Geometry of GL_n(C) on infinity: complete collineations, projective compactifications, and universal boundary

Consider a finite dimensional (generally reducible) polynomial representation \rho of GL_n. A projective compactification of GL_n is the closure of \rho(GL_n) in the space of all operators defined up to a factor (this class of spaces can be characterized as equivariant projective normal compactifications of GL_n). We give an expicit description for all projective compactifications. We also construct explicitly (in elementary geometrical terms) a universal object for all projective compactifications of GL_n.Comment: 24 pages, corrected varian

Bioelectrical impedance phase angle in clinical practice: implications for prognosis in stage IIIB and IV non-small cell lung cancer

<p>Abstract</p> <p>Background</p> <p>A frequent manifestation of advanced lung cancer is malnutrition, timely identification and treatment of which can lead to improved patient outcomes. Bioelectrical impedance analysis (BIA) is an easy-to-use and non-invasive technique to evaluate changes in body composition and nutritional status. We investigated the prognostic role of BIA-derived phase angle in advanced non-small cell lung cancer (NSCLC).</p> <p>Methods</p> <p>A case series of 165 stages IIIB and IV NSCLC patients treated at our center. The Kaplan Meier method was used to calculate survival. Cox proportional hazard models were constructed to evaluate the prognostic effect of phase angle, independent of stage at diagnosis and prior treatment history.</p> <p>Results</p> <p>93 were males and 72 females. 61 had stage IIIB disease at diagnosis while 104 had stage IV. The median phase angle was 5.3 degrees (range = 2.9 – 8). Patients with phase angle <= 5.3 had a median survival of 7.6 months (95% CI: 4.7 to 9.5; n = 81), while those with > 5.3 had 12.4 months (95% CI: 10.5 to 18.7; n = 84); (p = 0.02). After adjusting for age, stage at diagnosis and prior treatment history we found that every one degree increase in phase angle was associated with a relative risk of 0.79 (95% CI: 0.64 to 0.97, P = 0.02).</p> <p>Conclusion</p> <p>We found BIA-derived phase angle to be an independent prognostic indicator in patients with stage IIIB and IV NSCLC. Nutritional interventions targeted at improving phase angle could potentially lead to an improved survival in patients with advanced NSCLC.</p

Bioelectrical impedance phase angle as a prognostic indicator in breast cancer

<p>Abstract</p> <p>Background</p> <p>Bioelectrical impedance analysis (BIA) is an easy-to-use, non-invasive, and reproducible technique to evaluate changes in body composition and nutritional status. Phase angle, determined by bioelectrical impedance analysis (BIA), detects changes in tissue electrical properties and has been hypothesized to be a marker of malnutrition. Since malnutrition can be found in patients with breast cancer, we investigated the prognostic role of phase angle in breast cancer.</p> <p>Methods</p> <p>We evaluated a case series of 259 histologically confirmed breast cancer patients treated at Cancer Treatment Centers of America. Kaplan Meier method was used to calculate survival. Cox proportional hazard models were constructed to evaluate the prognostic effect of phase angle independent of stage at diagnosis and prior treatment history. Survival was calculated as the time interval between the date of first patient visit to the hospital and the date of death from any cause or date of last contact/last known to be alive.</p> <p>Results</p> <p>Of 259 patients, 81 were newly diagnosed at our hospital while 178 had received prior treatment elsewhere. 56 had stage I disease at diagnosis, 110 had stage II, 46 had stage III and 34 had stage IV. The median age at diagnosis was 49 years (range 25 – 74 years). The median phase angle score was 5.6 (range = 1.5 – 8.9). Patients with phase angle <= 5.6 had a median survival of 23.1 months (95% CI: 14.2 to 31.9; n = 129), while those > 5.6 had 49.9 months (95% CI: 35.6 to 77.8; n = 130); the difference being statistically significant (p = 0.031). Multivariate Cox modeling, after adjusting for stage at diagnosis and prior treatment history found that every one unit increase in phase angle score was associated with a relative risk of 0.82 (95% CI: 0.68 to 0.99, P = 0.041). Stage at diagnosis (p = 0.006) and prior treatment history (p = 0.001) were also predictive of survival independent of each other and phase angle.</p> <p>Conclusion</p> <p>This study demonstrates that BIA-derived phase angle is an independent prognostic indicator in patients with breast cancer. Nutritional interventions targeted at improving phase angle could potentially lead to an improved survival in patients with breast cancer.</p

Probabilistic machine learning and artificial intelligence.

How can a machine learn from experience? Probabilistic modelling provides a framework for understanding what learning is, and has therefore emerged as one of the principal theoretical and practical approaches for designing machines that learn from data acquired through experience. The probabilistic framework, which describes how to represent and manipulate uncertainty about models and predictions, has a central role in scientific data analysis, machine learning, robotics, cognitive science and artificial intelligence. This Review provides an introduction to this framework, and discusses some of the state-of-the-art advances in the field, namely, probabilistic programming, Bayesian optimization, data compression and automatic model discovery.The author acknowledges an EPSRC grant EP/I036575/1, the DARPA PPAML programme, a Google Focused Research Award for the Automatic Statistician and support from Microsoft Research.This is the author accepted manuscript. The final version is available from NPG at http://www.nature.com/nature/journal/v521/n7553/full/nature14541.html#abstract

Lymphatic mapping and sentinel node biopsy in gynecological cancers: a critical review of the literature

Although it does not have a long history of sentinel node evaluation (SLN) in female genital system cancers, there is a growing number of promising study results, despite the presence of some aspects that need to be considered and developed. It has been most commonly used in vulvar and uterine cervivcal cancer in gynecological oncology. According to these studies, almost all of which are prospective, particularly in cases where Technetium-labeled nanocolloid is used, sentinel node detection rate sensitivity and specificity has been reported to be 100%, except for a few cases. In the studies on cervical cancer, sentinel node detection rates have been reported around 80–86%, a little lower than those in vulva cancer, and negative predictive value has been reported about 99%. It is relatively new in endometrial cancer, where its detection rate varies between 50 and 80%. Studies about vulvar melanoma and vaginal cancers are generally case reports. Although it has not been supported with multicenter randomized and controlled studies including larger case series, study results reported by various centers around the world are harmonious and mutually supportive particularly in vulva cancer, and cervix cancer. Even though it does not seem possible to replace the traditional approaches in these two cancers, it is still a serious alternative for the future. We believe that it is important to increase and support the studies that will strengthen the weaknesses of the method, among which there are detection of micrometastases and increasing detection rates, and render it usable in routine clinical practice

Viral Information

Viruses are major drivers of global biogeochemistry and the etiological agents of many diseases. They are also the winners in the game of life; there are more viruses on the planet than cellular organisms and they encode most of the genetic diversity on the planet. In fact, it is reasonable to view life as a viral incubator. Nevertheless, most ecological and evolutionary theories were developed, and continue to be developed, without considering the virosphere. This means these theories need to be to reinterpreted in light of viral knowledge or we need to develop new theory from the viral point-of-view. Here we briefly introduce our viral planet and then address a major outstanding question in biology: why is most of life viral? Key insight is that during an infection cycle the original virus is completely broken down and only the associated information is passed on to the next generation. This is different than cellular organisms, which must pass on some physical part of themselves from generation to generation. Based on this premise, it is proposed that the thermodynamic consequences of physical information (e.g., Landauer's principle) are observed in natural viral populations. This link between physical and genetic information is then used to develop the Viral Information Hypothesis, which states that genetic information replicates itself to the detriment of system energy efficiency (i.e., is viral in nature). Finally, we show how viral information can be tested, and illustrate how this novel view can explain existing ecological and evolutionary theories from more fundamental principles