14 papers · ranked by Valyu relevance
Zezhen Wang, Weihao Mai, Yuming Chai, Kexin Qi + 8 more
'Chen Shen' 'Shiwu Zhang' 'Guodong Tan' 'Yu Hu' 'Quan Wen' 'Peter Latham' 'Panayiota Poirazi'] Understanding neural activity organization is vital for deciphering brain function. By recording whole-brain calcium activity in larval zebrafish during hunting and spontaneous behaviors, we find that the shape of the neural…
Michael Speckbacher
We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in ${\mathbb{R}}^2$. We first investigate the interplay between relative density of the trajectory and the reconstruction property. Later, we consider spiraling curves, a special class of trajectories…
Xueyang Yao, Natalie Baddour, Yilun Shang
The theory of the continuous two-dimensional (2D) Fourier Transform in polar coordinates has been recently developed but no discrete counterpart exists to date. In the first part of this two-paper series, we proposed and evaluated the theory of the 2D Discrete Fourier Transform (DFT) in polar coordinates. The theory of…
Jon Oñativia, Pier Luigi Dragotti
The current methods used to convert analogue signals into discrete-time sequences have been deeply influenced by the classical Shannon-Whittaker-Kotelnikov sampling theorem. This approach restricts the class of signals that can be sampled and perfectly reconstructed to bandlimited signals. During the last few years, a…
Yoonji Kim, Oksana A. Chkrebtii, Sebastian A. Kurtek
In many modern applications, discretely-observed data may be naturally understood as a set of functions. Functional data often exhibit two confounded sources of variability: amplitude (y-axis) and phase (x-axis). The extraction of amplitude and phase, a process known as registration, is essential in exploring the…
Amos A. Hari, Sefi Givli
This paper addresses a disconnect between the pivotal role of functional (path) integrals in modern theories, such as quantum mechanics and statistical thermodynamics, and the currently limited ability to perform the actual calculation. We present a new method for calculating functional integrals, based on a…
Yuanzheng Zhu, Antonio M. Scarfone
Sampling from constrained distributions has posed significant challenges in terms of algorithmic design and non-asymptotic analysis, which are frequently encountered in statistical and machine-learning models. In this study, we propose three sampling algorithms based on Langevin Monte Carlo with the Metropolis-Hastings…
Thomas A. Trikalinos, Yuliia Sereda, Abhik Ghosh
We introduce the nhppp package for simulating events from one dimensional non-homogeneous Poisson point processes (NHPPPs) in R fast and with a small memory footprint. We developed it to facilitate the sampling of event times in discrete event and statistical simulations. The package’s functions are based on three…
Paul Hauseux, Jack S. Hale, Stéphane P. A. Bordas, Xiao-Jun Yang
The Malliavin calculus is an extension of the classical calculus of variations from deterministic functions to stochastic processes. In this paper we aim to show in a practical and didactic way how to calculate the Malliavin derivative, the derivative of the expectation of a quantity of interest of a model with respect…
Michael R. Lindstrom, Hyuntae Jung, Denis Larocque
We present an unsupervised method to detect anomalous time series among a collection of time series. To do so, we extend traditional Kernel Density Estimation for estimating probability distributions in Euclidean space to Hilbert spaces. The estimated probability densities we derive can be obtained formally through…
Xiaohan Guo, Sebastian Kurtek, Karthik Bharath
Spatial, amplitude and phase variations in spatial functional data are confounded. Conclusions from the popular functional trace-variogram, which quantifies spatial variation, can be misleading when analyzing misaligned functional data with phase variation. To remedy this, we describe a framework that extends…
Weifeng Liu, Ying Jiang, Yuesheng Xu, Karsten Keller
Sample entropy, an approximation of the Kolmogorov entropy, was proposed to characterize complexity of a time series, which is essentially defined as $(-log(B/A))$, where B denotes the number of matched template pairs with length m and A denotes the number of matched template pairs with $(m+1)$, for a predetermined…
Timofey Shevgunov, Evgeny Efimov, Oksana Guschina, Oleg Varlamov
This article addresses the problem of estimating the spectral correlation function (SCF), which provides quantitative characterization in the frequency domain of wide-sense cyclostationary properties of random processes which are considered to be the theoretical models of observed time series or discrete-time signals.…
Mohammed B. Alamari, Fatimah A. Almulhim, Ibrahim M. Almanjahie, Salim Bouzebda + 2 more
'Salim Bouzebda' 'Ali Laksaci' 'José María Amigó'] In this paper, we investigate the recursive $L1$ estimator of the conditional mode when the input variable takes values in a pseudo-metric space. The new proposed estimator is constructed under an ergodicity assumption, which provides a robust alternative to the…