A Combinatorial Formula for Certain Elements of Upper Cluster Algebras

We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is properly contained in its upper cluster algebra

Stochastic Blockmodeling for Online Advertising

Online advertising is an important and huge industry. Having knowledge of the website attributes can contribute greatly to business strategies for ad-targeting, content display, inventory purchase or revenue prediction. Classical inferences on users and sites impose challenge, because the data is voluminous, sparse, high-dimensional and noisy. In this paper, we introduce a stochastic blockmodeling for the website relations induced by the event of online user visitation. We propose two clustering algorithms to discover the instrinsic structures of websites, and compare the performance with a goodness-of-fit method and a deterministic graph partitioning method. We demonstrate the effectiveness of our algorithms on both simulation and AOL website dataset

Wealth, Volume and Stock Market Volatility: Case of Hong Kong (1993-2001)

This paper attempts to answer the question of whether the gain and loss in property market speculations and rate of information flow play a significant role in stock market volatility in Hong Kong. To test for our wealth-volume-volatility hypothesis, two different measures of volatility: Absolute (absolute value of standard deviation from mean with monthly dimension) and conditional (EGARCH) are used and results are compared. In both measures we find evidence of a positive wealth effect on stock market volatility, in particular in the investment of upper luxury class of property in Hong Kong. To account for this result, we apply the newly developed conditional confidence theory. Although we fail to establish a volume-volatility relationship in our estimation, we offer additional dimensions to the explanation of our observation.

Sciatic neuropathy with preserved sensory nerve action potentials, a case series

Background: Sciatic neuropathy is differentiated from lumbosacral radiculopathy based on the finding of abnormal sensory nerve action potentials (SNAPs). Cases of sciatic neuropathy with intact SNAPS have not been well described. Methods: A retrospective analysis of 12 patients with sciatic neuropathy in a single institution. Results: We describe 12 patients in whom a sciatic neuropathy was diagnosed based on a combination of history, physical exam, radiological and electrodiagnostic (EDX) findings. Lower extremity SNAPs were found to be within normal range in all patients, although SNAP amplitude asymmetry between both sides was observed in 3. Included patients were young (mean age of 40.3 years) and mostly female (9 patients). Conclusions: Sciatic neuropathy may occur with a relative sparing of sensory fibers. Recognition of this group of patients should help to avoid making a misdiagnosis of lumbosacral radiculopathy

A nested mixture model for protein identification using mass spectrometry

Mass spectrometry provides a high-throughput way to identify proteins in biological samples. In a typical experiment, proteins in a sample are first broken into their constituent peptides. The resulting mixture of peptides is then subjected to mass spectrometry, which generates thousands of spectra, each characteristic of its generating peptide. Here we consider the problem of inferring, from these spectra, which proteins and peptides are present in the sample. We develop a statistical approach to the problem, based on a nested mixture model. In contrast to commonly used two-stage approaches, this model provides a one-stage solution that simultaneously identifies which proteins are present, and which peptides are correctly identified. In this way our model incorporates the evidence feedback between proteins and their constituent peptides. Using simulated data and a yeast data set, we compare and contrast our method with existing widely used approaches (PeptideProphet/ProteinProphet) and with a recently published new approach, HSM. For peptide identification, our single-stage approach yields consistently more accurate results. For protein identification the methods have similar accuracy in most settings, although we exhibit some scenarios in which the existing methods perform poorly.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS316 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org