Revealing structure-function relationships in functional flow networks via persistent homology

Complex networks encountered in biology are often characterized by significant structural diversity. Whether it be differences in the three-dimensional structure of allosteric proteins, or the variation among the micro-scale structures of organisms' cerebral vasculature systems, identifying relationships between structure and function often poses a difficult challenge. Here we showcase an approach to characterizing structure-function relationships in complex networks applied in the context of flow networks tuned to perform specific functions. Using persistent homology, we analyze flow networks tuned to perform complex multifunctional tasks, answering the question of how local changes in the network structure coordinate to create functionality at at the scale of the entire network. We find that the response of such networks encodes hidden topological features - sectors of uniform pressure - that are not apparent in the underlying network architectures, Regardless of differences in local connectivity, these features provide a universal topological description for all networks that perform these types of functions. We show that these features correlate strongly with the tuned response, providing a clear topological relationship between structure and function and structural insight into the limits of multifunctionality.Comment: 22 pages (double column), 12 figure

Operating Principles of Peristaltic Pumping through a Dense Array of Valves

Immersed nonlinear elements are prevalent in biological systems that require a preferential flow direction. A certain class of models is investigated where the fluid is driven by peristaltic pumping and the nonlinear elements are ideal valves that completely suppress backflow. This highly nonlinear system produces discontinuous solutions that are difficult to study. As the density of valves increases, the pressure and flow are well-approximated by a continuum of valves which can be analytically treated. Interestingly, two different pumping mechanisms emerge from this model. At low frequencies, diffusive transport pushes open all but one valve, and the radius takes the shape of the imposed force. At high frequencies, half of the valves open, and the flow is determined by the advective transport induced by peristalsis. In either case, the induced flow is linear in the amplitude of the peristaltic forces and is independent of pumping direction. Despite the continuum approximation used, the physical valve density is accounted for by modifying the resistance of the fluid appropriately. The suppression of backflow causes a net benefit in adding valves when the valve density is low, but once the density is high enough, the dominant valve effect is to suppress the forward flow, suggesting there is an optimum number of valves per wavelength.Comment: 11 pages, 7 figure

From localized to well-mixed: How commuter interactions shape disease spread

Interactions between commuting individuals can lead to large-scale spreading of rumors, ideas, or disease, even though the commuters have no net displacement. The emergent dynamics depend crucially on the commuting distribution of a population, that is how the probability to travel to a destination decays with distance from home. Applying this idea to epidemics, we will demonstrate the qualitatively different infection dynamics emerging from populations with different commuting distributions. If the commuting distribution is exponentially localized, we recover a reaction-diffusion system and observe Fisher waves traveling at a speed proportional to the characteristic commuting distance. If the commuting distribution has a long tail, then no finite-velocity waves can form, but we show that, in some regimes, there is nontrivial spatial dependence that the well-mixed approximation neglects. We discuss how, in all cases, an initial dispersal-dominated regime can allow the disease to go undetected for a finite amount of time before exponential growth takes over. This "offset time" is a quantity of huge importance for epidemic surveillance and yet largely ignored in the literature.Comment: 26 pages, 15 figures; made minor edits for clarit

An efficient spectral method for the dynamic behavior of truss structures

Truss structures at macro-scale are common in a number of engineering applications and are now being increasingly used at the micro-scale to construct metamaterials. In analyzing the properties of a given truss structure, it is often necessary to understand how stress waves propagate through the system and/or its dynamic modes under time dependent loading so as to allow for maximally efficient use of space and material. This can be a computationally challenging task for particularly large or complex structures, with current methods requiring fine spatial discretization or evaluations of sizable matrices. Here we present a spectral method to compute the dynamics of trusses inspired by results from fluid flow networks. Our model accounts for the full dynamics of linearly elastic truss elements via a network Laplacian; a matrix object which couples the motions of the structure joints. We show that this method is equivalent to the continuum limit of linear finite element methods as well as capable of reproducing natural frequencies and modes determined by more complex and computationally costlier methods

Collapse and Folding of Pressurized Rings in Two Dimensions

Hydrostatically pressurized circular rings confined to two dimensions (or cylinders constrained to have only z-independent deformations) undergo Euler-type buckling when the outside pressure exceeds a critical value. We perform a stability analysis of rings with arclength-dependent bending moduli and determine how weakened bending modulus segments affect the buckling critical pressure. Rings with a fourfold symmetric modulation are particularly susceptible to collapse. In addition we study the initial postbuckling stages of the pressurized rings to determine possible ring folding patterns.Engineering and Applied SciencesPhysicsOther Research Uni