The Complexity of Approximately Counting Stable Matchings

We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances between "preference points" and "attribute points". Irving and Leather proved that counting the number of stable matchings in the general case is #P-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph (#BIS). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibilty remains even in the restricted $k$-attribute setting when $k \geq 3$ (dot products) or $k \geq 2$ (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product setting.Comment: Fixed typos, small revisions for clarification, et

The Impact of Peer Accountability Groups in a Mathematics Classroom

This research study will examine student goal attainment through self- and peer analysis. The participants of this study will be students in an eighth grade mathematics class. Research was conducted through Google forms where students were able to list their goals, ideas for reaching those goals, and respond to weekly prompts. Overall, the peer accountability groups tended to be beneficial for most students

Utilitarian resource assignment

This paper studies a resource allocation problem introduced by Koutsoupias and Papadimitriou. The scenario is modelled as a multiple-player game in which each player selects one of a finite number of known resources. The cost to the player is the total weight of all players who choose that resource, multiplied by the ``delay'' of that resource. Recent papers have studied the Nash equilibria and social optima of this game in terms of the $L_\infty$ cost metric, in which the social cost is taken to be the maximum cost to any player. We study the $L_1$ variant of this game, in which the social cost is taken to be the sum of the costs to the individual players, rather than the maximum of these costs. We give bounds on the size of the coordination ratio, which is the ratio between the social cost incurred by selfish behavior and the optimal social cost; we also study the algorithmic problem of finding optimal (lowest-cost) assignments and Nash Equilibria. Additionally, we obtain bounds on the ratio between alternative Nash equilibria for some special cases of the problem.Comment: 19 page

Providence College Library+Commons Promotional Branding Material: Library+Commons Graphics

A PDF file containing Library+Commons images and grapics used at Providence College

Markov chain comparison

This is an expository paper, focussing on the following scenario. We have two Markov chains, $\mathcal {M}$ and $\mathcal {M}'$. By some means, we have obtained a bound on the mixing time of $\mathcal {M}'$. We wish to compare $\mathcal {M}$ with $\mathcal {M}'$ in order to derive a corresponding bound on the mixing time of $\mathcal {M}$. We investigate the application of the comparison method of Diaconis and Saloff-Coste to this scenario, giving a number of theorems which characterize the applicability of the method. We focus particularly on the case in which the chains are not reversible. The purpose of the paper is to provide a catalogue of theorems which can be easily applied to bound mixing times.Comment: Published at http://dx.doi.org/10.1214/154957806000000041 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Using Semantic Web Technologies to Support Enhanced Situation Awareness

The AKTiveSA project is using Semantic Web technologies to support information fusion and enhanced situational awareness in a simulated humanitarian relief scenario. We have developed an application that shows how situational awareness can be supported during humanitarian relief situations; often occurring alongside military conflict. Semantic Web technologies provide new opportunities for harvesting information from numerous, disparate and often heterogeneous information sources and can be used to better support complex knowledge fusion

\u3cem\u3eAlsea Valley Alliance v. Evans\u3c/em\u3e and the Meaning of Species Under the Endangered Species Act: A Return to Congressional Intent

This article examines whether the Alsea decision\u27s definition of species is consistent with the Endangered Species Act by examining the language of the ESA and Congressional intent. This article then examines some of the implications of the Alsea decision in the Northwest. Counting hatchery salmon would likely result in the removal of most salmon ESUs from the endangered or threatened list, ending many of the costly restrictions imposed by the ESA. In particular, Part I discusses the ESA provisions and congressional intent regarding the definition of species that is pertinent to understanding Alsea. Part II describes some of the effects of salmon listings in the Northwest. Part III describes the Alsea case, including the history of the Oregon coastal coho ESU listing and the procedural history of the case. Part IV analyzes the court\u27s legal reasoning in Alsea. Finally, Part V considers the implications of the case and the potential structure and outcome of the current NMFS\u27s policy review

\u3cem\u3eAlsea Valley Alliance v. Evans\u3c/em\u3e and the Meaning of Species Under the Endangered Species Act: A Return to Congressional Intent

This article examines whether the Alsea decision\u27s definition of species is consistent with the Endangered Species Act by examining the language of the ESA and Congressional intent. This article then examines some of the implications of the Alsea decision in the Northwest. Counting hatchery salmon would likely result in the removal of most salmon ESUs from the endangered or threatened list, ending many of the costly restrictions imposed by the ESA. In particular, Part I discusses the ESA provisions and congressional intent regarding the definition of species that is pertinent to understanding Alsea. Part II describes some of the effects of salmon listings in the Northwest. Part III describes the Alsea case, including the history of the Oregon coastal coho ESU listing and the procedural history of the case. Part IV analyzes the court\u27s legal reasoning in Alsea. Finally, Part V considers the implications of the case and the potential structure and outcome of the current NMFS\u27s policy review

Fine particulate matter pollution and risk of community-acquired sepsis

While air pollution has been associated with health complications, its effect on sepsis risk is unknown. We examined the association between fine particulate matter (PM2.5) air pollution and risk of sepsis hospitalization. We analyzed data from the 30,239 community-dwelling adults in the Reasons for Geographic and Racial Differences in Stroke (REGARDS) cohort linked with satellite-derived measures of PM2.5 data. We defined sepsis as a hospital admission for a serious infection with ≥2 systemic inflammatory response (SIRS) criteria. We performed incidence density sampling to match sepsis cases with 4 controls by age (±5 years), sex, and race. For each matched group we calculated mean daily PM2.5 exposures for short-term (30-day) and long-term (one-year) periods preceding the sepsis event. We used conditional logistic regression to evaluate the association between PM2.5 exposure and sepsis, adjusting for education, income, region, temperature, urbanicity, tobacco and alcohol use, and medical conditions. We matched 1386 sepsis cases with 5544 non-sepsis controls. Mean 30-day PM2.5 exposure levels (Cases 12.44 vs. Controls 12.34 µg/m3; p = 0.28) and mean one-year PM2.5 exposure levels (Cases 12.53 vs. Controls 12.50 µg/m3; p = 0.66) were similar between cases and controls. In adjusted models, there were no associations between 30-day PM2.5 exposure levels and sepsis (4th vs. 1st quartiles OR: 1.06, 95% CI: 0.85–1.32). Similarly, there were no associations between one-year PM2.5 exposure levels and sepsis risk (4th vs. 1st quartiles OR: 0.96, 95% CI: 0.78–1.18). In the REGARDS cohort, PM2.5 air pollution exposure was not associated with risk of sepsis