Semiclassical Approximations in Phase Space with Coherent States

We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman--Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.Comment: 80 pages, 4 figure

Overexpression of sphingosine kinase 1 is associated with salivary gland carcinoma progression and might be a novel predictive marker for adjuvant therapy

<p>Abstract</p> <p>Background</p> <p>Overexpression of sphingosine kinase-1 (SPHK1) has been demonstrated to be associated with the development and progression in various types of human cancers. The current study was to characterize the expression of SPHK1 in salivary gland carcinomas (SGC) and to investigate the association between SPHK1 expression and progression of SGC.</p> <p>Methods</p> <p>The expression of SPHK1 was examined in 2 normal salivary gland tissues, 8 SGC tissues of various clinical stages, and 5 pairs of primary SGC and adjacent salivary gland tissues from the same patient, using real-time PCR and western blot analysis. Furthermore, the SPHK1 protein expression was analyzed in 159 clinicopathologically characterized SGC cases by immunohistochemistry. Statistical analyses were performed to determine the prognostic and diagnostic associations.</p> <p>Results</p> <p>SPHK1 expression was found to be markedly upregulated in SGC tissues than that in the normal salivary gland tissues and paired adjacent salivary gland tissues, at both mRNA and protein levels. Statistical analysis revealed a significant correlation of SPHK1 expression with the clinical stage (<it>P </it>= 0.005), T classification (<it>P </it>= 0.017), N classification (<it>P </it>= 0.009), M classification (<it>P </it>= 0.002), and pathological differentiation (<it>P </it>= 0.013). Patients with higher SPHK1 expression had shorter overall survival time, whereas patients with lower SPHK1 expression had better survival. Importantly, patients in the group without adjuvant therapy who exhibited high SPHK1 expression had significantly lower overall survival rates compared with those with low SPHK1 expression. Moreover, multivariate analysis suggested that SPHK1 expression might be an independent prognostic indicator for the survival of SGC patients.</p> <p>Conclusions</p> <p>Our results suggest that SPHK1 expression is associated with SGC progression, and might represent as a novel and valuable predictor for adjuvant therapy to SGC patients.</p

Overexpression of sphingosine-1-phosphate receptor 1 and phospho-signal transducer and activator of transcription 3 is associated with poor prognosis in rituximab-treated diffuse large B-cell lymphomas

BACKGROUND: Sphingosine-1-phosphate receptor-1 (S1PR1) and signal transducer and activator of transcription-3 (STAT3) play important roles in immune responses with potential oncogenic roles. METHODS: We analyzed S1PR1/STAT3 pathway activation using immunohistochemistry in rituximab-treated diffuse large B-cell lymphomas (DLBCL; N = 103). RESULTS: Nuclear expression of pSTAT3 (but not S1PR1) was associated with non-GCB phenotype (p = 0.010). In univariate survival analysis, S1PR1 expression (S1PR1+) was a poor prognostic factor in total DLBCLs (p = 0.018), as well as in nodal (p = 0.041), high-stage (III, IV) (p = 0.002), and high-international prognostic index (IPI; 3–5) (p = 0.014) subgroups, while nuclear expression of pSTAT3 (pSTAT3+) was associated with poor prognosis in the low-stage (I, II) subgroup (p = 0.022). The S1PR1/pSTAT3 risk-categories, containing high-risk (S1PR1+), intermediate-risk (S1PR1-/pSTAT3+), and low-risk (S1PR1-/pSTAT3-), predicted overall survival (p = 0.010). This prognostication tended to be valid in each stage (p = 0.059 in low-stage; p = 0.006 in high-stage) and each IPI subgroups (p = 0.055 [low-IPI]; p = 0.034 [high-IPI]). S1PR1 alone and S1PR1/pSTAT3 risk-category were significant independent prognostic indicators in multivariate analyses incorporating IPI and B symptoms (S1PR1 [p = 0.005; HR = 3.0]; S1PR1/pSTAT3 risk-category [p = 0.019: overall; p = 0.024, HR = 2.7 for S1PR1-/pSTAT3+ vs. S1PR1+; p = 0.021, HR = 3.8 for S1PR1-/pSTAT3- vs. S1PR1+]). CONCLUSIONS: Therefore, S1PR1 and S1PR1/pSTAT3 risk-category may contribute to risk stratification in rituximab-treated DLBCLs, and S1PR1 and STAT3 might be therapeutic targets for DLBCL