113,840 research outputs found
Strong Collapse for Persistence
We introduce a fast and memory efficient approach to compute the persistent homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using strong collapses, as introduced by J. Barmak and E. Miniam [DCG (2012)], and to compute the PH of an induced sequence of reduced simplicial complexes that has the same PH as the initial one. Our approach has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for other types of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot of space and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel. As a result and as demonstrated by numerous experiments on publicly available data sets, our approach is extremely fast and memory efficient in practice
Edge Collapse and Persistence of Flag Complexes
In this article, we extend the notions of dominated vertex and strong collapse of a simplicial complex as introduced by J. Barmak and E. Miniam. We say that a simplex (of any dimension) is dominated if its link is a simplicial cone. Domination of edges appears to be a very powerful concept, especially when applied to flag complexes. We show that edge collapse (removal of dominated edges) in a flag complex can be performed using only the 1-skeleton of the complex. Furthermore, the residual complex is a flag complex as well. Next we show that, similar to the case of strong collapses, we can use edge collapses to reduce a flag filtration ? to a smaller flag filtration ?^c with the same persistence. Here again, we only use the 1-skeletons of the complexes. The resulting method to compute ?^c is simple and extremely efficient and, when used as a preprocessing for persistence computation, leads to gains of several orders of magnitude w.r.t the state-of-the-art methods (including our previous approach using strong collapse). The method is exact, irrespective of dimension, and improves performance of persistence computation even in low dimensions. This is demonstrated by numerous experiments on publicly available data
The notion of persistence applied to breathers in thermal equilibrium
We study the thermal equilibrium of nonlinear Klein-Gordon chains at the
limit of small coupling (anticontinuum limit). We show that the persistence
distribution associated to the local energy density is a useful tool to study
the statistical distribution of so-called thermal breathers, mainly when the
equilibrium is characterized by long-lived static excitations; in that case,
the distribution of persistence intervals turns out to be a powerlaw. We
demonstrate also that this generic behaviour has a counterpart in the power
spectra, where the high frequencies domains nicely collapse if properly
rescaled. These results are also compared to non linear Klein-Gordon chains
with a soft nonlinearity, for which the thermal breathers are rather mobile
entities. Finally, we discuss the possibility of a breather-induced anomalous
diffusion law, and show that despite a strong slowing-down of the energy
diffusion, there are numerical evidences for a normal asymptotic diffusion
mechanism, but with exceptionnally small diffusion coefficients.Comment: submitted to Physica
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Collapse of a desert bird community over the past century driven by climate change
Climate change has caused deserts, already defined by climatic extremes, to warm and dry more rapidly than other ecoregions in the contiguous United States over the last 50 years. Desert birds persist near the edge of their physiological limits, and climate change could cause lethal dehydration and hyperthermia, leading to decline or extirpation of some species. We evaluated how desert birds have responded to climate and habitat change by resurveying historic sites throughout the Mojave Desert that were originally surveyed for avian diversity during the early 20th century by Joseph Grinnell and colleagues. We found strong evidence of an avian community in collapse. Sites lost on average 43% of their species, and occupancy probability declined significantly for 39 of 135 breeding birds. The common raven was the only native species to substantially increase across survey sites. Climate change, particularly decline in precipitation, was the most important driver of site-level persistence, while habitat change had a secondary influence. Habitat preference and diet were the two most important species traits associated with occupancy change. The presence of surface water reduced the loss of site-level richness, creating refugia. The collapse of the avian community over the past century may indicate a larger imbalance in the Mojave and provide an early warning of future ecosystem disintegration, given climate models unanimously predict an increasingly dry and hot future
Radial Distribution Function of Rodlike Polyelectrolytes
We study the effect of electrostatic interactions on the distribution
function of the end-to-end distance of a single polyelectrolyte chain in a
rodlike configuration. We investigate the validity of the concept of
electrostatic persistence length for uniformly charged wormlike chains for both
screened and unscreened Coulomb interactions. We find that the distribution
function of a polyelectrolyte often differs significantly from the distribution
function of a wormlike chain.Comment: RevTeX 4, 7 pages, 6 figure
Magnetic Moment Collapse-Driven Mott Transition in MnO
The metal-insulator transition in correlated electron systems, where electron
states transform from itinerant to localized, has been one of the central
themes of condensed matter physics for more than half a century. The
persistence of this question has been a consequence both of the intricacy of
the fundamental issues and the growing recognition of the complexities that
arise in real materials, even when strong repulsive interactions play the
primary role. The initial concept of Mott was based on the relative importance
of kinetic hopping (measured by the bandwidth) and on-site repulsion of
electrons. Real materials, however, have many additional degrees of freedom
that, as is recently attracting note, give rise to a rich variety of scenarios
for a ``Mott transition.'' Here we report results for the classic correlated
insulator MnO which reproduce a simultaneous moment collapse, volume collapse,
and metallization transition near the observed pressure, and identify the
mechanism as collapse of the magnetic moment due to increase of crystal field
splitting, rather than to variation in the bandwidth.Comment: 18 pages, 5 figur
Collapse of a semiflexible polymer in poor solvent
We investigate the dynamics and the pathways of the collapse of a single,
semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations.
Earlier work indicates that the condensation of semiflexible polymers
generically proceeds via a cascade through metastable racquet-shaped,
long-lived intermediates towards the stable torus state. We investigate the
rate of decay of uncollapsed states, analyze the preferential pathways of
condensation, and describe likelihood and lifespan of the different metastable
states. The simulation are performed with a bead-stiff spring model with
excluded volume interaction and exponentially decaying attractive potential.
The semiflexible chain collapse is studied as functions of the three relevant
length scales of the phenomenon, i.e., the total chain length , the
persistence length and the condensation length , where is a measure of the attractive potential per unit
length. Two dimensionless ratios, and , suffice to describe
the decay rate of uncollapsed states, which appears to scale as . The condensation sequence is described in terms of the time series
of the well separated energy levels associated with each metastable collapsed
state. The collapsed states are described quantitatively through the spatial
correlation of tangent vectors along the chain. We also compare the results
obtained with a locally inextensible bead-rod chain and with a phantom
bead-spring model. Finally, we show preliminary results on the effects of
steady shear flow on the kinetics of collapse.Comment: 9 pages, 8 figure
Global persistence exponent of the double-exchange model
We obtained the global persistence exponent for a continuous spin
model on the simple cubic lattice with double-exchange interaction by using two
different methods. First, we estimated the exponent by following the
time evolution of probability that the order parameter of the model does
not change its sign up to time . Afterwards,
that exponent was estimated through the scaling collapse of the universal
function for different lattice sizes. Our results for
both approaches are in very good agreement each other.Comment: 4 pages, 3 figures, and 3 tables. To appear in Physical Review
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