Related papers: A geometrical setting for the classification of mu…
Real-world relations among entities can often be observed and determined by different perspectives/views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of…
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by…
Methods to increase the light scattered from small particles can help improve the sensitivity of many sensing techniques. Here, we investigate the role multiple scattering plays in perturbing the scattered signal when a particle is added to…
The transition from monolayers to multilayered structures in bacterial colonies is a fundamental step in biofilm development. Observed across different morphotypes and species, this transition is triggered within freely growing bacterial…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
We investigate factorized scattering from a reflecting and transmitting impurity. Bulk scattering is non trivial, provided that the bulk scattering matrix depends separately on the spectral parameters of the colliding particles, and not…
A categorical point of view about minimization in subrecursive classes is presented by extending the concept of Symmetric Monoidal Comprehension to that of Distributive Minimization Comprehension. This is achieved by endowing the former…
The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer operators with a generic cutting size which are applicable…
This paper supplements [17], showing that categorically the layered theory is the same as the theory of ordered monoids (e.g. the max-plus algebra) used in tropical mathematics. A layered theory is developed in the context of categories,…
Bilinear models has been shown to achieve impressive performance on a wide range of visual tasks, such as semantic segmentation, fine grained recognition and face recognition. However, bilinear features are high dimensional, typically on…
We recall the concept of Baxterisation of an R-matrix, or of a monodromy matrix, which corresponds to build, from one point in the $ R$-matrix parameter space, the algebraic variety where the spectral parameter(s) live. We show that the…
In this survey paper we study parametric versions of writing a matrix in $SL_n (\mathbb{C})$ as a product of lower and upper unitriangular matrices in interchanging order as well as generalizations to other classical groups. We give an…
We present an algorithm to compute all factorizations into linear factors of univariate polynomials over the split quaternions, provided such a factorization exists. Failure of the algorithm is equivalent to non-factorizability for which we…
We study how the field of definition of a rational function changes under iteration. We provide a complete classification of polynomials with the property that the field of definition of one of their iterates drops in degree (over a given…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…
We construct and investigate certain (unbalanced) superalgebra structures on $\text{End}_K(V)$, with $K$ a field of characteristic $0$ and $V$ a finite dimensional $K$-vector space (of dimension $n\geq 2$). These structures are induced by a…
Over the years data has become increasingly higher dimensional, which has prompted an increased need for dimension reduction techniques. This is perhaps especially true for clustering (unsupervised classification) as well as semi-supervised…
We first revisit impact-parameter dependent collisions of ultra-relativistic particles in quantum field theory. Two conditions sufficient for defining an impact-parameter dependent cross section are given, which could be violated in…