On the distribution of multiplicatively dependent vectors

In this paper, we study the distribution of multiplicatively dependent vectors. For example, although they have zero Lebesgue measure, they are everywhere dense both in $\R^n$ and \C^n. We also study this property in a more detailed manner by considering the covering radius of such vectors.Comment: 19 page

Feedback computability on Cantor space

We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show that the feedback computable functions are precisely the effectively Borel functions. With this as motivation we define the notion of a feedback computable function on a structure, independent of any coding of the structure as a real. We show that this notion is absolute, and as an example characterize those functions that are computable from a Gandy ordinal with some finite subset distinguished

A simple model for predicting snow albedo decay using observations from the Community Collaborative Rain, Hail, and Snow-Albedo (CoCoRAHS-Albedo) Network

The albedo of seasonal snow cover plays an important role in the global climate system due to its influence on Earth’s radiation budget and energy balance. Volunteer CoCoRaHS-Albedo observers collected 3,249 individual daily albedo, snow depth, and density measurements using standardized techniques at dozens of sites across New Hampshire, USA over four winter seasons. The data show that albedo increases rapidly with snow depth up to ~ 0.14 m. Multiple linear regression models using snowpack age, snow depth or density, and air temperature provide reasonable approximations of surface snow albedo during times of albedo decay. However, the linear models also reveal systematic biases that highlight an important non-linearity in snow albedo decay. Modeled albedo values are reasonably accurate within the range of 0.6 to 0.9, but exhibit a tendency to over-estimate lower albedo values and under-estimate higher albedo values. We hypothesize that rapid reduction in high albedo fresh snow results from a decrease in snow specific surface area, while during melt-events the presence of liquid water in the snowpack accelerates metamorphism and grain growth. We conclude that the CoCoRaHS-Albedo volunteer observer network provides useful snow albedo, depth, and density measurements and serves as an effective model for future measurement campaigns

Post-Pancreatoduodenectomy Outcomes and Epidural Analgesia: A 5-Year Single Institution Experience

Introduction Optimal pain control post-pancreatoduodenectomy is a challenge. Epidural analgesia (EDA) is increasingly utilized despite inherent risks and unclear effects on outcomes. Methods All pancreatoduodenectomies (PD) performed from 1/2013-12/2017 were included. Clinical parameters were obtained from retrospective review of a prospective clinical database, the ACS NSQIP prospective institutional database and medical record review. Chi-Square/Fisher’s Exact and Independent-Samples t-Tests were used for univariable analyses; multivariable regression (MVR) was performed. Results 671 consecutive PD from a single institution were included (429 EDA, 242 non-EDA). On univariable analysis, EDA patients experienced significantly less wound disruption (0.2% vs. 2.1%), unplanned intubation (3.0% vs. 7.9%), pulmonary embolism (0.5% vs. 2.5%), mechanical-ventilation >48hrs (2.1% vs. 7.9%), septic shock (2.6% vs. 5.8%), and lower pain scores. On MVR accounting for baseline group differences (gender, hypertension, pre-operative transfusion, labs, approach, pancreatic duct size), EDA was associated with less superficial wound infections (OR 0.34; CI 0.14-0.83; P=0.017), unplanned intubations (OR 0.36; CI 0.14-0.88; P=0.024), mechanical ventilation >48 hrs (OR 0.22; CI 0.08-0.62; P=0.004), and septic shock (OR 0.39; CI 0.15-1.00; P=0.050). EDA improved pain scores post-PD days 1-3 (P<0.001). No differences were seen in cardiac or renal complications; pancreatic fistula (B+C) or delayed gastric emptying; 30/90-day mortality; length of stay, readmission, discharge destination, or unplanned reoperation. Conclusion Based on the largest single institution series published to date, our data support the use of EDA for optimization of pain control. More importantly, our data document that EDA significantly improved infectious and pulmonary complications

The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations

In this paper, the third in a series illustrating the power of generalized linear models (GLMs) for the astronomical community, we elucidate the potential of the class of GLMs which handles count data. The size of a galaxy's globular cluster population $N_{\rm GC}$ is a prolonged puzzle in the astronomical literature. It falls in the category of count data analysis, yet it is usually modelled as if it were a continuous response variable. We have developed a Bayesian negative binomial regression model to study the connection between $N_{\rm GC}$ and the following galaxy properties: central black hole mass, dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude. The methodology introduced herein naturally accounts for heteroscedasticity, intrinsic scatter, errors in measurements in both axes (either discrete or continuous), and allows modelling the population of globular clusters on their natural scale as a non-negative integer variable. Prediction intervals of 99% around the trend for expected $N_{\rm GC}$comfortably envelope the data, notably including the Milky Way, which has hitherto been considered a problematic outlier. Finally, we demonstrate how random intercept models can incorporate information of each particular galaxy morphological type. Bayesian variable selection methodology allows for automatically identifying galaxy types with different productions of GCs, suggesting that on average S0 galaxies have a GC population 35% smaller than other types with similar brightness.Comment: 14 pages, 12 figures. Accepted for publication in MNRA