On the classification of certain 1-connected 7-manifolds and related problems

In this article, we give a classification of closed, smooth, spin, 1-connected 7-manifolds whose integral cohomology ring is isomorphic to that of $\mathbb{C}P^2\times S^3$. We also prove that if a closed, smooth, spin, 1-connected 7-manifold has integral cohomology ring isomorphic to that of $\mathbb{C}P^2\times S^3$ or $S^2\times S^5$, then it admits a Riemannian metric with positive Ricci curvature.Comment: 20 page

Bayesian Partially Ordered Probit and Logit Models with an Application to Course Redesign

Large entry-level courses are commonplace at public 2- and 4-year institutions of higher education (IHEs) across the United States. Low pass rates in these entry-level courses, coupled with tight budgets, have put pressure on IHEs to look for ways to teach more students more effectively at a lower cost. Efforts to improve student outcomes in such courses are often called ``course redesigns.\u27 The difficulty arises in trying to determine the impact of a particular course redesign; true random-controlled trials are expensive and time-consuming, and few IHEs have the resources or patience to implement them. As a result, almost all evaluations of efforts to improve student success at scale rely on observational studies. At the same time, standard multilevel models may be inadequate to extract meaningful information from the complex and messy sets of student data available to evaluators because they throw away information by treating all passing grades equally. We propose a new Bayesian approach that keeps all grading information: a partially ordered multinomial probit model with random effects fit using a Markov Chain Monte Carlo algorithm, and a logit model that can be fit with importance sampling. Simulation studies show that the Bayesian Partially Ordered Probit/Logit Models work well, and the parameter estimation is precise in large samples. We also compared this model with standard models considering Mean Squared Error and the area under the Receiver Operating Characteristic (ROC) curve. We applied these new models to evaluate the impact of a course redesign at a large public university using the students\u27 grade data from the Fall semester of 2012 and the Spring semester of 2013

Vasopressin-2 receptor antagonists in autosomal dominant polycystic kidney disease: from man to mouse and back

nephropathy, with an esti-mated prevalence of 1:1000. The disease is characterized by the development of multiple cysts from all nephron segments leading to the enlargement of both kidneys and replacement of normal parenchyma (see [1]). Change in total kidney volume over time is the strongest predictor of renal function decline in ADPKD [2]. Glomerular filtra-tion rate remains preserved up to the age of 40 years in most patients because glomerular hyperfiltration in functioning nephrons compensates for the ongoing loss of renal tissue, until end-stage renal failure ensues in>50 % of patients, usually in their fifth decade. Mutations in the PKD1 gene account for ~85 % of the affected families, whereas the remaining cases are caused by mutations in PKD2. PKD1 encodes polycystin-1, an integral membrane protein with a large extracellular domain that probably functions as a re-ceptor and/or an adhesion molecule, whereas PKD2 enco-des polycystin-2, a non-selective cation channel belonging to the family of transient receptor potential channels. The polycystins are located in the primary cilium and interact to form a mechanosensory complex that is involved in intra-cellular Ca21 homeostasis and various signalling pathways. Disruption of the complex leads to cyst development and enlargement resulting from tubular cell proliferation and transepithelial fluid secretion. The progressive understand-ing of these pathways has led to spectacular advances in the prospective treatment for ADPKD, including the blockade of vasopressin 2 receptor (V2R) to decrease the intracellu-lar level of 3#-5#-cyclic adenosine monophosphate (cAMP) in cyst-lining tubular cells [1]

Polarization Remote Sensing for Land Observation

In the real world, vegetation, liquid surfaces, rocks, buildings, snows, clouds, fogs, etc. can all be regarded as natural polarizers. In the process of reflecting, transmitting, and scattering of electromagnetic radiations, land surface objects can produce polarized features that are related to the nature of the materials. These polarized information can determine objects’ properties, and therefore, detecting the polarization information of objects becomes a new method of remote sensing. Polarization of reflected and scattered solar electromagnetic radiation adds a new dimension to the understanding of the Earth’s objects’ properties. The polarized bidirectional reflectance characteristics and polarized hyperspectral properties of land objects were methodically studied. The results of the polarized bidirectional reflectance characteristics can provide the theoretical basis for polarization remote sensing such as the detecting conditions, modeling and others. The polarized spectral property of the typical objects can be used as the spectral basis for polarization remote sensing. The atmospheric correction is a key problem when using polarization remote sensing method to detect land objects’ information, because scattered atmospheric particles exhibit stronger polarization phenomena than land objects do. A method of using atmospheric neutral point for the separation polarization effect between objects and atmosphere has been proposed

Gravity Effects on Information Filtering and Network Evolving

In this paper, based on the gravity principle of classical physics, we propose a tunable gravity-based model, which considers tag usage pattern to weigh both the mass and distance of network nodes. We then apply this model in solving the problems of information filtering and network evolving. Experimental results on two real-world data sets, \emph{Del.icio.us} and \emph{MovieLens}, show that it can not only enhance the algorithmic performance, but can also better characterize the properties of real networks. This work may shed some light on the in-depth understanding of the effect of gravity model