Quasi-Exact Solvability and the direct approach to invariant subspaces

We propose a more direct approach to constructing differential operators that preserve polynomial subspaces than the one based on considering elements of the enveloping algebra of sl(2). This approach is used here to construct new exactly solvable and quasi-exactly solvable quantum Hamiltonians on the line which are not Lie-algebraic. It is also applied to generate potentials with multiple algebraic sectors. We discuss two illustrative examples of these two applications: an interesting generalization of the Lam\'e potential which posses four algebraic sectors, and a quasi-exactly solvable deformation of the Morse potential which is not Lie-algebraic.Comment: 17 pages, 3 figure

Noncommutative effective theory of vortices in a complex scalar field

We derive a noncommutative theory description for vortex configurations in a complex field in 2+1 dimensions. We interpret the Magnus force in terms of the noncommutativity, and obtain some results for the quantum dynamics of the system of vortices in that context

Galactic Collapse of Scalar Field Dark Matter

We present a scenario for galaxy formation based on the hypothesis of scalar field dark matter. We interpret galaxy formation through the collapse of a scalar field fluctuation. We find that a cosh potential for the self-interaction of the scalar field provides a reasonable scenario for galactic formation, which is in agreement with cosmological observations and phenomenological studies in galaxies.Comment: 4 pages, 3 figue

Oscillatons revisited

In this paper, we study some interesting properties of a spherically symmetric oscillating soliton star made of a real time-dependent scalar field which is called an oscillaton. The known final configuration of an oscillaton consists of a stationary stage in which the scalar field and the metric coefficients oscillate in time if the scalar potential is quadratic. The differential equations that arise in the simplest approximation, that of coherent scalar oscillations, are presented for a quadratic scalar potential. This allows us to take a closer look at the interesting properties of these oscillating objects. The leading terms of the solutions considering a quartic and a cosh scalar potentials are worked in the so called stationary limit procedure. This procedure reveals the form in which oscillatons and boson stars may be related and useful information about oscillatons is obtained from the known results of boson stars. Oscillatons could compete with boson stars as interesting astrophysical objects, since they would be predicted by scalar field dark matter models.Comment: 10 pages REVTeX, 10 eps figures. Updated files to match version published in Classical and Quantum Gravit

Diagnostic and prognostic value of B4GALT1 hypermethylation and its clinical significance as a novel circulating cell-free DNA biomarker in colorectal cancer

Epigenetic modifications of glyco-genes have been documented in different types of cancer and are tightly linked to proliferation, invasiveness, metastasis, and drug resistance. This study aims to investigate the diagnostic, prognostic, and therapy-response predictive value of the glyco-gene B4GALT1 in colorectal cancer (CRC) patients. A Kaplan-Meier analysis was conducted in 1418 CRC patients (GEO and TCGA datasets) to assess the prognostic and therapy-response predictive values of the aberrant expression and methylation status of B4GALT1. Quantitative methylation-specific PCR (QMSP) and droplet digital quantitative methylation-specific PCR (dd-QMSP) were respectively used to detect hypermethylated B4GALT1 in metastasis and plasma in four cohorts of metastatic CRC cases (mCRC). Both the downregulated expression and promoter hypermethylation of B4GALT1 have a negative prognostic impact on CRC. Interestingly a low expression level of B4GALT1 was significantly associated with poor cetuximab response (progression-free survival (PFS) p = 0.01) particularly in wild-type (WT)-KRAS patients (p = 0.03). B4GALT1 promoter was aberrantly methylated in liver and lung metastases. The detection of hypermethylated B4GALT1 in plasma of mCRC patients showed a highly discriminative receiver operating characteristic (ROC) curve profile (area under curve (AUC) value 0.750; 95% CI: 0.592-0.908, p = 0.008), clearly distinguishing mCRC patients from healthy controls. Based on an optimal cut-off value defined by the ROC analysis, B4GALT1 yield a 100% specificity and a 50% sensitivity. These data support the potential value of B4GALT1 as an additional novel biomarker for the prediction of cetuximab response, and as a specific and sensitive diagnostic circulating biomarker that can be detected in CRC

Pass a Law, Any Law, Fast! State Legislative Responses to the Kelo Backlash

The Supreme Court in Kelo v. City of New London left protection of property against takings for economic development to the states. Since Kelo, thirty-seven states have enacted legislation to update their eminent domain laws. This paper is the first to theoretically and empirically analyze the factors that influence whether, in what manner, and how quickly states change their laws through new legislation. Fourteen of the thirty-seven new laws offer only weak protections against development takings. The legislative response to Kelo was responsive to measures of the backlash but only in the binary decision whether to pass any new law. The decision to enact a meaningful restriction was more a function of relevant political economy measures. States with more economic freedom, greater value of new housing construction, and less racial and income inequality are more likely to have enacted stronger restrictions, and sooner. Of the thirteen states that have not updated, Arkansas, Oklahoma and Mississippi are highly likely to do so in the future. Hawaii, Massachusetts and New York are unlikely to update ever if at all

Phenomenological Determination of the Beauty Meson Decay Parameter fBf_B and the CP-Violating Angle δ\delta

We fit the ${\cal CKM}$-matrix to all recent data with the following free parameters: three mixing angles, the CP-violating angle $\delta$ in the Maiani parametrisation, the top quark mass $m_t$, and the product f_B{\cal B}_{\B}^{1/2}, where $f_B$ is the $B$-meson decay parameter and {\cal B}_{\B} is the bag parameter. Our fits span a contiguous region in the (f_B{\cal B}_{\B}^{1/2},\ \cos\delta)--plane, limited by 0.117\lsim f_B{\cal B}_{\B}^{1/2}/{\rm GeV}\lsim 0.231 and --0.95 \lsim $\cos\delta$ \lsim 0.70. The parameters f_B{\cal B}_{\B}^{1/2} and $\cos\delta$ are strongly positively correlated.Comment: 9 pages + 1 figure available upon request, HU-TFT-94-3

Volumetric study of the maxillary sinus in patients with sinus pathology

OBJECTIVES: The aim of this study is 1) to obtain the area and volumes of the maxillary sinuses in patients affected by clinically unilateral sinus pathology by comparing the results to the contralateral sinus and 2) to determine the importance of the volumetric measures when diagnosing the percentage of sinus obliteration. MATERIALS AND METHODS: A single-centre observational retrospective clinical study was conducted in 214 patients with clinically unilateral sinus pathologies. Linear (mm), area (mm2) and volume (mm3) measurements were taken from Cone Beam Computed Tomography (CBCT) images of the affected sinus as well as from the contralateral ones. Histopathological study was performed using haematoxylin/eosin and PAS or Groccot stains. The lesions were classified into non-specific sinusitis, polyps, inverted papilloma, fungal sinusitis, cysts, mucocele and other lesions. Chi-squared test, ANOVA for independent samples and Pearson test were used for the statistical analysis. RESULTS: A total of 100 sinuses were measured in 50 patients (28 men and 22 women, with an age of 43.6 years (SD = 18.3), 50 pathological and 50 healthy contralateral sinuses. The three-dimensional occupation volume of the affected sinuses was 97.1 mm3 (62.5%) vs. 40.6 mm3 (22.8%) in the healthy ones (p<0.0001). The medial-lateral width of the sinus in the frontal plane was significantly higher in the cysts group (32.4 mm, CI: 23-41.8 mm). CONCLUSION: In medical terms, the global percentage of occupation determined using the classic manual determination method does not differ from the three-dimensional percentage calculated using specific complex software