Equidistribution in All Dimensions of Worst-Case Point Sets for the TSP

Given a set S of n points in the unit square [0, 1]d , an optimal traveling salesman tour of S is a tour of S that is of minimum length. A worst-case point set for the Traveling Salesman Problem in the unit square is a point set S(n) whose optimal traveling salesman tour achieves the maximum possible length among all point sets S ⊂ [0, 1]d , where |S| = n. An open problem is to determine the structure of S(n) . We show that for any rectangular parallelepiped R contained in [0, 1]d , the number of points in S(n) ∩ R is asymptotic to n times the volume of R. Analogous results are proved for the minimum spanning tree, minimum-weight matching, and rectilinear Steiner minimum tree. These equidistribution theorems are the first results concerning the structure of worst-case point sets like S(n)

Equidistribution of Point Sets for the Traveling Salesman and Related Problems

Given a set S of n points in the unit square [0, 1)2, an optimal traveling salesman tour of S is a tour of S that is of minimum length. A worst-case point set for the Traveling Salesman Problem in the unit square is a point set S(n) whose optimal traveling salesman tour achieves the maximum possible length among all point sets S C [0, 1)2, where JSI = n. An open problem is to determine the structure of S(n). We show that for any rectangle R contained in [0, 1 F, the number of points in S(n) n R is asymptotic to n times the area of R. One corollary of this result is an 0( n log n) approximation algorithm for the worst-case Euclidean TSP. Analogous results are proved for the minimum spanning tree, minimum-weight matching, and rectilinear Steiner minimum tree. These equidistribution theorems are the first results concerning the structure of worst-case point sets like S(n)

A Priori Bounds on the Euclidean Traveling Salesman

It is proved that there are constants $c_{1}$, $c_{2}$, and $c_{3}$ such that for any set S of n points in the unit square and for any minimum-length tour T of S the sum of squares of the edge lengths of T is bounded by $c_{1} \log n$. (2) the number of edges having length t or greater in T is at most $c_{2}/t^{2}$, and (3) the sum of edge lengths of any subset E of T is bounded by $c_{3}|E|^{1/2}$. The second and third bounds are independent of the number of points in S, as well as their locations. Extensions to dimensions $d \u3e 2$ are also sketched. The presence of the logarithmic term in (1) is engaging because such a term is not needed in the case of the minimum spanning tree and several analogous problems, and, furthermore, we know that there always exists some tour of S (which perhaps does not have minimal length) for which the sum of squared edges is bounded independently of n

Spontaneous Discharge Patterns in Cochlear Spiral Ganglion Cells Prior to the Onset of Hearing in Cats

Spontaneous neural activity has been recorded in the auditory nerve of cats as early as 2 days postnatal (P2 ), yet individual auditory neurons do not respond to ambient sound levels below 90–100 dB SPL until about P10. Significant refinement of the central projections from the spiral ganglion to the cochlear nucleus occurs during this neonatal period. This refinement may be dependent on peripheral spontaneous discharge activity. We recorded from single spiral ganglion cells in kittens aged P3 to P9. The spiral ganglion was accessed via the round window through the spiral lamina. A total of 112 ganglion cells were isolated for study in 9 animals. Spike rates in neonates were very low, ranging from 0.06 to 56 sp/s with a mean of 3.09 +/- 8.24 sp/s. Ganglion cells in neonatal kittens exhibited remarkable repetitive spontaneous bursting discharge patterns. The unusual patterns were evident in the large mean interval coefficient of variation (CVi = 2.9 +/-1.6) and burst index of 5.2 +/- 3.5 across ganglion cells. Spontaneous bursting patterns in these neonatal mammals were similar to those reported for cochlear ganglion cells of the embryonic chicken suggesting this may be a general phenomenon that is common across animal classes. Rhythmic spontaneous discharge of retinal ganglion cells has been shown to be important in the development of central retinotopic projections and normal binocular vision (Shatz, 1996, Proc Natl Acad Sci 93). Bursting rhythms in cochlear ganglion cells may play a similar role in the auditory system during pre-hearing periods. Originally published in Journal of Neurophysiology Vol. 98, No. 4 200

Opposing brain differences in 16p11.2 deletion and duplication carriers

Deletions and duplications of the recurrent ∼600 kb chromosomal BP4–BP5 region of 16p11.2 are associated with a broad variety of neurodevelopmental outcomes including autism spectrum disorder. A clue to the pathogenesis of the copy number variant (CNV)'s effect on the brain is that the deletion is associated with a head size increase, whereas the duplication is associated with a decrease. Here we analyzed brain structure in a clinically ascertained group of human deletion (N = 25) and duplication (N = 17) carriers from the Simons Variation in Individuals Project compared with age-matched controls (N = 29 and 33, respectively). Multiple brain measures showed increased size in deletion carriers and reduced size in duplication carriers. The effects spanned global measures of intracranial volume, brain size, compartmental measures of gray matter and white matter, subcortical structures, and the cerebellum. Quantitatively, the largest effect was on the thalamus, but the collective results suggest a pervasive rather than a selective effect on the brain. Detailed analysis of cortical gray matter revealed that cortical surface area displays a strong dose-dependent effect of CNV (deletion > control > duplication), whereas average cortical thickness is less affected. These results suggest that the CNV may exert its opposing influences through mechanisms that influence early stages of embryonic brain development

Nna1 Mediates Purkinje Cell Dendritic Development via Lysyl Oxidase Propeptide and NF-κB Signaling

SummaryThe molecular pathways controlling cerebellar Purkinje cell dendrite formation and maturation are poorly understood. The Purkinje cell degeneration (pcd) mutant mouse is characterized by mutations in Nna1, a gene discovered in an axonal regenerative context, but whose actual function in development and disease is unknown. We found abnormal development of Purkinje cell dendrites in postnatal pcdSid mice and linked this deficit to a deletion mutation in exon 7 of Nna1. With single cell gene profiling and virus-based gene transfer, we analyzed a molecular pathway downstream to Nna1 underlying abnormal Purkinje cell dendritogenesis in pcdSid mice. We discovered that mutant Nna1 dramatically increases intranuclear localization of lysyl oxidase propeptide, which interferes with NF-κB RelA signaling and microtubule-associated protein regulation of microtubule stability, leading to underdevelopment of Purkinje cell dendrites. These findings provide insight into Nna1's role in neuronal development and why its absence renders Purkinje cells more vulnerable

Physical drivers facilitating a toxigenic cyanobacterial bloom in a major Great Lakes tributary

The Maumee River is the primary source for nutrients fueling seasonal Microcystis-dominated blooms in western Lake Erie\u27s open waters though such blooms in the river are infrequent. The river also serves as source water for multiple public water systems and a large food services facility in northwest Ohio. On 20 September 2017, an unprecedented bloom was reported in the Maumee River estuary within the Toledo metropolitan area, which triggered a recreational water advisory. Here we (1) explore physical drivers likely contributing to the bloom\u27s occurrence, and (2) describe the toxin concentration and bacterioplankton taxonomic composition. A historical analysis using 10-years of seasonal river discharge, water level, and local wind data identified two instances when high-retention conditions occurred over ≥ 10 d in the Maumee River estuary: in 2016 and during the 2017 bloom. Observation by remote sensing imagery supported the advection of cyanobacterial cells into the estuary from the lake during 2017 and the lack of an estuary bloom in 2016 due to a weak cyanobacterial bloom in the lake. A rapid-response survey during the 2017 bloom determined levels of the cyanotoxins, specifically microcystins, in excess of recreational contact limits at sites within the lower 20 km of the river while amplicon sequencing found these sites were dominated by Microcystis. These results highlight the need to broaden our understanding of physical drivers of cyanobacterial blooms within the interface between riverine and lacustrine systems, particularly as such blooms are expected to become more prominent in response to a changing climate

Propulsion Investigation for Zero and Near-Zero Emissions Aircraft

As world emissions are further scrutinized to identify areas for improvement, aviation s contribution to the problem can no longer be ignored. Previous studies for zero or near-zero emissions aircraft suggest aircraft and propulsion system sizes that would perform propulsion system and subsystems layout and propellant tankage analyses to verify the weight-scaling relationships. These efforts could be used to identify and guide subsequent work on systems and subsystems to achieve viable aircraft system emissions goals. Previous work quickly focused these efforts on propulsion systems for 70- and 100-passenger aircraft. Propulsion systems modeled included hydrogen-fueled gas turbines and fuel cells; some preliminary estimates combined these two systems. Hydrogen gas-turbine engines, with advanced combustor technology, could realize significant reductions in nitrogen emissions. Hydrogen fuel cell propulsion systems were further laid out, and more detailed analysis identified systems needed and weight goals for a viable overall system weight. Results show significant, necessary reductions in overall weight, predominantly on the fuel cell stack, and power management and distribution subsystems to achieve reasonable overall aircraft sizes and weights. Preliminary conceptual analyses for a combination of gas-turbine and fuel cell systems were also performed, and further studies were recommended. Using gas-turbine engines combined with fuel cell systems can reduce the fuel cell propulsion system weight, but at higher fuel usage than using the fuel cell only

The ATLAS3D project - XXVII : Cold gas and the colours and ages of early-type galaxies

Date of Acceptance: 16/12/2013We present a study of the cold gas contents of the ATLAS3D early-type galaxies, in the context of their optical colours, near-ultraviolet colours and Hβ absorption line strengths. Early-type (elliptical and lenticular) galaxies are not as gas poor as previously thought, and at least 40 per cent of local early-type galaxies are now known to contain molecular and/or atomic gas. This cold gas offers the opportunity to study recent galaxy evolution through the processes of cold gas acquisition, consumption (star formation) and removal. Molecular and atomic gas detection rates range from 10 to 34 per cent in red sequence early-type galaxies, depending on how the red sequence is defined, and from 50 to 70 per cent in blue early-type galaxies. Notably, massive red sequence early-type galaxies (stellar masses >5 × 1010 M⊙, derived from dynamical models) are found to have H I masses up to M(H I)/M* ∼ 0.06 and H2 masses up to M(H2)/M* ∼ 0.01. Some 20 per cent of all massive early-type galaxies may have retained atomic and/or molecular gas through their transition to the red sequence. However, kinematic and metallicity signatures of external gas accretion (either from satellite galaxies or the intergalactic medium) are also common, particularly at stellar masses ≤5 × 1010 M⊙, where such signatures are found in ∼50 per cent of H2-rich early-type galaxies. Our data are thus consistent with a scenario in which fast rotator early-type galaxies are quenched former spiral galaxies which have undergone some bulge growth processes, and in addition, some of them also experience cold gas accretion which can initiate a period of modest star formation activity. We discuss implications for the interpretation of colour–magnitude diagramsPeer reviewedFinal Accepted Versio