Solving Hard Graph Problems with Combinatorial Computing and Optimization

Many problems arising in graph theory are difficult by nature, and finding solutions to large or complex instances of them often require the use of computers. As some such problems are $NP$-hard or lie even higher in the polynomial hierarchy, it is unlikely that efficient, exact algorithms will solve them. Therefore, alternative computational methods are used. Combinatorial computing is a branch of mathematics and computer science concerned with these methods, where algorithms are developed to generate and search through combinatorial structures in order to determine certain properties of them. In this thesis, we explore a number of such techniques, in the hopes of solving specific problem instances of interest. Three separate problems are considered, each of which is attacked with different methods of combinatorial computing and optimization. The first, originally proposed by ErdH{o}s and Hajnal in 1967, asks to find the Folkman number $F_e(3,3;4)$, defined as the smallest order of a $K_4$-free graph that is not the union of two triangle-free graphs. A notoriously difficult problem associated with Ramsey theory, the best known bounds on it prior to this work were $19 leq F_e(3,3;4) leq 941$. We improve the upper bound to $F_e(3,3;4) leq 786$ using a combination of known methods and the Goemans-Williamson semi-definite programming relaxation of MAX-CUT. The second problem of interest is the Ramsey number $R(C_4,K_m)$, which is the smallest $n$ such that any $n$-vertex graph contains a cycle of length four or an independent set of order $m$. With the help of combinatorial algorithms, we determine $R(C_4,K_9)=30$ and $R(C_4,K_{10})=36$ using large-scale computations on the Open Science Grid. Finally, we explore applications of the well-known Lenstra-Lenstra-Lov\u27{a}sz (LLL) algorithm, a polynomial-time algorithm that, when given a basis of a lattice, returns a basis for the same lattice with relatively short vectors. The main result of this work is an application to graph domination, where certain hard instances are solved using this algorithm as a heuristic

Patient-Reported Side Effects of Intradetrusor Botulinum Toxin Type A for Idiopathic Overactive Bladder Syndrome

Objective: The aim of the study was a prospective assessment of patient-reported side effects in an open-label study after intradetrusor botulinum toxin injections for idiopathic overactive bladder (OAB). Patients and Methods: Botulinum toxin A injection was performed in 56 patients with idiopathic OAB. Patients were followed up for 6 months concerning side effects and patients' satisfaction. Results: Different types of side effects were assessed such as dry mouth (19.6%), arm weakness (8.9%), eyelid weakness (8.9%), leg weakness (7.1%), torso weakness (5.4%), impaired vision (5.4%) and dysphagia (5.4%). In all cases, symptoms were mild and transient. Urological complications such as gross hematuria (17.9%), acute urinary retention (8.9%) and acute urinary tract infection (7.1%) were noticed. In all cases, acute urinary retention was transient and treated with temporary intermittent self-catheterization. There was no statistically significant correlation between dosage and observed side effects. Patients' satisfaction rate was high (71.4%). Conclusion: Intradetrusor injection of botulinum toxin was associated with a high rate of neurourological side effects. In general, side effects were transient, mild and did not require special treatment. Copyright (C) 2010 S. Karger AG, Base

The reaction between silylene and ammonia: some gas-phase kinetic and quantum chemical studies

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by 193 nm laser flash photolysis of silacyclopent-3-ene, have been carried out in the presence of ammonia, NH3. Second order kinetics were observed. The reaction was studied in the gas phase at 10 Torr total pressure in SF6 bath gas at each of the three temperatures, 299, 340 and 400 K. The second order rate constants (laser pulse energy of 60 mJ/pulse) fitted the Arrhenius equation: log(k/cm3 molecule-1 s-1) = (-10.37 ± 0.17) + (0.36 ± 1.12 kJ mol-1)/RTln10 Experiments at other pressures showed that these rate constants were unaffected by pressure in the range 10-100 Torr, but showed small decreases in value at 3 and 1 Torr. There was also a weak intensity dependence, with rate constants decreasing at laser pulse energies of 30 mJ/pulse. Ab initio calculations at the G3 level of theory, show that SiH2 + NH3 should form an initial adduct (donor-acceptor complex), but that energy barriers are too great for further reaction of the adduct. This implies that SiH2 + NH3 should be a pressure dependent association reaction. The experimental data are inconsistent with this and we conclude that SiH2 decays are better explained by reaction of SiH2 with the amino radical, NH2, formed by photodissociation of NH3 at 193 nm. The mechanism of this previously unstudied reaction is discussed

On the Initial Conditions for Brane Inflation

String theory gives rise to various mechanisms to generate primordial inflation, of which ``brane inflation'' is one of the most widely considered. In this scenario, inflation takes place while two branes are approaching each other, and the modulus field representing the separation between the branes plays the role of the inflaton field. We study the phase space of initial conditions which can lead to a sufficiently long period of cosmological inflation, and find that taking into account the possibility of nonvanishing initial momentum can significantly change the degree of fine tuning of the required initial conditions.Comment: 11 pages, 2 figure

Evidence of Linkage in a Hispanic Cohort with a Class III Dentofacial Phenotype

Despite the prevalence of craniofacial disorders, the genetic contribution remains poorly understood. Class III malocclusion represents a specific craniofacial problem that can be handicapping, both functionally and socially. We hypothesized that the Class III phenotype is genetically linked to specific loci that regulate maxillary or mandibular growth. To determine the region linked to the Class III phenotype in four Hispanic families, we performed a genome-wide scan and linkage analysis using 500 microsatellite markers. Pedigree and linkage analyses revealed that the Class III phenotype (primarily maxillary deficiency) segregates in an autosomal-dominant manner, and that 5 loci (1p22.1, 3q26.2, 11q22, 12q13.13, and 12q23) are suggestive of linkage. Candidate genes within the 12q23 region (ZLR = 2.93) include IGF1, HOXC, and COL2A1. Chromosome 1 results (ZLR = 2.92) were similar to those reported previously in an Asian cohort with mandibular prognathism, suggesting that a common upstream genetic element may be responsible for both mandibular prognathism and maxillary deficiency

Sox2 Is Required for Maintenance and Differentiation of Bronchiolar Clara, Ciliated, and Goblet Cells

The bronchioles of the murine lung are lined by a simple columnar epithelium composed of ciliated, Clara, and goblet cells that together mediate barrier function, mucociliary clearance and innate host defense, vital for pulmonary homeostasis. In the present work, we demonstrate that expression of Sox2 in Clara cells is required for the differentiation of ciliated, Clara, and goblet cells that line the bronchioles of the postnatal lung. The gene was selectively deleted in Clara cells utilizing Scgb1a1-Cre, causing the progressive loss of Sox2 in the bronchioles during perinatal and postnatal development. The rate of bronchiolar cell proliferation was decreased and associated with the formation of an undifferentiated, cuboidal-squamous epithelium lacking the expression of markers of Clara cells (Scgb1a1), ciliated cells (FoxJ1 and α-tubulin), and goblet cells (Spdef and Muc5AC). By adulthood, bronchiolar cell numbers were decreased and Sox2 was absent in extensive regions of the bronchiolar epithelium, at which time residual Sox2 expression was primarily restricted to selective niches of CGRP staining neuroepithelial cells. Allergen-induced goblet cell differentiation and mucus production was absent in the respiratory epithelium lacking Sox2. In vitro, Sox2 activated promoter-luciferase reporter constructs for differentiation markers characteristic of Clara, ciliated, and goblet cells, Scgb1a1, FoxJ1, and Agr2, respectively. Sox2 physically interacted with Smad3 and inhibited TGF-β1/Smad3-mediated transcriptional activity in vitro, a pathway that negatively regulates proliferation. Sox2 is required for proliferation and differentiation of Clara cells that serve as the progenitor cells from which Clara, ciliated, and goblet cells are derived

HIF-1alpha and HIF-2alpha are differentially activated in distinct cell populations in retinal ischaemia.

BACKGROUND: Hypoxia plays a key role in ischaemic and neovascular disorders of the retina. Cellular responses to oxygen are mediated by hypoxia-inducible transcription factors (HIFs) that are stabilised in hypoxia and induce the expression of a diverse range of genes. The purpose of this study was to define the cellular specificities of HIF-1alpha and HIF-2alpha in retinal ischaemia, and to determine their correlation with the pattern of retinal hypoxia and the expression profiles of induced molecular mediators. METHODOLOGY/PRINCIPAL FINDINGS: We investigated the tissue distribution of retinal hypoxia during oxygen-induced retinopathy (OIR) in mice using the bio-reductive drug pimonidazole. We measured the levels of HIF-1alpha and HIF-2alpha proteins by Western blotting and determined their cellular distribution by immunohistochemistry during the development of OIR. We measured the temporal expression profiles of two downstream mediators, vascular endothelial growth factor (VEGF) and erythropoietin (Epo) by ELISA. Pimonidazole labelling was evident specifically in the inner retina. Labelling peaked at 2 hours after the onset of hypoxia and gradually declined thereafter. Marked binding to Müller glia was evident during the early hypoxic stages of OIR. Both HIF-1alpha and HIF-2alpha protein levels were significantly increased during retinal hypoxia but were evident in distinct cellular distributions; HIF-1alpha stabilisation was evident in neuronal cells throughout the inner retinal layers whereas HIF-2alpha was restricted to Müller glia and astrocytes. Hypoxia and HIF-alpha stabilisation in the retina were closely followed by upregulated expression of the downstream mediators VEGF and EPO. CONCLUSIONS/SIGNIFICANCE: Both HIF-1alpha and HIF-2alpha are activated in close correlation with retinal hypoxia but have contrasting cell specificities, consistent with differential roles in retinal ischaemia. Our findings suggest that HIF-2alpha activation plays a key role in regulating the response of Müller glia to hypoxia

Alpha-band rhythms in visual task performance: phase-locking by rhythmic sensory stimulation

Oscillations are an important aspect of neuronal activity. Interestingly, oscillatory patterns are also observed in behaviour, such as in visual performance measures after the presentation of a brief sensory event in the visual or another modality. These oscillations in visual performance cycle at the typical frequencies of brain rhythms, suggesting that perception may be closely linked to brain oscillations. We here investigated this link for a prominent rhythm of the visual system (the alpha-rhythm, 8-12 Hz) by applying rhythmic visual stimulation at alpha-frequency (10.6 Hz), known to lead to a resonance response in visual areas, and testing its effects on subsequent visual target discrimination. Our data show that rhythmic visual stimulation at 10.6 Hz: 1) has specific behavioral consequences, relative to stimulation at control frequencies (3.9 Hz, 7.1 Hz, 14.2 Hz), and 2) leads to alpha-band oscillations in visual performance measures, that 3) correlate in precise frequency across individuals with resting alpha-rhythms recorded over parieto-occipital areas. The most parsimonious explanation for these three findings is entrainment (phase-locking) of ongoing perceptually relevant alpha-band brain oscillations by rhythmic sensory events. These findings are in line with occipital alpha-oscillations underlying periodicity in visual performance, and suggest that rhythmic stimulation at frequencies of intrinsic brain-rhythms can be used to reveal influences of these rhythms on task performance to study their functional roles