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pro vyhledávání: '"Tangents"'
Autor:
Käenmäki, Antti, Rutar, Alex
We study the fine scaling properties of planar self-affine carpets. For Gatzouras--Lalley carpets, we give a precise formula for maximal Hausdorff dimension of a tangent in terms of the Hausdorff dimension of the projection and the Assouad dimension
Externí odkaz:
http://arxiv.org/abs/2410.19404
Autor:
Eaton, Frederik
In this paper we describe an efficient method for providing a regression model with a sense of curiosity about its data. In the field of machine learning, our framework for representing curiosity is called Active Learning, which means automatically c
Externí odkaz:
http://arxiv.org/abs/2411.15292
Autor:
Caniato, Riccardo, Parise, Davide
We establish a direct log-epiperimetric inequality for Yang$-$Mills fields in arbitrary dimension and we leverage on it to prove uniqueness of tangent cones with isolated singularity for energy minimizing Yang$-$Mills fields and $\omega$-ASD connecti
Externí odkaz:
http://arxiv.org/abs/2410.15540
Activation functions are one of the key components of a deep neural network. The most commonly used activation functions can be classed into the category of continuously differentiable (e.g. tanh) and piece-wise linear functions (e.g. ReLU), both hav
Externí odkaz:
http://arxiv.org/abs/2406.09079
Autor:
Borzechowski, Michaela, Fearnley, John, Gordon, Spencer, Savani, Rahul, Schnider, Patrick, Weber, Simon
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 Sandwich proble
Externí odkaz:
http://arxiv.org/abs/2402.07683
Given a real cubic function $f(x)$ with three roots, take an equilateral triangle $ABC$, the projections of which vertices are the roots of $f(x)$. There is a folklore fact that the vertical lines through the extrema of $f(x)$ are tangent to the insc
Externí odkaz:
http://arxiv.org/abs/2401.12394
Characterizing rectifiability of Radon measures in Euclidean space has led to fundamental contributions to geometric measure theory. Conditions involving existence of principal values of certain singular integrals \cite{mattila1995rectifiable} and th
Externí odkaz:
http://arxiv.org/abs/2311.00589
Akademický článek
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Autor:
Kim, Shin-young
We describe varieties of minimal rational tangents on the wonderful symmetric varieties by marked Dynkin diagrams. An irreducible component of a variety of minimal rational tangents is a rational homogeneous space, and hence, we have a corresponding
Externí odkaz:
http://arxiv.org/abs/2306.10242