130 research outputs found
M\"obius Invariants of Shapes and Images
Identifying when different images are of the same object despite changes
caused by imaging technologies, or processes such as growth, has many
applications in fields such as computer vision and biological image analysis.
One approach to this problem is to identify the group of possible
transformations of the object and to find invariants to the action of that
group, meaning that the object has the same values of the invariants despite
the action of the group. In this paper we study the invariants of planar shapes
and images under the M\"obius group , which arises
in the conformal camera model of vision and may also correspond to neurological
aspects of vision, such as grouping of lines and circles. We survey properties
of invariants that are important in applications, and the known M\"obius
invariants, and then develop an algorithm by which shapes can be recognised
that is M\"obius- and reparametrization-invariant, numerically stable, and
robust to noise. We demonstrate the efficacy of this new invariant approach on
sets of curves, and then develop a M\"obius-invariant signature of grey-scale
images
Ambiguities in order-theoretic formulations of thermodynamics
Since the 1909 work of Carath\'eodory, formulations of thermodynamics have
gained ground which highlight the role of the the binary relation of adiabatic
accessibility between equilibrium states. A feature of Carath\'eodory's system
is that the version therein of the second law contains an ambiguity about the
nature of irreversible adiabatic processes, making it weaker than the
traditional Kelvin-Planck statement of the law. This paper attempts first to
clarify the nature of this ambiguity, by defining the arrow of time in
thermodynamics by way of the Equilibrium Principle ("Minus First Law"). It then
argues that the ambiguity reappears in the important 1999 axiomatisation due to
Lieb and Yngvason.Comment: 13 pages, 1 figur
Environmental boundary conditions for the origin of life converge to an organo-sulfur metabolism
Published in final edited form as:
Nat Ecol Evol. 2019 December ; 3(12): 1715–1724. doi:10.1038/s41559-019-1018-8.It has been suggested that a deep memory of early life is hidden in the architecture of metabolic networks, whose reactions could have been catalyzed by small molecules or minerals before genetically encoded enzymes. A major challenge in unravelling these early steps is assessing the plausibility of a connected, thermodynamically consistent proto-metabolism under different geochemical conditions, which are still surrounded by high uncertainty. Here we combine network-based algorithms with physico-chemical constraints on chemical reaction networks to systematically show how different combinations of parameters (temperature, pH, redox potential and availability of molecular precursors) could have affected the evolution of a proto-metabolism. Our analysis of possible trajectories indicates that a subset of boundary conditions converges to an organo-sulfur-based proto-metabolic network fuelled by a thioester- and redox-driven variant of the reductive tricarboxylic acid cycle that is capable of producing lipids and keto acids. Surprisingly, environmental sources of fixed nitrogen and low-potential electron donors are not necessary for the earliest phases of biochemical evolution. We use one of these networks to build a steady-state dynamical metabolic model of a protocell, and find that different combinations of carbon sources and electron donors can support the continuous production of a minimal ancient 'biomass' composed of putative early biopolymers and fatty acids.80NSSC17K0295 - Intramural NASA; 80NSSC17K0296 - Intramural NASA; T32 GM100842 - NIGMS NIH HHSAccepted manuscrip
The Community Simulator: A Python package for microbial ecology
Natural microbial communities contain hundreds to thousands of interacting
species. For this reason, computational simulations are playing an increasingly
important role in microbial ecology. In this manuscript, we present a new
open-source, freely available Python package called Community Simulator for
simulating microbial population dynamics in a reproducible, transparent and
scalable way. The Community Simulator includes five major elements: tools for
preparing the initial states and environmental conditions for a set of samples,
automatic generation of dynamical equations based on a dictionary of modeling
assumptions, random parameter sampling with tunable levels of metabolic and
taxonomic structure, parallel integration of the dynamical equations, and
support for metacommunity dynamics with migration between samples. To
significantly speed up simulations using Community Simulator, our Python
package implements a new Expectation-Maximization (EM) algorithm for finding
equilibrium states of community dynamics that exploits a recently discovered
duality between ecological dynamics and convex optimization. We present data
showing that this EM algorithm improves performance by between one and two
orders compared to direct numerical integration of the corresponding ordinary
differential equations. We conclude by listing several recent applications of
the Community Simulator to problems in microbial ecology, and discussing
possible extensions of the package for directly analyzing microbiome
compositional data.Comment: 14 pages, 6 figure
Currents and finite elements as tools for shape space
The nonlinear spaces of shapes (unparameterized immersed curves or
submanifolds) are of interest for many applications in image analysis, such as
the identification of shapes that are similar modulo the action of some group.
In this paper we study a general representation of shapes that is based on
linear spaces and is suitable for numerical discretization, being robust to
noise. We develop the theory of currents for shape spaces by considering both
the analytic and numerical aspects of the problem. In particular, we study the
analytical properties of the current map and the norm that it induces
on shapes. We determine the conditions under which the current determines the
shape. We then provide a finite element discretization of the currents that is
a practical computational tool for shapes. Finally, we demonstrate this
approach on a variety of examples
- …