From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

Prognostic Factors in Patients Undergoing Pulmonary Resection for Sarcomatoid Carcinomas of the Lung.

BACKGROUND: Pulmonary sarcomatoid carcinomas are very rare lung neoplasms, and no consensus exists regarding their optimal treatment. The prognosis of sarcomatoid carcinomas has been reported to be unfavorable compared with non-small-cell lung cancers; however, prognostic factors in patients undergoing surgery for sarcomatoid carcinomas remain unclear. AIMS: To analyze clinicopathologic prognostic factors and survival outcomes in patients who underwent surgery for pulmonary sarcomatoid carcinoma. STUDY DESIGN: Retrospective cross-sectional study. METHODS: We designed a retrospective cross-sectional study in patients who underwent surgery for pulmonary sarcomatoid carcinomas and statistically analyzed the prognostic factors regarding clinicopathologic features with respect to survival outcomes. RESULTS: We had a total of 44 patients with sarcomatoid carcinoma who had pulmonary resection. Sex distribution was 34 (77%) males and 10 (22.7%) females, which was determined by declaration. The mean age of patients was 57.3 ± 16 years with a median of 60 years. The 5-year progression-free survival and overall survival rates were 59% and 58%, respectively. The 5-year survival rates were significantly different for tumors > 5 cm (P = 0.044), tumorstatus (T) (P=0.016), lymph node status (N) (P=0.005), and pathologic tumor-node-metastasis (TNM) stage (P = 0.0001 ). However, histologic subtype (P = 0.628) and adjuvant treatment (P = 0.804) did not have any significant effect on survival. Similarly, the significant prognostic factors in univariate analysis were tumor size (P = 0.085), T status (P = 0.005), N status (P = 0.028), and pathologic TNM stage (P = 0.0001). Multivariate analysis showed only T status (P = 0.058), N status (P = 0.018), and pathologic TNM stage (P = 0.019) as independent prognostic factors, with statistical power of 87%, 43.1% and 21.2%. CONCLUSION: Surgery appears to be an optimal treatment with favorable outcomes for patients with pulmonary sarcomatoid carcinoma. Patients with small tumors at earlier stages are very likely to benefit from surgery, regardless of histologic subtype

An adolescent girl with obstructive uropathy requiring nephro-ureterectomy was subsequently diagnosed with renal tuberculosis: case report

A 15-year-old girl was followed up for 2 years in a district hospital for management of vesicoureteral reflux and, subsequently, hydronephrosis of both kidneys and required bilateral ureteroneocystostomy. Despite surgery, there was continuous progression of the left hydronephrosis. Referral to a tertiary hospital because of continued sterile pyuria prompted investigation for tuberculosis (TB): she was diagnosed with bilateral pulmonary TB and urine culture confirmedMycobacterium tuberculosis. Despite tuberculous chemotherapy and dexamethasone, she required a left nephrectomy. Histology demonstrated necrotising granulomatous pyelonephritis. She remains well with normal function of the right kidney. Despite the rarity, chronic urinary tract disorders should always prompt investigation for tuberculosis

Discrepancies between clinical and pathological findings seen at renal biopsy in rheumatological diseases

Objective. Renal biopsy contributes to the diagnosis, follow-up, and treatment of many rheumatic conditions. This study assessed the diagnostic role and safety of renal biopsies in a tertiary rheumatology clinic. Methods. Renal biopsies performed between June 2020 and December 2022 were screened, and demographic, clinical, histopathological, and safety data were collected from patient records. Results. In this study, 33 males and 38 females were included. Except for 1 patient who received acetylsalicylic acid, antiaggregant, and/or anticoagulant drugs were stopped before the biopsy. Complications included a decrease of hemoglobin in 8 patients (11.3%) and microscopic hematuria in 40 patients (56.3%). Control ultra-sonography was performed in 16 patients (22.5%), and a self-limiting hematoma was found in 4 of them (5.6%) without additional complications. While less than 10 glomeruli were obtained in 9 patients (9.9%), diagnosis success was 94.4%. Histopathological data were consistent with one of the pre-biopsy diagnoses in 54 of 67 cases (80.6%) but showed discrepancies in 19.4% (n=13) of patients. A repeat biopsy was performed in 7 patients for re-staging or insufficient biopsy. Conclusions. Renal biopsy significantly contributes to rheumatology practice, especially in patients with complex clinical and laboratory findings or in whom different treatments can be given according to the presence, severity, and type of renal involvement. Although the possibility of obtaining insufficient tissue and the need for re-staging and repeat biopsy in the follow-up might be expected, complication risk does not seem to be a big concern. Renal biopsy often evidenced discrepancies between pre-biopsy diagnosis and histopathological findings

Small Cell Carcinomas of the Bladder Highly Express Somatostatin Receptor Type 2A: Impact on Prognosis and Treatment--A Multicenter Study of Urooncology Society, Turkey.

Small cell carcinoma (SmCC) is a rare and aggressive neuroendocrine carcinoma of the bladder. Neuroendocrine carcinomas expressing somatostatin receptors (SSTR) in other viscera such as lung, pancreas, and gastrointestinal system respond to therapy with somatostatin analogs. In the present study, expressions of SSTRs 1 to 5 including type 2A are investigated by immunohistochemistry (IHC) and their relationship with clinicopathologic factors was evaluated. Hundred primary bladder SmCC cases were collected from 12 centers in Turkey. Forty-three cases were pure SmCC. Other cases had mostly papillary urothelial carcinoma as a second component. The percentage of the SmCC component ranged from 5% to 100%. SSTR-2A expression was membranous, whereas the other receptors showed cytoplasmic staining. The percentages of positive cases for SSTR-1, SSTR-2A, SSTR-3, SSTR-4, and SSTR-5 were 4% (3/75), 61.4% (54/88), 2.4% (2/84), 24.4% (20/82), and 6.25% (5/80), respectively. The percentage of SmCC component was positively correlated with the percentage of SSTR-2A expression (P=0.003) while negatively correlated with patient age (P=0.032). SSTR-2A expression was correlated with survival as a bad prognostic factor (P=0.018). SSTR-1, SSTR-3, SSTR-4, and SSTR-5 expressions did not show any statistical significance with any parameter. In conclusion, although the limited number of cases with adequate term follow-up, SSTR-2A expression could be a prognostic factor and somatostatin analogs therapeutic candidate for SmCCs of the bladder as these tumors show high percentage of SSTR-2A expression