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The ``evolving constants'' method of defining the quantum dynamics of time-reparametrization-invariant theories is investigated for a particular implementation of parametrized non-relativistic quantum mechanics (PNRQM). The wide range of…
We show that the existing methods for computing the f(\alpha) spectrum from a time series can be improved by using a new algorithmic scheme. The scheme relies on the basic idea that the smooth convex profile of a typical f(\alpha) spectrum…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
Leveraging the kernel trick in both the input and output spaces, surrogate kernel methods are a flexible and theoretically grounded solution to structured output prediction. If they provide state-of-the-art performance on complex data sets…
The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization…
Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover…
A central problem in parameterized algorithms is to obtain algorithms with running time $f(k)\cdot n^{O(1)}$ such that $f$ is as slow growing function of the parameter $k$ as possible. In particular, a large number of basic parameterized…
We study several numerical discretization techniques for the one-space plus one-time dimensional Dirac equation, including finite difference and space-time finite element methods. Two finite difference schemes and several space-time finite…
Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…
Detecting emergence of a low-rank signal from high-dimensional data is an important problem arising from many applications such as camera surveillance and swarm monitoring using sensors. We consider a procedure based on the largest…
Fractional learning algorithms are trending in signal processing and adaptive filtering recently. However, it is unclear whether the proclaimed superiority over conventional algorithms is well-grounded or is a myth as their performance has…
Stochastic differential equations can describe a wide range of dynamical systems, and obtaining the governing equations of these systems is the premise of studying the nonlinear dynamic behavior of the system. Neural networks are currently…
Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix…
We introduce a novel ensemble approach for feature selection based on hierarchical stacking for non-stationarity and/or a limited number of samples with a large number of features. Our approach exploits the co-dependency between features…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
Trajectory retiming is the task of computing a feasible time parameterization to traverse a path. It is commonly used in the decoupled approach to trajectory optimization whereby a path is first found, then a retiming algorithm computes a…
We consider the least-squares finite element method (lsfem) for systems of nonlinear ordinary differential equations and establish an optimal error estimate for this method when piecewise linear elements are used. The main assumptions are…
This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms. The parameterized approach articulates the running…
This work unifies pseudo-time and inexact regularization techniques for nonmonotone classes of partial differential equations, into a regularized pseudo-time framework. Convergence of the residual at the predicted rate is investigated…
Despite its impressive theory \& practical performance, Frequent Directions (\acrshort{fd}) has not been widely adopted for large-scale regression tasks. Prior work has shown randomized sketches (i) perform worse in estimating the…