A comparison of three heuristics to choose the variable ordering for CAD

Cylindrical algebraic decomposition (CAD) is a key tool for problems in real algebraic geometry and beyond. When using CAD there is often a choice over the variable ordering to use, with some problems infeasible in one ordering but simple in another. Here we discuss a recent experiment comparing three heuristics for making this choice on thousands of examples

Characterization of Aerodynamic Interactions with the Mars Science Laboratory Reaction Control System Using Computation and Experiment

On August 5 , 2012, the Mars Science Laboratory (MSL) entry capsule successfully entered Mars' atmosphere and landed the Curiosity rover in Gale Crater. The capsule used a reaction control system (RCS) consisting of four pairs of hydrazine thrusters to fly a guided entry. The RCS provided bank control to fly along a flight path commanded by an onboard computer and also damped unwanted rates due to atmospheric disturbances and any dynamic instabilities of the capsule. A preliminary assessment of the MSL's flight data from entry showed that the capsule flew much as predicted. This paper will describe how the MSL aerodynamics team used engineering analyses, computational codes and wind tunnel testing in concert to develop the RCS system and certify it for flight. Over the course of MSL's development, the RCS configuration underwent a number of design iterations to accommodate mechanical constraints, aeroheating concerns and excessive aero/RCS interactions. A brief overview of the MSL RCS configuration design evolution is provided. Then, a brief description is presented of how the computational predictions of RCS jet interactions were validated. The primary work to certify that the RCS interactions were acceptable for flight was centered on validating computational predictions at hypersonic speeds. A comparison of computational fluid dynamics (CFD) predictions to wind tunnel force and moment data gathered in the NASA Langley 31-Inch Mach 10 Tunnel was the lynch pin to validating the CFD codes used to predict aero/RCS interactions. Using the CFD predictions and experimental data, an interaction model was developed for Monte Carlo analyses using 6-degree-of-freedom trajectory simulation. The interaction model used in the flight simulation is presented

Oxidized low-density lipoprotein inhibits hepatitis C virus cell entry in human hepatoma cells.

Cell entry of hepatitis C virus, pseudoparticles (HCVpp) and cell culture grown virus (HCVcc), requires the interaction of viral glycoproteins with CD81 and other as yet unknown cellular factors. One of these is likely to be the scavenger receptor class B type I (SR-BI). To further understand the role of SR-BI, we examined the effect of SR-BI ligands on HCVpp and HCVcc infectivity. Oxidized low-density lipoprotein (oxLDL), but not native LDL, potently inhibited HCVpp and HCVcc cell entry. Pseudoparticles bearing unrelated viral glycoproteins or bovine viral diarrhea virus were not affected. A dose-dependent inhibition was observed for HCVpp bearing diverse viral glycoproteins with an approximate IC50 of 1.5 microg/mL apolipoprotein content, which is within the range of oxLDL reported to be present in human plasma. The ability of lipoprotein components to bind to target cells associated with their antiviral activity, suggesting a mechanism of action which targets a cell surface receptor critical for HCV infection of the host cell. However, binding of soluble E2 to SR-BI or CD81 was not affected by oxLDL, suggesting that oxLDL does not act as a simple receptor blocker. At the same time, oxLDL incubation altered the biophysical properties of HCVpp, suggesting a ternary interaction of oxLDL with both virus and target cells. In conclusion, the SR-BI ligand oxLDL is a potent cell entry inhibitor for a broad range of HCV strains in vitro. These findings suggest that SR-BI is an essential component of the cellular HCV receptor complex

Completing the Results of the 2013 Boston Marathon

The 2013 Boston marathon was disrupted by two bombs placed near the finish line. The bombs resulted in three deaths and several hundred injuries. Of lesser concern, in the immediate aftermath, was the fact that nearly 6,000 runners failed to finish the race. We were approached by the marathon's organizers, the Boston Athletic Association (BAA), and asked to recommend a procedure for projecting finish times for the runners who could not complete the race. With assistance from the BAA, we created a dataset consisting of all the runners in the 2013 race who reached the halfway point but failed to finish, as well as all runners from the 2010 and 2011 Boston marathons. The data consist of split times from each of the 5 km sections of the course, as well as the final 2.2 km (from 40 km to the finish). The statistical objective is to predict the missing split times for the runners who failed to finish in 2013. We set this problem in the context of the matrix completion problem, examples of which include imputing missing data in DNA microarray experiments, and the Netflix prize problem. We propose five prediction methods and create a validation dataset to measure their performance by mean squared error and other measures. The best method used local regression based on a K-nearest-neighbors algorithm (KNN method), though several other methods produced results of similar quality. We show how the results were used to create projected times for the 2013 runners and discuss potential for future application of the same methodology. We present the whole project as an example of reproducible research, in that we are able to make the full data and all the algorithms we have used publicly available, which may facilitate future research extending the methods or proposing completely different approaches

Completing the Results of the 2013 Boston Marathon

The 2013 Boston marathon was disrupted by two bombs placed near the finish line. The bombs resulted in three deaths and several hundred injuries. Of lesser concern, in the immediate aftermath, was the fact that nearly 6,000 runners failed to finish the race. We were approached by the marathon's organizers, the Boston Athletic Association (BAA), and asked to recommend a procedure for projecting finish times for the runners who could not complete the race. With assistance from the BAA, we created a dataset consisting of all the runners in the 2013 race who reached the halfway point but failed to finish, as well as all runners from the 2010 and 2011 Boston marathons. The data consist of split times from each of the 5 km sections of the course, as well as the final 2.2 km (from 40 km to the finish). The statistical objective is to predict the missing split times for the runners who failed to finish in 2013. We set this problem in the context of the matrix completion problem, examples of which include imputing missing data in DNA microarray experiments, and the Netflix prize problem. We propose five prediction methods and create a validation dataset to measure their performance by mean squared error and other measures. The best method used local regression based on a K-nearest-neighbors algorithm (KNN method), though several other methods produced results of similar quality. We show how the results were used to create projected times for the 2013 runners and discuss potential for future application of the same methodology. We present the whole project as an example of reproducible research, in that we are able to make the full data and all the algorithms we have used publicly available, which may facilitate future research extending the methods or proposing completely different approaches

Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition With Groebner Bases

Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the size of the input. Hence it is important to formulate the problem in the best manner for the CAD algorithm. One possibility is to precondition the input polynomials using Groebner Basis (GB) theory. Previous experiments have shown that while this can often be very beneficial to the CAD algorithm, for some problems it can significantly worsen the CAD performance. In the present paper we investigate whether machine learning, specifically a support vector machine (SVM), may be used to identify those CAD problems which benefit from GB preconditioning. We run experiments with over 1000 problems (many times larger than previous studies) and find that the machine learned choice does better than the human-made heuristic

Ubiquitination directly enhances activity of the deubiquitinating enzyme ataxin‐3

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/102210/1/emboj2008289-sup-0001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/102210/2/emboj2008289.pd