We prove strengthened lower bounds for constant-depth set-multilinear formulas. More precisely, we show that over any field, there is an explicit polynomial $f$ in VNP defined over $n^2$ variables, and of degree $n$, such that any product-depth $Δ$...
Let $G$ be an infinite group, $κ$ be an infinite cardinal, $κ\leq \mid G\mid$ and let $\mathcal{E}_κ$ denotes a coarse structure on $G$ with the base $\{\{ (x,y): y\in F x F\}: F\in [G]^{<κ}\}$. We prove that if either $κ< \mid G\mid$ or $κ= \m...
A Steiner quadruple system (briefly $SQS(n)$) is a pair $(X,B)$ where $|X|=n$ and $B$ is a collection of 4-element blocks such that every 3-subset of $X$ is contained in exactly one member of $B$. Hanani \cite{Hanani} proved that the necessary condit...
We study the complexity of Non-Gaussian Component Analysis (NGCA) in the Statistical Query (SQ) model. Prior work developed a general methodology to prove SQ lower bounds for this task that have been applicable to a wide range of contexts. In particu...
Stuttgart Vulgate. Scholars have identified families of variants, allowing tracing of influence or provenance of texts: for example, the Latin text of the
MapReduce has proven to be one of the most useful paradigms in the revolution of distributed computing, where cloud services and cluster computing become the standard venue for computing. The federation of cloud and big data activities is the next ch...
We prove that natural generating functions for enumeration of branched coverings of the pillowcase orbifold are level 2 quasimodular forms. This gives a way to compute the volumes of the strata of the moduli space of quadratic differentials....
Let B be a translation invariant Banach function space (BF-space). In this paper we prove that every temperate distribution f can be associated with a function F analytic in the convex tube Omega={z in C^d; |Im z|<1} such that the wave-front set...
We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a proof of up...
We introduce a simple transformation on two-player nonlocal games, called "anchoring", and prove an exponential-decay parallel repetition theorem for all anchored games in the setting of quantum entangled players. This transformation is inspired in p...
2 days ago · The White House has not ruled out eventually sending troops into Iran even as officials continue to hope it proves unnecessary.
In this paper we prove finiteness principles for $C^{m}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, and for $C^{m-1,1}\left( \mathbb{R}^{n}, \mathbb{R}^{D}\right) $-selection, in particular providing a proof for a conjecture of Brudyni-S...
We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As...
A woman who anonymously sued the rapper failed to prove that revealing her identity would cause mental harm, the judge ruled, saying "public humiliation’ is not enough.” A woman who anonymously s...
Internet advertising is a fast growing business which has proved to be significantly important in digital economics. It is vitally important for both web search engines and online content providers and publishers because web advertising provides them...
We prove first-order definability of the prime subring inside polynomial rings, whose coefficient rings are (commutative unital) reduced and indecomposable. This is achieved by means of a uniform formula in the language of rings with signature $(0,1,...
Vindicate means to justify, prove, or reinforce an idea — or to absolve from guilt. If your family thinks you hogged the last piece of pie on Thanksgiving, you'll be vindicated when your younger brother fesses up.
VINDICATE definition: 1. to prove that what someone said or did was right or true, after other people thought it was…. Learn more.
This is Part I of a two-part series regarding Ramsey properties of Fraisse structures satisfying a property called SDAP+, which strengthens the Disjoint Amalgamation Property. We prove that every Fraisse structure in a finite relational language with...
# Understanding the HCU Crisis Seeing your organic traffic disappear after a Google Helpful Content Update (HCU) is more than frustrating—it can threaten your entire business model. If you're facin...