Related papers: Lecture Notes: Temporal Point Processes and the Co…
Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…
Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one.…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…
Multistable processes, that is, processes which are, at each "time", tangent to a stable process, but where the index of stability varies along the path, have been recently introduced as models for phenomena where the intensity of jumps is…
In this paper we propose a data intensive approach for inferring sentence-internal temporal relations. Temporal inference is relevant for practical NLP applications which either extract or synthesize temporal information (e.g.,…
We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…
In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects…
Point processes are becoming very popular in modeling asynchronous sequential data due to their sound mathematical foundation and strength in modeling a variety of real-world phenomena. Currently, they are often characterized via intensity…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
Temporal point processes (TPPs) are a fundamental tool for modeling event sequences in continuous time, but most existing approaches rely on autoregressive parameterizations that are limited by their sequential sampling. Recent…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…
We study the process of suitably normalized successive return times to rare events in the setting of infinite-measure preserving dynamical systems. Specifically, we consider small neighborhoods of points whose measure tends to zero. We…
This is a series of lectures intended to introduce high energy theorists to the marvels of the Standard Model from an experimentalist's point of view.
This mini-course gives an introduction to the techniques used in experimental particle physics with an emphasis on the impact of technological advances. The basic detector types and particle accelerator facilities will be briefly covered…
These notes present some elements of causality theory. While they are not as complete as other treatments of the topic, there is some originality in that the whole approach is based on a definition of causal curves which allows to simplify…
We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…
When evaluating causal influence from one time series to another in a multivariate dataset it is necessary to take into account the conditioning effect of the other variables. In the presence of many variables, and possibly of a reduced…
The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…
These lecture notes, suitable for a two-semester introductory course or self-study, offer an elementary and self-contained exposition of the basic tools and concepts that are encountered in practical computations in perturbative thermal…