Related papers: Detecting discrete processes with the Epps effect
In complex physical systems, conventional differential equations often fall short in capturing non-local and memory effects, as they are limited to local dynamics and integer-order interactions. This study introduces a stepwise data-driven…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
Extracting and detecting spike activities from the fluorescence observations is an important step in understanding how neuron systems work. The main challenge lies in that the combination of the ambient noise with dynamic baseline…
The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture…
Instabilities in the price dynamics of a large number of financial assets are a clear sign of systemic events. By investigating a set of 20 high cap stocks traded at the Italian Stock Exchange, we find that there is a large number of high…
Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed and the usual…
Experiment, theory, and simulation are employed to understand the dispersion of colloidal particles in a periodic array of oscillating harmonic traps generated by optical tweezers. In the presence of trap oscillation, a non-monotonic and…
One of the most important quantities characterizing the microscopic properties of quantum systems are dynamical correlation functions. These correlations are obtained by time-evolving a perturbation of an eigenstate of the system, typically…
We study the dynamics of gradient flow in high dimensions for the multi-spiked tensor problem, where the goal is to estimate $r$ unknown signal vectors (spikes) from noisy Gaussian tensor observations. Specifically, we analyze the maximum…
We analyse how the sampling dynamics of distributions evolve in score-based diffusion models using cross-fluctuations, a centered-moment statistic from statistical physics. Specifically, we show that starting from an unbiased isotropic…
The Hawkes process is a simple point process with wide applications in finance, social networks, criminology, seismology, and many other fields. The Hawkes process is defined for continuous-time setting. However, data is also recorded in a…
Understanding how local perturbations induce the transient dynamics of a network of coupled units is essential to control and operate such systems. Often a perturbation initiated in one unit spreads to other units whose dynamical state they…
We propose an extension to Hawkes processes by treating the levels of self-excitation as a stochastic differential equation. Our new point process allows better approximation in application domains where events and intensities accelerate…
Data-driven modeling of non-Markovian dynamics is a recent topic of research with applications in many fields such as climate research, molecular dynamics, biophysics, or wind power modeling. In the frequently used standard Langevin…
Networks representation aims to encode vertices into a low-dimensional space, while preserving the original network structures and properties. Most existing methods focus on static network structure without considering temporal dynamics.…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
Univariate marked Hawkes processes are used to model a range of real-world phenomena including earthquake aftershock sequences, contagious disease spread, content diffusion on social media platforms, and order book dynamics. This paper…
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method…