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

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

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

Species, Rotation, and Life-Form Diversity Effects on Soil Carbon in Experimental Tropical Ecosystems

Extensive areas of species-rich forests in the tropics have been replaced by tree monocultures over the last two decades, and the impact on biogeochemical cycles is unclear. We characterized effects on soil carbon dynamics of species identity and rotation frequency in experimental plantations containing three native, non-N-fixing tree species, Hyeronima alchoreoides, Cedrela odorata, and Cordia alliodora, grown in monocultures and in polycultures with two monocot species, Euterpe oleracea and Heliconia imbricata. Over all treatments, change in total soil organic carbon (TSOC, 0–15 cm) after 10 years ranged from a loss of 24% (0.9 mg/ha in 1-yr rotation of Cedrela) to an increase of 14% (0.6 mg/ha under Hyeronima polycultures). Species differed in their effects on quantities of TSOC (P = 0.038), but differences were more pronounced in light particulate organic matter (LPOM; P = 0.001), a biologically active, sand-size soil fraction that constituted 6% of TSOC. Effects of rotation frequency were strong; in Cedrela and Cordia, the 4-yr rotations had higher soil C stocks than did long-term monocultures, where soil C stocks had declined under 10-yr-old trees. Under Cedrela and Cordia, polycultures had significantly higher stocks of soil C than monocultures, whereas soil C stocks were high under Hyeronima in both cultures. In polycultures, Hyeronima dominated detrital inputs, contributing 88% of litterfall and fine-root growth, whereas Cedrela and Cordia contributed R2 = 0.70 and 0.14, respectively). These data suggested that roots drove soil C accrual in long-term rotations, and that mechanisms involving root chemistry, and not quantity of detrital inputs, best explained effects of species on soil C sequestration

Childhood Sexual Abuse as an Antecedent of Problem Drinking and Sexual Dysfunction in Women

A number of studies have linked childhood sexual abuse to problems with alcohol and sexual dysfunction in adult women. Moreover, some researchers suggest temporal sequences in which either (a) early sexual abuse increases women\u27s risks of sexual dysfunction, which in turn leads to increased alcohol use, or (b) the reverse, in which sexual abuse contributes to excessive drinking, which in turn impairs sexual functioning. Most studies of these issues to date have had serious methodological problems (e.g., small samples, often from clinical populations lacking control groups). Additional limitations have been the limited range of variables measured and the lack of longitudinal data. This study was designed to overcome many limitations of earlier research. The study attempted, first, to determine if there is an association between childhood sexual abuse and adult alcohol abuse and sexual dysfunction in women, and, second, to test two potential temporal sequences of this relationship using path analysis. Subjects were 143 problem drinkers and 157 nonproblem drinkers from a large national sample of women in the U.S. The longitudinal data were gathered in 1981 and 1986 via structured personal interviews and private questionnaires for information of a more sensitive nature (e.g., sexual experience and sexual abuse). Results indicate that child sexual abuse predicts adult problem drinking and to a lesser degree sexual dysfunction. However, the temporal sequences among these variables are less clear. Child sexual abuse was a stronger predictor of both 1981 and 1986 problem drinking and 1986 sexual dysfunction among nonproblem drinkers than among problem drinkers. Often lacking a direct effect of its own among problem drinkers, child sexual abuse did predict a number of mediating variables (e.g., depression, suicidal thoughts or attempts, distrust, early sexual relations), some of which led to problem drinking in 1981. A surprising finding was that among problem drinkers, problem drinking in 1981 led to less sexual dysfunction in 1986 rather than more. Differences in predictors of problem drinking onset as compared with chronicity were discussed as a possible explanation for the different patterns among nonproblem and problem drinkers

The ties that bind: Jamaican elders\u27 testimonies of community life

This study explores the meanings of community, participation, activism and being old with eight older Jamaicans. The roles of culture and religion are examined in reference to the participants’ community and social aging experiences. The researcher used a culturally relevant research paradigm [Diasporic African] incorporating indigenous methods [testifying] grounded in the participants’ cultural and religious identifies and experiences as older Christian Jamaicans of African descent. The use of testimonies is described in Stanfield’s (1998) work on ethic modeling in qualitative research design. Demographic information and life histories focussing on community roles, sites for participation across the life span, and the meaning of community experiences in later years were derived from the participants’ testimonies. The participants, seven women interviewed in Jamaica and one man interviewed while he was on vacation in Canada, ranged in age from 70 to 102 years old. The average interview length was 45 minutes. The data analysis process involved an intuitive process of highlighting convergent and divergent experiences within the testimonies. Common words and phrases were coded as thematic categories. Memos, categorizing strategies and contextualizing strategies were also used as prescribed in Maxwell’s (1996) work on qualitative research design. Participants’ responses for the meanings of community and participation reflect the values of sharing, giving, and unity. The participants defined being old by making reference to the Biblical concept of “three-score and ten.” All of the participants identified themselves as old; however, they stated that “you are as old as you feel,” indicating that they perceived an attitudinal component to their identity as older persons. For the eight older persons in this study, activism was not a relevant term; however, a few individuals’ community involvements included activities that were more indicative of advocacy efforts. Overall the eight elders were involved in care-giving, income-generating, recreational, civic, and religious activities. “Sharing,” “giving,” and “being together” were the words participants used to describe community participation. Connectedness, relationship, and the concept of the collective are interpreted as extensions to the participants’ words. The findings are discussed in relation to cultural legacies and religious values found in Jamaican culture that is derived from the synthesis of African, Aboriginal and European elements. The author argues that the value for the collective [collectivism] is derived from the African cultural legacy within Jamaica. Jamaica is discussed as a sociocultural context embedded within the sociocultural contexts of the Caribbean and Latin America, the Americas, and the African diaspora. Descriptions of the traditional and changing roles of older persons within these sociocultural and geopolitical entities are presented to contextualize the participants’ experiences of community and growing older. Factors influencing the changing role of seniors in Jamaica are also discussed, as well as the opportunities that exist for capacity-building offers. Empowerment is inferred from the participants’ testimonies and the researcher’s observations. Arguments are presented supporting the relevance of the study’s findings to community psychology particularly where the experiences of older persons in the English-speaking Caribbean are unrepresented