A linear optimization technique for graph pebbling

Graph pebbling is a network model for studying whether or not a given supply of discrete pebbles can satisfy a given demand via pebbling moves. A pebbling move across an edge of a graph takes two pebbles from one endpoint and places one pebble at the other endpoint; the other pebble is lost in transit as a toll. It has been shown that deciding whether a supply can meet a demand on a graph is NP-complete. The pebbling number of a graph is the smallest t such that every supply of t pebbles can satisfy every demand of one pebble. Deciding if the pebbling number is at most k is NP 2 -complete. In this paper we develop a tool, called theWeight Function Lemma, for computing upper bounds and sometimes exact values for pebbling numbers with the assistance of linear optimization. With this tool we are able to calculate the pebbling numbers of much larger graphs than in previous algorithms, and much more quickly as well. We also obtain results for many families of graphs, in many cases by hand, with much simpler and remarkably shorter proofs than given in previously existing arguments (certificates typically of size at most the number of vertices times the maximum degree), especially for highly symmetric graphs. Here we apply theWeight Function Lemma to several specific graphs, including the Petersen, Lemke, 4th weak Bruhat, Lemke squared, and two random graphs, as well as to a number of infinite families of graphs, such as trees, cycles, graph powers of cycles, cubes, and some generalized Petersen and Coxeter graphs. This partly answers a question of Pachter, et al., by computing the pebbling exponent of cycles to within an asymptotically small range. It is conceivable that this method yields an approximation algorithm for graph pebbling.

On Borel equivalence relations in generalized Baire space

"Vegeu el resum a l'inici del document del fitxer adjunt."

Former eating disorder impairs 3rd person but not 1st person perspective taking. Does dance training help?

The mental ability to take the perspective of another person may depend on one's own bodily awareness and experience. In the present study, the former was defined as having a history of an eating disorder, and the latter variable was defined as formal experience with dance. The study used a 2 × 2 × 2 factorial design in which reaction times in two mental perspective taking tasks were compared between female dancers and non-dancers with and without a former eating disorder. Participants were asked to imagine two perspectives: i) the position of front-facing and back-facing figures (3rd person perspective taking task) and ii) that these same figures are a self reflection in a mirror (1st person perspective taking task). In both tasks, a particular hand was indicated in the presented figures, and the participants had to decide whether the hand represented their own left or right hand. Overall, responses were slower for front-facing than back-facing figures in the 3rd person perspective taking task, and for back-facing than front-facing figures in the 1st person perspective taking task. Importantly, having a former history of an eating disorder related to a decreased performance in the 3rd person perspective taking task, but only in participants without dance experience. Results from an additional control group (a history of exercise but no dance experience) indicated that dance is particularly beneficial for mental bodily perspective taking. Dance experience, more so than exercise in general, can benefit 3rd person or extrapersonal perspective taking, supporting the favourable impact this exercise has on own body processing

Spin-labeling coronary MR angiography with steady-state free precession and radial k-space sampling: initial results in healthy volunteers.

The purpose of this study was to prospectively compare free-breathing navigator-gated cardiac-triggered three-dimensional steady-state free precession (SSFP) spin-labeling coronary magnetic resonance (MR) angiography performed by using Cartesian k-space sampling with that performed by using radial k-space sampling. A new dedicated placement of the two-dimensional selective labeling pulse and an individually adjusted labeling delay time approved by the institutional review board were used. In 14 volunteers (eight men, six women; mean age, 28.8 years) who gave informed consent, signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), vessel sharpness, vessel length, and subjective image quality were investigated. Differences between groups were analyzed with nonparametric tests (Wilcoxon, Pearson chi2). Radial imaging, as compared with Cartesian imaging, resulted in a significant reduction in the severity of motion artifacts, as well as an increase in SNR (26.9 vs 12.0, P < .05) in the coronary arteries and CNR (23.1 vs 8.8, P < .05) between the coronary arteries and the myocardium. A tendency toward improved vessel sharpness and vessel length was also found with radial imaging. Radial SSFP imaging is a promising technique for spin-labeling coronary MR angiography.

MR spectroscopy of the human brain with enhanced signal intensity at ultrashort echo times on a clinical platform at 3T and 7T.

Recently, the spin-echo full-intensity acquired localized (SPECIAL) spectroscopy technique was proposed to unite the advantages of short TEs on the order of milliseconds (ms) with full sensitivity and applied to in vivo rat brain. In the present study, SPECIAL was adapted and optimized for use on a clinical platform at 3T and 7T by combining interleaved water suppression (WS) and outer volume saturation (OVS), optimized sequence timing, and improved shimming using FASTMAP. High-quality single voxel spectra of human brain were acquired at TEs below or equal to 6 ms on a clinical 3T and 7T system for six volunteers. Narrow linewidths (6.6 +/- 0.6 Hz at 3T and 12.1 +/- 1.0 Hz at 7T for water) and the high signal-to-noise ratio (SNR) of the artifact-free spectra enabled the quantification of a neurochemical profile consisting of 18 metabolites with Cramér-Rao lower bounds (CRLBs) below 20% at both field strengths. The enhanced sensitivity and increased spectral resolution at 7T compared to 3T allowed a two-fold reduction in scan time, an increased precision of quantification for 12 metabolites, and the additional quantification of lactate with CRLB below 20%. Improved sensitivity at 7T was also demonstrated by a 1.7-fold increase in average SNR (= peak height/root mean square [RMS]-of-noise) per unit-time.

Medicinal products: regulation of biosynthesis in space and time

We live in a "Demon-Haunted World". Human health care requires the ever increasing resistance of pathogens to be confronted by a correspondingly fast rate of discovery of novel antibiotics. One of the possible strategies towards this objective involves the rational localization of bioactive phytochemicals. The conceptual basis of the method consists in the surprisingly little known gearings of natural products with morphology, ecology and evolution of their plant source, i. e. an introspection into the general mechanisms of nature.

Closure of Space for health - PEL(13)05 (PDF 38KB)

This Professional Estates Letter informs HSC bodies of the closure of the Space for Health information service and the availability of DHSPPS estates and facilities management policy on the DHSSPS website.

Aerotropolis: an aviation-linked space

This paper examines the conditions allowing the formation of aeropolitan areas as large industrial areas with a high concentration of commercial activities in the proximity of selected airports. We assume that firms deliver their production by plane and land competition takes place among service operators, firms and farmers. Service operators supply facilities that firms can absorb. Our framework identifies a unique land equilibrium characterized by the spatial sequence Airport - Industrial park - Rural area (A-I-R). Aerotropolis-type configurations are associated with the level of transport costs and the degree of intensity of facilities. Keywords: aerotropolis; facilities; bid-rent function. JEL Classification Numbers: L29; L90; R14.

Oxygen-sensing reporter strain of Pseudomonas fluorescens for monitoring the distribution of low-oxygen habitats in soil.

The root-colonizing bacterium Pseudomonas fluorescens CHA0 was used to construct an oxygen-responsive biosensor. An anaerobically inducible promoter of Pseudomonas aeruginosa, which depends on the FNR (fumarate and nitrate reductase regulation)-like transcriptional regulator ANR (anaerobic regulation of arginine deiminase and nitrate reductase pathways), was fused to the structural lacZ gene of Escherichia coli. By inserting the reporter fusion into the chromosomal attTn7 site of P. fluorescens CHA0 by using a mini-Tn7 transposon, the reporter strain, CHA900, was obtained. Grown in glutamate-yeast extract medium in an oxystat at defined oxygen levels, the biosensor CHA900 responded to a decrease in oxygen concentration from 210 x 10(2) Pa to 2 x 10(2) Pa of O(2) by a nearly 100-fold increase in beta-galactosidase activity. Half-maximal induction of the reporter occurred at about 5 x 10(2) Pa. This dose response closely resembles that found for E. coli promoters which are activated by the FNR protein. In a carbon-free buffer or in bulk soil, the biosensor CHA900 still responded to a decrease in oxygen concentration, although here induction was about 10 times lower and the low oxygen response was gradually lost within 3 days. Introduced into a barley-soil microcosm, the biosensor could report decreasing oxygen concentrations in the rhizosphere for a 6-day period. When the water content in the microcosm was raised from 60% to 85% of field capacity, expression of the reporter gene was elevated about twofold above a basal level after 2 days of incubation, suggesting that a water content of 85% caused mild anoxia. Increased compaction of the soil was shown to have a faster and more dramatic effect on the expression of the oxygen reporter than soil water content alone, indicating that factors other than the water-filled pore space influenced the oxygen status of the soil. These experiments illustrate the utility of the biosensor for detecting low oxygen concentrations in the rhizosphere and other soil habitats.

New pre-dual space of Morrey space

In this paper we give new characterization of the classical Morrey space. Complementary global Morrey-type spaces are introduced. It is proved that for particular values of parameters these spaces give new pre-dual space of the classical Morrey space. We also show that our new pre-dual space of the Morrey space coincides with known pre-dual spaces.

MP2RAGE, a self bias-field corrected sequence for improved segmentation and T-1-mapping at high field

The large spatial inhomogeneity in transmit B, field (B-1(+)) observable in human MR images at hi h static magnetic fields (B-0) severely impairs image quality. To overcome this effect in brain T-1-weighted images the, MPRAGE sequence was modified to generate two different images at different inversion times MP2RAGE By combining the two images in a novel fashion, it was possible to create T-1-weigthed images where the result image was free of proton density contrast, T-2* contrast, reception bias field, and, to first order transmit field inhomogeneity. MP2RAGE sequence parameters were optimized using Bloch equations to maximize contrast-to-noise ratio per unit of time between brain tissues and minimize the effect of B-1(+) variations through space. Images of high anatomical quality and excellent brain tissue differentiation suitable for applications such as segmentation and voxel-based morphometry were obtained at 3 and 7 T. From such T-1-weighted images, acquired within 12 min, high-resolution 3D T-1 maps were routinely calculated at 7 T with sub-millimeter voxel resolution (0.65-0.85 mm isotropic). T-1 maps were validated in phantom experiments. In humans, the T, values obtained at 7 T were 1.15 +/- 0.06 s for white matter (WM) and 1.92 +/- 0.16 s for grey matter (GM), in good agreement with literature values obtained at lower spatial resolution. At 3 T, where whole-brain acquisitions with 1 mm isotropic voxels were acquired in 8 min the T-1 values obtained (0.81 +/- 0.03 S for WM and 1.35 +/- 0.05 for GM) were once again found to be in very good agreement with values in the literature. (C) 2009 Elsevier Inc. All rights reserved.

Imaging Properties of MS Lesions Correlate with Attention Deficits in Early Multiple Sclerosis

Introduction: Cognitive impairment affects 40-65% of multiple sclerosis (MS) patients, often since early stages of the disease (relapsing remitting MS, RRMS). Frequently affected functions are memory, attention or executive abilities but the most sensitive measure of cognitive deficits in early MS is the information processing speed (Amato, 2008). MRI has been extensively exploited to investigate the substrate of cognitive dysfunction in MS but the underlying physiopathological mechanisms remain unclear. White matter lesion load, whole-brain atrophy and cortical lesions' number play a role but correlations are in some cases modest (Rovaris, 2006; Calabrese, 2009). In this study, we aimed at characterizing and correlating the T1 relaxation times of cortical and sub-cortical lesions with cognitive deficits detected by neuropsychological tests in a group of very early RR MS patients. Methods: Ten female patients with very early RRMS (age: 31.6 ±4.7y; disease duration: 3.8 ±1.9y; EDSS disability score: 1.8 ±0.4) and 10 age- and gender-matched healthy volunteers (mean age: 31.2 ±5.8y) were included in the study. All participants underwent the following neuropsychological tests: Rao's Brief Repeatable Battery of Neuropsychological tests (BRB-N), Stockings of Cambridge, Trail Making Test (TMT, part A and B), Boston Naming Test, Hooper Visual Organization Test and copy of the Rey-Osterrieth Complex Figure. Within 2 weeks from neuropsychological assessment, participants underwent brain MRI at 3T (Magnetom Trio a Tim System, Siemens, Germany) using a 32-channel head coil. The imaging protocol included 3D sequences with 1x1x1.2 mm3 resolution and 256x256x160 matrix, except for axial 2D-FLAIR: -DIR (T2-weighted, suppressing both WM and CSF; Pouwels, 2006) -MPRAGE (T1-weighted; Mugler, 1991) -MP2RAGE (T1-weighted with T1 maps; Marques, 2010) -FLAIR SPACE (only for patient 4-10, T2-weighted; Mugler, 2001) -2D Axial FLAIR (0.9x0.9x2.5 mm3, 256x256x44 matrix). Lesions were identified by one experienced neurologist and radiologist using all contrasts, manually contoured and assigned to regional locations (cortical or sub-cortical). Lesion number, volume and T1 relaxation time were calculated for lesions in each contrast and in a merged mask representing the union of the lesions from all contrasts. T1 relaxation times of lesions were normalized with the mean T1 value in corresponding control regions of the healthy subjects. Statistical analysis was performed using GraphPad InStat software. Cognitive scores were compared between patients and controls with paired t-tests; p values ≤ 0.05 were considered significant. Spearmann correlation tests were performed between the cognitive tests, which differed significantly between patients and controls, and lesions' i) number ii) volume iii) T1 relaxation time iv) disease duration and v) years of study. Results: Cortical and sub-cortical lesions count, T1 values and volume are reported in Table 1 (A and B). All early RRMS patients showed cortical lesions (CLs) and the majority consisted of CLs type I (lesions with a cortical component extending to the sub-cortical tissue). The rest of cortical lesions were characterized as type II (intra-cortical lesions). No type III/IV lesions (large sub-pial lesions) were detected. RRMS patients were slightly less educated (13.5±2.5y vs. 16.3±1.8y of study, p=0.02) than the controls. Signs of cortical dysfunction (i.e. impaired learning, language, visuo-spatial skills or gnosis) were rare in all patients. However, patients showed on average lower scores on measures of visual attention and information processing speed (TMT-part A: p=0.01; TMT-part B: p=0.006; PASAT-included in the BRB-N: p=0.04). The T1 relaxation values of CLs type I negatively correlated with the TMT-part A score (r=0.78, p<0.01). The correlations of TMT-part B score and PASAT score with T1 relaxation time of lesions as well and the correlation between TMT-part A, TMT-part B and PASAT score with lesions' i) number ii) volume iii) disease duration and iv) years of study did not reach significance. In order to preclude possible influences from partial volume effects on the T1 values, the correlation between lesion volume and T1 value of CLs type I was calculated; no correlation was found, suggesting that partial volume effects did not affect the statistics. Conclusions: The present pilot study reports for the first time the presence and the T1 characteristics at 3 T of cortical lesions in very early RRMS (< 6 y disease duration). It also shows that CLS type I represents the most frequent cortical lesion type in this cohort of RRMS patients. In addition, it reveals a negative correlation between the attentional test TMT-part A and the T1 properties of cortical lesions type I. In other words, lower attention deficits are concomitant with longer T1-relaxation time in cortical lesions. In respect to this last finding, it could be speculated that long relaxation time correspond to a certain degree of tissue loss that is enough to stimulate compensatory mechanisms. This hypothesis is in line with previous fMRI studies showing functional compensatory mechanisms to help maintaining normal or sub-normal attention performances in RR MS patients (Penner, 2003).