gravity will act as a UV regulator in the low energy limit of quantum field theory. Earlier work has shown that if the path integral defining the quantum field theory…
An $n$-bit boolean function is resilient to coalitions of size $q$ if any fixed set of $q$ bits is unlikely to influence the function when the other $n-q$ bits are chosen uniformly. We give explicit constructions of depth-$3$ circuits that…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
CP violation by soft supersymmetry-breaking terms in orbifold compactifications is investigated. We include the universal part of the moduli-dependent threshold corrections in the construction of the non-perturbative effective potential due…