Related papers: Limit Theorems for Data with Network Structure
We investigate to what extent the degree sequence of a directed network constrains the number of driver nodes. We develop a pair of algorithms that take a directed degree sequence as input and aim to output a network with the maximum or…
A standard technique for understanding underlying dependency structures among a set of variables posits a shared conditional probability distribution for the variables measured on individuals within a group. This approach is often referred…
Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by…
In this paper, we study the problem of constructing a network by observing ordered connectivity constraints, which we define herein. These ordered constraints are made to capture realistic properties of real-world problems that are not…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
Characterising the capacity region for a network can be extremely difficult. Even with independent sources, determining the capacity region can be as hard as the open problem of characterising all information inequalities. The majority of…
This paper investigates the fundamental information-theoretic limits for the control and sensing of noiseless linear dynamical systems subject to a broad class of nonlinear observations. We analyze the interactions between the control and…
Spreading phenomena on networks are essential for the collective dynamics of various natural and technological systems, from information spreading in gene regulatory networks to neural circuits or from epidemics to supply networks…
Conventional studies of network growth models mainly look at the steady state degree distribution of the graph. Often long time behavior is considered, hence the initial condition is ignored. In this contribution, the time evolution of the…
There is a wide availability of methods for testing normality under the assumption of independent and identically distributed data. When data are dependent in space and/or time, however, assessing and testing the marginal behavior is…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…
We define a class of growing networks in which new nodes are given a spatial position and are connected to existing nodes with a probability mechanism favoring short distances and high degrees. The competition of preferential attachment and…
This paper presents new results and reinterpretation of existing conditions for strong structural controllability in a structured network determined by the zero/non-zero patterns of edges. For diffusively-coupled networks with self-loops,…
We introduce a new class of latent process models for dynamic relational network data with the goal of detecting time-dependent structure. Network data are often observed over time, and static network models for such data may fail to…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…
How are people linked in a highly connected society? Since in many networks a power-law (scale-free) node-degree distribution can be observed, power-law might be seen as a universal characteristics of networks. But this study of…
We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…