Related papers: Euclidean mirrors and first-order changepoints in …

Convolutional Neural Networks (CNN) have been successful in processing data signals that are uniformly sampled in the spatial domain (e.g., images). However, most data signals do not natively exist on a grid, and in the process of being…

Understanding the mutual interdependence between the behavior of dynamical processes on networks and the underlying topologies promises new insight for a large class of empirical networks. We present a generic approach to investigate this…

Over the last two decades, the Latent Position Model (LPM) has become a prominent tool to obtain model-based visualizations of networks. However, the geometric structure of the LPM is inherently symmetric, in the sense that outgoing and…

A social network grows over a period of time with the formation of new connections and relations. In recent years we have witnessed a massive growth of online social networks like Facebook, Twitter etc. So it has become a problem of extreme…

Graph neural networks face two fundamental challenges rooted in the linear structure of Euclidean vector spaces: (1) Current architectures represent geometry through vectors (directions, gradients), yet many tasks require matrix-valued…

Understanding the emergence of the thermodynamic arrow of time in microscopic systems is of fundamental importance, particularly given that unitary evolution preserves time-reversal symmetry. While projective measurements introduce temporal…

Dynamic networks exhibit temporal patterns that vary across different time scales, all of which can potentially affect processes that take place on the network. However, most data-driven approaches used to model time-varying networks…

In the following we are going to describe how macroscopic space-time is supposed to emerge as an orderparameter manifold or superstructure floating in a stochastic discrete network structure. As in preceeding work (mentioned below), our…

To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison…

We study the spectrum of a random matrix, whose elements depend on the Euclidean distance between points randomly distributed in space. This problem is widely studied in the context of the Instantaneous Normal Modes of fluids and is…

We introduce a stochastic geometry dynamics inspired by opinion dynamics that captures the essence of modern asymmetric social networks with leaders and followers. Points in the Euclidean space represent opinions, and the leader of an agent…

Building upon the one-step replica symmetry breaking formalism, duly understood and ramified, we show that the sequence of ordered extreme values of a general class of Euclidean-space logarithmically correlated random energy models…

Systems which can spontaneously reveal periodic evolution are dubbed time crystals. This is in analogy with space crystals that display periodic behavior in configuration space. While space crystals are modelled with the help of space…

Although static networks have been extensively studied in machine learning, data mining, and AI communities for many decades, the study of dynamic networks has recently taken center stage due to the prominence of social media and its…

Measuring the similarity between data points often requires domain knowledge, which can in parts be compensated by relying on unsupervised methods such as latent-variable models, where similarity/distance is estimated in a more compact…

We introduce a new methodology to analyze the evolution of epidemic time series, which is based on the construction of epidemic networks. First, we translate the time series into ordinal patterns containing information about local…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time…

We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge…

The primary objective of this thesis is to develop novel algorithmic approaches for Graph Representation Learning of static and single-event dynamic networks. In such a direction, we focus on the family of Latent Space Models, and more…