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The reversible Markov chains that drive the data augmentation (DA) and sandwich algorithms define self-adjoint operators whose spectra encode the convergence properties of the algorithms. When the target distribution has uncountable…

We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…

We present analytical results for the effect of preferential node deletion on the structure of networks that evolve via node addition and preferential attachment. To this end, we consider a preferential-attachment-preferential-deletion…

Through the distinction between ``real'' and ``virtual'' links between the nodes of a graph, we develop a set of simple rules leading to scale-free networks with a tunable degree distribution exponent. Albeit sharing some similarities with…

Much recent research activity has been devoted to empirical study and theoretical models of complex networks (random graphs) with three qualitative features: power-law degree distribution, local clustering of edges, and small diameter. We…

We use information-theoretic tools to derive a novel analysis of Multi-source Domain Adaptation (MDA) from the representation learning perspective. Concretely, we study joint distribution alignment for supervised MDA with few target labels…

We provide an analytic expression for the quantity described in the title. Namely, we perform a preferential attachment growth process to generate a scale-free network. At each stage we add a new node with $m$ new links. Let $k$ denote the…

Data augmentation is an effective technique to improve the generalization of deep neural networks. Recently, AutoAugment proposed a well-designed search space and a search algorithm that automatically finds augmentation policies in a…

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks…

An important question in statistical network analysis is how to estimate models of discrete and dependent network data with intractable likelihood functions, without sacrificing computational scalability and statistical guarantees. We…

We propose a fluctuation analysis to quantify spatial correlations in complex networks. The approach considers the sequences of degrees along shortest paths in the networks and quantifies the fluctuations in analogy to time series. In this…

We explore the possibility to interpret as a 'gas' the dynamical self-organized scale-free network recently introduced by Kim et al (2005). The role of 'momentum' of individual nodes is played by the degree of the node, the 'configuration…

Connectivity correlations play an important role in the structure of scale-free networks. While several empirical studies exist, there is no general theoretical analysis that can explain the largely varying behavior of real networks. Here,…

In real life, networks are dynamic in nature; they grow over time and often exhibit power-law degree sequences. To model the evolving structure of the internet, Barab\'{a}si and Albert introduced a simple dynamic model with a power-law…

The interest in dynamic processes on networks is steadily rising in recent years. In this paper, we consider the $(\alpha,\beta)$-Thresholded Network Dynamics ($(\alpha,\beta)$-Dynamics), where $\alpha\leq \beta$, in which only structural…

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower…

Data augmentation (DA) algorithms are widely used for Bayesian inference due to their simplicity. In massive data settings, however, DA algorithms are prohibitively slow because they pass through the full data in any iteration, imposing…

Millimeter wave (mmWave) communication with large array gains is a key ingredient of next generation (5G) wireless networks. Effective communication in mmWaves usually depends on the knowledge of the channel. We refer to the problem of…

In this work we investigate the spectra of Laplacian matrices that determine many dynamic properties of scale-free networks below and at the percolation threshold. We use a replica formalism to develop analytically, based on an integral…

The Ising model on a $restricted$ scale-free network (SFN) has been studied employing Monte Carlo simulations. This network is described by a power-law degree distribution in the form $P(k)~k^{-\alpha}$, and is called restricted, because…