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In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Dyson's integration theorem is widely used in the computation of eigenvalue correlation functions in Random Matrix Theory. Here we focus on the variant of the theorem for determinants, relevant for the unitary ensembles with Dyson index…
The equivalence of two formulations of Fokker's quantum theory is proved - based on the Feynman functional integral representation of the propagator for a system of charges with direct electromagnetic interaction and the quantum principle…
Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…
We study the algebraic and analytic structure of Feynman integrals by proposing an operation that maps an integral into pairs of integrals obtained from a master integrand and a corresponding master contour. This operation is a coaction. It…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
We obtain a good analytic fit to the joint Bjorken-x and Q^2 dependences of ZEUS data on the deep inelastic structure function F_2(x, Q^2). At fixed virtuality Q^2, as we showed previously, our expression is an expansion in powers of log…
We generalize module weak-* Haagerup tensor products to obtain complete quotients of normal Haagerup tensor product included in canonical Hilbert spaces associated to completely positive normal (covariance) maps $\eta$ on a finite von…
In perturbative calculations of quantum mechanical path integrals in curvilinear coordinates, Feynman diagrams involve multiple temporal integrals over products of distributions, which are mathematically undefined. We derive simple rules…
Feynman integrands are constructed as Hida distributions. For our approach we first have to construct solutions to a corresponding Schroedinger equation with time-dependent potential. This is done by a generalization of the Doss approach to…
The Poincare series of a multi-index filtration on the ring of germs of functions can be written as a certain integral with respect to the Euler characteristic over the projectivization of the ring. Here this integral is considered with…
We point out that a proper use of the Hoeffding--ANOVA decomposition for symmetric statistics of finite urn sequences, previously introduced by the author, yields a decomposition of the space of square-integrable functionals of a…
Quantifying the influence of infinitesimal changes in training data on model performance is crucial for understanding and improving machine learning models. In this work, we reformulate this problem as a weighted empirical risk minimization…
Evaluation of treatment effects and more general estimands is typically achieved via parametric modelling, which is unsatisfactory since model misspecification is likely. Data-adaptive model building (e.g. statistical/machine learning) is…
New physical insight into the correspondence between path integral concepts and the Schr\"odinger formulation is gained by the analysis of the effective classical potential, that is defined within the Feynman path integral formulation of…
An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. It is shown that…
Development generating diffraction-related valuable expressions and formulas capable of initiating new era for diffraction and for scientific domains that use it provided. The main expression, among these, gives diffracted intensity as…
The analytic integration and simplification of multi-loop Feynman integrals to special functions and constants plays an important role to perform higher order perturbative calculations in the Standard Model of elementary particles. In this…
In many applications, researchers are interested in the direct and indirect causal effects of a treatment or exposure on an outcome of interest. Mediation analysis offers a rigorous framework for identifying and estimating these causal…