We present MM-Food-100K, a public 100,000-sample multimodal food intelligence dataset with verifiable provenance. It is a curated approximately 10% open subset of an original 1.2 million, quality-accepted corpus of food images annotated for a wide ra...
We define the Toledo invariant of a G-Higgs bundle on a Riemann surface, where G is a real semisimple group of Hermitian type, and we prove a Milnor-Wood type bound for this invariant when the bundle is semistable. We prove rigidity results when th...
We prove that a complete family of linearly non-degenerate rational curves of degree $e > 2$ in $\mathbb{P}^n$ has at most $n-1$ moduli. For $e = 2$ we prove that such a family has at most $n$ moduli. It is unknown whether or not this is the best p...
Gigors (French pronunciation: [ʒigɔʁ]) is a commune in the Alpes-de-Haute-Provence department in southeastern France. Communes of the Alpes-de-Haute-Provence
Yolande of Aragon (11 August 1381 – 14 November 1442) was Duchess of Anjou and Countess of Provence by marriage, who acted as regent of Provence during
Following earlier results of Sondow, we propose another criterion of irrationality for Euler's constant $γ$. It involves similar linear combinations of logarithm numbers $L\_{n,m}$. To prove that $γ$ is irrational, it suffices to prove that, for...
We consider Lambek's invariants $\text{Ker}$ and $\text{Im}$ for commutative squares in Grandis homological categories. We prove that Nomura's null sequences exist in such categories and find sufficienct conditions for their exactness. We also prove...
#List of Proven Conspiracies This compilation of facts is the result of the /r/conspiracy community's efforts over the years to distribute information between ourselves. Many users contributed to thi...
In this paper, we prove that with high probability, random Reed-Solomon codes approach the half-Singleton bound - the optimal rate versus error tradeoff for linear insdel codes - with linear-sized alphabets. More precisely, we prove that, for any $ε...
Chaucer. The proverb, written in Middle English, being: "Right as diverse pathes leden diverse folk the righte way to Rome." The proverb is referencing the
# The letter that proves what Howard knew about ‘dogs on the docks’ By Helen Trinca 11 min. readView original This article contains features which are only available in the web version[Take me ...
# The letter that proves what Howard knew about ‘dogs on the docks’ By Helen Trinca 11 min. readView original This article contains features which are only available in the web version[Take me ...
We prove effective forms of the Sato-Tate conjecture for holomorphic cuspidal newforms which improve on the author's previous work (solo and joint with Lemke Oliver). We also prove an effective form of the joint Sato-Tate distribution for two twist-i...
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We prove an upper bound for the number of rational points of bounded height on irreducible affine hypersurfaces. More precisely, given an irreducible polynomial $f \in \mathbb{Z}[X_1, \dots, X_n]$, we prove an upper bound on the number of points $(x_...
In this paper, we study the skew mean curvature flow. The results are threefold. First, we prove the global regularity of solutions with initial data which are small perturbations of planes in Sobolev spaces. Second, we prove the modified scattering...
Points: 2 | Comments: 1 | Author: walterbell
In this article we define stable supercurves and super stable maps of genus zero via labeled trees. We prove that the moduli space of stable supercurves and super stable maps of fixed tree type are quotient superorbifolds. To this end, we prove a sli...
We prove classical Taylor polynomial theorems for sub-Riemannian manifolds that are obtained as the submetric image of a Carnot group. For these theorems we also prove a sufficient condition for real analyticity and a result on L-harmonicity of Taylo...