Related papers: The Average Spectrum Method for Analytic Continuat…
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…
The ideal spectral averaging method depends on one's science goals and the available information about one's data. Including low-quality data in the average can decrease the signal-to-noise ratio (SNR), which may necessitate an optimization…
This paper presents a very simple method ensuring the independence of consecutive spectra of the phase or frequency noise of an oscillator. This condition is essential for using cross-spectrum averages.
A simple method for numerical analytic continuation is developed. It is designed to analytically continue the imaginary time (Matsubara frequency) quantum Monte Carlo simulation results to the real time (real frequency) domain. Such a…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…
In order to remain competitive, Internet companies collect and analyse user data for the purpose of improving user experiences. Frequency estimation is a widely used statistical tool which could potentially conflict with the relevant…
We report multipronged progress on the stochastic averaging approach to numerical analytic continuation of quantum Monte Carlo data. With the sampled spectrum parametrized with delta-functions in continuous frequency space, a calculation of…
We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic…
Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. In a nutshell, spectral methods refer to a collection of algorithms built upon the eigenvalues…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter,…
Spectral Clustering is one of the most traditional methods to solve segmentation problems. Based on Normalized Cuts, it aims at partitioning an image using an objective function defined by a graph. Despite their mathematical attractiveness,…
A new approach of solving the ill-conditioned inverse problem for analytical continuation is proposed. The root of the problem lies in the fact that even tiny noise of imaginary-time input data has a serious impact on the inferred…
Intelligent spectrum management is crucial for improving spectrum efficiency and achieving secure utilization of spectrum resources. However, existing intelligent spectrum management methods, typically based on small-scale models, suffer…
Spectral clustering is one of the most popular clustering methods for finding clusters in a graph, which has found many applications in data mining. However, the input graph in those applications may have many missing edges due to error in…
Spectrum anomaly detection is of great importance in wireless communication to secure safety and improve spectrum efficiency. However, spectrum anomaly detection faces many difficulties, especially in unauthorized frequency bands. For…
The simplest and most widely applied method for guaranteeing differential privacy is to add instance-independent noise to a statistic of interest that is scaled to its global sensitivity. However, global sensitivity is a worst-case notion…
Frequency domain methods form a ubiquitous part of the statistical toolbox for time series analysis. In recent years, considerable interest has been given to the development of new spectral methodology and tools capturing dynamics in the…
Dynamic spectrum sharing is a promising technology for improving the spectrum utilization. In this paper, we study how secondary users can share the spectrum in a distributed fashion based on social imitations. The imitation-based mechanism…
We propose a new dynamic average consensus algorithm that is robust to information-sharing noise arising from differential-privacy design. Not only is dynamic average consensus widely used in cooperative control and distributed tracking, it…