Rigid colorings of hypergraphs and contiguity

©© 2019 Society for Industrial and Applied Mathematics We consider the problem of q-coloring a k-uniform random hypergraph, where q, k > 3, and determine the rigidity threshold. For edge densities above the rigidity threshold, we show that almost all solutions have a linear number of vertices that are linearly frozen, meaning that they cannot be recolored by a sequence of colorings that each change the color of a sublinear number of vertices. When the edge density is below the threshold, we prove that all but a vanishing proportion of the vertices can be recolored by a sequence of colorings that recolor only one vertex at a time. This change in the geometry of the solution space has been hypothesized to be the cause of the algorithmic barrier faced by naive coloring algorithms. Our calculations verify predictions made by statistical physicists using the nonrigorous cavity method. The traditional model for problems of this type is the random coloring model, where a random hypergraph is chosen and then a random coloring of that hypergraph is selected. However, it is often easier to work with the planted model, where a random coloring is selected first, and then edges are randomly chosen which respect the coloring. As part of our analysis, we show that up to the condensation phase transition, the random coloring model is contiguous with respect to the planted model. This result is of independent interest

Lower Bounds on the Chromatic Number of Random Graphs

We prove that a formula predicted on the basis of non-rigorous physics arguments [Zdeborová and Krzakala: Phys. Rev. E (2007)] provides a lower bound on the chromatic number of sparse random graphs. The proof is based on the interpolation method from mathematical physics. In the case of random regular graphs the lower bound can be expressed algebraically, while in the case of the binomial random we obtain a variational formula. As an application we calculate improved explicit lower bounds on the chromatic number of random graphs for small (average) degrees. Additionally, we show how asymptotic formulas for large degrees that were previously obtained by lengthy and complicated combinatorial arguments can be re-derived easily from these new results

Metal-catalyst-free growth of carbon nanotubes and their application in field-effect transistors

The metal-catalyst-free growth of carbon nanotubes (CNTs) using chemical vapor deposition and the application in field-effect transistors (FETs) is demonstrated. The CNT growth process used a 3-nm-thick Ge layer on SiO2 that was subsequently annealed to produce Ge nanoparticles. Raman measurements show the presence of radial breathing mode peaks and the absence of the disorder induced D-band, indicating single walled CNTs with a low defect density. The synthesized CNTs are used to fabricate CNTFETs and the best device has a state-of-the-art on/off current ratio of 3×108 and a steep sub-threshold slope of 110 mV/dec

Gamma-Ray Spectra & Variability of the Crab Nebula Emission Observed by BATSE

We report ~ 600 days of BATSE earth-occultation observations of the total gamma-ray (30 keV to 1.7 MeV) emission from the Crab nebula, between 1991 May 24 (TJD 8400) and 1994 October 2 (TJD 9627). Lightcurves from 35-100, 100-200, 200-300, 300-400, 400-700, and 700-1000 keV, show that positive fluxes were detected by BATSE in each of these six energy bands at significances of approximately 31, 20, 9.2, 4.5, 2.6, and 1.3 sigma respectively per day. We also observed significant flux and spectral variations in the 35-300 keV energy region, with time scales of days to weeks. The spectra below 300 keV, averaged over typical CGRO viewing periods of 6-13 days, can be well described by a broken power law with average indices of ~ 2.1 and ~ 2.4 varying around a spectral break at ~ 100 keV. Above 300 keV, the long-term averaged spectra, averaged over three 400 d periods (TJD 8400-8800, 8800-9200, and 9200-9628, respectively) are well represented by the same power law with index of ~ 2.34 up to ~ 670 keV, plus a hard spectral component extending from ~ 670 keV to ~ 1.7 MeV, with a spectral index of ~ 1.75. The latter component could be related to a complex structure observed by COMPTEL in the 0.7-3 MeV range. Above 3 MeV, the extrapolation of the power-law continuum determined by the low-energy BATSE spectrum is consistent with fluxes measured by COMPTEL in the 3-25 MeV range, and by EGRET from 30-50 MeV. We interpret these results as synchrotron emission produced by the interaction of particles ejected from the pulsar with the field in different dynamical regions of the nebula system, as observed recently by HST, XMM-Newton, and Chandra.Comment: To be published in the November 20, 2003, Vol 598 issue of the Astrophysical Journa

Implications of substrate geometry and coating thickness on the cracking resistance of polymer-based protective coatings

Welded steel T-sections of different weld fillet geometries coated with water ballast tank protective coatings were subjected to thermal cycling with a temperature range from 60°C to -10°C. Cracks developed in the coatings at the weld line, propagating longitudinally along it. The number of cycles required to create 1 mm cracks was strongly dependent on the weld geometry and the coating Dry Film Thickness (DFT). Finite Element Modelling (FEM) was employed to calculate thermally induced strain fields in the coatings subjected to the same temperature range. FEM predicted that the greatest strain concentrations are present at the coating surface within the weld fillet region. Increased DFT and decreased fillet radius leads to increased maximum principal strains. Numerical analysis predicts that greatest strain ranges promoting the earliest cracking/failure are found in thicker coatings applied to smaller weld radii. Experimental observations confirm this

Critical values for Lawshe's content validity ratio: revisiting the original methods of calculation

YesThe content validity ratio originally proposed by Lawshe is widely used to quantify content validity and yet methods used to calculate the original critical values were never reported. Methods for original calculation of critical values are suggested along with tables of exact binomial probabilities

Attention and fluctuating attention in patients with dementia with lewy bodies and alzheimer disease

Background: Attentional deficits are described in the consensus clinical criteria for the operationalized diagnosis of dementia with Lewy bodies (DLB) as characteristic of the condition. In addition, preliminary studies have indicated that both attentional impairments and fluctuation of attentional impairments are more marked in patients with DLB than in patients with Alzheimer disease (AD), although neuropsychological function has not previously been examined in a large prospective cohort with confirmed diagnostic accuracy against postmortem diagnosis. Methods: A detailed evaluation of attention and fluctuating attention was undertaken in 155 patients with dementia (85 with DLB and 80 with AD) from a representative hospital dementia case register and 35 elderly controls using the Cognitive Drug Research Computerized Assessment System for Dementia Patients computerized neuropsychological battery. Operationalized clinical diagnosis was made using the consensus criteria for DLB and the National Institute of Neurological and Communicative Disorders and Stroke-Alzheimer's Disease and Related Disorders Association criteria for AD. High levels of sensitivity and specificity have been achieved for the first 50 cases undergoing postmortem examination. Results: The groups were well matched for severity of cognitive impairments, bur the AD patients were older (mean age, 80 vs 78 years) and more likely to be female (55 vs 40). Patients with DLB were significantly more impaired than patients with AD on all measures of attention and fluctuating attention (for all comparisons, t � 2.5, P<.001), and patients from both dementia groups were significantly more impaired than elderly controls for all comparisons other than cognitive reaction time, which was significantly more impaired in DLB patients than controls but was comparable in controls and AD patients. There were, however, significant associations between the severity of cognitive impairment and the severity of both attentional deficits and fluctuations in attention. Conclusions: This large prospective study confirms that slowing of cognitive processing, attention, and fluctuations of attention are significantly more pronounced in DLB and AD patients, although fluctuating attention is common in patients with moderate-to-severe AD. Deficits of cognitive reaction rime appear to be specific to DLB, except in severe dementia. A detailed evaluation of attentional performance could make an important contribution to differential diagnosis, although the results need to be interpreted within the context of the overall severity of cognitive deficits

Immobilised teicoplanin does not demonstrate antimicrobial activity against Staphylococcus aureus

Abstract: Antibacterial bone biomaterial coatings appeal to orthopaedics, dentistry and veterinary medicine. Achieving the successful, stable conjugation of suitable compounds to biomaterial surfaces is a major challenge. A pragmatic starting point is to make use of existing, approved antibiotics which are known to remain functional in a stationary, immobilised state. This includes the macrocyclic glycopeptide, teicoplanin, following the discovery, in the 1990’s, that it could be used as a chiral selector in chromatographic enantiomeric separations. Importantly teicoplanin works at the level of the bacterial cell wall making it a potential candidate for biomaterial functionalisations. We initially sought to functionalise titanium (Ti) with polydopamine and use this platform to capture teicoplanin, however we were unable to avoid the natural affinity of the antibiotic to the oxide surface of the metal. Whilst the interaction between teicoplanin and Ti was robust, we found that phosphate resulted in antibiotic loss. Before contemplating the covalent attachment of teicoplanin to Ti we examined whether a commercial teicoplanin stationary phase could kill staphylococci. Whilst this commercially available material could bind N-Acetyl-L-Lys-D-Ala-D-Ala it was unable to kill bacteria. We therefore strongly discourage attempts at covalently immobilising teicoplanin and/or other glycopeptide antibiotics in the pursuit of novel antibacterial bone biomaterials

Neutron total cross sections on nuclei at Fermilab energies

We have measured total cross sections for neutrons on protons, deuteriom, beryllium, carbon, aluminium, iron, copper, cadmium, tungsten, lead, and uranium for momenta between 30 and 300 GeV/c. The measurements were carried out in a small-angle neutral beam at Fermilab. Typical accuracy of the data is 0.5 to 1%. The cross sections are consistent with an A0.77+/-0.01 dependence over the entire momentum range. The cross sections are compared with theoretical predictions. Agreement is found only if inelastic screening is included. Nuclear radii obtained from our data are in good agreement with previous determinations.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/22036/1/0000454.pd