Related papers: Killing Luzin and Sierpinski sets
We prove a removal lemma for systems of linear equations over finite fields: let $X_1,...,X_m$ be subsets of the finite field $\F_q$ and let $A$ be a $(k\times m)$ matrix with coefficients in $\F_q$ and rank $k$; if the linear system $Ax=b$…
We present a model where sterile neutrinos with rest masses in the range ~ keV to ~ MeV can be the dark matter and be consistent with all laboratory, cosmological, large-scale structure, as well as x-ray constraints. These sterile neutrinos…
We study a model of a keV-scale sterile neutrino with a relatively large mixing with the Standard Model sector. Usual considerations predict active generation of such particles in the early Universe, which leads to constraints from the…
It was proved by Avramov and Buchweitz that if A is a commutative local complete intersection ring with finitely generated modules M and N, then the Ext groups between M and N vanish from some step if and only if the Ext groups between N…
We find a distributive (v, 0, 1)-semilattice S of size $ aleph\_1$ that is not isomorphic to the maximal semilattice quotient of any Riesz monoid endowed with an order-unit of finite stable rank. We thus obtain solutions to various open…
We discuss a 331 model with three scalar triplets and neutral fermion singlets. We show that in the 331 model with right-handed neutrinos, it is possible to obtain small active neutrino masses via the double and inverse seesaw mechanisms,…
We reformulate the canonical seesaw mechanism in the case that the electroweak gauge symmetry is unbroken, and show that it can "formally" work and allow us to derive an exact seesaw formula for the light and heavy Majorana neutrinos. We…
We study connections between linear equations over various semigroups and recursively enumerable sets of positive integers. We give variants of the universal Diophantine representation of recursively enumerable sets of positive integers…
In the conventional type-(I+II) seesaw model, the effective mass matrix of three known light neutrinos is given by M_nu = M_L - M_D M^{-1}_R M^T_D in the leading-order approximation. We propose an intriguing scenario, in which the…
We perform a systematic and complete analysis of texture zeros in the lepton mass matrices and identify all viable and maximally restrictive cases of pairs (M_\ell, M_D) and (M_\ell, M_L), where M_\ell, M_D and M_L are the charged-lepton,…
We show that there are many (compact) convex semi-algebraic sets in euclidean space that do not have a semidefinite representation. This gives a negative answer to a question by Nemirovski, resp. it shows that the Helton-Nie conjecture is…
The appealing feature of inverse seesaw models is that the Standard Model (SM) neutrino mass emerges from the exchange of TeV scale singlets with sizable Yukawa couplings, which can be tested at colliders. However, the tiny Majorana mass…
Two Higgs Doublet Models (2HDM) are popular extensions of the Standard Model for several reasons, but do not explain neutrino masses. In this work, we investigate how one can incorporate neutrino masses within the framework of the…
We present a machine unlearning approach that is both retraining- and label-free. Most existing machine unlearning approaches require a model to be fine-tuned to remove information while preserving performance. This is computationally…
We show that under a new U(1) gauge symmetry, which is non-anomalous in the presence of one ``right-handed neutrino'' per generation and consistent with the standard model Yukawa couplings, the most general fermion charges are determined in…
We show that by adding to the standard model plus the type I seesaw different types of scalars, it is possible to construct models that satisfy the three requirements of (i) generating neutrino masses at the TeV scale, (ii) being testable…
A simple renormalizable U(1) gauge model is constructed to explain the smallness of the active neutrino masses and provide the stable cold dark matter candidate simultaneously. The local U(1) symmetry is assumed to be spontaneously broken…
We study a variation to the SUSY Left-Right symmetric model based on the gauge group $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_{BL}$. Beyond the quark and lepton superfields we only introduce a second Higgs bidoublet to produce…
We develop non-invertible Pesin theory for a new class of maps called cusp maps. These maps may have unbounded derivative, but nevertheless verify a property analogous to $C^{1+\epsilon}$. We do not require the critical points to verify a…
As experimental constraints on the parameter space of the MSSM and close variations thereof become stronger, the motivation to explore supersymmetric models that challenge some of the standard assumptions of the MSSM also become stronger.…