Related papers: Linear relations with disjoint supports and averag…

We show that various surface parameters in two-dimensional diffusion limited aggregation (DLA) grow linearly with the number of particles. We find the ratio of the average length of the perimeter and the accessible perimeter of a DLA…

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are…

Random tilings or packings in the plane are characterized by a size distribution of individual elements (domains) and by the statistics of neighbor relations between the domains. Most systems occurring in nature or technology have a…

Investigating the CKM matrix in different parametrization schemes, it is noticed that those schemes can be divided into a few groups where the sine values of the CP phase for each group are approximately equal. Using those relations,…

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

In this paper we generalize cellular algebras by allowing different partial orderings relative to fixed idempotents. For these relative cellular algebras we classify and construct simple modules, and we obtain other characterizations in…

We show that correlation matrices with particular average and variance of the correlation coefficients have a notably restricted spectral structure. Applying geometric methods, we derive lower bounds for the largest eigenvalue and the…

This paper considers generalised network, intended as networks where (a) the edges connecting the nodes are nonlinear, and (b) stochastic processes are continuously indexed over both vertices and edges. Such topological structures are…

In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- representations in terms of tensor products are directly…

We discuss the expansion of interaction kernels between anisotropic rigid molecules. The expansion decouples the correlated orientational variables so that it can be utilized to derive macroscopic models. Symmetries of two types are…

We discuss the relation of tiling, weak tiling and spectral sets in finite abelian groups. In particular, in elementary $p$-groups $(\mathbb{Z}_p)^d$, we introduce an averaging procedure that leads to a natural object of study: a 4-tuple of…

We develop a theory of graph algebras over general fields. This is modeled after the theory developed by Freedman, Lov\'asz and Schrijver in [22] for connection matrices, in the study of graph homomorphism functions over real edge weight…

Core-satellite graphs (sometimes referred to as generalized friendship graphs) are an interesting class of graphs that generalize many well known types of graphs. In this paper we show that two popular clustering measures, the average…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

The observed pattern of fermion masses and mixing is an outstanding puzzle in particle physics, generally known as the flavor problem. Over the years, guided by precision neutrino oscillation data, discrete flavor symmetries have often been…

We show that the probability for a finitely generated subgroup of the modular group, of size $n$, to be almost malnormal or non-parabolic, tends to 0 as $n$ tends to infinity -- where the notion of the size of a subgroup is based on a…

If $A$ is a unital associative ring and $\ell \geq 2$, then the general linear group $\mathrm{GL}(\ell, A)$ has root subgroups $U_\alpha$ and Weyl elements $n_\alpha$ for $\alpha$ from the root system of type $\mathsf A_{\ell - 1}$.…

A matrix A is image partition regular over Q provided that whenever Q - {0} is finitely coloured, there is a vector x with entries in Q - {0} such that the entries of Ax are monochromatic. It is kernel partition regular over Q provided that…

We study the learning properties of nonparametric ridge-less least squares. In particular, we consider the common case of estimators defined by scale dependent kernels, and focus on the role of the scale. These estimators interpolate the…

In the present paper we develop a small cancellation theory for associative algebras with a basis of invertible elements. Namely, we study quotients of a group algebra of a free group and introduce three axioms for the corresponding…