47,921 research outputs found
On morphological hierarchical representations for image processing and spatial data clustering
Hierarchical data representations in the context of classi cation and data
clustering were put forward during the fties. Recently, hierarchical image
representations have gained renewed interest for segmentation purposes. In this
paper, we briefly survey fundamental results on hierarchical clustering and
then detail recent paradigms developed for the hierarchical representation of
images in the framework of mathematical morphology: constrained connectivity
and ultrametric watersheds. Constrained connectivity can be viewed as a way to
constrain an initial hierarchy in such a way that a set of desired constraints
are satis ed. The framework of ultrametric watersheds provides a generic scheme
for computing any hierarchical connected clustering, in particular when such a
hierarchy is constrained. The suitability of this framework for solving
practical problems is illustrated with applications in remote sensing
A primer on noise-induced transitions in applied dynamical systems
Noise plays a fundamental role in a wide variety of physical and biological
dynamical systems. It can arise from an external forcing or due to random
dynamics internal to the system. It is well established that even weak noise
can result in large behavioral changes such as transitions between or escapes
from quasi-stable states. These transitions can correspond to critical events
such as failures or extinctions that make them essential phenomena to
understand and quantify, despite the fact that their occurrence is rare. This
article will provide an overview of the theory underlying the dynamics of rare
events for stochastic models along with some example applications
Maximum Flux Transition Paths of Conformational Change
Given two metastable states A and B of a biomolecular system, the problem is
to calculate the likely paths of the transition from A to B. Such a calculation
is more informative and more manageable if done for a reduced set of collective
variables chosen so that paths cluster in collective variable space. The
computational task becomes that of computing the "center" of such a cluster. A
good way to define the center employs the concept of a committor, whose value
at a point in collective variable space is the probability that a trajectory at
that point will reach B before A. The committor "foliates" the transition
region into a set of isocommittors. The maximum flux transition path is defined
as a path that crosses each isocommittor at a point which (locally) has the
highest crossing rate of distinct reactive trajectories. (This path is
different from that of the MaxFlux method of Huo and Straub.) It is argued that
such a path is nearer to an ideal path than others that have been proposed with
the possible exception of the finite-temperature string method path. To make
the calculation tractable, three approximations are introduced, yielding a path
that is the solution of a nonsingular two-point boundary-value problem. For
such a problem, one can construct a simple and robust algorithm. One such
algorithm and its performance is discussed.Comment: 7 figure
Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches
During tissue development, patterns of gene expression determine the spatial
arrangement of cell types. In many cases, gradients of secreted signaling
molecules - morphogens - guide this process. The continuous positional
information provided by the gradient is converted into discrete cell types by
the downstream transcriptional network that responds to the morphogen. A
mechanism commonly used to implement a sharp transition between two adjacent
cell fates is the genetic toggle switch, composed of cross-repressing
transcriptional determinants. Previous analyses emphasize the steady state
output of these mechanisms. Here, we explore the dynamics of the toggle switch
and use exact numerical simulations of the kinetic reactions, the Chemical
Langevin Equation, and Minimum Action Path theory to establish a framework for
studying the effect of gene expression noise on patterning time and boundary
position. This provides insight into the time scale, gene expression
trajectories and directionality of stochastic switching events between cell
states. Taking gene expression noise into account predicts that the final
boundary position of a morphogen-induced toggle switch, although robust to
changes in the details of the noise, is distinct from that of the deterministic
system. Moreover, stochastic switching introduces differences in patterning
time along the morphogen gradient that result in a patterning wave propagating
away from the morphogen source. The velocity of this wave is influenced by
noise; the wave sharpens and slows as it advances and may never reach steady
state in a biologically relevant time. This could explain experimentally
observed dynamics of pattern formation. Together the analysis reveals the
importance of dynamical transients for understanding morphogen-driven
transcriptional networks and indicates that gene expression noise can
qualitatively alter developmental patterning
A machine learning route between band mapping and band structure
The electronic band structure (BS) of solid state materials imprints the
multidimensional and multi-valued functional relations between energy and
momenta of periodically confined electrons. Photoemission spectroscopy is a
powerful tool for its comprehensive characterization. A common task in
photoemission band mapping is to recover the underlying quasiparticle
dispersion, which we call band structure reconstruction. Traditional methods
often focus on specific regions of interests yet require extensive human
oversight. To cope with the growing size and scale of photoemission data, we
develop a generic machine-learning approach leveraging the information within
electronic structure calculations for this task. We demonstrate its capability
by reconstructing all fourteen valence bands of tungsten diselenide and
validate the accuracy on various synthetic data. The reconstruction uncovers
previously inaccessible momentum-space structural information on both global
and local scales in conjunction with theory, while realizing a path towards
integrating band mapping data into materials science databases
Bistability of the climate around the habitable zone: a thermodynamic investigation
The goal of this paper is to explore the potential multistability of the
climate of a planet around the habitable zone. A thorough investigation of the
thermodynamics of the climate system is performed for very diverse conditions
of energy input and infrared atmosphere opacity. Using PlaSim, an Earth-like
general circulation model, the solar constant S* is modulated between 1160 and
1510 Wm-2 and the CO2 concentration, [CO2], from 90 to 2880 ppm. It is observed
that in such a parameter range the climate is bistable, i.e. there are two
coexisting attractors, one characterised by warm, moist climates (W) and one by
completely frozen sea surface (Snowball Earth, SB). Linear relationships are
found for the two transition lines (W\rightarrowSB and SB\rightarrowW) in
(S*,[CO2]) between S* and the logarithm of [CO2]. The dynamical and
thermodynamical properties - energy fluxes, Lorenz energy cycle, Carnot
efficiency, material entropy production - of the W and SB states are very
different: W states are dominated by the hydrological cycle and latent heat is
prominent in the material entropy production; the SB states are predominantly
dry climates where heat transport is realized through sensible heat fluxes and
entropy mostly generated by dissipation of kinetic energy. We also show that
the Carnot efficiency regularly increases towards each transition between W and
SB, with a large decrease in each transition. Finally, we propose well-defined
empirical functions allowing for expressing the global non-equilibrium
thermodynamical properties of the system in terms of either the mean surface
temperature or the mean planetary emission temperature. This paves the way for
the possibility of proposing efficient parametrisations of complex
non-equilibrium properties and of practically deducing fundamental properties
of a planetary system from a relatively simple observable
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