Related papers: Involution symmetries and the PMNS matrix
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
We introduce an ansatz of the PMNS matrix that consists of specific types of transformations. Bi-maximal mixing is taken for the neutrino masses, while a single-angle rotation in the 1-2 block is taken for the charged lepton masses.…
A candidate for the simple empirical neutrino mass formula is found, predicting the mass proportion m_1:m_2:m_3 = 0:4:24 and so, the mass ratio Delta m^2_{32}/Delta m^2_{21} = 35 not inconsistent with its experimental estimate. It involves…
It was recently argued that f(T) gravity could inherit "remnant symmetry" from the full Lorentz group, despite the fact that the theory is not locally Lorentz invariant. Confusion has arisen regarding the implication of this result for the…
Following a polynomial approach, many robust fixed-order controller design problems can be formulated as optimization problems whose set of feasible solutions is modelled by parametrized polynomial matrix inequalities (PMI). These…
Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which…
In this paper, we aim at introducing a new machine learning model, namely reconciled polynomial machine, which can provide a unified representation of existing shallow and deep machine learning models. Reconciled polynomial machine predicts…
We present the general form of the unitary matrices keeping invariant the Majorana neutrino mass matrix of specific texture suitable for explaining oscillation data. In the case of the Tri-bimaximal pattern with two degenerate masses we…
The problem of whether a metabolic idempotent of a central simple algebra with involution is contained in an invariant quaternion subalgebra is investigated. As an application, the similar problem is studied for skew-symmetric elements…
Deep learning frameworks commonly implement convolution operators with GEMM-based algorithms. In these algorithms, convolution is implemented on top of matrix-matrix multiplication (GEMM) functions, provided by highly optimized BLAS…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…
Several approximate equalities among the matrix elements of CKM and PMNS imply that hidden symmetries may exist and be common for both quark and neutrino sectors. The CP phase of the CKM matrix ($\delta_{\rm CKM}$) is involved in these…
We construct a neutrino mass matrix $M_{\nu}$ via a seesaw mechanism whith perturbed invariant under a cyclic permutation by introducing one parameter $\delta$ into the diagonal elements of $M_{\nu}$ with assumption that trace of the…
In this article, we develop a process to symmetrize the irreducible admissible representation of $GL_N(\mathbb{Q}_p)$, as a consequence we obtain a more geometric understanding of the coefficient $m(\mathbf{b}, \mathbf{a})$ appearing in the…
We provide a complete structure theorem for involutory matrices. This yields a new approach to principal angles between subspaces and provide a series of nice formulae for these angles.
Recently we have proposed a renormalizable grand unified theory, based on the SU(5) gauge symmetry, where the neutrino masses are generated through the type I and type III seesaw mechanisms. In this letter we study the supersymmetric…
Assuming that neutrinos are Majorana particles, we perform a complete classification of all possible mixing matrices which are fully determined by residual symmetries in the charged-lepton and neutrino mass matrices. The classification is…
We apply non-invertible selection rules coming from a fusion algebra to radiative neutrino mass models where fields are labeled by the elements in the algebra. Since non-invertible selection rules only hold at tree level, radiative…
Symmetries built into a neural network have appeared to be very beneficial for a wide range of tasks as it saves the data to learn them. We depart from the position that when symmetries are not built into a model a priori, it is…