We will establish lower bounds in terms of the level for the number of holomorphic cusp forms of weight k > 2 whose various L-functions do not vanish at the central critical point. This work generalizes the work of W. Duke [1] which was for the case of weight 2.

Scoring to identify high-affinity compounds remains a challenge in virtual screening. On one hand, protein-ligand scoring focuses on weighting favorable and unfavorable interactions between the two molecules. Ligand-based scoring, on the other hand, focuses on how well the shape and chemistry of each ligand candidate overlay on a three-dimensional reference ligand. Our hypothesis is that a hybr...

We have calculated the number of dormant, nearly isotropic Oort cloud comets in the solar system by (i) combining orbital distribution models with statistical models of dormant comet discoveries by well-defined surveys and (ii) comparing the model results to observations of a population of dormant comets. Dynamical models that assume that comets are not destroyed predict that we should have dis...

In this paper, we address the problem of quantifying the overall extent to which a testtaker’s essay deals with the topic it is assigned (prompt). We experiment with a number of models for word topicality, and a number of approaches for aggregating word-level indices into text-level ones. All models are evaluated for their ability to predict the holistic quality of essays. We show that the best...

In this equation, n represents the number of Figures of Merit (FoMs) that are to be combined, xi represents the output of the scoring function for the ith FoM and wi represents the weight of importance assigned to the ith FoM. The Product Tradeoff Function is commonly used for example in computing cost to benefit ratios and in doing risk analyses. Unfortunately, the published equation on page 1...

MS/MS and associated database search algorithms are essential proteomic tools for identifying peptides. Due to their widespread use, it is now time to perform a systematic analysis of the various algorithms currently in use. Using blood specimens used in the HUPO Plasma Proteome Project, we have evaluated five search algorithms with respect to their sensitivity and specificity, and have also ac...

We describe a study aimed at measuring the use of factual information in test-taker essays and assessing its effectiveness for predicting essay scores. We found medium correlations with the proposed measures, that remained significant after the effect of essay length was factored out. The correlations did not differ substantionally between a simple, relatively robust measure vs a more sophistic...

Let H0 be an arbitrary self-adjoint n × n matrix and H(n) be an n × n (random) Wigner matrix. We show that t 7→ Tr exp(H(n)−itH0) is positive definite in the average. This partially answers a long-standing conjecture. On the basis of asymptotic freeness our result implies that t 7→ τ(exp(a − itb)) is positive definite whenever the noncommutative random variables a and b are in free relation, wi...