Random walks on directed graphs and orientations of graphs

We apply spectral theory to study random processes involving directed graphs. In the first half of this thesis, we examine random walks on directed graphs, which is rooted in the study of non-reversible Markov chains. We prove bounds on key spectral invariants which play a role in bounding the rate of convergence of the walk and capture isoperimetric properties of the directed graph. We first focus on the principal ratio, which is the ratio of maximum to minimum values of vertices in the stationary distribution. Improving upon previous bounds, we give a sharp upper bound for this ratio over all strongly connected graphs on $n$ vertices. We characterize all graphs achieving the upper bound and give explicit constructions for these extremal graphs. Additionally, we show that under certain conditions, the principal ratio is tightly bounded. We then turn our attention to the first nontrivial Laplacian eigenvalue of a strongly connected directed graph. We give a lower bound for this eigenvalue, extending an analogous result for undirected graphs to the directed case. Our results on the principal ratio imply this lower bound can be factorially small in the number of vertices, and we give a construction having this eigenvalue factorially small. In the second half, we apply spectral tools to study orientations of graphs. We focus on counting orientations yielding strongly connected directed graphs, called strong orientations. Namely, we show that under a mild spectral and minimum degree condition, a possibly irregular, sparse graph $G$ has ``many" strong orientations. More precisely, given a graph $G$ on $n$ vertices, orient each edge in either direction with probability $1/2$ independently. We show that if $G$ satisfies a minimum degree condition of $(1+c_1)\log_2{n}$ and has Cheeger constant at least $c_2\frac{\log_2\log_2{n}}{\log_2{n}}$, then the resulting randomly oriented directed graph is strongly connected with high probability. This Cheeger constant bound can be replaced by an analogous spectral condition via the Cheeger inequality. Additionally, we provide an explicit construction to show our minimum degree condition is tight while the Cheeger constant bound is tight up to a $\log_2\log_2{n}$ factor. We conclude by exploring related future work

Relationship Between Genomic Damage and Clinical Features in Dialysis Patients

Patients with end-stage renal disease display enhanced genomic damage. We investigated the presence of genomic damage in the peripheral lymphocytes by using the micronucleus (MN) test and the factors associated with the MN frequency in hemodialysis (HD) and peritoneal dialysis (PD) patients. We studied 121 dialysis patients (60 HD and 61 PD) and 129 age-and gender-matched healthy controls. The MN analysis, used as a biomarker of chromosomal/DNA damage, was performed in peripheral lymphocytes by the cytokinesis-block method. Univariate analysis showed a significantly higher MN frequency in all patients in comparison with the controls (7.6% +/- 0.3% vs. 4.9% +/- 0.2%, respectively, p < 0.001). Significantly higher frequency of MN was observed in both HD and PD patients compared to controls (7.7% +/- 0.5% vs. 4.9% +/- 0.2%, p < 0.001 and 7.5% +/- 0.5% vs. 4.9% +/- 0.2%, p < 0.001, respectively). Multivariate analysis was performed, and it showed that the low-density lipoprotein level was the only independent determinant of increasing MN frequency in our patients (beta = 0.16, t = 2.172, p < 0.05). There is no significant difference in terms of genomic damage between two dialysis modalities, which suggests that PD may not be a more reliable choice in terms of genomic damage

Relationship Between Activity of Gluthatione Peroxidase and Nitric Oxide in Synovial Fluid and the Progression of Temporomandibular Joint Internal Derangement

SALMANOGLU, BERRIN/0000-0003-4344-5782WOS: 000355236700008PubMed: 25974819The purposes of this study were to measure the activity of glutathione peroxidase (GPX) and nitric oxide (NO) in the synovial fluid of patients with temporomandibular joint (TMJ) internal derangement (ID) and to indicate the relationship between the activity of GPX and NO and the progress of the ID. Twenty-six patients with TMJ ID were identified and classified according to Wilkes staging through clinical and radiologic examinations. Levels of GPX were determined indirectly by a coupled reaction with glutathione reductase. Levels of NO were measured colorimetrically. The activity of GPX and NO was observed to be progressively increasing as the stage of the TMJ ID progressed. There were significant correlations between the 2 substances and the Wilkes stages. Oxidative stress may have a role in the pathogenesis of TMJ ID. In synovial fluid, GPX and NO activities are increased as the stage of the disease increased. Increase in the activities of GPX might not be enough to prevent progression of the TMJ ID

DNA repair XRCC1 Arg399Gln polymorphism is associated with the risk of development of end-stage renal disease

Patients with end-stage renal disease (ESRD) display enhanced genomic damage. DNA repair gene polymorphisms may affect DNA repair capacity and modulate susceptibility to ESRD. In this study, we aimed to determine the frequency of polymorphisms in two DNA repair enzyme genes, Xeroderma pigmentosum complementation group D (XPD) and X-ray cross-complementing group 1 (XRCC1), in patients with ESRD and to evaluate their association with ESRD development. By using polymerase chain reaction (PCR) and restriction fragment length polymorphism (RFLP), we genotyped four single nucleotide polymorphisms (SNPs) in XPD codons 312 and 751 and XRCC1 codons 194 and 399 in 136 dialysis patients (71 patients undergoing hemodialysis and 65 subjected to peritoneal dialysis) and 147 healthy controls. Patients having XRCC1 399 Arg/Gln (OR:1.98; 95% CI: 1.21-3.25, P = 0.007) or XRCC1-399 Gln/Gln (OR: 3.95; 95% CI: 1.45-10.76, P = 0.005) genotype had a significantly higher risk of ESRD than those with XRCC1 399 Arg/Arg genotype. We also found a significantly higher frequency of the XRCC1 399Gln allele in patients with ESRD than in controls, with OR = 2.03 (95% CI = 1.08-3.81, P = 0.03). We further investigated the potential combined effect of these DNA repair variants on the risk of ESRD development. It was found that combination of the Arg/Gln or Gln/Gln genotypes of XRCC1 Arg399Gln polymorphism with the two possible genotypes of XPD-Asp312Asn or with the Lys/Gln or Gln/Gln genotypes of XPD Lys751Gln was significantly associated with the development of ESRD. This is the first report showing an association between DNA repair gene polymorphisms and ESRD development, and suggests that XRCC1 Arg399Gln polymorphism may confer increased risk for the development of the disease. Further larger studies should be conducted to confirm these results

Polymorphisms of the DNA Repair Genes XPD and XRCC1 and the Risk of Age-Related Macular Degeneration

PURPOSE. Oxidative stress seems to be an important factor in the development of age-related macular degeneration (AMD). The role of DNA repair mechanisms has also received attention recently in AMD pathogenesis. This case-control study was conducted to determine the frequency of polymorphisms in two DNA repair enzyme genes, xeroderma pigmentosum complementation group D (XPD), codons 312 and 751, and x-ray cross-complementing group 1 (XRCC1), codons 194 and 399, in patients with AMD and in disease-free control subjects

A comparison of panoramic radiography and cone beam computed tomography in the detection of osteosynthesis complications in sheep mandibular angle fractures.

Objective. The aim of this study was to compare the diagnostic efficacy of panoramic radiography (PANO) and cone beam computed tomography (CBCT) in detecting simulated complications of plate osteosynthesis applied to mandibular angle fractures (MAFs)

Sextant Biopsy-Based Criteria for Clinically Insignificant Prostate Cancer Are Also Valid for the 12-Core Prostate Biopsy Scheme: A Multicenter Study of Urooncology Association, Turkey

Background: Epstein criteria based on sextant biopsy are assumed to be valid for 12-core biopsies. However, very scarce information is present in the current literature to support this view. Objectives: To investigate the validity of Epstein criteria for clinically insignificant prostate cancer (PCa) in a cohort of the currently utilized 12-core prostate biopsy (TRUS-Bx) scheme in patients with low-risk and intermediate-risk PCa. Method: Pathological findings were separately evaluated in the areas matching the sextant biopsy (6-core paramedian) scheme and in all 12-core schemes. Patients were divided into 2 groups according to the final pathology report of RP as true clinically significant PCa (sPCa) and insignificant PCa (insPCa) groups. Predictive factors (including Epstein criteria) and cutoff values for the presence of insPCa were separately evaluated for 6- and 12-core TRUS-Bx schemes. Then, different predictive models based on Epstein criteria with or without additional biopsy findings were created. Results: A total of 442 patients were evaluated. PSA density, biopsy GS, percentage of tumor and number of positive cores, PNI, and HG-PIN were independent predictive factors for insPCa in both TRUS-Bx schemes. For the 12-core scheme, the best cutoff values of tumor percentage and number of positive cores were found to be = 50% (OR: 3.662) and 1.5 cores (OR: 2.194), respectively. The best predictive model was found to be that which added 3 additional factors (PNI and HG-PIN absence and number of positive cores) to Epstein criteria (OR: 6.041). Conclusions: Using a cutoff value of 1 for the number of positive biopsy cores and absence of biopsy PNI and HG-PIN findings can be more useful for improving the prediction model of the Epstein criteria in the 12-core biopsy scheme