Associahedra via spines

An associahedron is a polytope whose vertices correspond to triangulations of a convex polygon and whose edges correspond to flips between them. Using labeled polygons, C. Hohlweg and C. Lange constructed various realizations of the associahedron with relevant properties related to the symmetric group and the classical permutahedron. We introduce the spine of a triangulation as its dual tree together with a labeling and an orientation. This notion extends the classical understanding of the associahedron via binary trees, introduces a new perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's original approach, and sheds light upon the combinatorial and geometric properties of the resulting realizations of the associahedron. It also leads to noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction

Bringing Sexy Back: Unauthorized Film Editing, Copyright, and How Removing Reproductive Acts Violates Reproduction Rights

The Multicolored Asian Ladybird, Harmonia axyridis, is an extremely successful invasive species. Here we suggest that, in addition to many other traits, the dorsal spines of its larvae contribute to their success, as suggested by behavioral observations of agonistic interactions between H. axyridis and European coccinellids. In coccinellids, the role of dorsal spines in these interactions has been poorly studied and they could be a physical protection against intraguild predators. Dorsal spines of second instar H. axyridis larvae were removed with micro-scissors, which resulted in spineless larvae after molting (spineless group). These larvae were then exposed to starved Coccinella septempunctata larvae. Two control categories were also submitted to interactions: H. axyridis larvae with all their spines (control group) and with their spines, but injured by pin stings (injured group). Spine removal at the second instar did not hamper H. axyridis development. The bite rate by C. septempunctata was significantly higher on the spineless H. axyridis and more dorsally located compared to the control and injured groups, while no bite rate difference was observed between the injured and the control group. Our results suggest that in addition to behavioral and chemical defenses, the dorsal spines play a significant protective role against bites. Therefore, spines in ladybirds could be considered as a morphological defense against intraguild predation. In H. axyridis, these defenses might contribute to its success in food resources already exploited by other guild members and thus further facilitate the invasion of new areas.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Rapid, learning-induced inhibitory synaptogenesis in murine barrel field

The structure of neurons changes during development and in response to injury or alteration in sensory experience. Changes occur in the number, shape, and dimensions of dendritic spines together with their synapses. However, precise data on these changes in response to learning are sparse. Here, we show using quantitative transmission electron microscopy that a simple form of learning involving mystacial vibrissae results in approximately 70% increase in the density of inhibitory synapses on spines of neurons located in layer IV barrels that represent the stimulated vibrissae. The spines contain one asymmetrical (excitatory) and one symmetrical (inhibitory) synapse (double-synapse spines), and their density increases threefold as a result of learning with no apparent change in the density of asymmetrical synapses. This effect seems to be specific for learning because pseudoconditioning (in which the conditioned and unconditioned stimuli are delivered at random) does not lead to the enhancement of symmetrical synapses but instead results in an upregulation of asymmetrical synapses on spines. Symmetrical synapses of cells located in barrels receiving the conditioned stimulus also show a greater concentration of GABA in their presynaptic terminals. These results indicate that the immediate effect of classical conditioning in the "conditioned" barrels is rapid, pronounced, and inhibitory

Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Here we develop a computational framework that allows the study of multiple spiking events in a network of such spines embedded in a simple one-dimensional cable. This system is shown to support saltatory waves as a result of the discrete distribution of spines. Moreover, we demonstrate one of the ways to incorporate noise into the spine-head whilst retaining computational tractability of the model. The SDS model sustains a variety of propagating patterns

Dendritic Spine Shape Analysis: A Clustering Perspective

Functional properties of neurons are strongly coupled with their morphology. Changes in neuronal activity alter morphological characteristics of dendritic spines. First step towards understanding the structure-function relationship is to group spines into main spine classes reported in the literature. Shape analysis of dendritic spines can help neuroscientists understand the underlying relationships. Due to unavailability of reliable automated tools, this analysis is currently performed manually which is a time-intensive and subjective task. Several studies on spine shape classification have been reported in the literature, however, there is an on-going debate on whether distinct spine shape classes exist or whether spines should be modeled through a continuum of shape variations. Another challenge is the subjectivity and bias that is introduced due to the supervised nature of classification approaches. In this paper, we aim to address these issues by presenting a clustering perspective. In this context, clustering may serve both confirmation of known patterns and discovery of new ones. We perform cluster analysis on two-photon microscopic images of spines using morphological, shape, and appearance based features and gain insights into the spine shape analysis problem. We use histogram of oriented gradients (HOG), disjunctive normal shape models (DNSM), morphological features, and intensity profile based features for cluster analysis. We use x-means to perform cluster analysis that selects the number of clusters automatically using the Bayesian information criterion (BIC). For all features, this analysis produces 4 clusters and we observe the formation of at least one cluster consisting of spines which are difficult to be assigned to a known class. This observation supports the argument of intermediate shape types.Comment: Accepted for BioImageComputing workshop at ECCV 201

Micromechanics of sea urchin spines

The endoskeletal structure of the Sea Urchin, Centrostephanus rodgersii, has numerous long spines whose known functions include locomotion, sensing, and protection against predators. These spines have a remarkable internal microstructure and are made of single-crystal calcite. A finite-element model of the spine's unique porous structure, based on micro-computed tomography (microCT) and incorporating anisotropic material properties, was developed to study its response to mechanical loading. Simulations show that high stress concentrations occur at certain points in the spine's architecture; brittle cracking would likely initiate in these regions. These analyses demonstrate that the organization of single-crystal calcite in the unique, intricate morphology of the sea urchin spine results in a strong, stiff and lightweight structure that enhances its strength despite the brittleness of its constituent material