Planar bipartite graphs can be represented as touching graphs of horizontal and vertical segments in $\mathbb{R}^2$. We study a generalization in space: touching graphs of axis-aligned rectangles in $\mathbb{R}^3$, and prove that planar 3-colorable g...
Common knowledge and only knowing capture two intuitive and natural notions that have proven to be useful in a variety of settings, for example to reason about coordination or agreement between agents, or to analyse the knowledge of knowledge-based a...
The Snake-in-the-Box problem is that of finding a longest induced path in an $n$-dimensional hypercube. We prove new lower bounds for the values $n\in \{11,12,13\}$. The Coil-in-the-Box problem is that of finding a longest induced cycle in an $n$-dim...
Todo en argentina es malasangre y putear por todo: el verdulero te vende verde o podrido; el carnicero te vende carne dura; la granja, huevos pasados y pollo lleno de agua; el proveedor de cable/inter...
Consider the framework of topological aggregation introduced by Chichilnisky (1980). We prove that in this framework the Twin Paradox and the No Show Paradox cannot be avoided. Anonymity and unanimity are not needed to obtain these results....
For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers. We prove sufficient conditions for the $\ell^{p}$-improving inequality \beg...
I pulled a lot of this stuff from other users and pieces of this have made the rounds here as mini copy/pastes. I put it all together in one thread. Enjoy! - https://en.wikipedia.org/wiki/COINTELPRO ...
THEOREM. For every prime $p$ and each $n=2, 3, ... \infty$, there is an action of $G=\prod_{i=1}^{\infty}(Z/ pZ)$ on a two-dimensional compact metric space $X$ with $n$-dimensional orbit space. This theorem was proved in [DW: A.N. Dranishnikov an...
Jun 30, 2011 · There are many versions of this proverb, which suggests there are always several ways to do something. The earliest printed citation of this proverbial saying that I can find is in …
Jun 30, 2011 · There are many versions of this proverb, which suggests there are always several ways to do something. The earliest printed citation of this proverbial saying that I can find is in a short story …
Jun 30, 2011 · There are many versions of this proverb, which suggests there are always several ways to do something. The earliest printed citation of this proverbial saying that I can find is in a short story …
We prove sharp $\ell^2$-decoupling inequalities for non-degenerate complex curves via the bilinear argument due to Guo--Li--Yung--Zorin-Kranich. Secondly, quantifying the iteration in the cubic case, we obtain a logarithmic refinement of the decoupli...
Recent deep learning approaches in table detection achieved outstanding performance and proved to be effective in identifying document layouts. Currently, available table detection benchmarks have many limitations, including the lack of samples diver...
The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection of chance...
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We prove the existence of the operator product expansion (OPE) in Euclidean Yang-Mills theories as a short-distance expansion, to all orders in perturbation theory. We furthermore show that the Ward identities of the underlying gauge theory are refle...
In this paper we introduce techniques from complex harmonic analysis to prove a weaker version of the Geometric Arveson-Douglas Conjecture for complex analytic subsets that is smooth on the boundary of the unit ball and intersects transversally with...
In light of the well-known fact that the $n$th divided difference of any polynomial of degree $m$ must be zero while $m<n$,the present paper proves the $(α,β)$-inversion formula conjectured by Hsu and Ma [J. Math. Res. $\&$ Exposition 25(4) (2005)...
In this paper, we prove the Geometric Arveson-Douglas Conjecture for a special case which allow some singularity on $\partial{\mathbb{B}_n}$. More precisely, we show that if a variety can be decomposed into two varieties, each having nice properties...
We analyze a posteriori error bounds for stabilized finite element discretizations of second-order steady-state mean field games. We prove the local equivalence between the $H^1$-norm of the error and the dual norm of the residual. We then derive rel...