Mammalian rod terminal: Architecture of a binary synapse

AbstractThe mammalian rod synapse transmits a binary signal (one photon or none) using tonic, rapid exocytosis. We constructed a quantitative, physical model of the synapse. Presynaptically, a single, linear active zone provides docking sites for ∼130 vesicles, and a “ribbon” anchored to the active zone provides a depot for ∼640 vesicles. Postsynaptically, 4 processes invaginate the terminal: 2 (known to have low affinity glutamate receptors) lie near the active zone (16 nm), and 2 (known to have high affinity glutamate receptors) lie at a distance (130–640 nm). The presynaptic structure seems designed to minimize fluctuations in tonic rate owing to empty docking sites, whereas the postsynaptic geometry may permit 1 vesicle to evoke an all-or-none response at all 4 postsynaptic processes

Microwave Gaseous Discharges

Contains reports on three research projects.United States Atomic Energy Commission (Contract AT(30-1) 1842

Microwave Gaseous Discharges

Contains reports on five research projects.United States Atomic Energy Commission (Contract AT(30-1) 1842

Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Shapes of free resolutions over a local ring

We classify the possible shapes of minimal free resolutions over a regular local ring. This illustrates the existence of free resolutions whose Betti numbers behave in surprisingly pathological ways. We also give an asymptotic characterization of the possible shapes of minimal free resolutions over hypersurface rings. Our key new technique uses asymptotic arguments to study formal Q-Betti sequences.Comment: 14 pages, 1 figure; v2: sections have been reorganized substantially and exposition has been streamline

Microwave Gaseous Discharges

Contains reports on five research projects.United States Atomic Energy Commission (Contract AT (30-1) 1842

Resolution of null fiber and conormal bundles on the Lagrangian Grassmannian

We study the null fiber of a moment map related to dual pairs. We construct an equivariant resolution of singularities of the null fiber, and get conormal bundles of closed $K_C$-orbits in the Lagrangian Grassmannian as the categorical quotient. The conormal bundles thus obtained turn out to be a resolution of singularities of the closure of nilpotent $K_C$-orbits, which is a "quotient" of the resolution of the null fiber.Comment: 17 pages; completely revised and add reference

Microwave Gaseous Discharges

Contains research objectives and reports on five research projects

Triangle-Free Penny Graphs: Degeneracy, Choosability, and Edge Count

We show that triangle-free penny graphs have degeneracy at most two, list coloring number (choosability) at most three, diameter $D=\Omega(\sqrt n)$, and at most $\min\bigl(2n-\Omega(\sqrt n),2n-D-2\bigr)$ edges.Comment: 10 pages, 2 figures. To appear at the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Revisiting the tree Constraint

International audienceThis paper revisits the tree constraint introduced in [2] which partitions the nodes of a n-nodes, m-arcs directed graph into a set of node-disjoint anti-arborescences for which only certain nodes can be tree roots. We introduce a new filtering algorithm that enforces generalized arc-consistency in O(n + m) time while the original filtering algorithm reaches O(nm) time. This result allows to tackle larger scale problems involving graph partitioning