A family of multiple harmonic sum and multiple zeta star value identities

In this paper we present a new family of identities for multiple harmonic sums which generalize a recent result of Hessami Pilehrood et al [Trans. Amer. Math. Soc. (to appear)]. We then apply it to obtain a family of identities relating multiple zeta star values to alternating Euler sums. In such a typical identity the entries of the multiple zeta star values consist of blocks of arbitrarily long 2-strings separated by positive integers greater than two while the largest depth of the alternating Euler sums depends only on the number of 2-string blocks but not on their lengths

The empty opportunity : local control of secondary schools and student achievement in the Philippines

Decentralization policies are at the heart of education reform efforts in many countries internationally. Two important types of policies are those that: (a) remove barriers to private education; and (b) devolve authority and responsibility for schools from central level administrations to intermediate level organizations and ultimately to schools, relying more on local communities for financing, with an overall goal of improving effectiveness. While both types of policies are largely uninformed by empirical evidence regarding their impact on such education outcomes as student learning, in developing countries the evidence regarding the effects of local control is much weaker than that regarding private schools. This paper extends the literature on the impact of private education on achievement, while providing the first evidence on the impact of local control on achievement in a developing county. It analyzes data from 214 secondary schools in the Philippines to answer questions regarding: (a) the relative effectiveness of local, government and private secondary schools; and (b) the factors that account for observed differences.Education Reform and Management,Teaching and Learning,Gender and Education,Health Monitoring&Evaluation,Primary Education

A UNIFIED APPROACH TO SENSITIVITY ANALYSIS IN EQUILIBRIUM DISPLACEMENT MODELS: COMMENT

It is pointed out that the Chebychev confidence intervals and maximum p-values advocated by Davis and Espinoza for sensitivity analysis of equilibrium displacement models are unnecessary. Desired probability intervals and probabilities can be accurately estimated without resorting to gross approximations.simulation, probability distributions, empirical quantiles, Research Methods/ Statistical Methods,

Dynamics of liquid nano-threads : fluctuation-driven instability and rupture

The instability and rupture of nanoscale liquid threads is shown to strongly depend on thermal fluctuations. These fluctuations are naturally occurring within molecular dynamics (MD) simulations and can be incorporated via fluctuating hydrodynamics into a stochastic lubrication equation (SLE). A simple and robust numerical scheme is developed for the SLE that is validated against MD for both the initial (linear) instability and the nonlinear rupture process. Particular attention is paid to the rupture process and its statistics, where the `double-cone’ profile reported by Moseler & Landmann [Science, 2000, 289(5482): 1165-1169] is observed, as well as other distinct profile forms depending on the flow conditions. Comparison to the Eggers’ similarity solution [Physical Review Letters, 2002, 89(8): 084502], a power law of the minimum thread radius against time to rupture, shows agreement only at low surface tension; indicating that surface tension cannot generally be neglected when considering rupture dynamics

Intrinsically Motivated Learning of Visual Motion Perception and Smooth Pursuit

We extend the framework of efficient coding, which has been used to model the development of sensory processing in isolation, to model the development of the perception/action cycle. Our extension combines sparse coding and reinforcement learning so that sensory processing and behavior co-develop to optimize a shared intrinsic motivational signal: the fidelity of the neural encoding of the sensory input under resource constraints. Applying this framework to a model system consisting of an active eye behaving in a time varying environment, we find that this generic principle leads to the simultaneous development of both smooth pursuit behavior and model neurons whose properties are similar to those of primary visual cortical neurons selective for different directions of visual motion. We suggest that this general principle may form the basis for a unified and integrated explanation of many perception/action loops.Comment: 6 pages, 5 figure

Signaling and Tacit Collusion in an Infinitely Repeated Prisoners' Dilemma

In the context of an infinitely repeated Prisoners' Dilemma, we explore how cooperation is initiated when players signal and coordinate through their actions. There are two types of players - patient and impatient - and a player's type is private information. An impatient type is incapable of cooperative play, while if both players are patient types - and this is common knowledge - then they can cooperate with a grim trigger strategy. We find that the longer that players have gone without cooperating, the lower is the probability that they'll cooperate in the next period. While the probability of cooperation emerging is always positive, there is a positive probability that cooperation never occurs.