Related papers: Recursive parameterisation and invariant phases of…
In this paper we provide a general method to construct four-parameter families of complex Hadamard matrices of order six. Our approach is to write a 6-dimensional matrix as composed of four blocks, each one in the form of a circulant…
The paper is devoted to a discussion of general properties of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. First we propose a general method of a recursive construction of the CKM matrix for any number of generations. This allows to set up a…
Parameter fitting of data to a proposed equation almost always consider these parameters as independent variables. Here, the method proposed optimizes an arbitrary number of variables by the minimization of a function of a single variable.…
In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.
Various Non-negative Matrix factorization (NMF) based methods add new terms to the cost function to adapt the model to specific tasks, such as clustering, or to preserve some structural properties in the reduced space (e.g., local…
In this paper we introduce a six-parameter generalization of the four-parameter three-variable polynomials on the simplex and we investigate the properties of these polynomials. Sparse recurrence relations are derived by using ladder…
We give a complete structural characterisation of the map the positive branch of a one-way pattern implements. We start with the representation of the positive branch in terms of the phase map decomposition, which is then further analysed…
We introduce an efficient combination of polyhedral analysis and predicate partitioning. Template polyhedral analysis abstracts numerical variables inside a program by one polyhedron per control location, with a priori fixed directions for…
We provide an analysis of the structure of renormalisation scheme invariants for the case of $\phi^4$ theory, relevant in four dimensions. We give a complete discussion of the invariants up to four loops and include some partial results at…
A recursive algebraic method which allows to obtain the Feynman or Schwinger parametric representation of a generic L-loops and (E+1) external lines diagram, in a scalar $\phi ^{3}\oplus \phi ^{4}$ theory, is presented. The representation…
We propose a new and efficient method of reconstructing quark mass matrices from their eigenvalues and a complete set of mixing observables. By a combination of the principle of NNI (nearest neighbour interaction) bases which are known to…
In this paper we study a parametrized description of neutrino mixing from a phenomenological point of view. We concentrate on the parametrization in terms of higher order corrections to the leading order mixing matrix. A method to describe…
Consider a regression or some regression-type model for a certain response variable where the linear predictor includes an ordered factor among the explanatory variables. The inclusion of a factor of this type can take place is a few…
Procedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from…
Decompositions of the unitary group U(n) are useful tools in quantum information theory as they allow one to decompose unitary evolutions into local evolutions and evolutions causing entanglement. Several recursive decompositions have been…
These notes develop aspects of perturbation theory of matrices related to so-called diagonalisation schemes. Primary focus is on constructive tools to derive asymptotic expansions for small/large parameters of eigenvalues and…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
This work analyses a class of extensions of the Standard Model through the lens of a novel exact parameterisation. This parameterisation is specially suitable to the analysis of extensions of the Standard Model with non-unitary mixing…
Presented here is a matrix inversion method utilizing quantum searching algorithm. In this method, huge Hilbert space as a whole spanned by myriad of eigen states is searched and evaluated efficiently by sequential reduction in dimension…