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pro vyhledávání: '"Andersen, Lars P."'
Autor:
Andersen, Lars
Our main result is that chaos in dimension $n+1$ is a one-dimensional geometrical object embedded in a geometrical object of dimension $n$ which corresponds to a $n$ dimensional object which is either singular or non-singular. Our main result is then
Externí odkaz:
http://arxiv.org/abs/2407.17701
Autor:
Andersen, Lars
We discuss $\mathcal{D}$-modules and dynamical systems in the \'etale topology. We introduce the differential scheme associated to a morphism $f: X\to S$ of schemes of the same dimension. We introduce differential inertia group $I_{diff}^i$ which act
Externí odkaz:
http://arxiv.org/abs/2403.15806
Autor:
Andersen, Lars
We prove that to each real singularity $f: (\mathbb{R}^{n}, 0) \to (\mathbb{R}^k, 0)$ with $k\geq 2$ one can associate systems of differential equations $\mathfrak{g}^{k}_f$ which are pushforwards in the category of $\mathcal{D}$-modules over $\mathb
Externí odkaz:
http://arxiv.org/abs/2403.02174
Autor:
Borup, Kenneth, Andersen, Lars Nørvang
We propose two approaches to extend the notion of knowledge distillation to Gaussian Process Regression (GPR) and Gaussian Process Classification (GPC); data-centric and distribution-centric. The data-centric approach resembles most current distillat
Externí odkaz:
http://arxiv.org/abs/2304.02641
Autor:
Andersen, Lars
We prove that to each real singularity $f: (\mathbb{R}^{n+1}, 0) \to (\mathbb{R}, 0)$ one can associate two systems of differential equations $\mathfrak{g}^{k\pm}_f$ which are pushforwards in the category of $\mathcal{D}$-modules over $\mathbb{R}^{\p
Externí odkaz:
http://arxiv.org/abs/2206.06849
Learning often involves sensitive data and as such, privacy preserving extensions to Stochastic Gradient Descent (SGD) and other machine learning algorithms have been developed using the definitions of Differential Privacy (DP). In differentially pri
Externí odkaz:
http://arxiv.org/abs/2110.06255
Autor:
Andersen, Lars
In this article we apply the results in the article "On Isolated Real Singularities I" to the study of real $ADE$-singularities. We show that said results enables us to find the homology groups of the Milnor fibres of real $ADE$-singularities of curv
Externí odkaz:
http://arxiv.org/abs/2110.04417
Autor:
Andersen, Lars
In this article we prove two results concerning the motivic Milnor fibres $S^{\epsilon}(f)$ associated to a map germ $f: (\mathbb{R}^n,0)\to(\mathbb{R},0)$, defined by G. Comte and G. Fichou. Firstly, we prove that if $f,g:(\mathbb{R}^n,0)\to(\mathbb
Externí odkaz:
http://arxiv.org/abs/2110.04404
Autor:
Andersen, Lars
For analytic map germs $f: (\mathbb{R}^n, 0)\to (\mathbb{R}, 0)$ having an isolated critical value in the origin with $\dim V(f)>0$ and satisfying the transversality property of D.B. Massey we show that for $c>0$ a large enough constant, and $k$ a la
Externí odkaz:
http://arxiv.org/abs/2108.06877
Autor:
Andersen, Lars
Given a nonconstant polynomial map over the reals having an isolated critical point in the origin and with zero locus of positive dimension, we establish a formula for the singular homology groups of a Milnor fibre relative to its boundary.
Externí odkaz:
http://arxiv.org/abs/2105.04276