Related papers: Autoregressive description of biological phenomena
We investigate precursors and predictability of extreme increments in a time series. The events we are focusing on consist in large increments within successive time steps. We are especially interested in understanding how the quality of…
We develop a ``unified'' model that describes both ``micro'' and ``macro'' evolutions within a single theoretical framework. The eco-system is described as a dynamic network; the population dynamics at each node of this network describes…
Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-\alpha}$, with…
Rapid learning requires flexible representations to quickly adopt to new evidence. We develop a novel class of models called Attentive Recurrent Comparators (ARCs) that form representations of objects by cycling through them and making…
Autoregressive (AR) modeling is invaluable in signal processing, in particular in speech and audio fields. Attempts in the literature can be found that regularize or constrain either the time-domain signal values or the AR coefficients,…
Many researchers have investigated first hitting times as models for survival data. First hitting times arise naturally in many types of stochastic processes, ranging from Wiener processes to Markov chains. In a survival context, the state…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
A method is presented that, when used in conjunction with single molecule experimental techniques, allows for the extraction of rates and mechanical properties of a biomolecule undergoing transitions between mechanically distinct states.…
In practice, several time series exhibit long-range dependence or persistence in their observations, leading to the development of a number of estimation and prediction methodologies to account for the slowly decaying autocorrelations. The…
Rare events refer to qualitatively unlikely events whose realization can nevertheless have important consequences. Typically, the prediction of the kinetics of these events relies on Arrhenius laws, with exponentially distributed waiting…
We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphids in [Nilsen et al., PLOS One, 2013] and two random walk…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…
Autoregressive (AR) models have long dominated the landscape of large language models, driving progress across a wide range of tasks. Recently, diffusion-based language models have emerged as a promising alternative, though their advantages…
Most treatments of large scale anomalies in the microwave sky are a posteriori, with unquantified look-elsewhere effects. We contrast these with physical models of specific inhomogeneities in the early universe which then generate apparent…
Diffusion models have demonstrated appealing performance in both image and video generation. However, many works discover that they struggle to capture important, high-level relationships that are present in the real world. For example,…
Inhomogeneous temporal processes, like those appearing in human communications, neuron spike trains, and seismic signals, consist of high-activity bursty intervals alternating with long low-activity periods. In recent studies such bursty…