Deterministic Time-Space Tradeoffs for k-SUM

Given a set of numbers, the $k$-SUM problem asks for a subset of $k$ numbers that sums to zero. When the numbers are integers, the time and space complexity of $k$-SUM is generally studied in the word-RAM model; when the numbers are reals, the complexity is studied in the real-RAM model, and space is measured by the number of reals held in memory at any point. We present a time and space efficient deterministic self-reduction for the $k$-SUM problem which holds for both models, and has many interesting consequences. To illustrate: * $3$-SUM is in deterministic time $O(n^2 \lg\lg(n)/\lg(n))$ and space $O\left(\sqrt{\frac{n \lg(n)}{\lg\lg(n)}}\right)$. In general, any polylogarithmic-time improvement over quadratic time for $3$-SUM can be converted into an algorithm with an identical time improvement but low space complexity as well. * $3$-SUM is in deterministic time $O(n^2)$ and space $O(\sqrt n)$, derandomizing an algorithm of Wang. * A popular conjecture states that 3-SUM requires $n^{2-o(1)}$ time on the word-RAM. We show that the 3-SUM Conjecture is in fact equivalent to the (seemingly weaker) conjecture that every $O(n^{.51})$-space algorithm for $3$-SUM requires at least $n^{2-o(1)}$ time on the word-RAM. * For $k \ge 4$, $k$-SUM is in deterministic $O(n^{k - 2 + 2/k})$ time and $O(\sqrt{n})$ space

Post Traumatic Stress Disorder and The Reduction of Symptoms: A Review

Post-traumatic stress disorder (PTSD) is a life altering and often debilitating disorder that can have a profound effect on someone’s life. While there is currently no cure, research into different treatments for PTSD is ongoing. Conditions co-morbid with PTSD can cause difficulty in research. Several illegal drugs like psilocybin, cannabis, lysergic acid diethylamide, and mescaline have shown promise, but need further research as treatments for PTSD symptoms. Keywords: Post-traumatic stress disorder (PTSD), symptoms, reductio

Sex Differences in Otoacoustic Emissions to Examine Underlying Cochlear Mechanisms

This article was published in the Spring 2011 issue of the Journal of Undergraduate Researc

Nature of the appeal of the eighth-century prophets ..

Typewritten sheets in cover. Thesis (M.A.)--Boston University Bibliography: p. 108-110

WHEN MOLECULES AND MORPHOLOGY CLASH: REVISITING SPECIES TREE RECONSTRUCTION OF AMBYSTOMATID SALAMANDERS USING MULTIPLE NUCLEAR LOCI

The analysis of diverse data sets can yield different phylogenetic estimates that challenge systematists to explain the source of discordance. The Ambystomatidae are a classic example of this phylogenetic conflict. Previous attempts to resolve the ambystomatid species tree using allozymic, morphological, and mitochondrial sequence data have yielded different estimates, making it unclear which data source best approximates ambystomatid phylogeny. We present the first multi-locus DNA sequencebased phylogenetic study of the Ambystomatidae. Because independent loci can contain discordant gene tree histories, concatenating unlinked loci into a single data matrix can lead to strongly supported and erroneous results. Therefore, we utilized a range of analyses, including coalescent-based methods of phylogenetic estimation that account for incomplete lineage sorting and concordance-based methods that estimate the proportion of sampled loci that support a particular clade. We repeated these analyses with the removal of individual loci to determine if any locus has a disproportionate effect on our phylogenetic results. Many deep and relatively shallow clades within Ambystoma were robustly resolved. Analyses that excluded loci produced overlapping posterior distributions, suggesting no disproportionate influence of any particular locus. Our estimates differ from previous hypotheses, although there was greater similarity with previous molecular estimates, relative to morphological estimates