Related papers: Monotonicity Analysis over Chains and Curves

The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…

An important problem arising in the study of complex networks, for instance in community detection and motif finding, is the sampling of graphs with fixed degree sequence. The equivalent problem of generating random 0,1 matrices with fixed…

The inevitable noise in real measurements motivates the problem to continuously quantify the similarity between rigid objects such as periodic time series and proteins given by ordered points and considered up to isometry maintaining…

Much of the past work in network analysis has focused on analyzing discrete graphs, where binary edges represent the "presence" or "absence" of a relationship. Since traditional network measures (e.g., betweenness centrality) utilize a…

Scientists aim to extract simplicity from observations of the complex world. An important component of this process is the exploration of data in search of trends. In practice, however, this tends to be more of an art than a science. Among…

A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…

Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing.…

We introduce persistence spheres, a novel functional representation of persistence diagrams. Unlike existing embeddings (such as persistence images, landscapes, or kernel methods), persistence spheres provide a bi-continuous mapping: they…

Graph learning has emerged as a promising technique for multi-view clustering with its ability to learn a unified and robust graph from multiple views. However, existing graph learning methods mostly focus on the multi-view consistency…

Linear chains of quantum scatterers are studied in the process of lengthening, which is treated and analysed as a discrete dynamical system defined over the manifold of scattering matrices. Elementary properties of such dynamics relate the…

Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…

Graph Neural Networks (GNNs) have emerged as a powerful technique for learning on relational data. Owing to the relatively limited number of message passing steps they perform -- and hence a smaller receptive field -- there has been…

There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…

Uncertainty relations for particle motion in curved spaces are discussed. The relations are shown to be topologically invariant. New coordinate system on a sphere appropriate to the problem is proposed. The case of a sphere is considered in…

Symmetry is a key feature observed in nature (from flowers and leaves, to butterflies and birds) and in human-made objects (from paintings and sculptures, to manufactured objects and architectural design). Rotational, translational, and…

Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector…

This paper derives new results for the analysis of nonlinear systems by extending contraction theory in the framework of vector distances. A new tool, vector contraction analysis utilizing a notion of the vector-valued norm which evidently…

It is arguably believed that flatter minima can generalize better. However, it has been pointed out that the usual definitions of sharpness, which consider either the maxima or the integral of loss over a $\delta$ ball of parameters around…

Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…

Unveil the homophilic/heterophilic behaviors that characterize the wiring patterns of complex networks is an important task in social network analysis, often approached studying the assortative mixing of node attributes. Recent works…