Laplacian Distribution and Domination

Let $m_G(I)$ denote the number of Laplacian eigenvalues of a graph $G$ in an interval $I$, and let $\gamma(G)$ denote its domination number. We extend the recent result $m_G[0,1) \leq \gamma(G)$, and show that isolate-free graphs also satisfy $\gamma(G) \leq m_G[2,n]$. In pursuit of better understanding Laplacian eigenvalue distribution, we find applications for these inequalities. We relate these spectral parameters with the approximability of $\gamma(G)$, showing that $\frac{\gamma(G)}{m_G[0,1)} \not\in O(\log n)$. However, $\gamma(G) \leq m_G[2, n] \leq (c + 1) \gamma(G)$ for $c$-cyclic graphs, $c \geq 1$. For trees $T$, $\gamma(T) \leq m_T[2, n] \leq 2 \gamma(G)$

Preservation of glaciochemical time-series in snow and ice from the Penny Ice Cap, Baffin Island

A detailed investigation of major ion concentrations of snow and ice in the summit region of Penny Ice Cap (PIC) was performed to determine the effects of summer melt on the glaciochemical time-series. While ion migration due to meltwater percolation makes it difficult to confidently count annual layers in the glaciochemical profiles, time-series of these parameters do show good structure and a strong one year spectral component, suggesting that annual to biannual signals are preserved in PIC glaciochemical records

Potential implications of practice effects in Alzheimer's disease prevention trials.

IntroductionPractice effects (PEs) present a potential confound in clinical trials with cognitive outcomes. A single-blind placebo run-in design, with repeated cognitive outcome assessments before randomization to treatment, can minimize effects of practice on trial outcome.MethodsWe investigated the potential implications of PEs in Alzheimer's disease prevention trials using placebo arm data from the Alzheimer's Disease Cooperative Study donepezil/vitamin E trial in mild cognitive impairment. Frequent ADAS-Cog measurements early in the trial allowed us to compare two competing trial designs: a 19-month trial with randomization after initial assessment, versus a 15-month trial with a 4-month single-blind placebo run-in and randomization after the second administration of the ADAS-Cog. Standard power calculations assuming a mixed-model repeated-measure analysis plan were used to calculate sample size requirements for a hypothetical future trial designed to detect a 50% slowing of cognitive decline.ResultsOn average, ADAS-Cog 13 scores improved at first follow-up, consistent with a PE and progressively worsened thereafter. The observed change for a 19-month trial (1.18 points) was substantively smaller than that for a 15-month trial with 4-month run-in (1.79 points). To detect a 50% slowing in progression under the standard design (i.e., a 0.59 point slowing), a future trial would require 3.4 times more subjects than would be required to detect the comparable percent slowing (i.e., 0.90 points) with the run-in design.DiscussionAssuming the improvement at first follow-up observed in this trial represents PEs, the rate of change from the second assessment forward is a more accurate representation of symptom progression in this population and is the appropriate reference point for describing treatment effects characterized as percent slowing of symptom progression; failure to accommodate this leads to an oversized clinical trial. We conclude that PEs are an important potential consideration when planning future trials

Optimal Weighting of Preclinical Alzheimer’s Cognitive Composite (PACC) Scales to Improve their Performance as Outcome Measures for Alzheimer’s Disease Clinical Trials

Introduction: Cognitive composite scales constructed by combining existing neuropsychometric tests are seeing wide application as endpoints for clinical trials and cohort studies of Alzheimer’s disease (AD) predementia conditions. Preclinical Alzheimer’s Cognitive Composite (PACC) scales are composite scores calculated as the sum of the component test scores weighted by the reciprocal of their standard deviations at the baseline visit. Reciprocal standard deviation is an arbitrary weighting in this context, and may be an inefficient utilization of the data contained in the component measures. Mathematically derived optimal composite weighting is a promising alternative. Methods: Sample size projections using standard power calculation formulas were used to describe the relative performance of component measures and their composites when used as endpoints for clinical trials. Power calculations were informed by (n=1,333) amnestic mild cognitive impaired participants in the National Alzheimer’s Coordinating Center (NACC) Uniform Data Set. Results: A composite constructed using PACC reciprocal standard deviation weighting was both less sensitive to change than one of its component measures and less sensitive to change than its optimally weighted counterpart. In standard sample size calculations informed by NACC data, a clinical trial using the PACC weighting would require 38% more subjects than a composite calculated using optimal weighting. Discussion: These findings illustrate how reciprocal standard deviation weighting can result in inefficient cognitive composites, and underscore the importance of component weights to the performance of composite scales. In the future, optimal weighting parameters informed by accumulating clinical trial data may improve the efficiency of clinical trials in AD

Field Guide to Exhumed Major Faults in Southern California

This field guide provides an overview of exposures and provides a field trip guide to localities of exhumed faults in southern California. We focus on exposures of faults that are documented or inferred to be exhumed from seismogenic depths. The goal of this guidebook is to provide geoscientists who are interested in fault zone mechanics and earthquake processes a summary of the results of the work on these sites