Related papers: Involution symmetries and the PMNS matrix
Despite significant progress in transformer interpretability, an understanding of the computational mechanisms of large language models (LLMs) remains a fundamental challenge. Many approaches interpret a network's hidden representations but…
We show how the use of a see-saw mechanism based on a $3 \times 3$ neutrino mass matrix texture can considerably simplify Higgs sectors for quark-lepton symmetric models (and for Standard Model extensions generally). The main theory we…
In this short note we collect together known results on the use of Random Matrix Theory in lattice statistical mechanics. The purpose here is two fold. Firstly the RMT analysis provides an intrinsic characterization of integrability, and…
We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies.…
We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the…
We derive lattice invariants from the heat flux of a lattice. Using systems of harmonic polynomials, we obtain sums of products of spherical theta functions which give new invariants of integer lattices which are modular forms. In…
It is shown that if, from the starting point of a universal rank-one mass matrix long favoured by phenomenologists, one adds the assumption that it rotates (changes its orientation in generation space) with changing scale, one can…
Recent stringent experiment data of neutrino oscillations induces partial symmetries such as $Z_{2}$, $Z_{2}\times CP$ to derive lepton mixing patterns. New partial symmetries expressed with elements of group algebras are studied. A…
In the canonical seesaw mechanism of neutrino mass, lepton number is only multiplicatively conserved, which enables the important phenomenon of leptogenesis to occur, as an attractive explanation of the present baryon asymmetry of the…
Left-right symmetric models (LRSM) were proposed to reconcile the apparent parity violation in weak interactions with our intrinsic notion of fundamental parity symmetry. It was quickly realized that LRSM offers a viable framework for…
While neural networks have acted as a strong unifying force in the design of modern AI systems, the neural network architectures themselves remain highly heterogeneous due to the variety of tasks to be solved. In this chapter, we explore…
In a residual $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry approach, we investigate minimally perturbed Majorana neutrino mass matrices. Constraint relations among the low energy neutrino parameters are obtained. Baryogenesis is realized…
The lepton flavor mixing matrix having one row or one column in common with the bimaximal mixing up to permutations is still compatible with the present neutrino oscillation data. We provide a thorough exploration of generating such a…
The Seesaw extensions of the Standard Model not only provide a natural explanation for tiny neutrino masses, they also predict additional heavy states such as Majorana neutrinos, charged leptons, and scalar triplets. Distinguishing between…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
Presymmetry, the hidden symmetry underlying the charge and generational patterns of quarks and leptons, is utilized for repairing the left-right asymmetry of the standard model with Dirac neutrinos. It is shown that the restoration of…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
We analyze the possibility of the leptonic mixing matrix having a Wolfenstein form at the Grand Unified Theory scale. The renormalization group evolution of masses and mixing angles from the high scale to electroweak scale, in certain new…
Understanding what knowledge is implicitly encoded in deep learning models is essential for improving the interpretability of AI systems. This paper examines common methods to explain the knowledge encoded in word embeddings, which are core…
We consider two related problems arising from a question of R. Graham on quasirandom phenomena in permutation patterns. A ``pattern'' in a permutation $\sigma$ is the order type of the restriction of $\sigma : [n] \to [n]$ to a subset $S…