On the signature of positive braids and adjacency for torus knots

The objects of study in this thesis are knots. More precisely, positive braid knots, which include algebraic knots and torus knots. In the first part of this thesis, we compare two classical knot invariants - the genus g and the signature σ - for positive braid knots. Our main result on positive braid knots establishes a linear lower bound for the signature in terms of the genus. In the second part of the thesis, a positive braid approach is applied to the study of the local behavior of polynomial functions from the complex affine plane to the complex numbers. After endowing polynomial function germs with a suitable topology, the adjacency problem arises: for a fixed germ f, what classes of germs g can be found arbitrarily close to f? We introduce two purely topological notions of adjacency for knots and discuss connections to algebraic notions of adjacency and the adjacency problem.

The volume of positive braid links

Based on recent work by Futer, Kalfagianni and Purcell, we prove that the volume of sufficiently complicated positive braid links is proportional to the signature defect Δσ = 2g−σ.

Subtyping schizophrenia: A comparison of positive/negative and system-specific approaches

BACKGROUND Schizophrenia is a heterogeneous disorder. Over the years, different approaches have been proposed to approach this heterogeneity by categorizing symptom patterns. The study aimed to compare positive/negative and system-specific approaches to subtyping. METHODS We used the Positive and Negative Syndrome Scale (PANSS) and Bern Psychopathology Scale (BPS), which consists of subscales for three domains (language, affect and motor behavior) that are hypothesized to be related to specific brain circuits, to assess cross-sectional psychopathological characteristics in a sample of 100 inpatients with schizophrenia spectrum disorders. We then categorized participants into positive/negative and system-specific subgroups to allow comparisons of the two approaches. RESULTS The analyses revealed correlations between the PANSS positive subscore and the BPS affective subscore (r=.446, p<.001) and between the PANSS negative subscore and the BPS motor behavior subscore (r=.227, p=.023). As regards the positive and negative subtype, more participants were classified as positive in the language-dominant subtype (30.3%) and affect-dominant subtype (30.3%), whereas more were classified as negative in the motor behavior-dominant subtype (44.4%). However, most patients met the criteria for the mixed subtype. CONCLUSIONS The results suggest that the positive/negative and system-specific approaches can be regarded as complementary. Future studies should examine both approaches in a longitudinal assessment of psychopathological symptoms and link them with qualitative-phenomenological approaches.

Patterns of positive selection in seven ant genomes

The evolution of ants is marked by remarkable adaptations that allowed the development of very complex social systems. To identify how ant-specific adaptations are associated with patterns of molecular evolution, we searched for signs of positive selection on amino-acid changes in proteins. We identified 24 functional categories of genes which were enriched for positively selected genes in the ant lineage. We also reanalyzed genome-wide datasets in bees and flies with the same methodology, to check whether positive selection was specific to ants or also present in other insects. Notably, genes implicated in immunity were enriched for positively selected genes in the three lineages, ruling out the hypothesis that the evolution of hygienic behaviors in social insects caused a major relaxation of selective pressure on immune genes. Our scan also indicated that genes implicated in neurogenesis and olfaction started to undergo increased positive selection before the evolution of sociality in Hymenoptera. Finally, the comparison between these three lineages allowed us to pinpoint molecular evolution patterns that were specific to the ant lineage. In particular, there was ant-specific recurrent positive selection on genes with mitochondrial functions, suggesting that mitochondrial activity was improved during the evolution of this lineage. This might have been an important step toward the evolution of extreme lifespan that is a hallmark of ants.

Effects of Antiseptic Solutions Commonly Used in Dentistry on Bone Viability, Bone Morphology, and Release of Growth Factors

PURPOSE Antiseptic solutions are commonly used in dentistry for a number of sterilization procedures, including harvesting of bone chips, irrigation of extraction sockets, and sterilization of osteonecrotic bone. Despite its widespread use, little information is available regarding the effects of various antiseptic solutions on bone cell viability, morphology, and the release of growth factors. MATERIALS AND METHODS The antiseptic solutions included 1) 0.5% povidone iodine (PI), 2) 0.2% chlorhexidine diguluconate (CHX), 3) 1% hydrogen peroxide (H2O2), and 4) 0.25% sodium hypochlorite (HYP). Bone samples collected from porcine mandibular cortical bone were rinsed in the antiseptic solutions for 10 minutes and assessed for cell viability using an MTS assay and protein release of transforming growth factor (TGF-β1), bone morphogenetic protein 2 (BMP2), vascular endothelial growth factor (VEGF), interleukin (IL)-1β, and receptor activator of nuclear factor κB ligand (RANKL) using an enzyme-linked immunosorbent assay at 15 minutes and 4 hours after rinsing. RESULTS After antiseptic rinsing, changes to the surface protein content showed marked alterations, with an abundant protein layer remaining on CHX-rinsed bone samples. The amount of surface protein content gradually decreased in the following order: CHX, H2O2, PI, and HYP. A similar trend was also observed for the relative cell viability from within bone samples after rinsing, with up to 6 times more viable cells found in the CHX-rinsed bone samples than in the HYP- and PI-rinsed samples. An analysis of the growth factors found that both HYP and PI had significantly lower VEGF and TGF-β1 protein release from bone samples at 15 minutes and 4 hours after rinsing compared with CHX and H2O2. A similar trend was observed for RANKL and IL-1β protein release, although no change was observed for BMP2. CONCLUSIONS The results from the present study have demonstrated that antiseptic solutions present with very different effects on bone samples after 10 minutes of rinsing. Rinsing with CHX maintained significantly higher cell viability and protein release of growth factors potent to the bone remodeling cycle.

The Socioeconomics of Consumption: Solutions to the Problems of Interest, Knowledge, and Identity

This paper is a review of the socio-economic literature on consumption. Considering consumption as a social activity, it examines how consumption solves the problems of interest, knowledge, and identity. It also discusses the main themes and important contributions in each category and offers suggestions for further research.

A STUDY ON THE EPIDEMIOLOGY OF POSITIVE PHYSICAL HEALTH (NHANES I)

HANES 1 detailed sample data were used to operationalize a definition of health in the absence of disease and to describe and compare the characteristics of the normal (healthy) group versus an abnormal (unhealthy) group.^ Parallel screening gave a 3.8 percent prevalence proportion of physical health, with a female:male ratio of 2:1 and younger ages in the healthy group. Statistically significant Mantel-Haenszel gender-age-adjusted odds ratios (MHOR) were estimated among abnormal non-migrants (1.53), skilled workers/unemployed (1.76), annual family incomes of less than $10,000 (1.56), having ever smoked (1.58), and started smoking before 18 years of age (1.58). Significant MHOR were also found for abnormals for health promoting measures: non-iodized salt use (1.94), needed dental care (1.91); and for fair to poor perceived health (4.28), perceiving health problems (2.52), and low energy level (1.68). Significant protective effects for much to moderate recreational exercise (MHOR 0.42) and very active to moderate non-recreational activity (MHOR 0.49) were also obtained. Covariance analysis additive models detected statistically significant higher mean values for abnormals than normals for serum magnesium, hemoglobin, hematocrit, urinary creatinine, and systolic and diastolic blood pressures, and lower values for abnormals than normals for serum iron. No difference was detected for serum cholesterol. Significant non-additive joint effects were found for body mass index.^ The results suggest positive physical health can be measured with cross-sectional survey data. Gender differentials, and associations between ecologic, socioeconomic, hazardous risk factors, health promoting activities and physical health are in general agreement with published findings on studies of morbidity. Longitudinal prospective studies are suggested to establish the direction of the associations and to enhance present knowledge of health and its promoting factors. ^

Chemical composition of interstitial solutions from sediments of DSDP Legs 6-8, 11, 12, 14, 15, and 22

Through the Deep Sea Drilling Project samples of interstitial solutions of deeply buried marine sediments throughout the World Ocean have been obtained and analyzed. The studies have shown that in all but the most slowly deposited sediments pore fluids exhibit changes in composition upon burial. These changes can be grouped into a few consistent patterns that facilitate identification of the diagenetic reactions occurring in the sediments. Pelagic clays and slowly deposited (<1 cm/1000 yr) biogenic sediments are the only types that exhibit little evidence of reaction in the pore waters. In most biogenic sediments sea water undergoes considerable alteration. In sediments deposited at rates up to a few cm/1000 yr the changes chiefly involve gains of Ca(2+) and Sr(2+) and losses of Mg(2+) which balance the Ca(2+) enrichment. The Ca-Mg substitution may often reach 30 mM/kg while Sr(2+) may be enriched 15-fold over sea water. These changes reflect recrystallization of biogenic calcite and the substitution of Mg(2+) for Ca(2+) during this reaction. The Ca-Mg-carbonate formed is most likely a dolomitic phase. A related but more complex pattern is found in carbonate sediments deposited at somewhat greater rates. Ca(2+) and Sr(2+) enrichment is again characteristic, but Mg(2+) losses exceed Ca(2+) gains with the excess being balanced by SO4(post staggered 2-) losses. The data indicate that the reactions are similar to those noted above, except that the Ca(2+) released is not kept in solution but is precipitated by the HCO3(post staggered -) produced in SO4(post staggered 2-) reduction. In both these types of pore waters Na(+) is usually conservative, but K(+) depletions are frequent. In several partly consolidated sediment sections approaching igneous basement contact, very marked interstitial calcium enrichment has been found (to 5.5 g/kg). These phenomena are marked by pronounced depletion in Na(+), Si and CO2, and slight enhancement in Cl(-). The changes are attributed to exchange of Na(+) for Ca(2+) in silicate minerals forming from submarine weathering of igneous rocks such as basalts. Water is also consumed in these reactions, accounting for minor increases in total interstitial salinity. Terrigenous, organic-rich sediments deposited rapidly along continental margins also exhibit significant evidences of alteration. Microbial reactions involving organic matter lead to complete removal of SO4(post staggered 2-), strong HCO3(post staggered -) enrichment, formation of NH4(post staggered +), and methane synthesis from H2 and CO2 once SO4(post staggered 2-) is eliminated. K+ and often Na+ (slightly) are depleted in the interstitial waters. Ca(2+) depletion may occur owing to precipitation of CaCO3. In most cases interstitial Cl- remains relatively constant, but increases are noted over evaporitic strata, and decreases in interstitial Cl- are observed in some sediments adjacent to continents.

Geochemistry of hydrothermal solutions, ores, and biota from hydrothermal fields at the East Pacific Rise axis near 9°50'N

Hydrothermal solutions were examined in a circulation system that started to develop after the 1991 volcanic eruption in the axial segment of the EPR between 9°45'N and 9°52'N. Within twelve years after this eruption, diffusion outflow of hot fluid from fractures in basaltic lavas gave way to focused seeps of hot solutions through channels of hydrothermal sulfide edifices. An example of the field Q demonstrates that from 1991 to 2003 H2S concentrations decreased from 86 to 1 mM/kg, and the Fe/H2S ratio simultaneously increased by factor 1.7. This fact can explain disappearance of microbial mats that were widespread within the fields before 1991. S isotopic composition of H2S does not depend on H2S concentration. This fact testifies rapid evolution of the hydrothermal system in the early years of its evolution. Carbon in CH4 from hot fluid sampled in 2003 is richer in 12C isotope than carbon in fluid from the hydrothermal field at 21°N EPR. It suggests that methane comes to the Q field from more than one source. Composition of particulate matter in hydrothermal solutions indicates that it was contributed by biological material. Experimental solutions with labeled substrates (t<70°C) show evidence of active processes of methane oxidation and sulfate reduction. Our results indicate that, during 12-year evolution of the hydrothermal system, composition of its solutions evolved and approached compositions of solutions in mature hydrothermal systems of the EPR.