How large dimension guarantees a given angle?

We study the following two problems: (1) Given $n\ge 2$ and \al, how large Hausdorff dimension can a compact set A\su\Rn have if $A$ does not contain three points that form an angle \al? (2) Given \al and \de, how large Hausdorff dimension can a %compact subset $A$ of a Euclidean space have if $A$ does not contain three points that form an angle in the \de-neighborhood of \al? An interesting phenomenon is that different angles show different behaviour in the above problems. Apart from the clearly special extreme angles 0 and $180^\circ$, the angles $60^\circ,90^\circ$ and $120^\circ$ also play special role in problem (2): the maximal dimension is smaller for these special angles than for the other angles. In problem (1) the angle $90^\circ$ seems to behave differently from other angles

Gingival crevicular fluid MMP-8-concentrations in patients after acute myocardial infarction

<p>Abstract</p> <p>Background</p> <p>The aim of this study was to determine the presence of matrix metalloproteinase-8 in the gingival crevicular fluid (GCF) of patients after acute myocardial infarction (AMI).</p> <p>Methods</p> <p>A total of 48 GCF samples from 20 AMI patients, hospitalized at the Department of Cardiology and Angiology of the Johannes Gutenberg University Mainz, were investigated. Besides the myocardial infarction all patients suffered from chronic periodontal disease. Fifty-one GCF samples from 20 healthy age matched individuals with similar periodontal conditions served as controls. The dental examination included the assessment of oral hygiene, gingival inflammation, probing pocket depth, clinical attachment level and X-ray examination. The study was only carried out after the positive consent of the regional ethic commission. A quantitative assessment of aMMP-8 levels in the gingival crevicular fluid was performed with the help of the DentoAnalyzer (Dentognostics GmbH, Jena, Germany), utilising an immunological procedure.</p> <p>Results</p> <p>The aMMP-8 concentrations found in the gingival crevicular fluid of the AMI patients significantly differed (p = 0.001; mean value 30.33 ± 41.99 ng/ml aMMP-8) from the control group (mean value 10.0 ± 10.7 ng/ml aMMP-8). These findings suggest that periodontal inflammation in AMI patients might be associated with higher MMP-8-values compared to the healthy controls.</p> <p>Conclusions</p> <p>The acute myocardial infarction seems to influence the degree of periodontal inflammation, thus the measurement of the gingival crevicular fluid MMP8 levels seems to be a helpful biochemical test to obtain information about the severity of the periodontal disease.</p

Self-reported dental hygiene, obesity, and systemic inflammation in a pediatric rural community cohort

Background A growing body of epidemiologic evidence links oral health, obesity, and cardiovascular health, though few studies have reported on these relationships in children. While underlying mechanisms are unclear, adult studies have suggested sub-acute systemic inflammation, also implicated in the etiology of both obesity and cardiovascular disease. This study investigated associations between self-reported dental hygiene, obesity, and systemic inflammation in children. Methods 128 children \u3c 19 years of age from rural counties in West Virginia participated in a community-based health screening that included anthropometric assessments, blood collection, and a questionnaire about dental hygiene and self-assessed oral health. Results Participants ranged from 3.0-18.7 years. Univariate analysis demonstrated an association between parent-reported dental hygiene, including frequency of preventive dental care and parent-assessed overall dental health, and markers of systemic inflammation but not obesity. In multivariable regression, parent-assessed overall dental health and obesity were independent predictors of systemic inflammation, after adjustment for age, gender, and parent education. Conclusions This is the first known study of the association between dental hygiene, obesity, and systemic inflammation in children. These results highlight the importance of preventive dental care in overall, systemic health in children and are consistent with previous reports in adults

Garden and landscape-scale correlates of moths of differing conservation status: significant effects of urbanization and habitat diversity

Moths are abundant and ubiquitous in vegetated terrestrial environments and are pollinators, important herbivores of wild plants, and food for birds, bats and rodents. In recent years, many once abundant and widespread species have shown sharp declines that have been cited by some as indicative of a widespread insect biodiversity crisis. Likely causes of these declines include agricultural intensification, light pollution, climate change, and urbanization; however, the real underlying cause(s) is still open to conjecture. We used data collected from the citizen science Garden Moth Scheme (GMS) to explore the spatial association between the abundance of 195 widespread British species of moth, and garden habitat and landscape features, to see if spatial habitat and landscape associations varied for species of differing conservation status. We found that associations with habitat and landscape composition were species-specific, but that there were consistent trends in species richness and total moth abundance. Gardens with more diverse and extensive microhabitats were associated with higher species richness and moth abundance; gardens near to the coast were associated with higher richness and moth abundance; and gardens in more urbanized locations were associated with lower species richness and moth abundance. The same trends were also found for species classified as increasing, declining and vulnerable under IUCN (World Conservation Union) criteria

Multifractal tubes

Tube formulas refer to the study of volumes of $r$ neighbourhoods of sets. For sets satisfying some (possible very weak) convexity conditions, this has a long history. However, within the past 20 years Lapidus has initiated and pioneered a systematic study of tube formulas for fractal sets. Following this, it is natural to ask to what extend it is possible to develop a theory of multifractal tube formulas for multifractal measures. In this paper we propose and develop a framework for such a theory. Firstly, we define multifractal tube formulas and, more generally, multifractal tube measures for general multifractal measures. Secondly, we introduce and develop two approaches for analysing these concepts for self-similar multifractal measures, namely: (1) Multifractal tubes of self-similar measures and renewal theory. Using techniques from renewal theory we give a complete description of the asymptotic behaviour of the multifractal tube formulas and tube measures of self-similar measures satisfying the Open Set Condition. (2) Multifractal tubes of self-similar measures and zeta-functions. Unfortunately, renewal theory techniques do not yield "explicit" expressions for the functions describing the asymptotic behaviour of the multifractal tube formulas and tube measures of self-similar measures. This is clearly undesirable. For this reason, we introduce and develop a second framework for studying multifractal tube formulas of self-similar measures. This approach is based on multifractal zeta-functions and allow us obtain "explicit" expressions for the multifractal tube formulas of self-similar measures, namely, using the Mellin transform and the residue theorem, we are able to express the multifractal tube formulas as sums involving the residues of the zeta-function.Comment: 122 page

Periodontal disease and atherosclerosis from the viewpoint of the relationship between community periodontal index of treatment needs and brachial-ankle pulse wave velocity

BACKGROUND: It has been suggested that periodontal disease may be an independent risk factor for the development of atherosclerosis. However, the relationship between periodontal disease and atherosclerosis has not been fully elucidated. This study aimed to assess the effects of periodontal disease on atherosclerosis. METHODS: The study design was a cross-sectional study. Subjects were 291 healthy male workers in Japan. We used the Community Periodontal Index of Treatment Needs (CPITN) score, average probing depth and gingival bleeding index (rate of bleeding gums) to assess the severity of periodontal disease. We also used the Brachial-Ankle Pulse Wave Velocity (baPWV) as the index for the development of atherosclerosis. RESULTS: The unadjusted odds ratio (OR) of atherosclerosis in relation to the CPITN score was 1.41 [95% CI: 1.16–1.73]. However, after adjustment for age, systolic blood pressure and smoking, the CPITN score had no relationship with atherosclerosis (adjusted OR: 0.91 [0.68–1.20]). CONCLUSION: Our results show no relationship between mild periodontal disease and atherosclerosis after appropriate adjustments

Applicability of current staging/categorization of α-synuclein pathology and their clinical relevance

In Parkinson’s disease (PD) and dementia with Lewy bodies (DLB) α-synuclein (αS) pathology is seen that displays a predictable topographic distribution. There are two staging/categorization systems, i.e. Braak’s and McKeith’s, currently in use for the assessment of αS pathology. The aim of these diagnostic strategies in pathology is, in addition to assess the stage/severity of pathology, to assess the probabilities of the related clinical symptomatology i.e. dementia and extrapyramidal symptoms (EPS). Herein, we assessed the applicability of these two staging/categorization systems and the frequency of dementia and EPS in a cohort of 226 αS-positive-subjects. These subject were selected from a large autopsy sample (n = 1,720), irrespective of the clinical presentation, based on the detection of αS-immunoreactivity (IR) in one of the most vulnerable nuclei; in the dorsal motor nucleus of vagus, substantia nigra and basal forebrain. The frequency of αS-IR lesions in this large cohort was 14% (248 out of 1,720). If applicable, each of the 226 subjects with all required material available was assigned a neuropathological stage/category of PD/DLB and finally the neuropathological data was analyzed in relation to dementia and EPS. 83% of subjects showed a distribution pattern of αS-IR that was compatible with the current staging/categorization systems. Around 55% of subjects with widespread αS pathology (Braak’s PD stages 5–6) lacked clinical signs of dementia or EPS. Similarly, in respect to those subjects that fulfilled the McKeith criteria for diffuse neocortical category and displaying only mild concomitant Alzheimer’s disease-related pathology, only 48% were demented and 54% displayed EPS. It is noteworthy that some subjects (17%) deviated from the suggested caudo-rostral propagation suggesting alternative routes of progression, perhaps due to concomitant diseases and genetic predisposition. In conclusion, our results do indeed confirm that current staging/categorization systems can readily be applied to most of the subjects with αS pathology. However, finding that around half of the subjects with abundant αS pathology remain neurologically intact is intriguing and raises the question whether we do assess the actual disease process

Porphyromonas gingivalis suppresses adaptive immunity in periodontitis, atherosclerosis and Alzheimer’s disease

Porphyromonas gingivalis, a keystone pathogen in chronic periodontitis, has been found to associate with remote body organ inflammatory pathologies including atherosclerosis and Alzheimer’s disease (AD). Although P. gingivalis has a plethora of virulence factors, much of its pathogenicity is surprisingly related to the overall immunosuppression of the host. This review focuses on P. gingivalis aiding suppression of the host’s adaptive immune system involving manipulation of cellular immunological responses specifically T- and B-cells in periodontitis and related conditions. In periodontitis this bacterium inhibits the synthesis of IL-2 and increases humoral responses. This reduces inflammatory responses related to T- and B-cell activation, and subsequent IFN-ɤ secretion by a subset of T cells. The T cells further suppresses upregulation of programmed cell death-1 (PD-1)-receptor on CD+-cells and its ligand PD-L1 on CD11b+- subset of T-cells. IL-2 down-regulates immune response-regulated genes, induces a cytokine pattern in which the Th17 lineage is favored thereby modulating the Th17/ T-regulatory cell (Treg) imbalance. The suppression of IFN-ɤ stimulated release of interferon-inducible protein-10 (IP-10) chemokine ligands [ITAC (CXCL11) and Mig (CXCL9)] by P. gingivalis capsular serotypes, triggers distinct T-cell responses, and contributes to local immune evasion by release of its outer membrane vesicles. In atherosclerosis P. gingivalis reduces Tregs and transforming growth factor beta-1 (TGF-1) and causes imbalance in the Th17 lineage of the Treg population. In Alzheimer’s disease P. gingivalis may affect the blood-brain barrier permeability, and inhibit local IFN-ɤ response by preventing entry of immune cells into the brain. The scarcity of adaptive immune cells in Alzheimer’s disease neuropathology implies P. gingivalis infection of the brain likely causes impaired clearance of insoluble amyloid and induces immunosuppression. By the effective manipulation of the armory of adaptive immune suppression through a plethora of virulence factors P. gingivalis may act as a keystone organism in periodontitis and in related systemic diseases and other remote body inflammatory pathologies

An examination of periodontal treatment and per member per month (PMPM) medical costs in an insured population

BACKGROUND: Chronic medical conditions have been associated with periodontal disease. This study examined if periodontal treatment can contribute to changes in overall risk and medical expenditures for three chronic conditions [Diabetes Mellitus (DM), Coronary Artery Disease (CAD), and Cerebrovascular Disease (CVD)]. METHODS: 116,306 enrollees participating in a preferred provider organization (PPO) insurance plan with continuous dental and medical coverage between January 1, 2001 and December 30, 2002, exhibiting one of three chronic conditions (DM, CAD, or CVD) were examined. This study was a population-based retrospective cohort study. Aggregate costs for medical services were used as a proxy for overall disease burden. The cost for medical care was measured in Per Member Per Month (PMPM) dollars by aggregating all medical expenditures by diagnoses that corresponded to the International Classification of Diseases, 9(th )Edition, (ICD-9) codebook. To control for differences in the overall disease burden of each group, a previously calculated retrospective risk score utilizing Symmetry Health Data Systems, Inc. Episode Risk Groups™ (ERGs) were utilized for DM, CAD or CVD diagnosis groups within distinct dental services groups including; periodontal treatment (periodontitis or gingivitis), dental maintenance services (DMS), other dental services, or to a no dental services group. The differences between group means were tested for statistical significance using log-transformed values of the individual total paid amounts. RESULTS: The DM, CAD and CVD condition groups who received periodontitis treatment incurred significantly higher PMPM medical costs than enrollees who received gingivitis treatment, DMS, other dental services, or no dental services (p < .001). DM, CAD, and CVD condition groups who received periodontitis treatment had significantly lower retrospective risk scores (ERGs) than enrollees who received gingivitis treatment, DMS, other dental services, or no dental services (p < .001). CONCLUSION: This two-year retrospective examination of a large insurance company database revealed a possible association between periodontal treatment and PMPM medical costs. The findings suggest that periodontitis treatment (a proxy for the presence of periodontitis) has an impact on the PMPM medical costs for the three chronic conditions (DM, CAD, and CVD). Additional studies are indicated to examine if this relationship is maintained after adjusting for confounding factors such as smoking and SES