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The attention mechanism is a core component of the Transformer architecture. Various methods have been developed to compute attention scores, including multi-head attention (MHA), multi-query attention, group-query attention and so on. We…
We consider the Hamiltonian system of scalar wave field and a single nonrelativistic particle coupled in a translation invariant manner. The particle is also subject to a confining external potential. The stationary solutions of the system…
We consider the asymmetric simple exclusion process with Langmuir kinetics on a periodic lattice. We analytically obtain the exact time evolution of correlation functions with arbitrary length starting from the initial state with no…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
Sharpness-aware minimization (SAM) is a recently proposed training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains. Instead of minimizing the loss of the current…
Simulink is widely used in industrial design processes to model increasingly complex embedded control systems. Thus, their formal analysis is highly desirable. However, this comes with two major challenges: First, Simulink models often…
The non-linear collision-induced breakage equation has significant applications in particulate processes. Two semi-analytical techniques, namely homotopy analysis method (HAM) and accelerated homotopy perturbation method (AHPM) are…
A class of asymptotically autonomous systems on the plane with oscillatory coefficients is considered. It is assumed that the limiting system is Hamiltonian with a stable equilibrium. The effect of damped multiplicative stochastic…
In plasma physics, a hybrid fluid-kinetic model is composed of a magnetohydrodynamics (MHD) part that describes a bulk fluid component and a Vlasov kinetic theory part that describes an energetic plasma component. While most hybrid models…
In this paper, we consider numerical approximations for solving the inductionless magnetohydrodynamic (MHD) equations. By utilizing the scalar auxiliary variable (SAV) approach for dealing with the convective and coupling terms, we propose…
A proof of convergence is given for bulk--surface finite element semi-discretisation of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The semi-discretisation is studied in the weak…
Quantum annealing is a computational approach designed to leverage quantum fluctuations for solving large-scale classical optimization problems. Although incorporating standard transverse field (TF) terms in the annealing process can help…
We introduce an arbitrary order, stabilized finite element method for solving a unique continuation problem subject to the time-harmonic elastic wave equation with variable coefficients. Based on conditional stability estimates we prove…
Stability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable…
The paper deals with a nonlinear evolution equation describing the dynamics of a non homogeneous multiply hinged beam, subject to a nonlocal restoring force of displacement type. First, a spectral analysis for the associated weighted…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
We address the linear-mode analysis performed near an equilibrium configuration in the fluid rest frame with a dynamical magnetic field perturbed on a constant configuration. We develop a simple and general algorithm for an analytic…
Equilibrating proteins and other biomacromolecules is cardinal for molecular dynamics simulation of such biological systems in which they perform free dynamics without any externally-applied mechanical constraint, until thermodynamic…
To analyze non-stationary harmonic signals typically contained in geophysical observables is a quest that has seen continual advances in numerical techniques over the decades. In this paper, based on transient z-pole estimation (in Hankel…