Related papers: The Complex Langevin method: When can it be truste…
The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…
We suggest an approach for simulating theories with a sign problem that relies on optimisation of complex integration contours that are not restricted to lie along Lefschetz thimbles. To that end we consider the toy model of a…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
The three-dimensional SU(3) spin model is an effective Polyakov loop model for QCD at nonzero temperature and density. It suffers from a sign problem at nonzero chemical potential. We revisit this model using complex Langevin dynamics and…
Criteria are given for determining whether an irreducible sextic equation with rational coefficients is algebraically solvable over the complex numbers.
We study numerical methods for the generalized Langevin equation (GLE) with a positive Prony series memory kernel, in which case the GLE can be written in an extended variable Markovian formalism. We propose a new splitting method that is…
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds…
The three-dimensional XY model is studied at finite chemical potential using complex Langevin dynamics. The validity of the approach is probed at small chemical potential using imaginary chemical potential and continuity arguments, and at…
This study explores the potential of modern implicit solvers for stochastic partial differential equations in the simulation of real-time complex Langevin dynamics. Not only do these methods offer asymptotic stability, rendering the issue…
The classical approach to solvability of a mathematical problem is to define a method which includes certain rules of operation or algorithms. Then using the defined method, one can show that some problems are solvable or not solvable or…
This paper consider the problem of determining the reliability of a software system which can be decomposed in a number of modules. We have derived the expression of the reliability of a system using the Markovian model for the transfer of…
For a system at given temperature, with energy known as a function of a set of variables, we obtain the thermal fluctuation of the evolution of the variables by replacing the phase-space with a lattice and invoking the principle of detailed…
Hyperbolic problems can at times be solved employing symbolic arguments. This is especially true for the construction of forward (and backward) fundamental solutions. We formulate a corresponding abstract scheme and illustrate its…
The technology of formal software verification has made spectacular advances, but how much does it actually benefit the development of practical software? Considerable disagreement remains about the practicality of building systems with…
We propose a type system for a calculus of contracting processes. Processes can establish sessions by stipulating contracts, and then can interact either by keeping the promises made, or not. Type safety guarantees that a typeable process…
A key task in Bayesian statistics is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). However, without any assumptions, sampling (even approximately) can be #P-hard, and few…
Sign language is a visual language that enhances communication between people and is frequently used as the primary form of communication by people with hearing loss. Even so, not many people with hearing loss use sign language, and they…
Lefschetz thimbles and complex Langevin dynamics both provide a means to tackle the numerical sign problem prevalent in theories with a complex weight in the partition function, e.g. due to nonzero chemical potential. Here we collect some…
The following paper proposes a new approach to determine whether a logical (CNF) formula is satisfiable or not using probability theory methods. Furthermore, we will introduce an algorithm that speeds up the standard solution for (CNF-SAT)…
In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space,…