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In this Master's thesis, the graph properties of a multi-level drug-protein network are studied, as well as how the network's shape has informed discoveries over the years, identifying primarily crawling discoveries and a smaller number of…
The spatial localization or sequestering of motile cargo and their dispersal within cells is an important process in a number of physiological contexts. The morphology of the cytoskeletal network, along which active, motor-driven…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
We consider the problem of throughput-optimal broadcast- ing in time-varying wireless networks, whose underlying topology is restricted to Directed Acyclic Graphs (DAG). Previous broadcast algorithms route packets along spanning trees. In…
Water molecules confined between biological membranes exhibit a distinctive non-Gaussian displacement distribution, far different from bulk water. Here, we introduce a new transport equation for water molecules in the intermembrane space,…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
Topology provides a unifying framework for understanding robust transport through protected edge states arising from nontrivial wavenumber topology. Extending these concepts to active matter, however, remains largely unexplored…
We introduce a multi-species lattice gas model for motor protein driven collective cargo transport on cellular filaments. We use this model to describe and analyze the collective motion of interacting vesicle cargoes being carried by…
With the growing popularity of mobile smart devices, the existing networks are unable to meet the requirement of many complex scenarios; current network architectures and protocols do not work well with the network with high latency and…
A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of…
Epidemic spreading on complex networks depends on the topological structure as well as on the dynamical properties of the infection itself. Generally speaking, highly connected individuals play the role of hubs and are crucial to channel…
Many cellular networks rely on the regulated transport of their components to transduce extracellular information into precise intracellular signals. The dynamics of these networks is typically described in terms of compartmentalized…
A living cell's interior is one of the most complex and intrinsically dynamic systems, providing an elaborate interplay between cytosolic crowding and ATP-driven motion, which controls cellular functionality. Here, we investigated two…
Recent experiments show that both natural and artificial microswimmers in narrow channel-like geometries will self-organise to form steady, directed flows. This suggests that networks of flowing active matter could function as novel…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…
Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…
Networks of elastic fibers are ubiquitous in biological systems and often provide mechanical stability to cells and tissues. Fiber reinforced materials are also common in technology. An important characteristic of such materials is their…
The ability to reroute and control flow is vital to the function of venation networks across a wide range of organisms. By modifying individual edges in these networks, either by adjusting edge conductances or creating and destroying edges,…
Biological transport networks adapt through dynamic interactions between material transport and structural modification during growth and development. In this work, we present a model of transport network growth driven by local material…
To comprehend the multipartite organization of large-scale biological and social systems, we introduce a new information theoretic approach that reveals community structure in weighted and directed networks. The method decomposes a network…