An average case analysis of a greedy algorithm for the on-line Steiner tree problem

AbstractThis paper gives the average distance analysis for the Euclidean tree constructed by a simple greedy but efficient algorithm of the on-line Steiner tree problem. The algorithm accepts the data one by one following the order of input sequence. When a point arrives, the algorithm adds the shortest edge, between the new point and the points arriving already, to the previously constructed tree to form a new tree. We first show that, given n points uniformly on a unit disk in the plane, the expected Euclidean distance between a point and its jth (1 ≤ j ≤ n − 1) nearest neighbor is less than or equal to (53)√jn when n is large. Based upon this result, we show that the expected length of the tree constructed by the on-line algorithm is not greater than 4.34 times the expected length of the minimum Steiner tree when the number of input points is large

Manipulation of magnetic nanoparticle retention and hemodynamic consequences in microcirculation: assessment by laser speckle imaging

Magnetic nanoparticles (MNPs) have been proposed for targeted or embolization therapeutics. How MNP retention occurs in circulation may critically determine local hemodynamics, tissue distribution of MNPs, and the therapeutic effects. We attempted to establish a microcirculation model to study the magnetic capture of MNPs in small vessels and to determine the factors affecting MNP retention. Two-dimensional hemodynamic changes in response to magnet-induced MNP retention in the microvessels of the cremaster muscle in vivo were observed in a real-time manner using a laser speckle imaging technique. Changes in tissue perfusion of the cremaster muscle appeared to be closely correlated with the location of the magnet placement underneath the muscle in response to intra-arterial administration of dextran-coated MNPs. Magnet-related retention was observed along the edge of the magnet, as corroborated by the results of histology analysis and microcomputed tomography. In these preparations, tissue iron content almost doubled, as revealed by inductively coupled plasma optical emission spectroscopy. In addition, MNP retention was associated with reduced downstream flow in a dose-dependent manner. Dissipation of MNPs (5 mg/kg) occurred shortly after removal of the magnet, which was associated with significant recovery of tissue flow. However, MNP dissipation did not easily occur after administration of a higher MNP dose (10 mg/kg) or prolonged exposure to the magnetic field. An ultrasound after removal of the magnet may induce the partial dispersion of MNPs and thus partially improve hemodynamics. In conclusion, our results revealed the important correlation of local MNP retention and hemodynamic changes in microcirculation, which can be crucial in the application of MNPs for effective targeted therapeutics

The molecular basis of breast cancer pathological phenotypes

The histopathological evaluation of morphological features in breast tumours provides prognostic information to guide therapy. Adjunct molecular analyses provide further diagnostic, prognostic and predictive information. However, there is limited knowledge of the molecular basis of morphological phenotypes in invasive breast cancer. This study integrated genomic, transcriptomic and protein data to provide a comprehensive molecular profiling of morphological features in breast cancer. Fifteen pathologists assessed 850 invasive breast cancer cases from The Cancer Genome Atlas (TCGA). Morphological features were significantly associated with genomic alteration, DNA methylation subtype, PAM50 and microRNA subtypes, proliferation scores, gene expression and/or RPPA subtype. Marked nuclear pleomorphism, necrosis, inflammation and high mitotic count were associated with Basal-like subtype and have similar molecular basis. Omics-based signatures were constructed to predict morphological features. The association of morphology transcriptome signatures with overall survival in oestrogen receptor (ER)-positive and ER-negative breast cancer was first assessed using the METABRIC dataset; signatures that remained prognostic in the METABRIC multivariate analysis were further evaluated in five additional datasets. The transcriptomic signature of epithelial tubule formation was prognostic in ER-positive breast cancer. No signature was prognostic in ER-negative. This study provided new insights into the molecular basis of breast cancer morphological phenotypes. The integration of morphological with molecular data has potential to refine breast cancer classification, predict response to therapy, enhance our understanding of breast cancer biology and improve clinical management. This work is publicly accessible at www.dx.ai/tcga_breast

Identification of a robust gene signature that predicts breast cancer outcome in independent data sets

BACKGROUND: Breast cancer is a heterogeneous disease, presenting with a wide range of histologic, clinical, and genetic features. Microarray technology has shown promise in predicting outcome in these patients. METHODS: We profiled 162 breast tumors using expression microarrays to stratify tumors based on gene expression. A subset of 55 tumors with extensive follow-up was used to identify gene sets that predicted outcome. The predictive gene set was further tested in previously published data sets. RESULTS: We used different statistical methods to identify three gene sets associated with disease free survival. A fourth gene set, consisting of 21 genes in common to all three sets, also had the ability to predict patient outcome. To validate the predictive utility of this derived gene set, it was tested in two published data sets from other groups. This gene set resulted in significant separation of patients on the basis of survival in these data sets, correctly predicting outcome in 62–65% of patients. By comparing outcome prediction within subgroups based on ER status, grade, and nodal status, we found that our gene set was most effective in predicting outcome in ER positive and node negative tumors. CONCLUSION: This robust gene selection with extensive validation has identified a predictive gene set that may have clinical utility for outcome prediction in breast cancer patients

Pathologic and biologic response to preoperative endocrine therapy in patients with ER-positive ductal carcinoma in situ

Abstract Background Endocrine therapy is commonly recommended in the adjuvant setting for patients as treatment for ductal carcinoma in situ (DCIS). However, it is unknown whether a neoadjuvant (preoperative) anti-estrogen approach to DCIS results in any biological change. This study was undertaken to investigate the pathologic and biomarker changes in DCIS following neoadjuvant endocrine therapy compared to a group of patients who did not undergo preoperative anti-estrogenic treatment to determine whether such treatment results in detectable histologic alterations. Methods Patients (n = 23) diagnosed with ER-positive pure DCIS by stereotactic core biopsy were enrolled in a trial of neoadjuvant anti-estrogen therapy followed by definitive excision. Patients on hormone replacement therapy, with palpable masses, or with histologic or clinical suspicion of invasion were excluded. Premenopausal women were treated with tamoxifen and postmenopausal women were treated with letrozole. Pathologic markers of proliferation, inflammation, and apoptosis were evaluated at baseline and at three months. Biomarker changes were compared to a cohort of patients who had not received preoperative treatment. Results Median age of the cohort was 53 years (range 38–78); 14 were premenopausal. Following treatment, predominant morphologic changes included increased multinucleated histiocytes and degenerated cells, decreased duct extension, and prominent periductal fibrosis. Two postmenopausal patients had ADH only with no residual DCIS at excision. Postmenopausal women on letrozole had significant reduction of PR, and Ki67 as well as increase in CD68-positive cells. For premenopausal women on tamoxifen treatment, the only significant change was increase in CD68. No change in cleaved caspase 3 was found. Two patients had invasive cancer at surgery. Conclusion Preoperative therapy for DCIS is associated with significant pathologic alterations. These changes may be clinically significant. Further work is needed to identify which women may be the best candidates for such treatment for DCIS, and whether best responders may safely avoid surgical intervention. Trial Registration ClinicalTrials.gov NCT0029074

Mammographic density and risk of breast cancer by age and tumor characteristics

Introduction: Understanding whether mammographic density (MD) is associated with all breast tumor subtypes and whether the strength of association varies by age is important for utilizing MD in risk models. Methods: Data were pooled from six studies including 3414 women with breast cancer and 7199 without who underwent screening mammography. Percent MD was assessed from digitized film-screen mammograms using a computer-assisted threshold technique. We used polytomous logistic regression to calculate breast cancer odds according to tumor type, histopathological characteristics, and receptor (estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor (HER2)) status by age (51%) versus average density (11-25%). Women ages 2.1 cm) versus small tumors and positive versus negative lymph node status (P’s < 0.01). For women ages <55 years, there was a stronger association of MD with ER-negative breast cancer than ER-positive tumors compared to women ages 55–64 and ≥65 years (Page-interaction = 0.04). MD was positively associated with both HER2-negative and HER2-positive tumors within each age group. Conclusion: MD is strongly associated with all breast cancer subtypes, but particularly tumors of large size and positive lymph nodes across all ages, and ER-negative status among women ages <55 years, suggesting high MD may play an important role in tumor aggressiveness, especially in younger women