The homotopy type of the cobordism category

The embedded cobordism category under study in this paper generalizes the category of conformal surfaces, introduced by G. Segal in order to formalize the concept of field theories. Our main result identifies the homotopy type of the classifying space of the embedded d-dimensional cobordism category for all d. For d=2, our results lead to a new proof of the generalized Mumford conjecture, somewhat different in spirit from the original one.Comment: 40 pages. v2 has improved notation, added explanations, and minor mistakes fixed. v3 has minor corrections and improvements. Final submitted versio

The Impacts of External Patient Variables on Gene Expression Profiles of Lung Adenocarcinomas

The search for improvements to detection and treatment of cancers is a paramount goal for all of medicine. The most important step for oncological research is to expand the knowledge base of the genetic characteristics and abnormalities that give rise to cancer. In our present day, one of the most pressing and deadly forms of cancer is that of the lung, with lung adenocarcinomas being the most prevalent variation of the disease. Improving our cancer genomic insight can provide the seedings for improved cancer detection, novel cancer treatment, and serve as a guide for avenues to explore with future oncological research. Using The Cancer Genome Atlas (TCGA), a cancer genomics program from the National Cancer Institute, a data set of 512 lung adenocarcinoma samples was compiled for analysis into the interconnectivity of patient characteristics and their impact on gene expression profiles. For this sample population, patient sex, age, race, smoking history, and tumor stage were analyzed using a permutational multivariate analysis of variance (perMANOVA) modeled with non-metric multidimensional scaling (NMDS) to determine significant interactions between the variables on tumor genetic differentiation. Patient smoking history and tumor stage, sex and tumor stage, and sex and age were all found to have statistically significant impacts on gene expression, while race on its own was also found to have a significant impact. This analysis highlights that male and female cancers might differentiate quite differently and illuminates a need to explore sex related differences in cancer progression. Additionally, the research emphasizes the continued buildup of mutations throughout a cancer’s proliferation, showing the need for investigation into cancer development after it has been initially discovered. Lastly, this research demonstrates that patient variables interact significantly to impact gene expression profiles and accentuates the need for research about how external factors combine and interconnect to make each cancer unique

Further Evidence on Hedge Funds Performance.

In this analysis we identify dynamic hedge fund strategies quantitatively pursuing a Principal Component Analysis following Fung and Hsieh (1997). We extract five dominant hedge fund strategies each representing similar investment styles and analyse the performance of each strategy by employing a multi-factor model comprising both market indices and passive option strategies along the lines of Agerwal and Naik (2000). We find that the majority of the five homogenous strategies show superior performance. However, correcting for survivorship bias this superior performance disappears.Hedge funds; Investment in securities; Performance; Dynamic strategies; Hedge funds performance;

Multi-Periodic Climate Dynamics: Spectral Analysis of Instrumental, Short- and Long-length Proxy Temperature Records

Analyzing 26 short-length (less than 3000 years) instrumental and proxy temperature records and five long-length (greater than 3000 years) proxy temperature records using Discrete Fourier Transform has shown that as the length of significant periods increase in the time domain then so does the power at which the period is observed. A t-test verifies that a positive correlation exist between the length of the significant periods and the power with a confidence level of ∝ \u3e0.05. Significant frequencies with period greater than 30 years are confirmed using Monte Carlo simulations, which were created using a nonlinear approach known as fractional Brownian motion (FBM). While completing the spectral analysis it was observed in the spectral analysis is an absence of significant periods between about 1000 years and 20,000 years. Also, wavelet analysis of all short-length temperature records turned up no significant findings

Algebras of generalized functions with smooth parameter dependence

We show that spaces of Colombeau generalized functions with smooth parameter dependence are isomorphic to those with continuous parametrization. Based on this result we initiate a systematic study of algebraic properties of the ring $\widetilde{\mathbb{K}}_{sm}$ of generalized numbers in this unified setting. In particular, we investigate the ring and order structure of $\widetilde{\mathbb{K}}_{sm}$ and establish some properties of its ideals.Comment: 19 page