Related papers: Involution symmetries and the PMNS matrix
Nature features a plethora of extraordinary photonic architectures that have been optimized through natural evolution. While numerical optimization is increasingly and successfully used in photonics, it has yet to replicate any of these…
We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…
Phylogenetic models have polynomial parametrization maps. For symmetric group-based models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations. We employ this…
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution…
We provide a complete answer to the following question: what are the flavour groups and representations providing, in the symmetric limit, an approximate description of lepton masses and mixings? We assume that neutrinos masses are…
Using the fact that any linear representation of a group can be embedded into permutations, we propose a constructive description of quantum behavior that provides, in particular, a natural explanation of the appearance of complex numbers…
The Luminous Convolution Model (LCM) demonstrates that it is possible to predict the rotation curves of spiral galaxies directly from estimates of the luminous matter. We consider two frame-dependent effects on the light observed from other…
We consider Convolutional Neural Networks (CNNs) with 2D structured features that are symmetric in the spatial dimensions. Such networks arise in modeling pairwise relationships for a sequential recommendation problem, as well as secondary…
We propose a simple phenomenological model of quarks-leptons mass matrices having fundamentally universal symmetry structure. These mass matrices consist of democratic and semi-democratic mass matrix terms commonly to the neutrino and the…
We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…
We relate leptogenesis in a class of theories to low-energy experimental observables: quark and lepton masses and mixings. With reasonable assumptions motivated by grand unification, one can show that the CP-asymmetry parameter takes a…
We discuss the possibility of flavor symmetries to explain the pattern of charged lepton and neutrino masses and mixing angles. We emphasize what are the obstacles for the generation of an almost maximal atmospheric mixing and what are the…
An equivalence between an integro-differential operator M and an evolution operator Ln is determined. From this equivalence the fundamental solution of Ln is estimated in terms of the fundamental solution related to the third-order operator…
Simple deformations, with a parameter $\epsilon$, of classical $R$-matrices which follow from decomposition of appropriate Lie algebras, are considered. As a result nonstandard Lax representations for some well known integrable systems are…
Modulated symmetries are internal symmetries that are not invariant under spacetime symmetry actions. We propose a general way to describe the lattice translation modulated symmetries in 1+1D, including the non-invertible ones, via the…
We generalize a map by S. Mason regarding two combinatorial models for key polynomials, in a way that accounts for the major index. We also define similar variants of this map, that regards alternative models for the modified Macdonald…
The discovery of neutrino masses makes leptogenesis a very attractive scenario for explaining the puzzle of the baryon asymmetry of the Universe. We present the basic ingredients of leptogenesis, explain the predictive power of this…
We develop a machine learning method for mapping data originating from both Standard Model processes and various theories beyond the Standard Model into a unified representation (latent) space while conserving information about the…
Violated mirror symmetry (MS) is capable of reproducing observed qualitative properties of weak mixing for quarks and leptons. In violated MS, lepton phenomenology, that is, small neutrino masses and mixing properties different from those…
Treating neural network inputs and outputs as random variables, we characterize the structure of neural networks that can be used to model data that are invariant or equivariant under the action of a compact group. Much recent research has…