Partial zeta functions, partial exponential sums, and pp-adic estimates

Partial zeta functions of algebraic varieties over finite fields generalize the classical zeta function by allowing each variable to be defined over a possibly different extension field of a fixed finite field. Due to this extra variation their rationality is surprising, and even simple examples are delicate to compute. For instance, we give a detailed description of the partial zeta function of an affine curve where the number of unit poles varies, a property different from classical zeta functions. On the other hand, they do retain some properties similar to the classical case. To this end, we give Chevalley-Warning type bounds for partial zeta functions and $L$-functions associated to partial exponential sums.Comment: 8 page

Cutting the Cake: A Language for Fair Division

The fair division literature in economics considers how to divide resources between multiple agents such that the allocation is envy-free: each agent receives their favorite piece. Researchers have developed a variety of fair division protocols for the most standard setting, where the agents want to split a single item, however, the protocols are highly intricate and the proofs of envy-freeness involve tedious case analysis. We propose Slice, a domain specific language for fair-division. Programs in our language can be converted to logical formulas encoding envy-freeness and other target properties. Then, the constraints can be dispatched to automated solvers. We prove that our constraint generation procedure is sound and complete. We also report on a prototype implementation of Slice, which we have used to automatically check envy-freeness for several protocols from the fair division literature.Comment: 31 pages, 15 figures, PLDI 202

AWLCO: All-Window Length Co-Occurrence

Analyzing patterns in a sequence of events has applications in text analysis, computer programming, and genomics research. In this paper, we consider the all-window-length analysis model which analyzes a sequence of events with respect to windows of all lengths. We study the exact co-occurrence counting problem for the all-window-length analysis model. Our first algorithm is an offline algorithm that counts all-window-length co-occurrences by performing multiple passes over a sequence and computing single-window-length co-occurrences. This algorithm has the time complexity $O(n)$ for each window length and thus a total complexity of $O(n^2)$ and the space complexity $O(|I|)$ for a sequence of size n and an itemset of size $|I|$. We propose AWLCO, an online algorithm that computes all-window-length co-occurrences in a single pass with the expected time complexity of $O(n)$ and space complexity of $O( \sqrt{ n|I| })$. Following this, we generalize our use case to patterns in which we propose an algorithm that computes all-window-length co-occurrence with expected time complexity $O(n|I|)$ and space complexity $O( \sqrt{n|I|} + e_{max}|I|)$, where $e_{max}$ is the length of the largest pattern

Library Analytics Investigation Team Recommendations

The University of Michigan Library’s Technology Alignment and Stewardship Committee charged the Library Analytics Investigation Team in the Winter 2016 cycle. The team met from April through September of 2016 to investigate processes to provide library-generated data to library staff for service improvement and/or research investigations.http://deepblue.lib.umich.edu/bitstream/2027.42/134406/1/Library Analytics Investigation Team Report.pdfDescription of Library Analytics Investigation Team Report.pdf : Investigation Team Repor

SNPs Associated with Cerebrospinal Fluid Phospho-Tau Levels Influence Rate of Decline in Alzheimer's Disease

Alzheimer's Disease (AD) is a complex and multifactorial disease. While large genome-wide association studies have had some success in identifying novel genetic risk factors for AD, case-control studies are less likely to uncover genetic factors that influence progression of disease. An alternative approach to identifying genetic risk for AD is the use of quantitative traits or endophenotypes. The use of endophenotypes has proven to be an effective strategy, implicating genetic risk factors in several diseases, including anemia, osteoporosis and heart disease. In this study we identify a genetic factor associated with the rate of decline in AD patients and present a methodology for identification of other such factors. We have used an established biomarker for AD, cerebrospinal fluid (CSF) tau phosphorylated at threonine 181 (ptau181) levels as an endophenotype for AD, identifying a SNP, rs1868402, in the gene encoding the regulatory sub-unit of protein phosphatase B, associated with CSF ptau181 levels in two independent CSF series . We show no association of rs1868402 with risk for AD or age at onset, but detected a very significant association with rate of progression of disease that is consistent in two independent series . Our analyses suggest that genetic variants associated with CSF ptau181 levels may have a greater impact on rate of progression, while genetic variants such as APOE4, that are associated with CSF Aβ42 levels influence risk and onset but not the rate of progression. Our results also suggest that drugs that inhibit or decrease tau phosphorylation may slow cognitive decline in individuals with very mild dementia or delay the appearance of memory problems in elderly individuals with low CSF Aβ42 levels. Finally, we believe genome-wide association studies of CSF tau/ptau181 levels should identify novel genetic variants which will likely influence rate of progression of AD

Systematic review of the validity and reliability of consumer-wearable activity trackers

Abstract Background Consumer-wearable activity trackers are electronic devices used for monitoring fitness- and other health-related metrics. The purpose of this systematic review was to summarize the evidence for validity and reliability of popular consumer-wearable activity trackers (Fitbit and Jawbone) and their ability to estimate steps, distance, physical activity, energy expenditure, and sleep. Methods Searches included only full-length English language studies published in PubMed, Embase, SPORTDiscus, and Google Scholar through July 31, 2015. Two people reviewed and abstracted each included study. Results In total, 22 studies were included in the review (20 on adults, 2 on youth). For laboratory-based studies using step counting or accelerometer steps, the correlation with tracker-assessed steps was high for both Fitbit and Jawbone (Pearson or intraclass correlation coefficients (CC) > =0.80). Only one study assessed distance for the Fitbit, finding an over-estimate at slower speeds and under-estimate at faster speeds. Two field-based studies compared accelerometry-assessed physical activity to the trackers, with one study finding higher correlation (Spearman CC 0.86, Fitbit) while another study found a wide range in correlation (intraclass CC 0.36–0.70, Fitbit and Jawbone). Using several different comparison measures (indirect and direct calorimetry, accelerometry, self-report), energy expenditure was more often under-estimated by either tracker. Total sleep time and sleep efficiency were over-estimated and wake after sleep onset was under-estimated comparing metrics from polysomnography to either tracker using a normal mode setting. No studies of intradevice reliability were found. Interdevice reliability was reported on seven studies using the Fitbit, but none for the Jawbone. Walking- and running-based Fitbit trials indicated consistently high interdevice reliability for steps (Pearson and intraclass CC 0.76–1.00), distance (intraclass CC 0.90–0.99), and energy expenditure (Pearson and intraclass CC 0.71–0.97). When wearing two Fitbits while sleeping, consistency between the devices was high. Conclusion This systematic review indicated higher validity of steps, few studies on distance and physical activity, and lower validity for energy expenditure and sleep. The evidence reviewed indicated high interdevice reliability for steps, distance, energy expenditure, and sleep for certain Fitbit models. As new activity trackers and features are introduced to the market, documentation of the measurement properties can guide their use in research settings