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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 science explores intricate connections among objects, employed in diverse domains like social interactions, fraud detection, and disease spread. Visualization of networks facilitates conceptualizing research questions and forming…
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
This mini-course was given in the First Yaroslavl Summer School on Discrete and Computational Geometry in August 2012, organized by International Delaunay Laboratory "Discrete and Computational Geometry" of Demidov Yaroslavl State…
The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. There has been abundant interest in studying how the…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…
Robust and efficient design of networks on a realistic geographical space is one of the important issues for the realization of dependable communication systems. In this paper, based on a percolation theory and a geometric graph property,…
Node-link diagrams are widely used to visualise networks. However, even the best network layout algorithms ultimately result in 'hairball' visualisations when the graph reaches a certain degree of complexity, requiring simplification…
Neural networks have been used prominently in several machine learning and statistics applications. In general, the underlying optimization of neural networks is non-convex which makes their performance analysis challenging. In this paper,…
We consider the minimum spanning tree problem with predictions, using the weight-arrival model, i.e., the graph is given, together with predictions for the weights of all edges. Then the actual weights arrive one at a time and an…
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we…
We study agents playing a pure coordination game on a large social network. Agents are restricted to coordinate locally, without access to a global communication device, and so different regions of the network will converge to different…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
Symmetric networks designed for energy minimization such as Boltzman machines and Hopfield nets are frequently investigated for use in optimization, constraint satisfaction and approximation of NP-hard problems. Nevertheless, finding a…
This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the…
The success of deep neural networks hinges on our ability to accurately and efficiently optimize high-dimensional, non-convex functions. In this paper, we empirically investigate the loss functions of state-of-the-art networks, and how…
A fundamental problem in network science is the normalization of the topological or physical distance between vertices, that requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the…
Large bundles of myelinated axons, called white matter, anatomically connect disparate brain regions together and compose the structural core of the human connectome. We recently proposed a method of measuring the local integrity along the…
Previous work on undirected small-world networks established the paradigm that locally structured networks tend to have high density of short loops. On the other hand, many realistic networks are directed. Here we investigate the local…
A mechanism for self-organization of the degree of connectivity in model neural networks is studied. Network connectivity is regulated locally on the basis of an order parameter of the global dynamics which is estimated from an observable…