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Contrary to standard statistical models, unnormalised statistical models only specify the likelihood function up to a constant. While such models are natural and popular, the lack of normalisation makes inference much more difficult. Here…
We study renormalizable extensions of the standard model that contain vector-like fermions in a (single) complex representation of the standard model gauge group. There are 11 models where the vector-like fermions Yukawa couple to the…
There have been a great deal of works on the precision test of the standard model (SM) because of the incredibly precise data obtained at the LEP and the new measurements of $M_W$ and $m_t$ at the Fermilab Tevatron as well as the recent…
In this thesis, we perform a comprehensive renormalization group analysis of two- and three-dimensional Fermi systems at low and zero temperature. We examine systems with spontaneous symmetry-breaking and quantum critical behavior by…
Methods of determination of constants of the Standard Model are considered. The constants values obtained now are presented and experiments for improving some values are pointed out. A few possible generalized models are considered together…
We present the first unquenched, continuum limit, lattice QCD results for the matrix elements of the operators describing neutral kaon oscillations in extensions of the Standard Model. Owing to the accuracy of our calculation on \Delta S=2…
The Dualized Standard Model which gives explanations for both fermion generations and Higgs fields has already been used to calculate fermion mass and mixing parameters with success. In this paper, we extend its application to low energy…
The Functional Renormalisation Group approach is applied the imbalanced many-fermion systems. The system is found to exhibit the first order phase transition from the superfluid to normal phase when the density (chemical potential) mismatch…
When solving renormalisation group equations in a quantum field theory, one often specifies the boundary conditions at multiple renormalisation scales, such as the weak and grand-unified scales in a theory beyond the standard model. A point…
Various precision determinations of the Fermi constant are compared. Included are muon and (leptonic) tau decays as well as indirect prescriptions employing $\alpha, m_Z, m_W, \ssthwmzms, \Gamma(Z\to\ell^+\ell^-)$, and $\Gamma(Z \to \nu\bar…
The massive Schwinger model is studied, using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit…
A general calculational method is applied to investigate symmetry relations among divergent amplitudes in a free fermion model. A very traditional work on this subject is revisited. A systematic study of one, two and three point functions…
A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual…
Functional renormalisation group approach is applied to a imbalanced many- fermion system with a short-range attractive force. Composite boson field is introduced to describe the pairing between different flavour fermions. A set of…
In a previous study, the flavor-changing fermion-graviton interactions have been analyzed in the framework of the standard model, where analytical results for the relevant form factors were obtained at the leading order in the external…
A connection between the General Linear Model (GLM) in combination with classical statistical inference and the machine learning (MLE)-based inference is described in this paper. Firstly, the estimation of the GLM parameters is expressed as…
We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an ${\it extended}$ non-supersymmetric SO(10) model, where the Higgs sector contains the ${\bf 10}_{\rm H}$, ${\bf…
A variant of variationally optimized perturbation, incorporating renormalization group properties in a straightforward way, uniquely fixes the variational mass interpolation in terms of the anomalous mass dimension. It is used at three…
In this thesis we use renormalization group methods to study the critical behaviour of the staggered F-model. This model is a six vertex model that can be used to calculate the thermodynamic properties of a facet of a BCC crystal in the…
Reliable estimation of feature contributions in machine learning models is essential for trust, transparency and regulatory compliance, especially when models are proprietary or otherwise operate as black boxes. While permutation-based…