Chromatic quasisymmetric functions

We introduce a quasisymmetric refinement of Stanley's chromatic symmetric function. We derive refinements of both Gasharov's Schur-basis expansion of the chromatic symmetric function and Chow's expansion in Gessel's basis of fundamental quasisymmetric functions. We present a conjectural refinement of Stanley's power sum basis expansion, which we prove in special cases. We describe connections between the chromatic quasisymmetric function and both the $q$-Eulerian polynomials introduced in our earlier work and, conjecturally, representations of symmetric groups on cohomology of regular semisimple Hessenberg varieties, which have been studied by Tymoczko and others. We discuss an approach, using the results and conjectures herein, to the $e$-positivity conjecture of Stanley and Stembridge for incomparability graphs of $(3+1)$-free posets.Comment: 57 pages; final version, to appear in Advances in Mat

Eulerian quasisymmetric functions

We introduce a family of quasisymmetric functions called {\em Eulerian quasisymmetric functions}, which specialize to enumerators for the joint distribution of the permutation statistics, major index and excedance number on permutations of fixed cycle type. This family is analogous to a family of quasisymmetric functions that Gessel and Reutenauer used to study the joint distribution of major index and descent number on permutations of fixed cycle type. Our central result is a formula for the generating function for the Eulerian quasisymmetric functions, which specializes to a new and surprising $q$-analog of a classical formula of Euler for the exponential generating function of the Eulerian polynomials. This $q$-analog computes the joint distribution of excedance number and major index, the only of the four important Euler-Mahonian distributions that had not yet been computed. Our study of the Eulerian quasisymmetric functions also yields results that include the descent statistic and refine results of Gessel and Reutenauer. We also obtain $q$-analogs, $(q,p)$-analogs and quasisymmetric function analogs of classical results on the symmetry and unimodality of the Eulerian polynomials. Our Eulerian quasisymmetric functions refine symmetric functions that have occurred in various representation theoretic and enumerative contexts including MacMahon's study of multiset derangements, work of Procesi and Stanley on toric varieties of Coxeter complexes, Stanley's work on chromatic symmetric functions, and the work of the authors on the homology of a certain poset introduced by Bj\"orner and Welker.Comment: Final version; to appear in Advances in Mathematics; 52 pages; this paper was originally part of the longer paper arXiv:0805.2416v1, which has been split into three paper

Social protection: Opportunities for Africa

"Social protection involves policies and programs that protect people against risk and vulnerability, mitigate the impacts of shocks, and support people who suffer from chronic incapacities to secure basic livelihoods. It can also build assets, reducing both short-term and intergenerational transmission of poverty. It includes social insurance (such as health, life, and asset insurance, which may involve contributions from employers and/or beneficiaries); social assistance (mainly cash, food, vouchers, or subsidies); and services (such as maternal and child health and nutrition programs). Interventions that provide training and credit for income-generating activities also have a social protection component. Interest in social protection is growing across Africa, fueled by persistent high rates of poverty and malnutrition; the undermining of livelihoods and family-based support systems by shocks such as the AIDS epidemic; volatile food prices and the calamities of weather and war; extensive evidence that denying children basic nutrition, health, and education has lifelong, irreversible, and intergenerational consequences; and growing evidence of the effectiveness of social protection in low-income countries throughout the world—particularly in contributing to poverty reduction and improved health, nutrition, and education. Approaches vary across regions and countries, with a notable introduction or scale-up of cash transfers for the very poor in southern and East Africa. While many programs have been undertaken on a pilot basis, successful implementation of large-scale social protection programs in Ethiopia and South Africa—each with more than 8 million beneficiaries—has demonstrated that social protection systems are no longer only within the reach of rich countries." from Author's textSocial protection, Poverty reduction, Hunger, Cash transfers,

Conditional cash transfer programs: A "magic bullet" for reducing poverty?

Hunger, Poor households, Cash transfer programs, Inequality, Poverty reduction, Micronutrient deficiencies, Developing countries,

Robustness of Network Measures to Link Errors

In various applications involving complex networks, network measures are employed to assess the relative importance of network nodes. However, the robustness of such measures in the presence of link inaccuracies has not been well characterized. Here we present two simple stochastic models of false and missing links and study the effect of link errors on three commonly used node centrality measures: degree centrality, betweenness centrality, and dynamical importance. We perform numerical simulations to assess robustness of these three centrality measures. We also develop an analytical theory, which we compare with our simulations, obtaining very good agreement.Comment: 9 pages, 9 figure

Saddam Hussein is “dangerous to the extreme”: The ethics of professional commentary on public figures

People are intrinsically interested in the personalities of public figures such as the celebrities they follow, political leaders, and citizens at the center of newsworthy events. The goal of the present article is to examine the key issues that surround ethical commentary on public figures by psychologists, psychiatrists, and other mental health professionals. Public commentaries carry with them a host of issues from representing a given discipline such as psychology well, to potentially harming an individual who is discussed, to furthering public education about personality and mental health issues. For this reason such commentary deserves special consideration as to when and how it is appropriate to carry out

Tracking the Trends 2013: 12th Edition

This report contains current and historical demographic and socio-economic data from the Edmonton region. Areas of focus in this report include statistics on education and employment, the cost of living and housing, wages and incomes, poverty, government income supports, social wellbeing, and the demographics of Edmonton