Related papers: Singularities in bivariate normal mixtures
Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…
We define the dual F-signature of modules, which is equivalent to the F-signature if the module is the base ring. By using this invariant, We give characterizations of regular, F-regular, F-rational, and Gorenstein singularities.
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…
We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. Such mixtures have a history of application to the problem of detecting differentially…
We study quenched mixing rates for two classes of random interval maps characterized by the presence of two indifferent fixed points and singular points. Using a random tower construction we prove the existence of an equivariant absolutely…
We introduce a unified method for study of 2-dimensional invariant subspaces of matrices and their corresponding super-eigenvalues. As a novel application to non-commutative algebra, we present a connection between the eigenvalues of…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
We study germs of analytic maps $f:(X,S)\rightarrow(\mathbb{C}^p,0)$, when $X$ is an ICIS of dimension $n<p$. We define an image Milnor number, generalizing Mond's definition, $\mu_I(X,f)$ and give results known for the smooth case such as…
This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…
In this paper, we study the behaviour of TF-isomorphisms, a natural generalisation of isomorphisms. TF-isomorphisms allow us to simplify the approach to seemingly unrelated problems. In particular, we mention the Neighbourhood…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
We first find the combinatorial degree of any map $f:V\to F$ where $F$ is a finite field and $V$ is a finite-dimensional vector space over $F$. We then simplify and generalize a certain construction due to Chein and Goodaire that was used…
In this work, the dual flatness, which is connected with Statistics and Information geometry, of general $(\alpha,\beta)$-metrics (a new class of Finsler metrics) is studied. A nice characterization for such metrics to be dually flat under…
For given natural numbers $d_1,d_2$ let $\Omega_2(d_1,d_2)$ be the set off all polynomial mappings $F=(f,g):\mathbb{C}^2\to\mathbb{C}^2$ such that deg $f\le d_1$, deg $g\le d_2$. We say that the mapping $F$ is topologically stable in…
We study renormalization of highly dissipative analytic three dimensional H\'enon maps $$ F(x,y,z) = (f(x) - \varepsilon(x,y,z),\ x,\ \delta(x,y,z)) $$ where $ \varepsilon(x,y,z) $ is a sufficiently small perturbation of $…
Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…
This work considers a problem of estimating a mixing probability density $f$ in the setting of discrete mixture models. The paper consists of three parts. The first part focuses on the construction of an $L_1$ consistent estimator of $f$.…
We investigate regularity properties of generalized conjugate functions induced by a general coupling function and the associated generalized proximal mapping. Our main results provide verifiable conditions ensuring local single-valuedness,…
The goal of this note is to define biparametric persistence diagrams for smooth generic mappings $h=(f,g):M\to V\cong \mathbb{R}^2$ for smooth compact manifold $M$. Existing approaches to multivariate persistence are mostly centered on the…
For a pair (X,L) consisting of a projective variety X over a perfect field of characteristic p>0 and an ample line bundle L on X, we introduce and study a positive characteristic analog of the $\alpha$-invariant introduced by Tian, which we…