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Using the auxiliary field method, we give an analytical expression for the eigenenergies of a system composed of two non-relativistic particles interacting via a potential of type $\sqrt{a^2 r^2 + b}$. This situation is usual in the case of…
Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…
Eigenfunctions and eigenvalues of the operator of the square of the angular momentum are studied. It is shown that neither from the requirement for the eigenfunctions be normalizable nor from the commutation relations it is possible to…
For polynomials of degree two which have no zeros, the method of accompanying variables is developed and zeros of associated vector polynomials are determined. Our flexible method uses a wide variety of possible vector-valued vector…
We provide a sufficient condition for avoiding squared propagators in the intermediate stages of setting up differential equations for loop integrals. This condition is satisfied in a large class of two- and three-loop diagrams. For these…
In this paper we entertain a simple idea that the action of ghost free massive gravity (in metric formulation) depends not on the full structure of the square root of a matrix but rather on its invariants given by elementary symmetric…
We propose and analyze an algorithm for the solution of the $L^2$-subgradient flow of the total variation functional. The algorithm involves no regularization, thus the numerical solution preserves the main features that motivate…
We compute the sum and the alternating sum of the reciprocals of triangular numbers using two standard methods from calculus: a telescoping series approach and a power series approach. We then extend these results to generalized…
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being…
We demonstrate that the use of analytical on-shell methods involving calculation of the discontinuity across the t-channel cut associated with the exchange of a pair of massless particles (photons or gravitons) can be used to evaluate…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
We consider fluctuations of magnetic field excited by external force and advected by isotropic turbulent flow. It appears that non-Gaussian velocity gradient statistics and finite region of pumping force provide the existence of stationary…
In this paper, we propose a transformed na\"ive ratio and product based estimators using the characterizing scalar in presence of auxiliary information of the study variable for estimating the population mode following simple random…
Many causal estimands, such as average treatment effects under unconfoundedness, can be written as continuous linear functionals of an unknown regression function. We study a weighting estimator that sets weights by a minimax procedure:…
This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to certain inner product spaces. Those spaces are then endowed with the Gaussian probability…
We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions…
We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…
Balancing square and rectangular tables by rotation has been a interesting way to illustrate the intermediate value theorem. The aim of this note is to show that the balancing act but with non-rectangular tables can be a nice application of…
In continuous-time system identification, the intersample behavior of the input signal is known to play a crucial role in the performance of estimation methods. One common input behavior assumption is that the spectrum of the input is…
A gauge-independent approach to resonant transition amplitudes with nonconserved external currents is presented, which is implemented by the pinch technique. The analytic expressions derived with this method are $U(1)_{em}$ invariant,…