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We present a model for the evolution of networks of occupied sites on undirected regular graphs. At every iteration step in a parallel update I randomly chosen empty sites are occupied and occupied sites having degree outside of a given…
The evolution of communities in dynamic (time-varying) network data is a prominent topic of interest. A popular approach to understanding these dynamic networks is to embed the dyadic relations into a latent metric space. While methods for…
Interactions among people or objects are often dynamic in nature and can be represented as a sequence of networks, each providing a snapshot of the interactions over a brief period of time. An important task in analyzing such evolving…
Comparability graphs are the undirected graphs whose edges can be directed so that the resulting directed graph is transitive. They are related to posets and have applications in scheduling theory. This paper considers the problem of…
Many types of pairwise interaction take the form of a fixed set of nodes with edges that appear and disappear over time. In the case of discrete-time evolution, the resulting evolving network may be represented by a time-ordered sequence of…
Percolation establishes the connectivity of complex networks and is one of the most fundamental critical phenomena for the study of complex systems. On simple networks, percolation displays a second-order phase transition; on multiplex…
Many random growth models have the property that the set of discovered sites, scaled properly, converges to some deterministic set as time grows. Such results are known as shape theorems. Typically, not much is known about the shapes. For…
We present a new model for time series classification, called the hidden-unit logistic model, that uses binary stochastic hidden units to model latent structure in the data. The hidden units are connected in a chain structure that models…
We propose an extended local-world evolving network model including a triad formation step. In the process of network evolution, random fluctuation in the number of new edges is involved. We derive analytical expressions for degree…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly…
Disentangling the mechanisms underlying the social network evolution is one of social science's unsolved puzzles. Preferential attachment is a powerful mechanism explaining social network dynamics, yet not able to explain all scaling-laws…
Contagions such as the spread of popular news stories, or infectious diseases, propagate in cascades over dynamic networks with unobservable topologies. However, "social signals" such as product purchase time, or blog entry timestamps are…
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…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
In this paper, we propose an encoder-decoder convolutional neural network (CNN) architecture for estimating camera pose (orientation and location) from a single RGB-image. The architecture has a hourglass shape consisting of a chain of…
We define nearest-neighbour point processes on graphs with Euclidean edges and linear networks. They can be seen as the analogues of renewal processes on the real line. We show that the Delaunay neighbourhood relation on a tree satisfies…
We study the evolution of branching trees embedded in Euclidean spaces with suppressed branching of spatially close nodes. This cooperative branching process accounts for the effect of overcrowding of nodes in the embedding space and mimics…
Existing online change-point detection (CPD) methods rely on fixed-dimensional Euclidean summaries, implicitly assuming that distributional changes are well captured by moment-based or feature-based representations. They can obscure…
Borrowing inspiration from Marcone and Mont\'{a}lban's one-one correspondence between the class of signed trees and the equimorphism classes of indecomposable scattered linear orders, we find a subclass of signed trees which has an…