In this paper, we study how many inequality signs we should include in the design of Futoshiki puzzle. A problem instance of Futoshiki puzzle is given as an n × n grid of cells such that some cells are empty, other cells are filled with integers in [n] = {1, 2, . . . , n}, and some pairs of two adjacent cells have inequality signs. A solver is then asked to fill all the empty cells with integer...

We explore the connection between inequality and civil conflict by focusing on the mediating role of ethnic identity. Using over 200 individual-level surveys from 89 countries, we provide a new data set with countryand group-level measures of inequality within and across ethnic groups. We then show that consistent with Esteban and Ray’s (2011) argument about the need for labor and capital to fi...

STUDY OBJECTIVE To investigate whether the income distribution in a Russian region has a "contextual" effect on individuals' self rated health, and whether the regional income distributions are related to regional health differences. METHODS The Russia longitudinal monitoring survey (RLMS) is a survey (n = 7696) that is representative of the Russian population. With multilevel regressions bot...

The most limiting weakness of the human development index (HDI) is that it looks only at average achievements and does not take into account the distribution of human development within a country or population subgroups. All previous attempts to capture inequality in the HDI have also used aggregate information and there exists no HDI at the household level. This paper provides a method and ill...

We interpret the Leggett-Garg (LG) inequality as a kind of contextual probabilistic inequality in which one combines data collected in experiments performed for three different contexts. In the original version of the inequality these contexts have the temporal nature and they are given by three pairs of instances of time, (t1, t2), (t2, t3), (t3, t4), where t1 < t2 < t3. We generalize LG condi...

Article history: Received 1 January 2012 Received in revised form 10 July 2012 Accepted 18 February 2013 Available online 26 February 2013

BACKGROUND Although measuring socioeconomic inequality in population health indicators like infant mortality is important, more interesting for policy purposes is to try to explain infant mortality inequality. The objective of this paper is to quantify for the first time the determinants' contributions of socioeconomic inequality in infant mortality in Iran. METHODS A nationally representativ...

We establish a Penrose-Like Inequality for general (not necessarily time symmetric) initial data sets of the Einstein equations which satisfy the dominant energy condition. More precisely, it is shown that the ADM energy is bounded below by an expression which is proportional to the square root of the area of the outermost future (or past) apparent horizon.

In this paper, we introduce a class of generalized vector equilibrium problems for set-valued mappings which include a number of vector equilibrium problems, generalized vector variational-like inequality problems and generalized vector variational inequality problems as special cases. By using the KKM-Fan theorem and Nadler’s lemma, we prove the existence of solution to this class of generaliz...

Notice that nR̂n(h) ∼ binom(n,R(h)) and so E [ R̂n(h) ] = R(h). We would like to understand how accurate R̂n(h) is as an estimate of R(h). Thankfully there are many well known concentration inequalities that provide us with quantitative answers to this question. The goal of this lecture is to establish one such bound: Hoeffding’s inequality [2]. This inequality was originally proved in the 1960’s ...