Charter School Replication: Growing a Quality Charter School Sector

NACSA's Policy Guide series is intended to support state legislatures and charter school advocates in creating policy environments that result in high quality authorizing and high quality schools. This guide outlines key considerations for policymakers committed to supporting the replication of existing successful charter school models

Containerless protein crystal growth technology: Electrostatic multidrop positioner

A brief discussion of containerless protein crystal growth in space and a diagram of the electrostatic multidrop positioner are presented. A picture of lysome crystals growing in a drop and a graph of levitation voltage versus time (minutes) are also presented

Noncontact electrical resistivity measurement technique for molten metals

A noncontact technique of measuring the changes in electrical conductivity (or resistivity) of conducting liquids is reported. The technique is based on a conducting drop that is levitated by the high-temperature electrostatic levitator in a high vacuum. This technique, which utilizes the principle of the asynchronous induction motor, measures the relative changes in torque as a function of temperature by applying a rotating magnetic field to the sample. Changes in electrical resistivity are related to the changes in measured torque using the formula developed for the induction motor. Validity of this technique was demonstrated using a pure aluminum sample around its melting temperature. When the measurement results were calibrated by a literature value of resistivity at the melting point, our resistivity data around the melting point could be expressed by rliq = 24.19 + 1.306 × 10–2(T – Tm) µOmega cm over Tm ~ 1160 K, rsolid = 10.77 + 1.421 × 10–2(T – Tm) µOmega cm over 700 K ~ Tm, and the thermal conductivity as determined by the Wiedemann–Franz–Lorenz law from the resistivity data was given by kappaliq(T) = 94.61 + 4.41 × 10–2(T – Tm) W m – 1 K – 1, kappasolid(T) = 211.13 – 7.57 × 10–2(T – Tm) W m – 1 K – 1. Both electrical resistivity and thermal conductivity are in close agreement with the literature, confirming the validity of the present technique

Keep Ballots Secret: On the Futility of Social Learning in Decision Making by Voting

We show that social learning is not useful in a model of team binary decision making by voting, where each vote carries equal weight. Specifically, we consider Bayesian binary hypothesis testing where agents have any conditionally-independent observation distribution and their local decisions are fused by any L-out-of-N fusion rule. The agents make local decisions sequentially, with each allowed to use its own private signal and all precedent local decisions. Though social learning generally occurs in that precedent local decisions affect an agent's belief, optimal team performance is obtained when all precedent local decisions are ignored. Thus, social learning is futile, and secret ballots are optimal. This contrasts with typical studies of social learning because we include a fusion center rather than concentrating on the performance of the latest-acting agents

Classification of flat bands according to the band-crossing singularity of Bloch wave functions

We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band, its Bloch wave function possesses immovable discontinuities generated by the band-crossing with other bands, and thus the vector bundle associated with the flat band cannot be defined. This singularity precludes the compact localized states from forming a complete set spanning the flat band. Once the degeneracy at the band crossing point is lifted, the singular flat band becomes dispersive and can acquire a finite Chern number in general, suggesting a new route for obtaining a nearly flat Chern band. On the other hand, the Bloch wave function of a nonsingular flat band has no singularity, and thus forms a vector bundle. A nonsingular flat band can be completely isolated from other bands while preserving the perfect flatness. All one-dimensional flat bands belong to the nonsingular class. We show that a singular flat band displays a novel bulk-boundary correspondence such that the presence of the robust boundary mode is guaranteed by the singularity of the Bloch wave function. Moreover, we develop a general scheme to construct a flat band model Hamiltonian in which one can freely design its singular or nonsingular nature. Finally, we propose a general formula for the compact localized state spanning the flat band, which can be easily implemented in numerics and offer a basis set useful in analyzing correlation effects in flat bands.Comment: 23 pages, 13 figure

Distributed Hypothesis Testing with Social Learning and Symmetric Fusion

We study the utility of social learning in a distributed detection model with agents sharing the same goal: a collective decision that optimizes an agreed upon criterion. We show that social learning is helpful in some cases but is provably futile (and thus essentially a distraction) in other cases. Specifically, we consider Bayesian binary hypothesis testing performed by a distributed detection and fusion system, where all decision-making agents have binary votes that carry equal weight. Decision-making agents in the team sequentially make local decisions based on their own private signals and all precedent local decisions. It is shown that the optimal decision rule is not affected by precedent local decisions when all agents observe conditionally independent and identically distributed private signals. Perfect Bayesian reasoning will cancel out all effects of social learning. When the agents observe private signals with different signal-to-noise ratios, social learning is again futile if the team decision is only approved by unanimity. Otherwise, social learning can strictly improve the team performance. Furthermore, the order in which agents make their decisions affects the team decision.Comment: 10 pages, 7 figure