Symmetry implies independence

Given a quantum system consisting of many parts, we show that symmetry of the system's state, i.e., invariance under swappings of the subsystems, implies that almost all of its parts are virtually identical and independent of each other. This result generalises de Finetti's classical representation theorem for infinitely exchangeable sequences of random variables as well as its quantum-mechanical analogue. It has applications in various areas of physics as well as information theory and cryptography. For example, in experimental physics, one typically collects data by running a certain experiment many times, assuming that the individual runs are mutually independent. Our result can be used to justify this assumption.Comment: LaTeX, contains 4 figure

Photodynamic therapy of early stage oral cavity and oropharynx neoplasms: an outcome analysis of 170 patients

The indications of photodynamic therapy (PDT) of oral cavity and oropharynx neoplasms are not well defined. The main reason is that the success rates are not well established. The current paper analyzes our institutional experience of early stage oral cavity and oropharynx neoplasms (Tis-T2) to identify the success rates for each subgroup according to T stage, primary or non-primary treatment and subsites. In total, 170 patients with 226 lesions are treated with PDT. From these lesions, 95 are primary neoplasms, 131 were non-primaries (recurrences and multiple primaries). The overall response rate is 90.7% with a complete response rate of 70.8%. Subgroup analysis identified oral tongue, floor of mouth sites with more favorable outcome. PDT has more favorable results with certain subsites and with previously untreated lesions. However, PDT can find its place for treating lesions in previously treated areas with acceptable results

Parity-related molecular signatures and breast cancer subtypes by estrogen receptor status

INTRODUCTION: Relationships of parity with breast cancer risk are complex. Parity is associated with decreased risk of postmenopausal hormone receptor–positive breast tumors, but may increase risk for basal-like breast cancers and early-onset tumors. Characterizing parity-related gene expression patterns in normal breast and breast tumor tissues may improve understanding of the biological mechanisms underlying this complex pattern of risk. METHODS: We developed a parity signature by analyzing microRNA microarray data from 130 reduction mammoplasty (RM) patients (54 nulliparous and 76 parous). This parity signature, together with published parity signatures, was evaluated in gene expression data from 150 paired tumors and adjacent benign breast tissues from the Polish Breast Cancer Study, both overall and by tumor estrogen receptor (ER) status. RESULTS: We identified 251 genes significantly upregulated by parity status in RM patients (parous versus nulliparous; false discovery rate = 0.008), including genes in immune, inflammation and wound response pathways. This parity signature was significantly enriched in normal and tumor tissues of parous breast cancer patients, specifically in ER-positive tumors. CONCLUSIONS: Our data corroborate epidemiologic data, suggesting that the etiology and pathogenesis of breast cancers vary by ER status, which may have implications for developing prevention strategies for these tumors