Related papers: Optimal Smoothing for N-Body Codes
In this work, we propose a novel and efficient method for smoothing polylines in motion planning tasks. The algorithm applies to motion planning of vehicles with bounded curvature. In the paper, we show that the generated path: 1) has…
This report describes a modification of the orthogonal function Poisson solver for n-body simulations that minimizes relaxation caused by small particle number fluctuations. With the standard algorithm, the noise leading to relaxation can…
Cosmological N-Body simulations are used for a variety of applications. Indeed progress in the study of large scale structures and galaxy formation would have been very limited without this tool. For nearly twenty years the limitations…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
The typical model for measurement noise in quantum error correction is to randomly flip the binary measurement outcome. In experiments, measurements yield much richer information - e.g., continuous current values, discrete photon counts -…
In this paper, we present a new smoothing approach to solve general nonlinear complementarity problems. Under the $P_0$ condition on the original problems, we prove some existence and convergence results . We also present an error estimate…
In self-consistent N-body simulations of collisionless systems, gravitational interactions are modified on small scales to remove singularities and simplify the task of numerically integrating the equations of motion. This `gravitational…
We propose an adaptive accelerated smoothing technique for a nonsmooth convex optimization problem where the smoothing update rule is coupled with the momentum parameter. We also extend the setting to the case where the objective function…
We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit $N…
A smoothing algorithm is presented for solving the soft-margin Support Vector Machine (SVM) optimization problem with an $\ell^{1}$ penalty. This algorithm is designed to require a modest number of passes over the data, which is an…
This paper computationally obtains optimal bounded-weight, binary, error-correcting codes for a variety of distance bounds and dimensions. We compare the sizes of our codes to the sizes of optimal constant-weight, binary, error-correcting…
Decoders that provide an estimate of the probability of a logical failure conditioned on the error syndrome ("soft-output decoders") can reduce the overhead cost of fault-tolerant quantum memory and computation. In this work, we construct…
We derive a three-term recurrence relation for computing the polynomial of best approximation in the uniform norm to $x^{-1}$ on a finite interval with positive endpoints. As application, we consider two-level methods for scalar elliptic…
We estimate optimal thresholds for surface code in the presence of loss via an analytical method developed in statistical physics. The optimal threshold for the surface code is closely related to a special critical point in a…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…
The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold…
In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
It has been widely recognized that the 0/1 loss function is one of the most natural choices for modelling classification errors, and it has a wide range of applications including support vector machines and 1-bit compressed sensing. Due to…
Data shaping is a coding technique that has been proposed to increase the lifetime of flash memory devices. Several data shaping codes have been described in recent work, including endurance codes and direct shaping codes for structured…