Related papers: A Linear-Time Branching-Time Spectrum for Behavior…

Large language models often achieve strong benchmark gains without corresponding improvements in broader capability. We hypothesize that this discrepancy arises from differences in training regimes induced by data distribution. To…

Behavior trees represent a hierarchical and modular way of combining several low-level control policies into a high-level task-switching policy. Hybrid dynamical systems can also be seen in terms of task switching between different…

To make informed decisions in natural environments that change over time, humans must update their beliefs as new observations are gathered. Studies exploring human inference as a dynamical process that unfolds in time have focused on…

Over the last 30 years, extensive work has been devoted to developing central limit theory for partial sums of subordinated long memory linear time series. A much less studied problem, motivated by questions that are ubiquitous in extreme…

An introduction into the theory of boundary critical phenomena and the application of the field-theoretical renormalization group method to these is given. The emphasis is on a discussion of surface critical behavior at bulk critical points…

This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less…

Motivated by the recent interest in formal methods-based control for dynamic robots, we discuss the applicability of prescribed performance control to nonlinear systems subject to signal temporal logic specifications. Prescribed performance…

Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…

The general acceptance of sequence diagrams can be attributed to their relatively intuitive nature and ability to describe partial behaviors (as opposed to such diagrams as state charts). However, studies have shown that over 80 percent of…

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…

Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic…

Many models such as Long Short Term Memory (LSTMs), Gated Recurrent Units (GRUs) and transformers have been developed to classify time series data with the assumption that events in a sequence are ordered. On the other hand, fewer models…

A system driven in the vicinity of its critical point by varying a relevant field in an arbitrary function of time is a generic system that possesses a long relaxation time compared with the driving time scale and thus represents a large…

We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected stopping time is obtained via the uniform integrability of…

This paper investigates locally linear regression for locally stationary time series and develops theoretical results for locally linear smoothing and transfer learning. Existing analyses have focused on local constant estimators and given…

In "The Organization of Behavior" (Hebb, 1949), Hebb suggested that the propagation of activity between transiently grouped neurons plays an important role in behavior. Since then, multiple studies have provided evidence supporting Hebb's…

While it is widely recognised that linear (structural) VARs may fail to capture important aspects of economic time series, the use of nonlinear SVARs has to date been almost entirely confined to the modelling of stationary time series,…

Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…

There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…

Sensory stimuli are usually composed of different features (the what) appearing at irregular times (the when). Neural responses often use spike patterns to represent sensory information. The what is hypothesized to be encoded in the…