Related papers: Approximation of potential function in the problem…
We consider the phase diagram of a classical fluid in the presence of a random pinning potential of arbitrary strength. Introducing replicas for averaging over the quenched disorder, we use the hypernetted chain approximation to calculate…
Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution…
A dynamical theory which incorporates the electron-electron correlations and the effects of external magnetic fields for an electron escaping from a helium surface is presented. The degrees of freedom in the calculation of the escape rate…
We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
We construct and analyze a group of immersed finite element (IFE) spaces formed by linear, bilinear and rotated Q1 polynomials for solving planar elasticity equation involving interface. The shape functions in these IFE spaces are…
We introduce a theoretical framework for the rational approximation of optical response functions in resonant photonic systems. The framework is based on the AAA algorithm and further allows to solve the underlying nonlinear eigenproblems…
We study dynamics of a classical particle in a one-dimensional potential, which is composed of two periodic components, that are time-independent, have equal amplitudes and periodicities. One of them is externally driven by a random force…
The area of parameterized approximation seeks to combine approximation and parameterized algorithms to obtain, e.g., (1+eps)-approximations in f(k,eps)n^{O(1)} time where k is some parameter of the input. We obtain the following results on…
From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to…
We consider a stochastic optimal exit time feedback control problem. The Bellman equation is solved approximatively via the Policy Iteration algorithm on a polynomial ansatz space by a sequence of linear equations. As high degree…
We present an analytic study for subdiffusive escape of overdamped particles out of a cusp-shaped parabolic potential well which are driven by thermal, fractional Gaussian noise with a $1/\omega^{1-\alpha}$ power spectrum. This…
We extend the static theory of disorder-induced exponential decay of the averaged Green function of a quantum charged particle in a classical one-component plasma to the dynamic regime by incorporating the temporal evolution of the ionic…
In reinforcement learning (RL), an agent must explore an initially unknown environment in order to learn a desired behaviour. When RL agents are deployed in real world environments, safety is of primary concern. Constrained Markov decision…
We introduce and initiate the study of a new model of reductions called the random noise model. In this model, the truth table $T_f$ of the function $f$ is corrupted on a randomly chosen $\delta$-fraction of instances. A randomized…
The reactive process of barrier escaping from the metastable potential well is studied together with the extension of Kramers' rate formula to the fractional case. Characteristic quantities are computed for an thimbleful of insight into the…
The use of electrostatic ion beam traps require to set many potentials on the electrodes (ten in our case), making the tuning much more difficult than with quadrupole traps. In order to obtain the best trapping conditions, an analytical…
The problem of noise-induced transitions is often associated with Hendrik Kramers due to his seminal paper of 1940, where an archetypal example - one-dimensional potential system subject to linear damping and weak white noise - was…