Related papers: Topological exploration of artificial neuronal net…

In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…

This paper considers the problem of detecting topology variations in dynamical networks. We consider a network whose behavior can be represented via a linear dynamical system. The problem of interest is then that of finding conditions under…

We present a unified pipeline for univariate time series classification via complex networks and persistent homology. A time series is mapped to a graph through one of five constructions across three families (visibility (natural and…

Topology learning of networked dynamical systems is an important problem with implications to optimal control, decision-making over networks, cybersecurity and safety. The majority of prior work in consistent topology estimation relies on…

We present a topological pipeline for automated multiclass emotion recognition from eye-tracking data. Delay embeddings of gaze trajectories are analyzed using persistent homology. From the resulting persistence diagrams, we extract…

Homeostasis is widely observed in biological systems and refers to their ability to maintain an output quantity approximately constant despite variations in external disturbances. Mathematically, homeostasis can be formulated through an…

Complex networks are a powerful modeling tool, allowing the study of countless real-world systems. They have been used in very different domains such as computer science, biology, sociology, management, etc. Authors have been trying to…

Artificial neural networks thrive in solving the classification problem for a particular rigid task, acquiring knowledge through generalized learning behaviour from a distinct training phase. The resulting network resembles a static entity…

In many networks, vertices have hidden attributes, or types, that are correlated with the networks topology. If the topology is known but these attributes are not, and if learning the attributes is costly, we need a method for choosing…

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field.…

We investigate online network topology identification from smooth nodal observations acquired in a streaming fashion. Different from non-adaptive batch solutions, our distinctive goal is to track the (possibly) dynamic adjacency matrix with…

Most research concerning the influence of network structure on phenomena taking place on the network focus on relationships between global statistics of the network structure and characteristic properties of those phenomena, even though…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

This study explores the design and control of the behaviour of agents and robots using simple circuits of spiking neurons and Spike Timing Dependent Plasticity (STDP) as a mechanism of associative and unsupervised learning. Based on a…

High-quality training data is the foundation of machine learning and artificial intelligence, shaping how models learn and perform. Although much is known about what types of data are effective for training, the impact of the data's…

Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…

Topology applied to real world data using persistent homology has started to find applications within machine learning, including deep learning. We present a differentiable topology layer that computes persistent homology based on level set…

We introduce the concept of dynamical score networks for the representation and analysis of tonal compositions: a score is interpreted as a dynamical network where every chord is a node and each progression links successive chords. This…

Motivated by the recent surge of criminal activities with cross-cryptocurrency trades, we introduce a new topological perspective to structural anomaly detection in dynamic multilayer networks. We postulate that anomalies in the underlying…

Persistent homology has recently emerged as a powerful technique in topological data analysis for analyzing the emergence and disappearance of topological features throughout a filtered space, shown via persistence diagrams. Additionally,…