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We prove the existence of the exact density-functional theory formalism for open electronic systems, and develop subsequently an exact time-dependent density-functional theory (TDDFT) formulation for the dynamic response. The TDDFT…
Most generalized fractional operators rely on prescribed memory kernels, restricting hereditary behavior to predefined forms and limiting flexibility in modeling diverse memory effects. Motivated by these limitations, this paper develops a…
It has been known for some time that the Green's function of a planar domain can be defined in terms of the exit time of Brownian motion, and this definition has been extended to stopping times more general than exit times. In this paper,…
We introduce a Lagrangian-space Effective Field Theory (LEFT) formalism for the study of cosmological large scale structures. Unlike the previous Eulerian-space construction, it is naturally formulated as an effective field theory of…
In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is…
We derive an approximation approach to evolution of the longitudinal structure function, by using a Laplace-transform method. We solve the master equation and derive the longitudinal structure function as a function of the initial condition…
Optical aberrations prevent telescopes from reaching their theoretical diffraction limit. Once estimated, these aberrations can be compensated for using deformable mirrors in a closed loop. Focal plane wavefront sensing enables the…
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was…
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…
We construct an explicit Green's function for the conjugated Laplacian $e^{-\omega \cdot x/h}\Delta e^{-\omega \cdot x/h}$, which let us control our solutions on roughly half of the boundary. We apply the Green's function to solve a partial…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
The work is devoted to the construction of efficient and applicable to real tasks first-order methods of convex optimization, that is, using only values of the target function and its derivatives. Construction uses OGM-G, fast gradient…
Score-based diffusion models generate samples from a complex underlying data distribution by time-reversal of a diffusion process and represent the state-of-the-art in many generative AI applications. Here, I show how a generative diffusion…
We present the first-principles quantization of a damped scalar field within the framework of classical action principle of non-conservative systems using doubled dynamical variables. We consider a non-conservative potential term…
Marchenko algorithms retrieve the wavefields excited by virtual sources in the subsurface, these are the Green's functions consisting of the primary and multiple reflected waves. The requirements for these algorithms are the same as for…
Seismic inversion refers to the process of estimating reservoir rock properties from seismic reflection data. Conventional and machine learning-based inversion workflows usually work in a trace-by-trace fashion on seismic data, utilizing…
Domain shifts in the training data are common in practical applications of machine learning; they occur for instance when the data is coming from different sources. Ideally, a ML model should work well independently of these shifts, for…
The first passage time problem is considered for stochastic logistic growth model with constant harvesting and multiplicative environmental noise. Explicit expressions for the moments and cumulants of both upcrossing and downcrossing FPTs…
Practical methods to compute dipole strengths for a three-body system by using a discretized continuum are analyzed. New techniques involving Green's function are developed, either by correcting the tail of the approximate wave function in…
In this brief report we discuss the action functional of a particle with damping, showing that it can be obtained from the dissipative equation of motion through a modification which makes the new dissipative equation invariant for time…