264 research outputs found
High Resolution Maps of the Vasculature of An Entire Organ
The structure of vascular networks represents a great, unsolved problem in anatomy. Network geometry and topology differ dramatically from left to right and person to person as evidenced by the superficial venation of the hands and the vasculature of the retinae. Mathematically, we may state that there is no conserved topology in vascular networks. Efficiency demands that these networks be regular on a statistical level and perhaps optimal. We have taken the first steps towards elucidating the principles underlying vascular organization, creating the rst map of the hierarchical vasculature (above the capillaries) of an entire organ. Using serial blockface microscopy and fluorescence imaging, we are able to identify vasculature at 5 ÎĽm resolution. We have designed image analysis software to segment, align, and skeletonize the resulting data, yielding a map of the individual vessels. We transformed these data into a mathematical graph, allowing computationally efficient storage and the calculation of geometric and topological statistics for the network. Our data revealed a complexity of structure unexpected by theory. We observe loops at all scales that complicate the assignment of hierarchy within the network and the existence of set length scales, implying a distinctly non-fractal structure of components within
Depth Lower Bounds in Stabbing Planes for Combinatorial Principles
We prove logarithmic depth lower bounds in Stabbing Planes for the classes of
combinatorial principles known as the Pigeonhole principle and the Tseitin
contradictions. The depth lower bounds are new, obtained by giving almost
linear length lower bounds which do not depend on the bit-size of the
inequalities and in the case of the Pigeonhole principle are tight.
The technique known so far to prove depth lower bounds for Stabbing Planes is
a generalization of that used for the Cutting Planes proof system. In this work
we introduce two new approaches to prove length/depth lower bounds in Stabbing
Planes: one relying on Sperner's Theorem which works for the Pigeonhole
principle and Tseitin contradictions over the complete graph; a second proving
the lower bound for Tseitin contradictions over a grid graph, which uses a
result on essential coverings of the boolean cube by linear polynomials, which
in turn relies on Alon's combinatorial Nullenstellensatz
On the Relative Strength of Pebbling and Resolution
The last decade has seen a revival of interest in pebble games in the context
of proof complexity. Pebbling has proven a useful tool for studying
resolution-based proof systems when comparing the strength of different
subsystems, showing bounds on proof space, and establishing size-space
trade-offs. The typical approach has been to encode the pebble game played on a
graph as a CNF formula and then argue that proofs of this formula must inherit
(various aspects of) the pebbling properties of the underlying graph.
Unfortunately, the reductions used here are not tight. To simulate resolution
proofs by pebblings, the full strength of nondeterministic black-white pebbling
is needed, whereas resolution is only known to be able to simulate
deterministic black pebbling. To obtain strong results, one therefore needs to
find specific graph families which either have essentially the same properties
for black and black-white pebbling (not at all true in general) or which admit
simulations of black-white pebblings in resolution. This paper contributes to
both these approaches. First, we design a restricted form of black-white
pebbling that can be simulated in resolution and show that there are graph
families for which such restricted pebblings can be asymptotically better than
black pebblings. This proves that, perhaps somewhat unexpectedly, resolution
can strictly beat black-only pebbling, and in particular that the space lower
bounds on pebbling formulas in [Ben-Sasson and Nordstrom 2008] are tight.
Second, we present a versatile parametrized graph family with essentially the
same properties for black and black-white pebbling, which gives sharp
simultaneous trade-offs for black and black-white pebbling for various
parameter settings. Both of our contributions have been instrumental in
obtaining the time-space trade-off results for resolution-based proof systems
in [Ben-Sasson and Nordstrom 2009].Comment: Full-length version of paper to appear in Proceedings of the 25th
Annual IEEE Conference on Computational Complexity (CCC '10), June 201
Stochastic transport in complex environments : applications in cell biology
Living organisms would not be functional without active processes. This general statement is valid down to the cellular level. Transport processes are necessary to create, maintain and support cellular structures. In this thesis, intracellular transport processes, driven by concentration gradients and active matter, as well as the dynamics of migrating cells are studied. Many studies deal with diffusive intracellular transport in the complex environment of neuronal dendrites, however, focusing on a few spines. In this thesis, a model was developed for diffusive transport in a full dendritic tree. A link was established between complex structural changes by diseases and transport characteristics. Furthermore, recent experimental studies of search processes in migration of dendritic cells show a link between speed and persistence. In this thesis, a correlation between them was included in a stochastic model, which lead to increased search efficiency. Finally, this thesis deals with the question of how active, bidirectional transport by molecular motors in axons can be efficient. Generically, traffic jams are expected in confined environments. Limitations of bypassing mechanisms are discussed with a bidirectional non-Markovian exclusion process, developed in this thesis. Experimental findings of cooperative effects and microtubule modifications have been incorporated in a stochastic model, leading to self-organized lane-formation and thus, efficient bidirectional transport.Ohne aktive Prozesse wären lebendige Organismen nicht funktionsfähig. Dies gilt bis herab zur Zellebene. Transportprozesse sind notwendig um zelluläre Strukturen aufzubauen und zu erhalten. In dieser Arbeit werden intrazelluläre Transportprozesse, getrieben von Konzentrationsgradienten und aktiver Materie, sowie die Dynamik in Zellmigration untersucht. Viele Studien beschäftigen sich mit passivem Transport in der komplexen Umgebung von neuronalen Dendriten, vorwiegend jedoch mit einzelnen Dornvortsätzen (spines). In dieser Arbeit wurde ein Modell zu Diffusion in einer vollständigen Dendritenstruktur entwickelt und eine Relation zwischen Krankheitsverläufen und neuronalen Funktionen gefunden. Die Migration von dendritischen Zellen zeigen einen Zusammenhang zwischen ihrer Geschwindigkeit und Persistenz. Dieser wurde in ein stochastisches Modell übernommen welches zeigte, dass die Sucheffizienz der Zellen damit gesteigert werden kann. Außerdem geht es um die Frage wie aktiver, bidirektionaler Transport durch molekulare Motoren in Axonen effizient sein kann. In einem so begrenzten Raum sind Verkehrsstaus zu erwarten. In dieser Arbeit wurden lokale Austauschmechanismen anhand des entwickelten Nicht-Markovschen, bidirektionalen Exklusionsprozess diskutiert. Experimentell entdeckte kooperative Effekte und Mikrotubulimodifikationen wurde in ein stochastisches Modell übernommen, was zu selbstorganisierter Spurbildung und damit zu effizientem bidirektionalem Transport führte
Critical phenomena in complex networks
The combination of the compactness of networks, featuring small diameters,
and their complex architectures results in a variety of critical effects
dramatically different from those in cooperative systems on lattices. In the
last few years, researchers have made important steps toward understanding the
qualitatively new critical phenomena in complex networks. We review the
results, concepts, and methods of this rapidly developing field. Here we mostly
consider two closely related classes of these critical phenomena, namely
structural phase transitions in the network architectures and transitions in
cooperative models on networks as substrates. We also discuss systems where a
network and interacting agents on it influence each other. We overview a wide
range of critical phenomena in equilibrium and growing networks including the
birth of the giant connected component, percolation, k-core percolation,
phenomena near epidemic thresholds, condensation transitions, critical
phenomena in spin models placed on networks, synchronization, and
self-organized criticality effects in interacting systems on networks. We also
discuss strong finite size effects in these systems and highlight open problems
and perspectives.Comment: Review article, 79 pages, 43 figures, 1 table, 508 references,
extende
Monitoring Rice Phenology Based on Backscattering Characteristics of Multi-Temporal RADARSAT-2 Datasets
Accurate estimation and monitoring of rice phenology is necessary for the management and yield prediction of rice. The radar backscattering coefficient, one of the most direct and accessible parameters has been proved to be capable of retrieving rice growth parameters. This paper aims to investigate the possibility of monitoring the rice phenology (i.e., transplanting, vegetative, reproductive, and maturity) using the backscattering coefficients or their simple combinations of multi-temporal RADARSAT-2 datasets only. Four RADARSAT-2 datasets were analyzed at 30 sample plots in Meishan City, Sichuan Province, China. By exploiting the relationships of the backscattering coefficients and their combinations versus the phenology of rice, HH/VV, VV/VH, and HH/VH ratios were found to have the greatest potential for phenology monitoring. A decision tree classifier was applied to distinguish the four phenological phases, and the classifier was effective. The validation of the classifier indicated an overall accuracy level of 86.2%. Most of the errors occurred in the vegetative and reproductive phases. The corresponding errors were 21.4% and 16.7%, respectively
Persistent homology analysis of brain artery trees
New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries
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