105,793 research outputs found
A relation on 132-avoiding permutation patterns
Rudolph conjectures that for permutations and of the same length,
for all if and only if the spine structure of is
less than or equal to the spine structure of in refinement order. We
prove one direction of this conjecture, by showing that if the spine structure
of is less than or equal to the spine structure of , then for all . We disprove the opposite direction by giving a
counterexample, and hence disprove the conjecture
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Geometric principles of second messenger dynamics in dendritic spines.
Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14-19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity
The Spine of the Cosmic Web
We present the SpineWeb framework for the topological analysis of the Cosmic
Web and the identification of its walls, filaments and cluster nodes. Based on
the watershed segmentation of the cosmic density field, the SpineWeb method
invokes the local adjacency properties of the boundaries between the watershed
basins to trace the critical points in the density field and the separatrices
defined by them. The separatrices are classified into walls and the spine, the
network of filaments and nodes in the matter distribution. Testing the method
with a heuristic Voronoi model yields outstanding results. Following the
discussion of the test results, we apply the SpineWeb method to a set of
cosmological N-body simulations. The latter illustrates the potential for
studying the structure and dynamics of the Cosmic Web.Comment: Accepted for publication HIGH-RES version:
http://skysrv.pha.jhu.edu/~miguel/SpineWeb
Inverse limits as attractors in parameterized families
We show how a parameterized family of maps of the spine of a manifold can be
used to construct a family of homeomorphisms of the ambient manifold which have
the inverse limits of the spine maps as global attractors. We describe
applications to unimodal families of interval maps, to rotation sets, and to
the standard family of circle maps.Comment: 11 pages, 1 figur
Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium.
Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines
Sticky central limit theorems on open books
Given a probability distribution on an open book (a metric space obtained by
gluing a disjoint union of copies of a half-space along their boundary
hyperplanes), we define a precise concept of when the Fr\'{e}chet mean
(barycenter) is sticky. This nonclassical phenomenon is quantified by a law of
large numbers (LLN) stating that the empirical mean eventually almost surely
lies on the (codimension and hence measure ) spine that is the glued
hyperplane, and a central limit theorem (CLT) stating that the limiting
distribution is Gaussian and supported on the spine. We also state versions of
the LLN and CLT for the cases where the mean is nonsticky (i.e., not lying on
the spine) and partly sticky (i.e., is, on the spine but not sticky).Comment: Published in at http://dx.doi.org/10.1214/12-AAP899 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
On the origin of the hard X-Ray excess of high-synchrotron-peaked BL Lac object Mrk 421
For the first time, Kataoka \& Stawarz reported a clear detection of a hard
X-ray excess, above 20 keV, in the high-synchrotron-peaked BL Lac
object Mrk 421. We find that this feature may not be produced by the low-energy
part of the same electron population that produced the Fermi/LAT -ray.
Because of that it is required that the power-law electron energy go down to
, which predicts a very strong radio emission (radio
flux larger than the observed) even considering the synchrotron self-absorption
effect. We investigate the possibility of this excess being produced from the
spine/layer jet structure, which has been clearly detected in Mrk 421. We find
that (1) similar to one-zone modeling, the spine emissions provide good
modeling of the broadband spectral energy distribution, except for the hard
X-ray excess; and (2) the hard X-ray excess can be well represented by the
synchrotron photons (from the layer) being inverse Compton scattered by the
spine electrons.Comment: 20 pages, 3 figures, published versio
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