Related papers: Transit Functions and Clustering Systems
Higher order interactions are increasingly recognised as a fundamental aspect of complex systems ranging from the brain to social contact networks. Hypergraph as well as simplicial complexes capture the higher-order interactions of complex…
Many real-world interactions (e.g., researcher collaborations and email communication) occur among multiple entities. These group interactions are naturally modeled as hypergraphs. In graphs, transitivity is helpful to understand the…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
A clustering algorithm partitions a set of data points into smaller sets (clusters) such that each subset is more tightly packed than the whole. Many approaches to clustering translate the vector data into a graph with edges reflecting a…
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these…
This paper discusses the topological and transport properties of binary heterostructures of different topological materials. The creation of multilayer devices is an alternative to building synthetic topological materials. By adjusting the…
Functorial maps and weak parities are equivalent descriptions of rules of substitution virtual crossings for classical in diagrams of a knot in a way compatible with Reidemeister moves. We introduce the notion of maximal weak parity and…
The spatial arrangement of urban hubs and centers and how individuals interact with these centers is a crucial problem with many applications ranging from urban planning to epidemiology. We utilize here in an unprecedented manner the large…
We offer a solution to a long-standing problem in the physics of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity -- the propensity for two neighbors of a network node also to be…
Transfer learning has recently become the dominant paradigm of machine learning. Pre-trained models fine-tuned for downstream tasks achieve better performance with fewer labelled examples. Nonetheless, it remains unclear how to develop…
The steady state reached by a system of particles sliding down a fluctuating surface has interesting properties. Particle clusters form and break rapidly, leading to a broad distribution of sizes and large fluctuations. The density-density…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering…
The objective of this paper is to study wandering subspaces for commuting tuples of bounded operators on Hilbert spaces. It is shown that, for a large class of analytic functional Hilbert spaces $\mathcal{H}_K$ on the unit ball in $\mathbb…
Quantum walks, both discrete (coined) and continuous time, form the basis of several quantum algorithms and have been used to model processes such as transport in spin chains and quantum chemistry. The enhanced spreading and mixing…
In this paper, we deal with the problem of curves clustering. We propose a nonparametric method which partitions the curves into clusters and discretizes the dimensions of the curve points into intervals. The cross-product of these…
The undirected technique for evaluating belief networks [Jensen, et.al., 1990, Lauritzen and Spiegelhalter, 1988] requires clustering the nodes in the network into a junction tree. In the traditional view, the junction tree is constructed…
Public-transit systems face a number of operational challenges: (a) changing ridership patterns requiring optimization of fixed line services, (b) optimizing vehicle-to-trip assignments to reduce maintenance and operation codes, and (c)…
Characteristic functions are shown to be useful for highly sensitive measurements. Redistributions of motional Fock states of a trapped atom can be directly monitored via the most fragile nonclassical part of the characteristic function.…
We review the general relativistic theory of the motion, and of the timing, of binary systems containing compact objects (neutron stars or black holes). Then we indicate the various ways one can use binary pulsar data to test the…