Geometric Quantization on the Super-Disc

In this article we discuss the geometric quantization on a certain type of infinite dimensional super-disc. Such systems are quite natural when we analyze coupled bosons and fermions. The large-N limit of a system like that corresponds to a certain super-homogeneous space. First, we define an example of a super-homogeneous manifold: a super-disc. We show that it has a natural symplectic form, it can be used to introduce classical dynamics once a Hamiltonian is chosen. Existence of moment maps provide a Poisson realization of the underlying symmetry super-group. These are the natural operators to quantize via methods of geometric quantization, and we show that this can be done.Comment: 17 pages, Latex file. Subject: Mathematical physics, geometric quantizatio

Finitely Many Dirac-Delta Interactions on Riemannian Manifolds

This work is intended as an attempt to study the non-perturbative renormalization of bound state problem of finitely many Dirac-delta interactions on Riemannian manifolds, S^2, H^2 and H^3. We formulate the problem in terms of a finite dimensional matrix, called the characteristic matrix. The bound state energies can be found from the characteristic equation. The characteristic matrix can be found after a regularization and renormalization by using a sharp cut-off in the eigenvalue spectrum of the Laplacian, as it is done in the flat space, or using the heat kernel method. These two approaches are equivalent in the case of compact manifolds. The heat kernel method has a general advantage to find lower bounds on the spectrum even for compact manifolds as shown in the case of S^2. The heat kernels for H^2 and H^3 are known explicitly, thus we can calculate the characteristic matrix. Using the result, we give lower bound estimates of the discrete spectrum.Comment: To be published in JM

Carotid Artery Stenting: A Single Center “Real World” Experience

BACKGROUND:Percutaneous carotid artery stenting (CAS) became a widely used procedure in patients with symptomatic and asymptomatic carotid artery stenosis. However its role compared to carotid endarterectomy (CAD) remains questioned. We analysed the safety of carotid artery stenting program of a prospective CAS register program of a tertiary teaching hospital. METHOD:Between July 2003 and December 2010, 208 patients underwent CAS procedure. Baseline, procedural and follow-up data were prospectively collected. Primary peri-interventional outcome was defined as 30-day major adverse events (MAE), including death, stroke or myocardial infarction, and mid- to long-term follow-up outcome included ipsilateral stroke, myocardial infarction or death. Secondary outcome was restenosis rate ≥ 50% per lesion. RESULTS:Unilateral carotid artery interventions were performed in 186 patients. In 22 patients CAS was performed bilaterally as stages procedures. The 30-day MAE rate was 1.9% consisting of two contralateral strokes and two ipsilateral stroke. Mean clinically follow-up was 22 months. Mid- to long-term MAE was 8.1% with 6.3% (n = 13) deaths, 1.9% (n = 4) myocardial infarctions and 0.9% (n = 2) ipsilateral stroke. The restenosis rate ≥ 50% per lesion was 4.3% at a mean follow-up of 22 months. Target lesion revascularization was performed in one patient, because of restenosis at 9 months follow-up after first CAS. CONCLUSION:Implementation of a carotid artery stenting program at a tertiary, teaching hospital is a safe method for treatment of carotid artery stenosis. The adverse event rate during mid-to-long-term follow-up suggests an appropriate patient selection

Leptin and resistin levels in serum of patients with hematologic malignancies: correlation with clinical characteristic

Aim:To evaluate leptin and resistin levels in patients with various hematologic malignancies. Methods: We included 21 patients with lymphoma, 14 with multiple myeloma (MM), 14 with acute leukemia, 13 with chronic lymphocytic leukemia (CLL), and 25 healthy control subjects into our study. The subjects’ body mass indexes (BMI) were calculated; hematological and acute phase response parameters, serum lipid were determined; serum leptin and resistin levels were determined by ELISA. Results: Serum leptin level was significantly increased in CLL and MM groups when compared to the control group (p < 0.01). Resistin level was significantly higher in lymphoma patients than in CLL, acute leukemia and control groups (p < 0.01). In the control group, leptin level was negatively correlated with hemoglobin level (r = –0.44, p = 0.047); and in all patients with hematologic malignancies, leptin level was correlated with BMI (r = 0.32, p = 0.02). Leptin in lymphoma subjects correlated with hemoglobin level (r = 0.64, p = 0.005), resistin level correlated with the platelet count in patients with hematologic malignancies (r = 0.26, p = 0.044). In addition, leptin level had negative correlations with international prognostic score (IPS) in Hodgkin lymphoma (r = –0.9, p = 0.002) and with international prognostic index (IPI) in non-Hodgkin lymphoma (r = –0.77, p = 0.03). In CLL patients, leptin level had a correlation with the poor prognostic marker — CD38 level (r = 0.68, p = 0.03). Conclusion: We found higher leptin levels in MM and CLL patients, and higher resistin levels in lymphoma patients: this fact demonstrates that changes in adipose tissue and metabolism occur in these disease states.Цель: определить уровни содержания лептина и резистина в сыворотке крови больных с различными онкогематологическими заболеваниями. Методы: обследован 21 больной лимфомой, 14 — множественной миеломой (ММ), 14 — острой лейкемией, 13 — хронической лимфоцитарной лейкемией (ХЛЛ), и 25 здоровых доноров. У пациентов определены такие характеристики: индекс массы тела (ИМТ), гематологические параметры, содержание липидов в сыворотке крови. Содержание лептина и резистина в сыворотке крови определяли иммуноферментным методом. Результаты: уровень лептина в сыворотке крови был значительно выше у больных с ХЛЛ и ММ, чем таковой у контрольной группы (р < 0,01). Уровень резистина был значительно выше в группе больных с лимфомами по сравнению с ХЛЛ, острой лейкемией и контрольной группами (р < 0,01). В контрольной группе уровень лептина отрицательно коррелировал с уровнем гемоглобина (r = –0,44, р = 0,047), а во всех группах больных уровень лептина коррелировал с ИМТ (r = 0,32, р = 0,02). Уровень лептина при лимфомах коррелировал с уровнем гемоглобина (r = 0,64, р = 0,005), уровень резистина коррелировал с количеством тромбоцитов у больных всех групп (r = 0,26, р = 0,044). При лимфоме Ходжкина выявлена отрицательная корреляция между уровнем лептина и величиной международной прогностической шкалы (r = -0,9, р = 0,002), при неходжкинской лимфоме — величиной международного прогностического индекса (r = –0,77, р = 0,03), у больных ХЛЛ — с уровнем экспрессии CD38 (r = 0,68, р = 0,03). Выводы: у больных ММ и ХЛЛ выявлен высокий уровень лептина, а с лимфомами — высокий уровень резистина: этот факт указывает на то, что у больных указанными онкогематологическими заболеваниями могут возникать изменения в структуре жировой ткани и обмене веществ

Extensive central nervous system involvement in Merkel cell carcinoma: a case report and review of the literature

<p>Abstract</p> <p>Introduction</p> <p>Merkel cell carcinoma is a rare malignant cutaneous neoplasm that is locally invasive and frequently metastasizes to lymph nodes, liver, lungs, bone and brain. The incidence of Merkel cell carcinoma has increased in the past three decades.</p> <p>Case presentation</p> <p>A 65-year-old Caucasian man presented with a sudden onset of severe headache and a three-month history of balance disturbance. Magnetic resonance imaging revealed a large meningeal metastasis. The radiologic workup showed retroperitoneal and inguinal lymph node metastases. Biopsy of the inguinal lymph nodes showed metastases of Merkel cell carcinoma. Biopsy from three different suspected skin lesions revealed no Merkel cell carcinoma, and the primary site of Merkel cell carcinoma remained unknown. Leptomeningeal metastases, new axillary lymph node metastases, and intraspinal (epidural and intradural) metastases were detected within six, seven and eight months, respectively, from the start of symptoms despite treating the intracranial metastasis with gamma knife and the abdominal metastases with surgical dissection and external radiotherapy. This indicates the aggressive nature of the disease.</p> <p>Conclusion</p> <p>To the best of our knowledge, this is the first report in the literature of an intracranial meningeal metastasis of Merkel cell carcinoma treated with gamma knife and of intraspinal intradural metastases of Merkel cell carcinoma. Despite good initial response to radiotherapy, recurrence and occurrence of new metastases are common in Merkel cell carcinoma.</p

Point Interaction in two and three dimensional Riemannian Manifolds

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac delta interactions on two and three dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator. In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for general class of manifolds, e.g., for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the beta-function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by S. G. Rajeev.Comment: 43 page

Existence of Hamiltonians for Some Singular Interactions on Manifolds

The existence of the Hamiltonians of the renormalized point interactions in two and three dimensional Riemannian manifolds and that of a relativistic extension of this model in two dimensions are proven. Although it is much more difficult, the proof of existence of the Hamiltonian for the renormalized resolvent for the non-relativistic Lee model can still be given. To accomplish these results directly from the resolvent formula, we employ some basic tools from the semigroup theory.Comment: 33 pages, no figure

A Many-body Problem with Point Interactions on Two Dimensional Manifolds

A non-perturbative renormalization of a many-body problem, where non-relativistic bosons living on a two dimensional Riemannian manifold interact with each other via the two-body Dirac delta potential, is given by the help of the heat kernel defined on the manifold. After this renormalization procedure, the resolvent becomes a well-defined operator expressed in terms of an operator (called principal operator) which includes all the information about the spectrum. Then, the ground state energy is found in the mean field approximation and we prove that it grows exponentially with the number of bosons. The renormalization group equation (or Callan-Symanzik equation) for the principal operator of the model is derived and the $\beta$ function is exactly calculated for the general case, which includes all particle numbers.Comment: 28 pages; typos are corrected, three figures are adde

Diagnostic value of combined serum biomarkers for the evaluation of liver fibrosis in chronic hepatitis C infection: A multicenter, noninterventional, observational study

Background/Aims: The hepatitis C virus (HCV) infection is important cause of chronic hepatitis. Liver biopsy is considered the gold standard for assessment of fibrosis but this procedure is an invasive procedure. We aimed to evaluate the diagnostic efficiency of non-invasive serum biomarkers, separately and in combinations, on liver fibrosis in treatment-naive chronic hepatitis C (CHC) patients. Materials and Methods: Two hundred and sixteen treatment-naive CHC patients were enrolled from 32 locations across Turkey in this open-labelled, non-interventional prospective observational study. FibroTest®, aspartate aminotransferase-to-platelet ratio index(APRI), aspartate aminotransferase and alanine aminotransferase ratio (AAR), fibrosis index based on four factors (FIB-4), Age-platelet(AP) index and Forns index were measured and compared with Metavir scores got from liver biopsies. Results: Data from 182 patients with baseline liver biopsy were suitable for analysis. One hundred and twenty patients (65.9%) had F0-F1 fibrosis and 62 patients (34.1%) had F2-F4 fibrosis. APRI 0.732 area under the curve(AUC) indicated advanced fibrosis with 69% sensitivity and 77% specificity. FIB-4 0.732 AUC and FibroTest 0.715 AUC indicated advanced fibrosis with 69% and 78.4% sensitivity, and 75% and 71.4% specificity, respectively. The combined use of tests also led to an increase in AUC and specificity. Combinations of FibroTest with APRI and/or FIB-4, and FIB-4 with APRI were optimal for the evaluation of liver fibrosis. Conclusion: Fibrotest, FIB-4, APRI, AP index and Forns index exhibit good diagnostic performance for determining liver fibrosis in CHC patients, and the use of at least two tests together will increase their diagnostic value still further. © Copyright 2018 by The Turkish Society of Gastroenterology