Improved Algorithms for Recognizing Perfect Graphs and Finding Shortest Odd and Even Holes

Various classes of induced subgraphs are involved in the deepest results of graph theory and graph algorithms. A prominent example concerns the {\em perfection} of $G$ that the chromatic number of each induced subgraph $H$ of $G$ equals the clique number of $H$. The seminal Strong Perfect Graph Theorem confirms that the perfection of $G$ can be determined by detecting odd holes in $G$ and its complement. Chudnovsky et al. show in 2005 an $O(n^9)$ algorithm for recognizing perfect graphs, which can be implemented to run in $O(n^{6+\omega})$ time for the exponent $\omega<2.373$ of square-matrix multiplication. We show the following improved algorithms. 1. The tractability of detecting odd holes was open for decades until the major breakthrough of Chudnovsky et al. in 2020. Their $O(n^9)$ algorithm is later implemented by Lai et al. to run in $O(n^8)$ time, leading to the best formerly known algorithm for recognizing perfect graphs. Our first result is an $O(n^7)$ algorithm for detecting odd holes, implying an $O(n^7)$ algorithm for recognizing perfect graphs. 2. Chudnovsky et al. extend in 2021 the $O(n^9)$ algorithms for detecting odd holes (2020) and recognizing perfect graphs (2005) into the first polynomial algorithm for obtaining a shortest odd hole, which runs in $O(n^{14})$ time. We reduce the time for finding a shortest odd hole to $O(n^{13})$. 3. Conforti et al. show in 1997 the first polynomial algorithm for detecting even holes, running in about $O(n^{40})$ time. It then takes a line of intensive efforts in the literature to bring down the complexity to $O(n^{31})$, $O(n^{19})$, $O(n^{11})$, and finally $O(n^9)$. On the other hand, the tractability of finding a shortest even hole has been open for 16 years until the very recent $O(n^{31})$ algorithm of Cheong and Lu in 2022. We improve the time of finding a shortest even hole to $O(n^{23})$.Comment: 29 pages, 5 figure

Effect of diabetes on mortality and length of hospital stay in patients with renal or perinephric abscess

OBJECTIVES: We compared the risk of in-hospital mortality and the length of hospital stay between diabetic and non-diabetic patients hospitalized for renal or perinephric abscess. METHOD: The data analyzed in this study were retrieved from Taiwan's National Health Insurance claims. The risk of in-hospital mortality and the length of hospital stay were compared between 1,715 diabetic patients, hospitalized because of renal or perinephric abscess in Taiwan between 1997 and 2007, and a random sample of 477 non-diabetes patients with renal or perinephric abscess. RESULTS: The in-hospital mortality rates from renal or perinephric abscess for the diabetic patients and the non-diabetic patients were not different, at 2.3% and 3.4%, respectively. However, diabetes was significantly associated with a longer length of hospital stay among patients with renal abscess, by 3.38 days (95% confidence interval [CI]: 1.59-5.17). CONCLUSIONS: Diabetes does not increase the risk of in-hospital mortality from renal or perinephric abscess. Nevertheless, appropriate management of patients with diabetes and concurrent renal or perinephric abscess is essential to reduce the length of hospital stay

Using DMA to Simultaneously Acquire Young's Relaxation Modulus and Time-dependent Poisson's Ratio of a Viscoelastic Material

AbstractA method to obtain the Young's relaxation modulus and time-dependent Poisson's ratio simultaneously by using DMA is developed with the assumption of constant bulk modulus instead of constant Poisson's ratio. The constant bulk modulus is then calculated by either instantaneous response or the equilibrium response of the time-dependent Poisson's ratio. The modulating Young's moduli and characteristic times that measured by DMA are corrected analytically by using the developed formulas. The time-dependent Poisson's ratio is then obtained from the corrected modulating Young's moduli and the constant bulk modulus. As an application example, the method is applied to the DMA measurement of an epoxy molding compound (EMC). Although the correction to Young's relaxation modulus is very small, the viscoelastic Poisson's ratio varies significantly over time from 0.4 to 0.496, and can’t be assumed as a constant

Investigation of a Photoelectrochemical Passivated ZnO-Based Glucose Biosensor

A vapor cooling condensation system was used to deposit high quality intrinsic ZnO thin films and intrinsic ZnO nanorods as the sensing membrane of extended-gate field-effect-transistor (EGFET) glucose biosensors. The sensing sensitivity of the resulting glucose biosensors operated in the linear range was 13.4 μA mM−1 cm−2. To improve the sensing sensitivity of the ZnO-based glucose biosensors, the photoelectrochemical method was utilized to passivate the sidewall surfaces of the ZnO nanorods. The sensing sensitivity of the ZnO-based glucose biosensors with passivated ZnO nanorods was significantly improved to 20.33 μA mM−1 cm−2 under the same measurement conditions. The experimental results verified that the sensing sensitivity improvement was the result of the mitigation of the Fermi level pinning effect caused by the dangling bonds and the surface states induced on the sidewall surface of the ZnO nanorods

Quantitative thermal testing as a screening and follow-up tool for diabetic sensorimotor polyneuropathy in patients with type 2 diabetes and prediabetes

IntroductionThe diagnosis and assessment of neuropathy severity of diabetic sensorimotor polyneuropathy (DSPN) are mainly based on clinical neuropathy scores and electrophysiologic studies. This study aimed to determine whether quantitative thermal testing (QTT) can be used as a screening and follow-up tool for DSPN of prediabetes and type 2 diabetes at baseline and at 1-year follow-up.MethodsAll patients were assessed using the Toronto Clinical Neuropathy Score (TCNS) and underwent electrophysiological testing, including a nerve conduction study (NCS) and QTT, at baseline and at a 1-year follow-up. The TCNS and the composite scores of nerve conduction were used to assess the severity of DSPN. The DSPN status at the 1-year follow-up was classified as remaining no DSPN, remaining DSPN, regression to no DSPN, or progression to DSPN.ResultsDiabetic sensorimotor polyneuropathy was initially diagnosed in 89 patients with prediabetes and type 2 diabetes (22%). The regressed to no DSPN in 29 patients and progressed to DSPN in 20 patients at the 1-year follow-up. TCNS was significantly correlated with composite scores of nerve conduction, hand cold detection threshold (CDT), hand warm detection threshold (WDT), foot CDT, and foot WDT. Stepwise logistic regression demonstrated that the foot CDT (p &lt; 0.0001) was independently associated with the presence of DSPN. The TCNS, composite scores of the nerve conduction, hand WDT, hand CDT, foot WDT, and foot CDT were all statistically significant among the four different DSPN status groups at two different time periods (baseline and the 1-year follow-up).ConclusionThe foot CDT can be used as an initial screening tool for DSPN alternatively. The characteristics of nerve damage after 1 year of DSPN can be progressive or reversible, and the neurological functions of large and small fibers have a parallel trend, which can be objectively measured by NCS and QTT

A novel deep intronic variant strongly associates with Alkaptonuria.

Alkaptonuria is a rare autosomal recessive inherited disorder of tyrosine metabolism, which causes ochronosis, arthropathy, cardiac valvular calcification, and urolithiasis. The epidemiology of alkaptonuria in East Asia is not clear. In this study, patients diagnosed with alkaptonuria from January 2010 to June 2020 were reviewed. Their clinical and molecular features were further compared with those of patients from other countries. Three patients were found to have alkaptonuria. Mutation analyses of the homogentisate 1,2-dioxygenase gene (HGD) showed four novel variants c.16-2063 A > C, p.(Thr196Ile), p.(Gly344AspfsTer25), and p.(Gly362Arg) in six mutated alleles (83.3%). RNA sequencing revealed that c.16-2063 A > C activates a cryptic exon, causing protein truncation p.(Tyr5_Ile6insValTer17). A literature search identified another 6 patients with alkaptonuria in East Asia; including our cases, 13 of the 18 mutated alleles have not been reported elsewhere in the world. Alkaptonuria is rare in Taiwan and East Asia, with HGD variants being mostly novel and private

Non-Typhoidal Salmonella and the Risk of Kawasaki Disease: A Nationwide Population-Based Cohort Study

ObjectiveThe aim of this study was to investigate the relationship between non-typhoidal Salmonella (NTS) infection and the risk of Kawasaki disease (KD) by using a nationwide population-based data set in Taiwan.MethodsIn this retrospective cohort study, we enrolled 69,116 patients under 18 years of age, with NTS from January 1st, 2000, to December 31st, 2013, using the population-based National Health Insurance Research Database of Taiwan. A comparison group without NTS was matched (at a 1:4 ratio) by propensity score. The two cohorts were followed from the initial diagnosis of NTS until the date of KD development or December 31st, 2013. Cox proportional hazard regression analysis was conducted to estimate hazard ratios (HRs) and 95% confidence intervals (CIs) after adjusting for covariates. Also, we conducted sensitivity analyses to examine our findings.ResultsAfter adjusting for covariates, the risk of KD for the children with NTS was significantly higher than that of the comparison group (hazard ratio = 1.31; 95% confidence interval = 1.03-1.66; p &lt; 0.01). Stratified analysis showed that the associated risk of the investigated outcome was significant in children aged ≤2 years (aHR= 1.31, 95% C.I. 1.02-1.69), in female patients (aHR= 1.46, 95% C.I. 1.03-2.08), and in those without allergic diseases.ConclusionsNTS is associated with an increased risk of KD in Taiwanese children

What Drives Animal Fluency Performance in Cantonese-Speaking Chinese Patients with Adult-Onset Psychosis?

Among the numerous studies investigating semantic factors associated with functioning in psychotic patients, most have been conducted on western populations. By contrast, the current cross-sectional study involved native Cantonese-speaking Chinese participants. Using the category fluency task, we compared performance between patients and healthy participants and examined clinical and sociodemographic correlates. First-episode psychosis patients (n = 356) and gender- and age-matched healthy participants (n = 35) were asked to generate as many ‘animals’ as they could in a minute. As expected, patients generated fewer correct responses (an average of 15.5 vs. 22.9 words), generated fewer clusters (an average of 3.7 vs. 5.4 thematically grouped nouns), switched less between clusters (on average 8.0 vs. 11.9 switches) and, interestingly, produced a larger percentage of Chinese zodiac animals than healthy participants (an average of 37.7 vs. 24.2). However, these significant group differences in the clusters and switches disappeared when the overall word production was controlled for. Within patients, education was the strongest predictor of category fluency performance (namely the number of correct responses, clusters, and switches). The findings suggest that an overall slowness in patients may account for the group differences in category fluency performance rather than any specific abnormality per se

HbA1C Variability Is Strongly Associated With the Severity of Peripheral Neuropathy in Patients With Type 2 Diabetes

Variability in HbA1c is associated with a higher risk of cardiovascular disease and microvascular complications in patients with type 2 diabetes. The present study evaluated the severity of somatic nerve dysfunction at different stages of chronic glycemic impairment, and its correlation with different cardio-metabolic parameters. The study was conducted on 223 patients with type 2 diabetes. We calculated the intrapersonal mean, standard deviation (SD), and coefficient of variation of HbA1c for each patient using all measurements obtained for 3 years prior to the study. Patients were divided into quartiles according to the SD of HbA1c, and we constructed composite scores of nerve conduction as the severity of peripheral neuropathy. Linear regression analysis was performed to evaluate the influence of independent variables on mean composite scores. Those with higher SD-HbA1c had a higher body mass index, mean and index HbA1c, triglyceride and uric acid level, urinary albumin excretion and albumin-creatinine ratio, proportion of insulin therapy, and prevalence of hypertension as the underlying diseases, but lower estimate glomerular filtration rate (eGFR). In addition, those with higher SD-HbA1c showed lower amplitudes and reduced motor nerve conduction velocity in tested nerves, and lower sensory nerve conduction velocity in the sural nerve. Furthermore, those with higher SD-HbA1c had higher composite scores of low extremities. Multiple linear regression analysis revealed that diabetes duration, SD-HbA1c, and eGFR were independently associated with mean composite scores. Based on our results, HbA1c variability plus chronic glycemic impairment is strongly associated with the severity of peripheral neuropathy in patients with type 2 diabetes. Aggressively control blood glucose to an acceptable range and avoid blood glucose fluctuations by individualized treatment to prevent further nerve damage