Results 81 to 90 of about 1,230 (193)

Hyperplane Arrangements of Trained ConvNets Are Biased

, 2023
We investigate the geometric properties of the functions learned by trained ConvNets in the preactivation space of their convolutional layers, by performing an empirical study of hyperplane arrangements induced by a convolutional layer.
Björkman, Mårten, Carlsson, Stefan, Gamba, Matteo, Azizpour, Hossein   +3 more
core  

A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
wiley   +1 more source

k-Adjoint of hyperplane arrangements

Journal of Combinatorial Theory, Series A
In this paper, we introduce the $k$-adjoint of a given hyperplane arrangement $\mathcal{A}$ associated with rank-$k$ elements in the intersection lattice $L(\mathcal{A})$, which generalizes the classical adjoint proposed by Bixby and Coullard. The $k$-adjoint of $\mathcal{A}$ induces a decomposition of the Grassmannian, which we call the $\mathcal{A ...
Weikang Liang, Suijie Wang, Chengdong Zhao   +2 more
openaire   +2 more sources

Critical Points and Resonance of Hyperplane Arrangements

, 2011
If is a master function corresponding to a hyperplane arrangement 𝒜 and a collection of weights ⋋, we investigate the relationship between the critical set of , the variety defined by the vanishing of the one-form ⩊⋋ = d log , and the resonance of ...
Varchenko, A., D. Cohen, G. Denham, Denham, G., A. Varchenko, M. Falk, Cohen, D., Falk, M.   +7 more
core   +1 more source

A note on kinematic flow and differential equations for two-site one-loop graph in FRW spacetime

Journal of High Energy Physics
In this work, we systematically study the differential systems governing loop-level wavefunction coefficients of conformally-coupled scalar field theory within a general power-law FRW cosmology.
Yanfeng Hang, Cong Shen
doaj   +1 more source

Hyperplane arrangements

, 2014
Cette thèse étudie la fibre de Milnor d'un arrangement d'hyperplans complexe central, et l'opérateur de monodromie sur ses groupes de cohomologie. On s'intéresse à la problématique suivante : peut-on déterminer l'opérateur de monodromie, ou au moins les ...
Bailet, Pauline
core  

On free and plus-one generated curves arising from free curves by addition–deletion of a line

Bulletin of Mathematical Sciences
In a recent paper, after introducing the notion of plus-one generated hyperplane arrangements, Takuro Abe has shown that if we add (respectively, delete) a line to (respectively, from) a free line arrangement, then the resulting line arrangement is ...
Alexandru Dimca
doaj   +1 more source

Group Actions on Hyperplane Arrangements

, 2012
In this dissertation, we will look at two families of algebras with connections to hyperplane arrangements that admit actions of finite groups. One of the fundamental questions to ask is how these decompose into irreducible representations. For the first
Moseley, Daniel
core  

Jumping Numbers of Hyperplane Arrangements [PDF]

Communications in Algebra, 2010
M. Saito recently proved that the jumping numbers of a hyperplane arrangement depend only on the combinatorics of the arrangement. However, a formula in terms of the combinatorial data was still missing. In this note, we give a formula and a different proof of the fact that the jumping numbers of a hyperplane arrangement depend only on the ...
openaire   +2 more sources

Integral hyperplane arrangements and graphs determined by Laplacian spectra

, 2010
This thesis studies two subjects. Chapters 1-4 study integral hyperplane arrangements. Chapters 5-8 are devoted to graphs determined by their Laplacian spectra. In Chapter 1, we introduce hyperplane arrangements, characteristic polynomials, and some well
Wang, Suijie
core