Differential Privacy (DP) has received increasing attention as a rigorous privacy framework. Many existing studies employ traditional DP mechanisms (e.g., the Laplace mechanism) as primitives to continuously release private data for protecting privacy at each time point (i.e., event-level privacy), which assume that the data at different time points are independent, or that adversaries do not h...

When X is an associative H-space, the bar spectral sequence computes the homology of the delooping, H∗(BX). If X is an n-fold loop space for n ≥ 2 this is a spectral sequence of Hopf algebras. Using machinery by Sugawara and Clark, we show that the spectral sequence filtration respects the Browder bracket structure on H∗(BX), and so it is moreover a spectral sequence of Poisson algebras. Throug...

An analysis is presented of how the space in which principal component analysis is performed can affect the colorimetric and spectral accuracy of spectral reconstruction. The spectral reconstruction is performed using digital counts given by a new concept of spectral image acquisition constituted by a trichromatic camera combined with absorption filters, instead of the traditional monochrome ca...

An analogue of the Bernstein inequality is derived for partial sums of a vector-valued function on a finite reversible Markov chain. The inequality gives an upper bound for the probability of a large deviation of the partial sum. The bound depends on the chain’s spectral gap, the dimension of the space where the function takes values, and the upper bound on the size and the variance of the func...

In this paper we introduce a novel method for nonnegative matrix factorization (NMF) using a genetic algorithm. The method finds the optimal basis functions for the spectral colors in both spectral and color spaces. We show that one version of the proposed algorithm works as well as the standard NMF algorithm in spectral space. Further, this algorithm is modified to obtain a functionality to wo...

Responses of Gabor wavelets in the mid-frequency space build a local spectral representation scheme with optimal properties regarding the time-frequency uncertainty principle. However, when using Gabor wavelets we observe a skewness in the mid-frequency space caused by the spreading effect of Gabor wavelets. Though in most current applications the skewness does not obstruct the sampling of the ...

Previous studies on social networks are often focused on networks with only positive relations between individual nodes. As a significant extension, we conduct the spectral analysis on graphs with both positive and negative edges. Specifically, we investigate the impacts of introducing negative edges and examine patterns in the spectral space of the graph’s adjacency matrix. Our theoretical res...

Previous studies on social networks are often focused on networks with only positive relations between individual nodes. As a significant extension, we conduct the spectral analysis on graphs with both positive and negative edges. Specifically, we investigate the impacts of introducing negative edges and examine patterns in the spectral space of the graph’s adjacency matrix. Our theoretical res...

In this paper, we study systems of functional equations (FEs) and first-order partial differential equations (PDEs) suggested in [SIAM J. Sci. Statist. Comput., 12 (1991), pp. 607–647 and SIAM J. Numer. Anal., 29 (1992), pp. 1741–1768] as approximations for the computation of invariant tori. The main new ideas of this paper are, first, to investigate these systems in the setting of Hilbert spac...