Uncategorized – Page 4 – Mahadevan Natural Philosophy

Cutting into shape

Mathematical framework turns any sheet of material into any shape using kirigami cuts

Using math to help treat Alzheimer’s, Parkinson’s and other diseases

Insights into treatments for protein aggregation diseases from control theory and chemical kinetics

Using origami memory to encode geometric information in floppy structures

Researchers develop method to control the rigidity of structures through origami folds

How termite mounds get their shape

Shedding light on the principles of termite mound size and shape with a model coupling insect behavior and environmental remodeling

Planar morphometrics using Teichmüller maps

Inspired by the question of quantifying wing shape,
we propose a computational approach for analysing
planar shapes. We first establish a correspondence
between the boundaries of two planar shapes with
boundary landmarks using geometric functional data
analysis and then compute a landmark-matching
curvature-guided Teichmüller mapping with uniform
quasi-conformal distortion in the bulk. This allows
us to analyse the pair-wise difference between the
planar shapes and construct a similarity matrix on
which we deploy methods from network analysis
to cluster shapes. We deploy our method to study
a variety of Drosophila wings across species to
highlight the phenotypic variation between them,
and Lepidoptera wings over time to study the
developmental progression of wings. Our approach
of combining complex analysis, computation and
statistics to quantify, compare and classify planar
shapes may be usefully deployed in other biological
and physical systems.

Generalized Erdös numbers for network analysis

The identification of relationships in complex networks is critical
in a variety of scientific contexts. This includes the identification of
globally central nodes and analysing the importance of pairwise
relationships between nodes. In this paper, we consider the
concept of topological proximity (or ‘closeness’) between nodes
in a weighted network using the generalized Erdo´´s numbers
(GENs). This measure satisfies a number of desirable properties
for networks with nodes that share a finite resource. These
include: (i) real-valuedness, (ii) non-locality and (iii) asymmetry.
We show that they can be used to define a personalized
measure of the importance of nodes in a network with a natural
interpretation that leads to new methods to measure centrality.
We show that the square of the leading eigenvector of an
importance matrix defined using the GENs is strongly correlated
with well-known measures such as PageRank, and define a
personalized measure of centrality that is also well correlated
with other existing measures. The utility of this measure
of topological proximity is demonstrated by showing the
asymmetries in both the dynamics of random walks and the
mean infection time in epidemic spreading are better
predicted by the topological definition of closeness provided
by the GENs than they are by other measures.

Deep-reinforcement learning for gliding and perching

Deep-reinforcement learning for gliding and perching G. Novati, L. Mahadevan, P. Koumoutsakos, arXiv

Shaking the swarm

Researchers explore how bees collaborate to stabilize swarm clusters

A photosynthetic engine for artificial cells

Researchers engineered a cell-like structure that harnesses photosynthesis to perform designer reactions

Controllable biomimetic birdsong

Birdsong is the product of the controlled generation of sound embodied in a
neuromotor system. From a biophysical perspective, a natural question is
that of the difficulty of producing birdsong. To address this, we built a biomimetic syrinx consisting of a stretched simple rubber tube through which
air is blown, subject to localized mechanical squeezing with a linear actuator. A large static tension on the tube and small dynamic variations in the
localized squeezing allow us to control transitions between three states: a
quiescent state, a periodic state and a solitary wave state. The static load
brings the system close to threshold for spontaneous oscillations, while
small dynamic loads allow for rapid transitions between the states. We use
this to mimic a variety of birdsongs via the slow– fast modulated nonlinear
dynamics of the physical substrate, the syrinx, regulated by a simple controller. Finally, a minimal mathematical model of the system inspired by our
observations allows us to address the problem of song mimicry in an
excitable oscillator for tonal songs