126 research outputs found
A random tunnel number one 3-manifold does not fiber over the circle
We address the question: how common is it for a 3-manifold to fiber over the
circle? One motivation for considering this is to give insight into the fairly
inscrutable Virtual Fibration Conjecture. For the special class of 3-manifolds
with tunnel number one, we provide compelling theoretical and experimental
evidence that fibering is a very rare property. Indeed, in various precise
senses it happens with probability 0. Our main theorem is that this is true for
a measured lamination model of random tunnel number one 3-manifolds.
The first ingredient is an algorithm of K Brown which can decide if a given
tunnel number one 3-manifold fibers over the circle. Following the lead of
Agol, Hass and W Thurston, we implement Brown's algorithm very efficiently by
working in the context of train tracks/interval exchanges. To analyze the
resulting algorithm, we generalize work of Kerckhoff to understand the dynamics
of splitting sequences of complete genus 2 interval exchanges. Combining all of
this with a "magic splitting sequence" and work of Mirzakhani proves the main
theorem.
The 3-manifold situation contrasts markedly with random 2-generator 1-relator
groups; in particular, we show that such groups "fiber" with probability
strictly between 0 and 1.Comment: This is the version published by Geometry & Topology on 15 December
200
Random division of an interval
The well-known relation between random division of an interval and the Poisson process is interpreted as a Laplace transformation. With the use of this interpretation a number of (in part known) results is derived very easily
The structure of typical clusters in large sparse random configurations
The initial purpose of this work is to provide a probabilistic explanation of
a recent result on a version of Smoluchowski's coagulation equations in which
the number of aggregations is limited. The latter models the deterministic
evolution of concentrations of particles in a medium where particles coalesce
pairwise as time passes and each particle can only perform a given number of
aggregations. Under appropriate assumptions, the concentrations of particles
converge as time tends to infinity to some measure which bears a striking
resemblance with the distribution of the total population of a Galton-Watson
process started from two ancestors. Roughly speaking, the configuration model
is a stochastic construction which aims at producing a typical graph on a set
of vertices with pre-described degrees. Specifically, one attaches to each
vertex a certain number of stubs, and then join pairwise the stubs uniformly at
random to create edges between vertices. In this work, we use the configuration
model as the stochastic counterpart of Smoluchowski's coagulation equations
with limited aggregations. We establish a hydrodynamical type limit theorem for
the empirical measure of the shapes of clusters in the configuration model when
the number of vertices tends to . The limit is given in terms of the
distribution of a Galton-Watson process started with two ancestors
Random Neighbor Theory of the Olami-Feder-Christensen Earthquake Model
We derive the exact equations of motion for the random neighbor version of
the Olami-Feder-Christensen earthquake model in the infinite-size limit. We
solve them numerically, and compare with simulations of the model for large
numbers of sites. We find perfect agreement. But we do not find any scaling or
phase transitions, except in the conservative limit. This is in contradiction
to claims by Lise & Jensen (Phys. Rev. Lett. 76, 2326 (1996)) based on
approximate solutions of the same model. It indicates again that scaling in the
Olami-Feder-Christensen model is only due to partial synchronization driven by
spatial inhomogeneities. Finally, we point out that our method can be used also
for other SOC models, and treat in detail the random neighbor version of the
Feder-Feder model.Comment: 18 pages, 6 ps-figures included; minor correction in sec.
Self-organized model of cascade spreading
We study simultaneous price drops of real stocks and show that for high drop
thresholds they follow a power-law distribution. To reproduce these collective
downturns, we propose a minimal self-organized model of cascade spreading based
on a probabilistic response of the system elements to stress conditions. This
model is solvable using the theory of branching processes and the mean-field
approximation. For a wide range of parameters, the system is in a critical
state and displays a power-law cascade-size distribution similar to the
empirically observed one. We further generalize the model to reproduce
volatility clustering and other observed properties of real stocks.Comment: 8 pages, 6 figure
Early Detection of Tuberculosis Outbreaks among the San Francisco Homeless: Trade-Offs Between Spatial Resolution and Temporal Scale
BACKGROUND: San Francisco has the highest rate of tuberculosis (TB) in the U.S. with recurrent outbreaks among the homeless and marginally housed. It has been shown for syndromic data that when exact geographic coordinates of individual patients are used as the spatial base for outbreak detection, higher detection rates and accuracy are achieved compared to when data are aggregated into administrative regions such as zip codes and census tracts. We examine the effect of varying the spatial resolution in the TB data within the San Francisco homeless population on detection sensitivity, timeliness, and the amount of historical data needed to achieve better performance measures. METHODS AND FINDINGS: We apply a variation of space-time permutation scan statistic to the TB data in which a patient's location is either represented by its exact coordinates or by the centroid of its census tract. We show that the detection sensitivity and timeliness of the method generally improve when exact locations are used to identify real TB outbreaks. When outbreaks are simulated, while the detection timeliness is consistently improved when exact coordinates are used, the detection sensitivity varies depending on the size of the spatial scanning window and the number of tracts in which cases are simulated. Finally, we show that when exact locations are used, smaller amount of historical data is required for training the model. CONCLUSION: Systematic characterization of the spatio-temporal distribution of TB cases can widely benefit real time surveillance and guide public health investigations of TB outbreaks as to what level of spatial resolution results in improved detection sensitivity and timeliness. Trading higher spatial resolution for better performance is ultimately a tradeoff between maintaining patient confidentiality and improving public health when sharing data. Understanding such tradeoffs is critical to managing the complex interplay between public policy and public health. This study is a step forward in this direction
A Spatial Cluster Analysis of Tractor Overturns in Kentucky from 1960 to 2002
Agricultural tractor overturns without rollover protective structures are the leading cause of farm fatalities in the United States. To our knowledge, no studies have incorporated the spatial scan statistic in identifying high-risk areas for tractor overturns. The aim of this study was to determine whether tractor overturns cluster in certain parts of Kentucky and identify factors associated with tractor overturns.A spatial statistical analysis using Kulldorff's spatial scan statistic was performed to identify county clusters at greatest risk for tractor overturns. A regression analysis was then performed to identify factors associated with tractor overturns.The spatial analysis revealed a cluster of higher than expected tractor overturns in four counties in northern Kentucky (RR = 2.55) and 10 counties in eastern Kentucky (RR = 1.97). Higher rates of tractor overturns were associated with steeper average percent slope of pasture land by county (p = 0.0002) and a greater percent of total tractors with less than 40 horsepower by county (p<0.0001).This study reveals that geographic hotspots of tractor overturns exist in Kentucky and identifies factors associated with overturns. This study provides policymakers a guide to targeted county-level interventions (e.g., roll-over protective structures promotion interventions) with the intention of reducing tractor overturns in the highest risk counties in Kentucky
Spatial variations in the incidence of breast cancer and potential risks associated with soil dioxin contamination in Midland, Saginaw, and Bay Counties, Michigan, USA
<p>Abstract</p> <p>Background</p> <p>High levels of dioxins in soil and higher-than-average body burdens of dioxins in local residents have been found in the city of Midland and the Tittabawassee River floodplain in Michigan. The objective of this study is threefold: (1) to evaluate dioxin levels in soils; (2) to evaluate the spatial variations in breast cancer incidence in Midland, Saginaw, and Bay Counties in Michigan; (3) to evaluate whether breast cancer rates are spatially associated with the dioxin contamination areas.</p> <p>Methods</p> <p>We acquired 532 published soil dioxin data samples collected from 1995 to 2003 and data pertaining to female breast cancer cases (<it>n </it>= 4,604) at ZIP code level in Midland, Saginaw, and Bay Counties for years 1985 through 2002. Descriptive statistics and self-organizing map algorithm were used to evaluate dioxin levels in soils. Geographic information systems techniques, the Kulldorff's spatial and space-time scan statistics, and genetic algorithms were used to explore the variation in the incidence of breast cancer in space and space-time. Odds ratio and their corresponding 95% confidence intervals, with adjustment for age, were used to investigate a spatial association between breast cancer incidence and soil dioxin contamination.</p> <p>Results</p> <p>High levels of dioxin in soils were observed in the city of Midland and the Tittabawassee River 100-year floodplain. After adjusting for age, we observed high breast cancer incidence rates and detected the presence of spatial clusters in the city of Midland, the confluence area of the Tittabawassee, and Saginaw Rivers. After accounting for spatiotemporal variations, we observed a spatial cluster of breast cancer incidence in Midland between 1985 and 1993. The odds ratio further suggests a statistically significant (<it>α </it>= 0.05) increased breast cancer rate as women get older, and a higher disease burden in Midland and the surrounding areas in close proximity to the dioxin contaminated areas.</p> <p>Conclusion</p> <p>These findings suggest that increased breast cancer incidences are spatially associated with soil dioxin contamination. Aging is a substantial factor in the development of breast cancer. Findings can be used for heightened surveillance and education, as well as formulating new study hypotheses for further research.</p
Interpopulation variation in female remating is attributable to female and male effects in Callosobruchus chinensis
The evolution of female multiple mating is best understood by consideration of male and female reproductive perspectives. Females should usually be selected to remate at their optimum frequencies whereas males should be selected to manipulate female remating to their advantage. Female remating behavior may therefore be changed by variation of male and female traits. In this study, our objective was to separate the effects of female and male strains on female remating for the adzuki bean beetle, Callosobruchus chinensis, for which there is interstrain variation in female remating frequency. We found that interstrain variation in female remating is primarily attributable to female traits, suggesting genetic variation in female receptivity to remating in C. chinensis. Some interstrain variation in female remating propensity was attributable to an interaction between female and male strains, however, with the males of some strains being good at inducing nonreceptivity in females from one high-remating strain whereas others were good at inducing copulation in nonvirgin females from the high-remating strain. There is, therefore, interstrain variation in male ability to deter females from remating and in male ability to mate successfully with nonvirgin females. These results suggest that mating traits have evolved along different trajectories in different strains of C. chinensis.</p
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