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We evaluate various sources of errors that occur when attempting to produce a specified coherent change of a two-state quantum system using six popular coherent control techniques: resonant excitation, adiabatic following, composite…
The method of constructing spline classes in the form of trigonometric Fourier series whose coefficients have a certain decreasing order are considered. in turn, this decrement determines the number of continuous derivatives of sum of this…
Parameterized quantum circuits (PQCs) are ubiquitous in the design of hybrid quantum-classical algorithms. In this work, we propose an interpolation-based coordinate descent (ICD) method to address the parameter optimization problem in…
Interpolation and smoothing using cubic and generalized splines are fundamental tools in data analysis and statistical modeling. Recently, fast computational algorithms were developed for natural $L$-splines of order four, which arise as…
A new method to correct the emulsion deformation, mainly produced in the development process, is developed to recover the high accuracy of nuclear emulsion as a tracking device. The method is based on a precise photomask and a careful…
The material point method (MPM) has been increasingly used for the simulation of large deformation processes in fluid-infiltrated porous materials. For undrained poromechanical problems, however, standard MPMs are numerically unstable…
The Immersed Boundary (IB) method is a mathematical framework for constructing robust numerical methods to study fluid-structure interaction in problems involving an elastic structure immersed in a viscous fluid. The IB formulation uses an…
Mesh refinement in pseudospectral (PS) optimal control is embarrassingly easy --- simply increase the order $N$ of the Lagrange interpolating polynomial and the mathematics of convergence automates the distribution of the grid points.…
We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the…
Video interpolation is an important problem in computer vision, which helps overcome the temporal limitation of camera sensors. Existing video interpolation methods usually assume uniform motion between consecutive frames and use linear…
A robust control strategy for autonomous vehicles can improve system stability, enhance riding comfort, and prevent driving accidents. This paper presents a novel interpolation-tube-based constrained iterative linear quadratic regulator…
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
In this paper we consider the cubic regularization (CR) method for minimizing a twice continuously differentiable function. While the CR method is widely recognized as a globally convergent variant of Newton's method with superior iteration…
This paper introduces a new framework for constructing the Discrete Empirical Interpolation Method DEIM projection operator. The interpolation node selection procedure is formulated using the QR factorization with column pivoting, and it…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
This paper considers the problem of temporal video interpolation, where the goal is to synthesize a new video frame given its two neighbors. We propose Cross-Video Neural Representation (CURE) as the first video interpolation method based…
We present a general method to quickly generate high-fidelity control pulses for any continuously-parameterized set of quantum gates after calibrating a small number of reference pulses. We find that interpolating between optimized control…
Texture synthesis models are important tools for understanding visual processing. In particular, statistical approaches based on neurally relevant features have been instrumental in understanding aspects of visual perception and of neural…
Scalable quantum computing can only be achieved if qubits are manipulated fault-tolerantly. Topological error correction - a novel method which combines topological quantum computing and quantum error correction - possesses the highest…