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One of the challenges for future infrastructures is how to design a network with high efficiency and strong connectivity at low cost. We propose self-organized geographical networks beyond the vulnerable scale-free structure found in many…
Generative flow networks utilize a flow-matching loss to learn a stochastic policy for generating objects from a sequence of actions, such that the probability of generating a pattern can be proportional to the corresponding given reward.…
From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
Diffusion models are important in tissue engineering as they enable an understanding of molecular delivery to cells in tissue constructs. As three-dimensional (3D) tissue constructs become larger, more intricate, and more clinically…
A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be…
Suppose that under the action of gravity, liquid drains through the unit $d$-cube via a minimal-length network of channels constrained to pass through random sites and to flow with nonnegative component in one of the canonical orthogonal…
Networks are mathematical structures that are universally used to describe a large variety of complex systems such as the brain or the Internet. Characterizing the geometrical properties of these networks has become increasingly relevant…
We review the recent fast progress in statistical physics of evolving networks. Interest has focused mainly on the structural properties of random complex networks in communications, biology, social sciences and economics. A number of giant…
Cardiovascular networks span the body by branching across many generations of vessels. The resulting structure delivers blood over long distances to supply all cells with oxygen via the relatively short-range process of diffusion at the…
A determinant property of the structure of a biological network is the distribution of local connectivity patterns, i.e., network motifs. In this work, a method for creating directed, unweighted networks while promoting a certain…
From the vasculature of animals to the porous media making up batteries, the core task of flow networks is to transport solutes and perfuse all cells or media equally with resources. Yet, living flow networks have a key advantage over…
The metabolic networks are very well characterized for a large set of organisms, a unique case in within the large-scale biological networks. For this reason they provide a a very interesting framework for the construction of analytically…
Many machine learning algorithms have been developed under the assumption that data sets are already available in batch form. Yet in many application domains data is only available sequentially overtime via compute nodes in different…
To explore the coupling between a growing population of microorganisms such as E. coli and a nonuniform nutrient distribution, we formulate a minimalistic model. It consists of active Brownian particles that divide and grow at a…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
We study a mathematical model of social diffusion on a symmetric weighted network where individual nodes' states gradually assimilate to local social norms made by their neighbors' average states. Unlike physical diffusion, this process is…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
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…
We analyze the structure of networks minimizing the global resistance to flow (or dissipated energy) with respect to two different constraints: fixed total channel volume and fixed total channel surface area. First, we determine the shape…