We introduce a concept of tree-graded metric space and we use it to show quasi-isometry invariance of certain classes of relatively hyperbolic groups, to obtain a characterization of relatively hyperbolic groups in terms of their asymptotic cones, to find geometric properties of Cayley graphs of relatively hyperbolic groups, and to construct the first example of finitely generated group with a ...

The distribution of growth cones was studied in the optic nerve of monkeys during the first half of prenatal development using quantitative electron microscopic methods. Our aim was to test the hypothesis that ganglion cell growth cones extend predominantly along the surfaces of the nerve, just beneath the pia mater. A complete census of growth cones in cross sections of the nerve during the ea...

We sought to characterize the regenerated cells, if any, when photoreceptor ablation was mostly limited to a particular cone subtype. This allowed us to uniquely assess whether the remaining cells influence specification of regenerating photoreceptors. The ability to replace lost photoreceptors via stem cell therapy holds promise for treating many retinal degenerative diseases. Zebrafish are po...

The cyclic GMP-gated cationic channels of vertebrate photoreceptors are essential for visual phototransduction. We have examined the developmental regulation of cGMP-gated channels in morphologically identified cones in the chick retina. Expression of cone-type cGMP-gated channel mRNA can be detected at embryonic day 6 (E6), but expression of functional channels, as accessed by patch-clamp reco...

The analysis of classical consensus algorithms relies on contraction properties of adjoints of Markov operators, with respect to Hilbert’s projective metric or to a related family of seminorms (Hopf’s oscillation or Hilbert’s seminorm). We generalize these properties to abstract consensus operators over normal cones, which include the unital completely positive maps (Kraus operators) arising in...

We have examined the question of scarcity-driven competition for outgrowth among growth cones of a single neuron. We measured spontaneous neurite elongation rates from 85 hours of videotape of the arbors of 31 chick sensory neurons in culture. These rate measurements were analyzed in ten minute periods that allowed cell bodies to be classified as to the number of their growth cones and the elon...

The need for robust solutions for sets of non-linear multivariate constraints or equations needs no motivation. Subdivision-based multivariate constraint solvers [1–3] typically employ the convex hull and subdivision/domain clipping properties of the Bézier/B-spline representation to detect all regions that may contain a feasible solution. Once such a region has been identified, a numerical imp...

We present an algorithm which is capable of globally solving a well-constrained transcendental system over some sub-domainD ⊂ R, isolating all roots. Such a system consists of n unknowns and n regular functions, where each may contain non-algebraic (transcendental) functions like sin, exp or log. Every equation is considered as a hyper-surface in R and thus a bounding cone of its normal (gradie...