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In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by…

There exists the phase ambiguity problem in the coherent beam combining (CBC) system with centrosymmetric arrays, which means that multiple different piston aberrations may generate the same far-field image. This will cause that the…

This paper addresses the problem of fault diagnosis in multistation assembly systems. Fault diagnosis is to identify process faults that cause the excessive dimensional variation of the product using dimensional measurements. For such…

We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…

Several modern accelerator facilities require the synchronization of equipment, which is distributed over large distances, down to the femto-second scale. This document describes the resulting problems, gives a basic description of concepts…

Laplacian matrices of graphs arise in large-scale computational applications such as semi-supervised machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits;…

We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…

Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…

Laplace transform method has proved to be very efficient and easy to parallelize for the solution of time-dependent problems. However, the synchronization delay among processors implies an upper bound on the expectable acceleration factor,…

We describe how to overcome some problems that usually prevent from obtaining an efficient algorithm to fix a generic covariant gauge on the lattice. This gauge is the lattice equivalent of the generic gauge usually adopted in perturbative…

As a pivotal component to attaining generalizable solutions in human intelligence, reasoning provides great potential for reinforcement learning (RL) agents' generalization towards varied goals by summarizing part-to-whole arguments and…

In this paper, we propose a new framework for solving a general dynamic optimal stopping problem without time consistency. A sophisticated solution is proposed and is well-defined for any time setting with general flows of objectives. A…

Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have…

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is the main source of Galilean…

We study causal discovery from observational data in linear Gaussian systems affected by \emph{mixed latent confounding}, where some unobserved factors act broadly across many variables while others influence only small subsets. This…

A generic model for alternating lags in QPO harmonics is presented where variations in the photon spectrum are caused by oscillations in two parameters that characterize the spectrum. It is further assumed that variations in one of the…

This paper is concerned with optimal power flow (OPF), which is the problem of optimizing the transmission of electricity in power systems. Our main contributions are as follows: (i) we propose a novel parabolic relaxation, which transforms…

We propose a time-adaptive predictor/multi-corrector method to solve hyperbolic partial differential equations, based on the generalized-$\alpha$ scheme that provides user-control on the numerical dissipation and second-order accuracy in…

In this paper is provided a new representation of periodic solution to the impulsive Logistic equation considered in [7].

Analog-mixed-signal (AMS) circuits are highly non-linear and operate on continuous real-world signals, making them far more difficult to model with data-driven AI than digital blocks. To close the gap between structured design data (device…