Weighted Szeg\H{o} Kernels on Planar Domains

We study properties of weighted Szeg\H{o} and Garabedian kernels on planar domains. Motivated by the unweighted case as explained in Bell's work, the starting point is a weighted Kerzman-Stein formula that yields boundary smoothness of the weighted Szeg\H{o} kernel. This provides information on the dependence of the weighted Szeg\H{o} kernel as a function of the weight. When the weights are close to the constant function $1$ (which corresponds to the unweighted case), it is shown that some properties of the unweighted Szeg\H{o} kernel propagate to the weighted Szeg\H{o} kernel as well. Finally, it is shown that the reduced Bergman kernel and higher order reduced Bergman kernels can be written as a rational combination of three unweighted Szeg\H{o} kernels and their conjugates, thereby extending Bell's list of kernel functions that are made up of simpler building blocks that involve the Szeg\H{o} kernel.Comment: 26 page

Weighted Bergman Kernels on Planar Domains

For a planar domain $D \subset \mathbb{C}$ and an admissible weight function $\mu$ on it, some aspects of the corresponding weighted Bergman kernel $K_{D, \mu}$ are studied. First, we obtain a precise relation between $K_{D, \mu}$ and the classical Bergman kernel $K_D$ near a smooth boundary point of $D$. Second, the weighted kernel $K_{D, \mu}$ gives rise to weighted metrics in the same way as the classical Bergman kernel does. Motivated by work of Mok, Ng, Chan--Yuan and Chan--Xiao--Yuan among others, we study the nature of holomorphic isometries from the disc $\mathbb{D} \subset \mathbb{C}$ with respect to the weighted Bergman metrics arising from weights of the form $\mu = K_{\mathbb{D}}^{-d}$ for some integer $d \ge 0$. Specific examples that are studied in detail include those in which the isometry takes values in $\mathbb{D}^n$ and $\mathbb{D} \times \mathbb{B}^n$ where each factor admits a weighted Bergman metric as above for possibly different non-negative integers $d$. Finally, the case of isometries between polydisks in possibly different dimensions, in which each factor has a different weighted Bergman metric as above, is also presented.Comment: 33 pages. Comments and suggestions are welcom

Data Mining Based on Semantic Similarity to mine new Association Rules

The problem of mining association rules in a database are introduced. Most of association rule mining approaches aim to mine association rules considering exact matches between items in transactions. A new algorithm called 201C;Improved Data Mining Based on Semantic Similarity to mine new Association Rules201D; which considers not only exact matches between items, but also the semantic similarity between them. Improved Data Mining (IDM) Based on Semantic Similarity to mine new Association Rules uses the concepts of an expert to represent the similarity degree between items, and proposes a new way of obtaining support and confidence for the association rules containing these items. An association rule is for ex: i.e. for a grocery store say 201C;30% of transactions that contain bread also contain milk; 2% of all transactions contain both of these items201D;. Here 30% is called the confidence of the rule, and 2% the support of the rule and this rule is represented as Bread F0E0; Milk. The problem is to find all association rules that satisfy user-specified minimum support and minimum confidence constraints. This paper then results that new rules bring more information about the database

Transformation formula for the Reduced Bergman kernel and its Application

In this article, we prove the transformation formula for the reduced Bergman kernels under proper holomorphic correspondences between bounded domains in the complex plane. As a corollary, we obtain the transformation formula for the reduced Bergman kernels under proper holomorphic maps. We also establish the transformation formula for the weighted reduced Bergman kernels under proper holomorphic maps. Finally, we provide an application of this transformation formula.Comment: 11 page

A comparative study of clinical and radiological outcome between cages and morselized bone graft in transforaminal lumbar interbody fusion surgery: a hospital-based study

Background: Degenerative spinal diseases resulting in neuropathic backache are managed by nerve root decompression with instrumented interbody fusion is the treatment of choice for these groups of patients when not managed conservatively.Methods: Hospital based, comparative, retrospective study was carried out in such patients who underwent transforaminal lumbar interbody fusion (TLIF) with either cage with bone graft or stand-alone autologous morselized bone graft. The clinical and radiological outcomes were compared in these two methods of interbody fusion to assess any significant difference between them. A total of 20 patients with lumbar canal stenosis and degenerative grade 1/2 spondylolisthesis who failed conservative management were operated by TLIF approach and were evaluated for post-operative improvement in Oswestry disability index (ODI) and interbody fusion on imaging at 6 months and 1 year postoperatively. Vertebral level of surgical intervention, intra-operative blood loss and duration of surgery were recorded for each patient along with complications, if any.Results: In our study there was no significant difference in the clinical and radiological outcome between the two methods of interbody fusion. Although the group which was offered morselized bone graft with cage showed slightly better clinical outcome at 6 months of follow up, both showed no significant difference in ODI at 1 year of follow up.Conclusions: With this study, we can conclude that both the methods have similar clinical and radiological outcome with similar patient satisfaction and can be interchangeably employed for interbody fusion according to surgeon’s and patient’s preferences

The sigma-1 receptor curtails endogenous opioid analgesia during sensitization of TRPV1 nociceptors

Background and Purpose: Peripheral sensitization contributes to pathological pain. While prostaglandin E2 (PGE2) and nerve growth factor (NGF) sensitize peptidergic C-nociceptors (TRPV1+), glial cell line-derived neurotrophic factor (GDNF) sensitizes non-peptidergic C-neurons (IB4+). Sigma-1 receptor (σ1R) is a Ca2+-sensing chaperone known to modulate analgesia induced by opioid drugs. This receptor binds both to TRPV1 and the µ-opioid receptor (MOPr), although the functional repercussions of these physical interactions in peripheral sensitization are unknown. Experimental Approach: We tested the effect of sigma-1 antagonism on PGE2-, NGF- and GDNF-induced mechanical and heat hyperalgesia in mice. We used immunohistochemistry to determine the presence of endomorphin-2, an endogenous MOPr agonist, on dorsal root ganglion (DRG) neurons. Recombinant proteins were used to study the interactions between σ1R, MOPr and TRPV1. We used calcium imaging to study the effects of sigma-1 antagonism on PGE2-induced sensitization of TRPV1+ nociceptors. Key Results: σ1R antagonists reversed PGE2- and NGF-induced hyperalgesia, but not GDNF-induced hyperalgesia. Endomorphin-2 was detected on TRPV1+ but not on IB4+ neurons. Peripheral opioid receptor antagonism by naloxone methiodide or administration of an anti-endomorphin-2 antibody to a sensitized paw, reversed the antihyperalgesia induced by sigma-1 antagonists. Sigma-1 antagonism transfers σ1R from TRPV1 to MOPr, suggesting that σ1R participate in TRPV1-MOPr crosstalk. Moreover, σ1R antagonism reversed, in a naloxone-sensitive manner, PGE2-induced sensitization of DRG neurons to the calcium flux elicited by capsaicin, the prototypic TRPV1 agonist. Conclusion and Implications: σ1R antagonism harnesses endogenous opioids produced by TRPV1+ neurons to reduce hyperalgesia by increasing MOPr activity

An international prospective study of INICC analyzing the incidence and risk factors for catheter-associated urinary tract infections in 235 ICUs across 8 Asian Countries

Background: Identify urinary catheter (UC)-associated urinary tract infections (CAUTI) incidence and risk factors (RF) in 235 ICUs in 8 Asian countries: India, Malaysia, Mongolia, Nepal, Pakistan, the Philippines, Thailand, and Vietnam. Methods: From January 1, 2014, to February 12, 2022, we conducted a prospective cohort study. To estimate CAUTI incidence, the number of UC days was the denominator, and CAUTI was the numerator. To estimate CAUTI RFs, we analyzed 11 variables using multiple logistic regression. Results: 84,920 patients hospitalized for 499,272 patient days acquired 869 CAUTIs. The pooled CAUTI rate per 1,000 UC-days was 3.08; for those using suprapubic-catheters (4.11); indwelling-catheters (2.65); trauma-ICU (10.55), neurologic-ICU (7.17), neurosurgical-ICU (5.28); in lower- middle-income countries (3.05); in upper-middle-income countries (1.71); at public-hospitals (5.98), at private-hospitals (3.09), at teaching-hospitals (2.04). The following variables were identified as CAUTI RFs: Age (adjusted odds ratio [aOR] = 1.01; 95% CI = 1.01-1.02; P < .0001); female sex (aOR = 1.39; 95% CI = 1.21-1.59; P < .0001); using suprapubic-catheter (aOR = 4.72; 95% CI = 1.69-13.21; P < .0001); length of stay before CAUTI acquisition (aOR = 1.04; 95% CI = 1.04-1.05; P < .0001); UC and device utilization-ratio (aOR = 1.07; 95% CI = 1.01-1.13; P = .02); hospitalized at trauma-ICU (aOR = 14.12; 95% CI = 4.68-42.67; P < .0001), neurologic-ICU (aOR = 14.13; 95% CI = 6.63-30.11; P < .0001), neurosurgical-ICU (aOR = 13.79; 95% CI = 6.88-27.64; P < .0001); public-facilities (aOR = 3.23; 95% CI = 2.34-4.46; P < .0001). Discussion: CAUTI rate and risk are higher for older patients, women, hospitalized at trauma-ICU, neurologic-ICU, neurosurgical-ICU, and public facilities. All of them are unlikely to change. Conclusions: It is suggested to focus on reducing the length of stay and the Urinary catheter device utilization ratio, avoiding suprapubic catheters, and implementing evidence-based CAUTI prevention recommendations