Related papers: Consistent Conformal Extensions of the Standard Mo…
The Kaczmarz and Gauss-Seidel methods both solve a linear system $\bf{X}\bf{\beta} = \bf{y}$ by iteratively refining the solution estimate. Recent interest in these methods has been sparked by a proof of Strohmer and Vershynin which shows…
We propose a classically scale-invariant extension of the Georgi--Machacek model by augmenting its custodial \(SU(2)_L \times SU(2)_R\)-symmetric Higgs sector -- originally composed of a doublet and two triplets -- with a gauge-singlet…
In this paper, we derive the standard model with classical conformal invariance from the Yang--Mills--Higgs model in noncommutative geometry (NCG). In the ordinary context of the NCG, the {\it distance matrix} $M_{nm}$ which corresponds to…
We perform a systematic analysis of an extension of the Standard Model that includes a complex singlet scalar field and is scale invariant at the tree level. We call such a model the Minimal Scale Invariant extension of the Standard Model…
We consider a class of sigma models that appears from a generalisation of the gauged WZW model parametrised by a constant matrix $Q$. Particular values of $Q$ correspond to the standard gauged WZW models, chiral gauged WZW models and a…
We use the conformal bootstrap program to derive necessary conditions for emergent symmetry enhancement from discrete symmetry (e.g. $\mathbb{Z}_n$) to continuous symmetry (e.g. $U(1)$) under the renormalization group flow. In three…
We point out a novel possible mechanism by which the electroweak hierarchy problem can be avoided in the (effective) quantum field theory. Assuming the existence of a UV complete underlying fundamental theory and treating the cutoff scale…
Mathematical models of the real world are simplified representations of complex systems. A caveat to using mathematical models is that predicted causal effects and conditional independences may not be robust under model extensions, limiting…
We prove the uniform in space and time convergence of the scaled heights of large classes of deterministic growth models that are monotone and equivariant under translations by constants. The limits are characterized as the unique…
The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both…
We improve and generalize in several accounts the recent rigorous proof of convergence of delta expansion - order dependent mappings (variational perturbation expansion) for the energy eigenvalues of anharmonic oscillator. For the…
A scale-invariant extension of the Standard Model with a singlet-scalar and hidden-QCD sector is studied. The scale of electroweak symmetry breaking is generated dynamically in an asymptotic-free hidden-QCD sector, and mediated by the…
Concerning bivariate least squares linear regression, the classical results obtained for extreme structural models in earlier attempts are reviewed using a new formalism in terms of deviation (matrix) traces which, for homoscedastic data,…
A stepped wedge design is a unidirectional crossover design where clusters are randomized to distinct treatment sequences. While model-based analysis of stepped wedge designs is standard practice to evaluate treatment effects accounting for…
The dimer model is the study of random dimer covers (perfect matchings) of a graph. A double-dimer configuration on a graph $G$ is a union of two dimer covers of $G$. We introduce quaternion weights in the dimer model and show how they can…
We consider the minimal U(1)' extension of the standard model (SM) with the classically conformal invariance, where an anomaly-free U(1)' gauge symmetry is introduced along with three generations of right-handed neutrinos and a U(1)' Higgs…
In this thesis, various extensions of the scalar sector have been considered comprising of different ${SU(2)_L}$ multiplets. If the extended scalar sector participates in the electroweak symmetry breaking then these extra scalars need to…
Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…
We consider two different versions of the double dimer model on a planar domain, where we either fold a single dimer cover on a symmetric domain onto itself across the line of symmetry, or we superimpose two independent dimer covers on two,…
Suppose that $\lambda=\lambda^{<\lambda} \ge\aleph_0$, and we are considering a theory $T$. We give a criterion on $T$ which is sufficient for the consistent existence of $\lambda^{++}$ universal models of $T$ of size $\lambda^+$ for models…