Related papers: The spatial Lambda-Fleming-Viot process: an event-…

We construct a class of discontinuous superprocesses with dependent spatial motion and general branching mechanism. The process arises as the weak limit of critical interacting-branching particle systems where the spatial motions of the…

Despite achieving significant progress in 2D image understanding, large multimodal models (LMMs) struggle in the physical world due to the lack of spatial representation. Typically, existing 3D LMMs mainly embed 3D positions as fixed…

We propose a Leaked Motion Video Predictor (LMVP) to predict future frames by capturing the spatial and temporal dependencies from given inputs. The motion is modeled by a newly proposed component, motion guider, which plays the role of…

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition but define a…

There exists a correlation between geospatial activity temporal patterns and type of land use. A novel self-supervised approach is proposed to stratify landscape based on mobility activity time series. First, the time series signal is…

Reinforcement learning algorithms typically rely on the assumption that the environment dynamics and value function can be expressed in terms of a Markovian state representation. However, when state information is only partially observable,…

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help…

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…

We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state…

In this paper, we study the Galton-Watson process in the random environment for the particular case when the number of the offsprings in each generation has the fractional linear generation function with random parameters. In this case, the…

A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching…

We introduce supervised latent Dirichlet allocation (sLDA), a statistical model of labelled documents. The model accommodates a variety of response types. We derive an approximate maximum-likelihood procedure for parameter estimation, which…

Positive self-similar Markov processes (pssMp) are positive Markov processes that satisfy the scaling property and it is known that they can be represented as the exponential of a time-changed L\'evy process via Lamperti representation. In…

There are numerous contexts where one wishes to describe the state of a randomly evolving system. Effective solutions combine models that quantify the underlying uncertainty with available observational data to form relatively optimal…

Spatio-Temporal predictive Learning is a self-supervised learning paradigm that enables models to identify spatial and temporal patterns by predicting future frames based on past frames. Traditional methods, which use recurrent neural…

Identifying systematic patterns in seismicity that precede large earthquakes remains a central challenge in statistical seismology. In this work, we present a methodological framework for detecting spatiotemporal anomalies in seismicity…

The first chapter concerns monotype population models. We first study general birth and death processes and we give non-explosion and extinction criteria, moment computations and a pathwise representation. We then show how different scales…

Retrieval and recommendation are two essential tasks in modern search tools. This paper introduces a novel retrieval-reranking framework leveraging Large Language Models (LLMs) to enhance the spatiotemporal and semantic associated mining…

We study a stochastic model based on a modified fragmentation of a finite interval. The mechanism consists in cutting the interval at a random location and substituting a unique fragment on the right of the cut to regenerate and preserve…

In self-supervised learning (SSL), representations are learned via an auxiliary task without annotated labels. A common task is to classify augmentations or different modalities of the data, which share semantic content (e.g. an object in…