相关论文: Counting $S_5$-fields with a power saving error te…

Many hard problems in the computational sciences are equivalent to counting the leaves of a decision tree, or, more generally, summing a cost function over the nodes. These problems include calculating the permanent of a matrix, finding the…

Data centers are high power consumers and the energy consumption of data centers keeps on rising in spite of all the efforts for increasing the energy efficiency. The need for energy-awareness in data centers makes the use of power modeling…

The scheduling problem in additive manufacturing is receiving increasing attention; however, few have considered the effect of scheduling decisions on machine energy consumption. This research focuses on the nesting and scheduling problem…

Support Vector Machines (SVM) is a computational technique which has been used in various fields of sciences as a classifier with k-class classification capability, k being 2,3,4, etc. Seismograms of volcanic tremors often contain noises…

In the paper, we describe in operator form classes of PDEs that admit PINN's error estimation. Also, for $L^p$ spaces, we obtain a Bramble-Hilbert type lemma that is a tool for PINN's residuals bounding.

Data entry constitutes a fundamental component of the machine learning pipeline, yet it frequently results in the introduction of labelling errors. When a model has been trained on a dataset containing such errors its performance is…

This paper aims at refined error analysis for binary classification using support vector machine (SVM) with Gaussian kernel and convex loss. Our first result shows that for some loss functions such as the truncated quadratic loss and…

Although empirical studies have confirmed the effectiveness of spectrum-based fault localization (SBFL) techniques, their performance may be degraded due to presence of some undesired circumstances such as the existence of coincidental…

We prove an asymptotic formula with a power saving error term for the (pure or mixed) second moment of central values of L-functions of any two (possibly equal) fixed cusp forms f, g twisted by all primitive characters modulo q, valid for…

In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on…

As a signal recovery algorithm, compressed sensing is particularly useful when the data has low-complexity and samples are rare, which matches perfectly with the task of quantum phase estimation (QPE). In this work we present a new…

We introduce a scheme for fault tolerantly dealing with losses (or other "leakage" errors) in cluster state computation that can tolerate up to 50% qubit loss. This is achieved passively using an adaptive strategy of measurement - no…

The effective Lagrangian and power counting rules for non-relativistic gauge theories are derived via an expansion in $1/c$. It is shown that the $1/c$ expansion leads to an effective field theory which incorporates a multipole expansion.…

We improve the error terms of some estimates related to counting lattices from recent work of L. Fukshansky, P. Guerzhoy and F. Luca (2017). This improvement is based on some analytic techniques, in particular on bounds of exponential sums…

The heavy quark effective theory makes model independent predictions for semileptonic $\Lambda_b \to \Lambda_c$ decays in terms of a small set of parameters. No subleading Isgur-Wise function occurs at order $\Lambda_{\rm QCD}/m_{c,b}$, and…

An estimation problem of fundamental interest is that of phase synchronization, in which the goal is to recover a collection of phases using noisy measurements of relative phases. It is known that in the Gaussian noise setting, the maximum…

Errors due to hardware or low level software problems, if detected, can be fixed by various schemes, such as recomputation from a checkpoint. Silent errors are errors in application state that have escaped low-level error detection. At…

In 2011, the fundamental gap conjecture for Schr\"odinger operators was proven. This can be used to estimate the ground state energy of the time-independent Schr\"odinger equation with a convex potential and relative error \epsilon.…

We prove a quantitative estimate with a power saving error term for the number of points in a mapping class group orbit of Teichm\"uller space that lie within a Teichm\"uller metric ball of given center and large radius. Estimates of the…

Polynomial--time constant--space quantum Turing machines (QTMs) and logarithmic--space probabilistic Turing machines (PTMs) recognize uncountably many languages with bounded error (Say and Yakary\i lmaz 2014, arXiv:1411.7647). In this…