Related papers: Higher-order correlation functions and nonlinear r…

A possible mechanism leading to anomalous diffusion is the presence of long-range correlations in time between the displacements of the particles. Fractional Brownian motion, a non-Markovian self-similar Gaussian process with stationary…

The relative timing of action potentials in neurons recorded from local cortical networks often shows a non-trivial dependence, which is then quantified by cross-correlation functions. Theoretical models emphasize that such spike train…

Complete information on the equilibrium behaviour and dynamics of a quantum field theory (QFT) is provided by multipoint correlation functions. However, their theoretical calculation is a challenging problem, even for exactly solvable…

We compute analytically and in closed form the four-point correlation function in the plane, and the two-point correlation function in the upper half-plane, of layering vertex operators in the two dimensional conformally invariant system…

A fundamental problem in statistical neuroscience is to model how neurons encode information by analyzing electrophysiological recordings. A popular and widely-used approach is to fit the spike trains with an autoregressive point process…

Recent work has demonstrated the strong qualitative differences between the dynamics near a glass transition driven by short-ranged repulsion and one governed by short-ranged attraction. Here, we study in detail the behavior of non-linear,…

We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…

We study the correlation function and mean linear response function of the velocity Fourier mode of statistically steady-state, homogeneous and isotropic turbulence in the Eulerian and Lagrangian coordinates through direct numerical…

Multi-task learning requires accurate identification of the correlations between tasks. In real-world time-series, tasks are rarely perfectly temporally aligned; traditional multi-task models do not account for this and subsequent errors in…

Correlation functions in the restricted primitive model are calculated within a field-theoretic approach in the one-loop self-consistent Hartree approximation. The correlation functions exhibit damped oscillatory behavior as found before in…

A methodology for high dimensional causal inference in a time series context is introduced. It is assumed that there is a monotonic transformation of the data such that the dynamics of the transformed variables are described by a Gaussian…

In nature, active inference agents must learn how observations of the world represent the state of the agent. In engineering, the physics behind sensors is often known reasonably accurately and measurement functions can be incorporated into…

The nonlinear response of molecular systems undergoing Markovian stochastic reorientations is calculated up to fifth order in the amplitude of the external field. Time-dependent perturbation theory is used to compute the relevant response…

Gaussian processes are a widely embraced technique for regression and classification due to their good prediction accuracy, analytical tractability and built-in capabilities for uncertainty quantification. However, they suffer from the…

We propose a method that allows for a rigorous statistical analysis of neural responses to natural stimuli which are non-Gaussian and exhibit strong correlations. We have in mind a model in which neurons are selective for a small number of…

Established techniques for simulation and prediction with Gaussian process (GP) dynamics often implicitly make use of an independence assumption on successive function evaluations of the dynamics model. This can result in significant error…

A functional risk curve gives the probability of an undesirable event as a function of the value of a critical parameter of a considered physical system. In several applicative situations, this curve is built using phenomenological…

Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…

A new type of nonstationary Gaussian process model is developed for approximating computationally expensive functions. The new model is a composite of two Gaussian processes, where the first one captures the smooth global trend and the…

Nonlinear interference is modeled by a time-varying conditionally Gaussian channel. It is shown that approximating this channel with a time-invariant channel imposes considerable loss in the performance of channel decoding. An adaptive…