Non-Central Potentials and Spherical Harmonics Using Supersymmetry and Shape Invariance

It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be applied to several problems with non-central vector and scalar potentials. As examples, we analyze the bound state spectra of an electron in a Coulomb plus an Aharonov-Bohm field and/or in the magnetic field of a Dirac monopole.Comment: Latex, 12 pages. To appear in American Journal of Physic

Broken Supersymmetric Shape Invariant Systems and Their Potential Algebras

Although eigenspectra of one dimensional shape invariant potentials with unbroken supersymmetry are easily obtained, this procedure is not applicable when the parameters in these potentials correspond to broken supersymmetry, since there is no zero energy eigenstate. We describe a novel two-step shape invariance approach as well as a group theoretic potential algebra approach for solving such broken supersymmetry problems.Comment: Latex file, 10 page

Shape invariance and the exactness of quantum Hamilton-Jacobi formalism

Quantum Hamilton-Jacobi Theory and supersymmetric quantum mechanics (SUSYQM) are two parallel methods to determine the spectra of a quantum mechanical systems without solving the Schr\"odinger equation. It was recently shown that the shape invariance, which is an integrability condition in SUSYQM formalism, can be utilized to develop an iterative algorithm to determine the quantum momentum functions. In this paper, we show that shape invariance also suffices to determine the eigenvalues in Quantum Hamilton-Jacobi Theory.Comment: Accepted for publication in Phys. Lett.

Semiclassical Approach to Quantum-mechanical Problems with Broken Supersymmetry

The semiclassical WKB approximation method is reexamined in the context of nonrelativistic quantum-mechanical bound-state problems with broken supersymmetry (SUSY). This gives rise to an alternative quantization condition (denoted by BSWKB) which is different from the standard WKB formula and also different from the previously studied supersymmetric (SWKB) formula for unbroken SUSY. It is shown that to leading order in ħ, the BSWKB condition yields exact energy eigenvalues for shape-invariant potentials with broken SUSY (harmonic oscillator, Pöschl-Teller I and II) which are known to be analytically solvable. Further, we show explicitly that the higher-order corrections to these energy eigenvalues, up to sixth order in ħ, vanish identically. We also consider a number of examples of potentials with broken supersymmetry that are not analytically solvable. In particular, for the broken SUSY superpotential W=Ax2d [A\u3e0, d=(integer)], we evaluate contributions up to the sixth order and show that these results are in excellent agreement with numerical solutions of the Schrödinger equation. While the numerical BSWKB results in lowest order are not always better than the corresponding WKB results, they are still a considerable improvement because they guarantee equality of the corresponding energy eigenvalues for the supersymmetric partner potentials V+ and V-. This is of special importance in those situations where these partner potentials are not related by parity

Epidemiology and Host Factors

In 2014, WHO reported approximately 9.6 million new cases of tuberculosis (TB) in the world, more than half of which are contributed by developing countries in Asia and Africa. Lack of modern diagnostic tools, underreporting of the new cases and underutilization of directly observed therapy (DOT) remain a concern in developing countries. Transient resurgence of TB during the HIV epidemic has subsided and the annual decline has resumed in developed countries including the USA. In 2014 though, the rate of decline has slowed down resulting in leveling of TB incidence in the USA. In developed countries like the USA, the incidence of TB remains high in those with certain risk factors for TB. This group includes immunocompromised patients, particularly those with positive HIV infection. Others at high risk include those with diabetes, cancer, those taking immunosuppressive drugs, and those with other medical conditions that reduce host immunity. If we look at age and ethnicity, elderly patients are at higher risk of developing TB. African-American, foreign-born, and homeless populations are also at higher risk of developing tuberculosis. Virulence of the mycobacteria, and immunological and genetically mediated factors are also mentioned, but these topics are not the primary goal of this article. This review, thus discusses the epidemiology, host factors, and those at high risk for developing active TB. A brief review of the current trends in drug resistance of mycobacteria is also presented

Epidemiology and Host Factors

In 2014, WHO reported approximately 9.6 million new cases of tuberculosis (TB) in the world, more than half of which are contributed by developing countries in Asia and Africa. Lack of modern diagnostic tools, underreporting of the new cases and underutilization of directly observed therapy (DOT) remain a concern in developing countries. Transient resurgence of TB during the HIV epidemic has subsided and the annual decline has resumed in developed countries including the USA. In 2014 though, the rate of decline has slowed down resulting in leveling of TB incidence in the USA. In developed countries like the USA, the incidence of TB remains high in those with certain risk factors for TB. This group includes immunocompromised patients, particularly those with positive HIV infection. Others at high risk include those with diabetes, cancer, those taking immunosuppressive drugs, and those with other medical conditions that reduce host immunity. If we look at age and ethnicity, elderly patients are at higher risk of developing TB. African-American, foreign-born, and homeless populations are also at higher risk of developing tuberculosis. Virulence of the mycobacteria, and immunological and genetically mediated factors are also mentioned, but these topics are not the primary goal of this article. This review, thus discusses the epidemiology, host factors, and those at high risk for developing active TB. A brief review of the current trends in drug resistance of mycobacteria is also presented

Weekly osimertinib dosing prevents EGFR mutant tumor cells destined to home mouse lungs

The recently conducted ADAURA trial concludes daily dosing of adjuvant osimertinib, a third-generation EGFR tyrosine kinase inhibitor (TKI), improves disease-free survival with stage IB/II/IIIA EGFR -mutated non-small cell lung cancer patients in comparison to placebo. We have developed a preclinical orthotopic mouse model, using luciferase tagged lung adenocarcinoma cells harboring EGFR TKI sensitive exon 19 deletion to model and extend trial implications comparing a weekly vs daily dosing outcome of osimertinib to a first-generation TKI- erlotinib. We find that 100% of mice in both the groups receiving osimertinib daily or weekly before injection of cells show a complete absence of homing of cells in mice's lungs from day three until day 18 post-injection of cells. On the other hand, 25% and 75% of mice receiving erlotinib daily and weekly before injecting cells show homing of cells to the lungs. The tumors observed in the lungs, when dissected at day 30, confirmed the colonization of the injected cells homing to the organ. Thus, our study establishes the efficacy of pretreatment with osimertinib in reducing tumor cells' homing to mouse lungs in an in vivo mouse model

Thermodynamics of a free q-fermion gas

We study the thermodynamics of a q-fermion gas for complex values of q on the unit circle. Special emphasis is given to the study of the virial coefficients and the specific heat of this gas. In particular, it is shown that if any state can accommodate up to p q-fermions, then the first p virial coefficients of such a gas are the same as that of a gas of free bosons. Explicit expressions for the deviation of higher virial coefficients from the corresponding values for a Bose gas are obtained. Further, as for ordinary fermions, it is shown that the specific heat of a q-fermion gas at low temperature is proportional to T. Numerical computations show that the derivative of the specific heat as a function of T has no discontinuity

Integrated Genomic Analysis of Early Stage Tongue Tumors Revealed Recurrent Transcript Fusions

Introduction: Tongue cancer is the most predominant form of oral cancer in developed countries with varying incidence in developing countries. In India, tongue cancer accounts for 21% of head and neck squamous cell carcinoma (HNSCC) and known to display occult node metastasis during early stages of disease. The major etiological factors associated with tongue cancer includes tobacco related products, alcohol and human papilloma virus (HPV) infections. Objective: Portrait of genomic aberrations underlying the genome of tobacco/nut chewing HPV-negative early stage tongue tumors. Materials and Methods: Whole transcriptome sequencing of 17 HPV-negative early stage tongue squamous cell carcinoma (TSCC) tumors and 4 HNSCC cell lines. Validation of findings in an additional set of 44 paired HPV-negative early stage TSCC tumor samples. Results: Using bioinformatics approaches, we present the first glance of a portrait of 242 tumor specific transcript fusions, followed by exhaustive validation of 12 candidate fusion transcripts across 44 paired HPV-negative early TSCC tumor samples and 4 HNSCC cell lines. Comparative analysis of our data with various fusion databases revealed 48 previously described transcript fusions in various cancer types. We have identified and validated novel somatic recurrent fusion transcripts in tumor samples. Here, we present a comprehensive landscape of transcript fusions underlying the genome of HPV-negative early stage tongue tumors. Conclusions: Characterization of the recurrent transcript fusions described here could serve as attractive candidates to facilitate in diagnosis of HPV-negative early stage TSCC patients

Elucidating the mechanisms of resistance to tyrosine kinase inhibitors in lung cancer patients

Introduction: Lung tumors with mutations in epidermal growth factor receptor (EGFR) gene represent a clinically distinct subtype of lung cancer and are observed at a frequency of 23% among Indian patients. The standard practice for treatment of EGFR mutated lung cancer patients includes tyrosine kinase inhibitors (TKIs) erlotinib and gefitinib. Although initial clinical responses are observed, resistance to TKIs develops within year from the start of treatment. In about fifty percent of cases, the resistance is caused due to a secondary T790M mutation in the EGFR gene. Additionally, MET amplification and histological transformation of tumors are known to confer TKI resistance in a small subset of patients. Nonetheless, there is an unmet need to elucidate novel ways by which lung tumors acquire resistance to EGFR targeting TKIs. Objectives: To delineate novel mechanisms of acquired resistance to EGFR-TKIs by characterizing the differential profile of drug sensitive and resistant state among lung tumors using integrated genomics approaches. Material and Methods: A retrospective collection of FFPE DNA samples (n=45) from tumors at baseline and rebiopsy along with paired blood sample was done for a total of 15 EGFR mutated lung cancer patients. Only tumor samples which were negative for EGFR T790M (as confirmed by orthologous technologies) were selected in the study with an anticipation that such samples would be enriched novel resistance mechanisms. Whole exome sequencing at an average coverage of 100X was performed for these samples. Results: The whole exome data was analyzed using an in-house developed pipeline. Of all the known resistance mutations, we identified EGFR T790M mutation in five out of fifteen patients. Other than T790M we expect to identify novel resistance causing mutations from the analysis of ten patients with unknown resistance mechanisms. Functional validation of these resistance specific alterations would be performed in vitro using drug sensitive lung cancer cell lines