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Understanding the loss surface of neural networks is essential for the design of models with predictable performance and their success in applications. Experimental results suggest that sufficiently deep and wide neural networks are not…
We study spatial networks that are designed to distribute or collect a commodity, such as gas pipelines or train tracks. We focus on the cost of a network, as represented by the total length of all its edges, and its efficiency in terms of…
Understanding of vascular organization is a long-standing problem in quantitative biology and biophysics and is essential for the growth of large cultured tissues. Approaches are needed that (1) make predictions of optimal arteriovenous…
Designing strong and robust bio-inspired structures requires an understanding of how function arises from the architecture and geometry of materials found in nature. We draw from trabecular bone, a lightweight bone tissue that exhibits a…
Understanding the mechanisms of neural communication in large-scale brain networks remains a major goal in neuroscience. We investigated whether navigation is a parsimonious routing model for connectomics. Navigating a network involves…
The architecture of the human connectome supports efficient communication protocols relying either on distances between brain regions or on the intensities of connections. However, none of these protocols combines information about the two…
The relationship between brain structure and function has been probed using a variety of approaches, but how the underlying structural connectivity of the human brain drives behavior is far from understood. To investigate the effect of…
Supplementing a lattice with long-range connections effectively models small-world networks characterized by a high local and global interconnectedness observed in systems ranging from society to the brain. If the links have a wiring cost…
Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…
The cerebral arteries are difficult to reproduce from first principles, featuring interwoven territories, and intricate layers of grey and white matter with differing metabolic demand. The aim of this study was to identify the ideal…
Recent developments in network neuroscience have highlighted the importance of developing techniques for analyzing and modeling brain networks. A particularly powerful approach for studying complex neural systems is to formulate generative…
The branching geometry of biological transport networks is characterized by a diameter scaling exponent $\alpha$. Two structural attractors compete: impedance matching ($\alpha \sim 2$) for pulsatile flow and viscous-metabolic minimization…
Stochastic network design is a general framework for optimizing network connectivity. It has several applications in computational sustainability including spatial conservation planning, pre-disaster network preparation, and river network…
Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we…
Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics…
We show that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our results offer an explanation as to why so many diverse species of network structure…
The underlying anatomical structure is fundamental to the study of brain networks, but the role of brainstem from a structural perspective is not very well understood. We conduct a computational and graph-theoretical study of the human…
This paper optimizes path planning for a trunkand-branch topology network in an irregular 2-dimensional manifold embedded in 3-dimensional Euclidean space with application to submarine cable network planning. We go beyond our earlier focus…
Power lines, roadways, pipelines and other physical infrastructure are critical to modern society. These structures may be viewed as spatial networks where geographic distances play a role in the functionality and construction cost of…
Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific…