Complete CAT Research Articles

Lim's theorems for multivalued mappings in CAT(0) spaces

Let X be a complete CAT(0) space. We prove that, if E is a nonempty bounded closed convex subset of X and T : E → K ( X ) a nonexpansive mapping satisfying the weakly inward condition, i.e., there exists p ∈ E such that α p ⊕ ( 1 − α ) T x ⊂ I E ( x ) ¯ ∀ x ∈ E , ∀ α ∈ [ 0 , 1 ] , then T has a fixed point. In Banach spaces, this is a result of Lim [On asymptotic centers and fixed points of nonexpansive mappings, Canad. J. Math. 32 (1980) 421–430]. The related result for unbounded R -trees is given.

A game of cat and mouse: xenografting of testis tissue from domestic kittens results in complete cat spermatogenesis in a mouse host.

Loss of genetic diversity because of infertility or the premature death of valuable individuals is a significant problem in the conservation of rare and endangered felid species, as well as in the maintenance of lines of cats used to study inherited feline and human disease. Attempts to overcome loss of genetic diversity have focused on freezing sperm; however, sperm cannot be collected from immature males. Previously, we reported completion of spermatogenesis in testis tissue from newborn pigs and goats grafted ectopically into host mice. The objective of this study was to extend the technique of testis tissue xenografting to the domestic cat as a model for felid species. Testes from 1- to 5-week-old domestic shorthaired kittens (n = 9) were cut into small fragments (about 0.5-1 mm3 each), and up to 8 fragments were grafted under the back skin of each castrated immunodeficient host mouse (n = 16). Histologic examination of the testis xenografts was performed between 5 and 54 weeks posttransplantation. At the time of grafting, the seminiferous cords of the donor testis tissue contained only immature Sertoli cells and gonocytes. At 14 weeks after grafting, tubular expansion was evidently caused by the proliferation of Sertoli cells and tubular lumen formation. By 18 weeks after transplantation, the seminiferous epithelium contained spermatocytes, and by 20 weeks, round spermatids were the most advanced types of germ cells. By 36 weeks after transplantation, xenografts of cat testis tissue had completed spermatogenesis. These results demonstrate the potential of xenografting to achieve full spermatogenesis in testis tissue from kittens. Therefore, sperm production in a mouse host can provide an alternative for germ line preservation from immature felids where sperm cryopreservation is not an option.

A sphere theorem for 2-dimensional CAT(1)-spaces

We study sphere theorems for compact, geodesically complete 2-dimensional CAT(1)-spaces. As one of the main results, for compact, geodesically complete, 2-dimensional CAT(1)-spaces, we obtain the optimal volume condition to ensure being homeomorphic to the 2-sphere.

Convex Hulls in Singular Spaces of Negative Curvature

The paper gives a simple example of a complete CAT(–1)-space containing a set S with the following property: the boundary at infinity ∂ ∞CH(S)of the convex hull of S differs from S by an isolated point. In contrast to this it is shown that if S is a union of finitely many convex subsets of a complete CAT(–1)-space X, then ∂ ∞CH(S) = ∂ ∞ S. Moreover, this identity holds without restrictions on S if CH is replaced by some notion of 'almost convex hull'.

Computer simulation of shared input among projection neurons in the dorsal cochlear nucleus.

Computer simulations of a network model of an isofrequency patch of the dorsal cochlear nucleus (DCN) were run to explore possible mechanisms for the level-dependent features observed in the cross-correlograms of pairs of type IV units in the cat and nominal type IV units in the gerbil DCN. The computer model is based on the conceptual model (of a cat) that suggests two sources of shared input to DCN's projection neurons (type IV units): excitatory input for auditory nerves and inhibitory input from interneurons (type II units). Use of tonal stimuli is thought to cause competition between these sources resulting in the decorrelation of type IV unit activities at low levels. In the model, P-cells (projection neurons), representing type IV units, receive inhibitory input from I-cells (interneurons), representing type II units. Both sets of model neurons receive a simulated excitatory auditory nerve (AN) input from same-CF AN fibers, where the AN input is modeled as a dead-time modified Poisson process whose intensity is given by a computationally tractable discharge rate versus sound pressure level function. Subthreshold behavior of each model neuron is governed by a set of normalized state equations. The computer mode has previously been shown to reproduce the major response properties of both type IV and type II units (e.g., rate-level curves and peri-stimulus time histograms) and the level-dependence of the functional type II-type IV inhibitory interaction. This model is adapted for the gerbil by simulating a reduced population of I-cells. Simulations were carried out for several auditory nerve input levels, and cross-correlograms were computed from the activities of pairs of P-cells for a complete (cat model) and reduced (gerbil model) population of I-cells. The resultant correlograms show central mounds (CMs), indicative of either shared excitatory or inhibitory input, for both spontaneous and tone-evoked driven activities. Similar to experimental results, CM amplitudes are a non-monotonic function of level and CM widths decrease as a function of level. These results are consistent with the hypothesis that shared excitatory input correlates the spontaneous activities of type IV units adn shared inhibitory input correlates their driven activities. The results also suggest that the decorrelation of the activities of type IV units can result from a reduced effectiveness of the AN input as a function of increasing level. Thus, competition between the excitatory and inhibitory inputs is not required.

Comparison of fish catches from a buoyant pop net and a beach seine net in a shallow seagrass habitat

A large (25 m2), remote-release buoyant pop net, 1989), and to do this, a buoyant pop net was designed floorless to permit normal behaviour by benthic fish, and a with the aim of making a more complete cat&. The beach seine net were comparing the catch seine net is also unwieldy when fish need to be collected the 2 net types. Both nets were made of 1 mm mesh, aimed at catchina fish from 10 to 100 mm Iona. The Q ~ Q net cauaht from defined The pop net permits 1 . more figh than the selne net, mainlydbecause 9 tlmes mzre tlon of fish from such areas, for example from experiFavonigobius lateraLis were caught in the pop net. Apart from mental plots in which habitat has been manipulated. species such as E lateralis that dwell on the sea bed, the seine ~~~~~~t pop nets usually consist of 4 mesh walls, net catches small fish as well as the pop net, and for some species is a faster, cheaper collection method for survey work. depressed prior to release, and a mesh floor. Such traps H ~ ~ ~ ~ ~ ~ , as net catches can about rank can be lifted clear of the water to collect ensnared fish. order of abundances of species, its main use may be in colSmall pop nets (area 5.6 m2) have been used in vegeletting presence'absence data. The POP net gives a more tated backwaters of a river (Dewey et al. 1989) while a accurate estimate of bottom-dwelling species, and is useful larger net (14,5 m2) was tested for estimating fish where fish need to be collected from small, deflned areas such as ex~erimental ~ l o t s . abundance associated with artificial structures in lakes (Larson et al. 1986). In the present study, a floorless

Coerulospinal fiber regeneration in transected feline spinal cord

After complete cat spinal cord transection, a collagen matrix was used to bridge the gap. Vascular supply was increased to the transection site with an omental pedicle. Before hardening, either 4-aminopyridine, laminin, glia maturation factor, or lipid angiogenic factor were mixed into the collagen. Surgically reconstructed animals were compared to transection-only controls and observed for 90 days. Fluoro-Gold was injected distal to the transection site on day 75. Immunocytochemical examination of brain and spinal cord tissue was done on day 90. Examination revealed supraspinal catecholaminergic fibers present in the collagen bridge and distal cord tissue only in cats with surgical reconstruction. Fluoro-Gold particles were found localized in locus coeruleus and other noradrenergic pontine neurons. Distal to the transection, double immunostaining with synaptophysin and tyrosine hydroxylase or dopamine-β-hydroxylase revealed dot-like deposits closely apposed to preganglionic sympathetic neurons suggestive of synaptic connectivity to these targets. Results indicate that considerable outgrowth of specific supraspinal fibers can be induced following spinal transection and reconstruction, and that such fibers may be extending and contacting appropriate distal target tissue in the cord.