Related papers: Matched Topological Subspace Detector
We propose a new approach, the calibrated nonparametric scan statistic (CNSS), for more accurate detection of anomalous patterns in large-scale, real-world graphs. Scan statistics identify connected subgraphs that are interesting or…
We introduce an easily computable topological measure which locates the effective crossover between segregation and integration in a modular network. Segregation corresponds to the degree of network modularity, while integration is…
The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally…
Cooperation in cellular networks is a promising scheme to improve system performance. Existing works consider that a user dynamically chooses the stations that cooperate for his/her service, but such assumption often has practical…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
Non-Hermitian systems have been discussed mostly in the context of open systems and nonequilibrium. Recent experimental progress is much from optical, cold-atomic, and classical platforms due to the vast tunability and clear identification…
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…
Recently emerged Topological Deep Learning (TDL) methods aim to extend current Graph Neural Networks (GNN) by naturally processing higher-order interactions, going beyond the pairwise relations and local neighborhoods defined by graph…
Topologically nontrivial states are common in symmetry broken phases at macroscopic scales. Low dimensional systems bring them to a microscopic level where solitons emerge as single particles. The earliest and latest applications are…
Exceptional points (EPs) with their intriguing spectral topology have attracted considerable attention in a broad range of physical systems, with potential sensing applications driving much of the present research in this field. Here we…
The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact…
To incorporate spatial (neighborhood) and bidirectional hierarchical relationships as well as features and priors of the samples into their classification, we formulated the classification problem on three variants of multiresolution…
This paper studies the classical problem of detecting the locations of signal occurrences in a one-dimensional noisy measurement. Assuming the signal occurrences do not overlap, we formulate the detection task as a constrained likelihood…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
The topological information of a network can be retrieved equivalently from its complement consisting of the same nodes but complementary edges. Hence the partition of a network into certain substructures based on given criteria should be…
While tremendous research has revealed that symmetry enriches topological phases of matter, more general principles that protect topological phases have yet to be explored. In this Letter, we elucidate the roles of subspaces in…
In this paper, we consider the problem of detecting signals in multiple, sequentially observed data streams. For each stream, the exact distribution is unknown, but characterized by a parameter that takes values in either of two disjoint…
Semi-supervised learning on real-world graphs is frequently challenged by heterophily, where the observed graph is unreliable or label-disassortative. Many existing graph neural networks either rely on a fixed adjacency structure or attempt…
Higher-order networks have so far been considered primarily in the context of studying the structure of complex systems, i.e., the higher-order or multi-way relations connecting the constituent entities. More recently, a number of studies…
Detecting multiple planes in images is a challenging problem, but one with many applications. Recent work such as J-Linkage and Ordered Residual Kernels have focussed on developing a domain independent approach to detect multiple…