Related papers: Addressing $\gamma_5$ in Nondimensional Regulariza…
Gamma-ray bursts (GRBs) offer a powerful probe of the cosmic expansion history far beyond the redshift range accessible to Type Ia supernovae. However, the study of cosmological models using GRBs is hindered by the circularity problem,…
This work introduces a new cubic regularization method for nonconvex unconstrained multiobjective optimization problems. At each iteration of the method, a model associated with the cubic regularization of each component of the objective…
We propose and analyze a perturbative regularization method to approximate quadratic optimization problems with finite-dimensional degeneracy. The original problem is first approximated by a regularized problem depending on a small positive…
With an eye toward understanding complexity control in deep learning, we study how infinitesimal regularization or gradient descent optimization lead to margin maximizing solutions in both homogeneous and non-homogeneous models, extending…
The density matrix renormalization group (DMRG) method is applied to the interaction round a face (IRF) model. When the transfer matrix is asymmetric, singular-value decomposition of the density matrix is required. A trial numerical…
We demonstrate how to parallelize the density matrix renormalization group (DMRG) algorithm in real space through a straightforward modification of serial DMRG. This makes it possible to apply at least an order of magnitude more…
Quantum impurity problems can be solved using the numerical renormalization group (NRG), which involves discretizing the free conduction electron system and mapping to a `Wilson chain'. It was shown recently that Wilson chains for different…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
Implicit Neural Representations (INRs) are a learning-based approach to accelerate Magnetic Resonance Imaging (MRI) acquisitions, particularly in scan-specific settings when only data from the under-sampled scan itself are available.…
Segmented regression models offer model flexibility and interpretability as compared to the global parametric and the nonparametric models, and yet are challenging in both estimation and inference. We consider a four-regime segmented model…
A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
Coherent optical transmission systems naturally lead to a four dimensional (4D) signal space, i.e., two polarizations each with two quadratures. In this paper we derive an analytical model to quantify the impact of Kerr nonlinearity on such…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…
Envelope methods perform dimension reduction of predictors or responses in multivariate regression, exploiting the relationship between them to improve estimation efficiency. While most research on envelopes has focused on their estimation…
The polarizable embedding (PE) approach is a flexible embedding model where a pre-selected region out of a larger system is described quantum mechanically while the interaction with the surrounding environment is modeled through an…
We study a consistent infrared and ultraviolet regularization scheme for the cosmological perturbations. The infrared divergences are cured by assuming that the Universe undergoes a transition between a non-singular pre-inflationary,…
We compare a momentum space implicit regularisation (IR) framework with other renormalisation methods which may be applied to dimension specific theories, namely Differential Renormalisation (DfR) and the BPHZ formalism. In particular, we…
Subspace recycling techniques have been used quite successfully for the acceleration of iterative methods for solving large-scale linear systems. These methods often work by augmenting a solution subspace generated iteratively by a known…