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Flexible duplex networks allow users to dynamically employ uplink and downlink channels without static time scheduling, thereby utilizing the network resources efficiently. This work investigates the sum-rate maximization of flexible duplex…
Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards…
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
Complex networks representing social interactions, brain activities, molecular structures have been studied widely to be able to understand and predict their characteristics as graphs. Models and algorithms for these networks are used in…
Many applications donot have the benefit of the laws of physics to derive succinct descriptive models for observed data. In alternative, interdependencies among $N$ time series $\{ x_{nk}, k>0 \}_{n=1}^{N}$ are nowadays often captured by a…
We propose a general approach to the description of spectra of complex networks. For the spectra of networks with uncorrelated vertices (and a local tree-like structure), exact equations are derived. These equations are generalized to the…
Knowledge Graph Embedding (KGE) aims to represent entities and relations of knowledge graph in a low-dimensional continuous vector space. Recent works focus on incorporating structural knowledge with additional information, such as entity…
Using the recently proposed model of combinatorial landscapes: local optima networks, we study the distribution of local optima in two classes of instances of the quadratic assignment problem. Our results indicate that the two problem…
The fitness landscape encodes the mapping of genotypes to fitness and provides a succinct representation of possible trajectories followed by an evolving population. Evolutionary accessibility is quantified by the existence of…
Tensor networks were developed in the context of many-body physics as compressed representations of multiparticle quantum states. These representations mitigate the exponential complexity of many-body systems by capturing only the most…
Graph Neural Networks (GNNs) are widely used to compute representations of node pairs for downstream tasks such as link prediction. Yet, theoretical understanding of their expressive power has focused almost entirely on graph-level…
One of the most prominent attributes of Neural Networks (NNs) constitutes their capability of learning to extract robust and descriptive features from high dimensional data, like images. Hence, such an ability renders their exploitation as…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…
Exploratory landscape analysis and fitness landscape analysis in general have been pivotal in facilitating problem understanding, algorithm design and endeavors such as automated algorithm selection and configuration. These techniques have…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
Network geometry, characterized by nodes with associated latent variables, is a fundamental feature of real-world networks. Still, when only the network edges are given, it may be difficult to assess whether the network contains an…
Upon a matrix representation of a binary bipartite network, via the permutation invariance, a coupling geometry is computed to approximate the minimum energy macrostate of a network's system. Such a macrostate is supposed to constitute the…
This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…
Convolutional neural networks (CNNs) have achieved superior accuracy in many visual related tasks. However, the inference process through intermediate layers is opaque, making it difficult to interpret such networks or develop trust in…