Variance and Covariance of Several Simultaneous Outputs of a Markov Chain

The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial characterization of Markov sources which satisfy this condition is given in terms of cycles of the underlying graph of the Markov chain. Also Markov sources with higher dimensional alphabets are considered. Furthermore, the case of an unbounded covariance between two coordinates of the Markov source is combinatorically characterized. If the covariance is bounded, then the two coordinates are asymptotically independent. The results are illustrated by several examples, like the number of specific blocks in $0$-$1$-sequences and the Hamming weight of the width-$w$ non-adjacent form

Inspiring girls to be strong, smart, and bold: girls’ organizations change with the times

While Girls Incorporated and other organizations have evolved with the changing times, many of the old problems remain.Women - Education

Roll-off at the top of the ballot: intentional undervoting in American presidential elections

Every four years, more than 2% of voters fail to cast a valid vote in the U.S. presidential contest. The 2000 election highlighted the fact that many intended votes are voided because of voter confusion associated with complicated ballot designs or voting equipment. Using survey data, this study provides estimates of the proportion of voided presidential ballots that do not represent errors but rather intentional undervotes. Voters who are older, poorer, and who do not identify with either major party are more likely to intentionally refrain from casting a presidential vote. African American-white differences are very minor, implying that racial disparities in the rate of voided votes cannot be attributed to a stronger tendency among African American voters to intentionally skip the presidential contest.voting, elections, turnout

Who Uses Inferior Voting Technology?

In this article, we report on the incidence of punch-card and other voting equipment by ethnicity, incomes and other variables, combining county-level demographic data from the Census Bureau with county-level data on voting equipment collected by Election Data Services, Inc. Our findings, widely reported in the national print and electronic media in late January and February of 2001, provide remarkably little support for the view that resource constraints cause poorer counties with large minority populations to retain antiquated or inferior voting equipment.voting, elections

Effective dynamics of disordered quantum systems

We derive general evolution equations describing the ensemble-average quantum dynamics generated by disordered Hamiltonians. The disorder average affects the coherence of the evolution and can be accounted for by suitably tailored effective coupling agents and associated rates which encode the specific statistical properties of the Hamiltonian's eigenvectors and eigenvalues, respectively. Spectral disorder and isotropically disordered eigenvector distributions are considered as paradigmatic test cases.Comment: 20 page

Viewers like you: community norms and contributions to public broadcasting

The logic of collective action (Olson 1965) suggests that public broadcasting may be underprovided, because non-contributors are not excluded from receiving the benefits. Why do so many individuals voluntarily contribute to public television, even though they can obtain the benefits of public television without contributing? We explore the hypothesis that giving to public broadcasting is determined in part by the strength of "civic norms" that limit the opportunistic behavior of individuals in large-numbers prisoners' dilemma settings. We also explore a variety of other explanations for charitable giving and collective action, including group size, tax deductibility, crowd out, and selective incentives. Our findings provide evidence linking civic norms and giving to public broadcasting. Education and income have indirect effects through strengthening civic norms. We find some evidence that selective incentives increase the average size of contributions among those who contribute.collective action, selective incentives, norms, free riding, social capital, public goods

Automata in SageMath---Combinatorics meet Theoretical Computer Science

The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and transducers and solved using SageMath. In particular, we compute the asymptotic Hamming weight of a non-adjacent-form-like digit expansion, which was not known before