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We apply Koide's mass relation of charged leptons to neutrinos and quarks, with both the normal and inverted mass schemes of neutrinos discussed. We introduce the parameters $k_{\nu}$, $k_u$ and $k_d$ to describe the deviations of neutrinos…
Neutrinos are perhaps the most elusive known particles in the universe. We know they have some nonzero mass, but unlike all other particles, the absolute scale remains unknown. In addition, their fundamental nature is uncertain; they can…
A typical form of mass formula is re-explained in terms of nuclear structure. For $ N \approx Z $ nuclei, we propose to start with the shell model picture and to consider the T=0 $2n-2p$ ($\alpha$-like) correlations as the fundamental…
We discuss some of the challenges that future nuclear modeling may face in order to improve the description of the nuclear structure. One challenge is related to the need for A-body nuclear interactions justified by various contemporary…
In this work, we study the inverse problem of analog gravity systems which admit rotation and energy-dependent boundary conditions. By extending two recent results, we provide a recipe that allows one to relate resonant transmission spectra…
This paper studies an inverse boundary value problem for a semilinear Helmholtz equation with Neumann boundary conditions in a bounded domain $\Omega \subset \mathbb{R}^n$ ($n\ge2$). The objective is to recover the unknown linear and…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
By using a machine learning algorithms, we present an improved nuclear mass table with a root mean square deviation of less than $200$\.keV. The model is equipped with statistical error bars in order to compare with available experimental…
In this work, we have done a completely microscopic calculation using a many-body variational method based on the cluster expansion of energy to compute the asymmetry energy of nuclear matter. In our calculations, we have employed the…
In this paper, we study the inverse scattering problem for energy-dependent Schr\"{o}dinger equations on the half-line with energy-dependent boundary conditions at the origin. Under certain positivity and very mild regularity assumptions,…
The nuclear matter parameters (NMPs), those underlie in the construction of the equation of state (EoS) of neutron star matter, are not directly accessible. The Bayesian approach is applied to reconstruct the posterior distributions of NMPs…
Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…
Neural networks functions are supposed to be able to encode the desired solution of an inverse problem very efficiently. In this paper, we consider the problem of solving linear inverse problems with neural network coders. First we…
In this paper is presented a general-relativistic approach of cuasi-neutral bodies endowed with magnetic field. Starting from the similarity of neutron particles with neutron stars for which the general-relativistic framework is imposed,…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
We analyse the fermion masses and mixings in the flipped SU(5) model. The fermion mass matrices are evolved from the GUT scale down to $m_W$ by solving the renormalization group equations for the Yukawa couplings. The constraints imposed by…
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function…
We generalize the problem of strongly interacting neutron matter by adding a periodic external modulation. This allows us to study from first principles a neutron system that is extended and inhomogeneous, with connections to the physics of…