Related papers: Variational approach for pair optimization in the …
Nuclear pairing properties are studied within an approach that includes the quasiparticle-number fluctuation (QNF) and coupling to the quasiparticle-pair vibrations at finite temperature and angular momentum. The formalism is developed to…
Classical Principal Component Analysis (PCA) approximates data in terms of projections on a small number of orthogonal vectors. There are simple procedures to efficiently compute various functions of the data from the PCA approximation. The…
Unitary transformations can allow one to study open quantum systems in situations for which standard, weak-coupling type approximations are not valid. We develop here an extension of the variational (polaron) transformation approach to open…
Quantum few-body systems are deceptively simple. Indeed, with the notable exception of a few special cases, their associated Schrodinger equation cannot be solved analytically for more than two particles. One has to resort to approximation…
We present a new technique called contrastive principal component analysis (cPCA) that is designed to discover low-dimensional structure that is unique to a dataset, or enriched in one dataset relative to other data. The technique is a…
Atomic nuclei exhibit deformation, pairing correlations, and rotational symmetries. To meet these competing demands in a computationally tractable formalism, we revisit the use of general pair condensates with good particle number as a…
Despite major advances in oncology, many chemotherapeutic agents still cause severe side effects that reduce quality of life, motivating new approaches for early detection and targeted elimination of cancer cells. Luminescent transition…
The analysis of shape transitions in Nd isotopes, based on the framework of relativistic energy density functionals and restricted to axially symmetric shapes in Ref. \cite{PRL99}, is extended to the region $Z = 60$, 62, 64 with $N \approx…
Complexity is often exhibited in dynamical systems, where certain parameters evolve with time in a strange and chaotic nature. These systems lack predictability and are common in the physical world. Dissipative systems are one of such…
Inverse problems involving partial differential equations (PDEs) are widely used in science and engineering. Although such problems are generally ill-posed, different regularisation approaches have been developed to ameliorate this problem.…
Variational approaches, such as variational Monte Carlo (VMC) or the variational quantum eigensolver (VQE), are powerful techniques to tackle the ground-state many-electron problem. Often, the family of variational states is not invariant…
We formulate a new Hartree-Fock-Bogoliubov method applicable to weakly bound deformed nuclei using the coordinate-space Green's function technique. An emphasis is put on treatment of quasiparticle states in the continuum, on which we impose…
We have utilized the non-conjugate Variational Bayesian (VB) method for the problem of the sparse Poisson regression model. To provide approximate conjugacy in the model, the likelihood is approximated by a quadratic function, yielding…
A multi-channel algebraic scattering theory has been used to study the properties of nucleon scattering from 12C and of the sub-threshold compound nuclear states, accounting for properties in the compound nuclei to ~10 MeV. All compound and…
Data analysis often requires methods that are invariant with respect to specific transformations, such as rotations in case of images or shifts in case of images and time series. While principal component analysis (PCA) is a widely-used…
Quantum simulation has begun to penetrate the field of quantum chemistry in hopes of efficiently calculating ground state energies and approximating real-time evolution. With modern research highlighting nonadiabatic dynamics, tunably…
Starting from state-by-state calculations of exclusive rates of the ordinary muon capture (OMC), we evaluated total muon-capture rates for a set of light- and medium-weight nuclear isotopes. We employed a version of the proton-neutron…
Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event…
Combining classical optimization with parameterized quantum circuit evaluation, variational quantum algorithms (VQAs) are among the most promising algorithms in near-term quantum computing. Similar to neural networks (NNs), VQAs iteratively…
We propose kernel PCA as a method for analyzing the dependence structure of multivariate extremes and demonstrate that it can be a powerful tool for clustering and dimension reduction. Our work provides some theoretical insight into the…