Related papers: Modeling Time-Varying Random Objects and Dynamic N…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
Time series similarity measures are highly relevant in a wide range of emerging applications including training machine learning models, classification, and predictive modeling. Standard similarity measures for time series most often…
Models of complex networks often incorporate node-intrinsic properties abstracted as hidden variables. The probability of connections in the network is then a function of these variables. Real-world networks evolve over time, and many…
The degree distribution is an important characteristic of complex networks. In many data analysis applications, the networks should be represented as fixed-length feature vectors and therefore the feature extraction from the degree…
Dynamic networks are ubiquitous for modelling sequential graph-structured data, e.g., brain connectome, population flows and messages exchanges. In this work, we consider dynamic networks that are temporal sequences of graph snapshots, and…
Many systems of scientific interest can be conceptualized as multipartite networks. Examples include the spread of sexually transmitted infections, scientific collaborations, human friendships, product recommendation systems, and metabolic…
Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed…
Over the past two decades, complex network theory provided the ideal framework for investigating the intimate relationships between the topological properties characterizing the wiring of connections among a system's unitary components and…
Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…
Multivariate time series are ubiquitous objects in signal processing. Measuring a distance or similarity between two such objects is of prime interest in a variety of applications, including machine learning, but can be very difficult as…
This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…
In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In 2011, Mileyko and his collaborators made the first study of the properties of the…
Feature propagation in Deep Neural Networks (DNNs) can be associated to nonlinear discrete dynamical systems. The novelty, in this paper, lies in letting the discretization parameter (time step-size) vary from layer to layer, which needs to…
Nowadays, neural networks are widely used in many applications as artificial intelligence models for learning tasks. Since typically neural networks process a very large amount of data, it is convenient to formulate them within the…
In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and…
The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by…
Many dynamical processes on real world networks display complex temporal patterns as, for instance, a fat-tailed distribution of inter-events times, leading to heterogeneous waiting times between events. In this work, we focus on…
A `trajectory' refers to a trace generated by a moving object in geographical spaces, usually represented by of a series of chronologically ordered points, where each point consists of a geo-spatial coordinate set and a timestamp. Rapid…
Dynamic multilayer networks are frequently used to describe the structure and temporal evolution of multiple relationships among common entities, with applications in fields such as sociology, economics, and neuroscience. However,…