Related papers: The Fourier Spectral Characterization for the Corr…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
In this short note, we initiate the study of the Linear Isomorphism Testing Problem in the setting of communication complexity, a natural linear algebraic generalization of the classical Equality problem. Given Boolean functions $f, g :…
We study the relation among some security parameters for vectorial Boolean functions which prevent attacks on the related block cipher. We focus our study on a recently-introduced security criterion, called weak differential uniformity,…
In this note, we investigate $C^2$ differential images of the homogeneous self-similar measure associated with an IFS $\mathcal{I}=\{\rho x+a_j\}_{j=1}^m$ satisfying the strong separation condition and a positive probability vector…
Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are…
Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution,…
We present a multi-modal spectroscopic paradigm that enables independent measurement of charge and spin degrees of freedom (DOF) in strongly correlated materials. This spin-based technique probes symmetry-specific Hamiltonian parameters by…
We define and study symmetrized and antisymmetrized multivariate exponential functions. They are defined as determinants and antideterminants of matrices whose entries are exponential functions of one variable. These functions are…
The physics that governs quantum monitoring may involve other degrees of freedom than the ones initialised and controlled for probing. In this context we address the simultaneous estimation of phase and dephasing characterizing a dispersive…
Characterizing the privacy degradation over compositions, i.e., privacy accounting, is a fundamental topic in differential privacy (DP) with many applications to differentially private machine learning and federated learning. We propose a…
We study Boolean functions with sparse Fourier coefficients or small spectral norm, and show their applications to the Log-rank Conjecture for XOR functions f(x\oplus y) --- a fairly large class of functions including well studied ones such…
Let $\mathcal{F}_{n}^*$ be the set of Boolean functions depending on all $n$ variables. We prove that for any $f\in \mathcal{F}_{n}^*$, $f|_{x_i=0}$ or $f|_{x_i=1}$ depends on the remaining $n-1$ variables, for some variable $x_i$. This…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
This chapter discusses correlation analysis of stationary multivariate Gaussian time series in the spectral or Fourier domain. The goal is to identify the hub time series, i.e., those that are highly correlated with a specified number of…
A new approach to the correlation functions is presented for the XXZ model in the anti-ferroelectric regime. The method is based on the recent realization of the quantum affine symmetry using vertex operators. With the aid of a boson…
The complex Fourier transform of the two-point correlator of the energy spectrum of a quantum system is known as the spectral form factor (SFF). It constitutes an essential diagnostic tool for phases of matter and quantum chaos. In black…
Machine learning on encrypted data has received a lot of attention thanks to recent breakthroughs in homomorphic encryption and secure multi-party computation. It allows outsourcing computation to untrusted servers without sacrificing…
Infrared object detection is crucial for perception in autonomous driving and surveillance but remains vulnerable to physical adversarial attacks. Unlike in the RGB domain, where attacks rely on color texture, infrared attacks must…
Orbital-free density functional theory (OF-DFT) constitutes a computationally highly effective tool for modeling electronic structures of systems ranging from room-temperature materials to warm dense matter. Its accuracy critically depends…
The convergence of DP Fourier series which are neither strongly convergent nor strongly divergent is discussed in terms of the Taylor series of the corresponding inner analytic functions. These are the cases in which the maximum disk of…