Merit Pay for Educators: An Investigation of Components Significantly Impacting Student Achievement

With teacher evaluations, school ratings, and ultimately school funding being linked more and more to student achievement data, U.S. public schools are searching for new and effective ways to boost academic testing scores. This study examined teachers’ and administrators’ experiences with and perceptions of merit pay, with the goal of identifying key program components positively impacting student success. With this information, solid and successful merit pay structures could be implemented in schools across the nation. Professional educators from two Midwest states who were involved in performance pay programs participated in the study through both a survey instrument and personal interviews. Surveys were crafted using the review of related literature, then distributed and collected via SurveyMonkey to educators in selected merit pay schools. Likert scale selections and open response inquiries were utilized to assess educator opinions and experiences. Personal interviews were scheduled and conducted within one Arkansas school district. This district employed an innovative merit pay program for educational stakeholders. Experiences, perceived strengths and weaknesses, and results of the merit pay structure were discussed during the interview sessions. Valuable perceptions regarding merit pay structure and implementation were gained. Three important factors of any successful school motivation program emerged. These three components included development of a purpose driven structure, fair measurement of student growth, and educator empowerment. Further research is recommended to determine varied and effective ways to structure programs to sustainably increase student achievement gains

Physics-based analysis of Affymetrix microarray data

We analyze publicly available data on Affymetrix microarrays spike-in experiments on the human HGU133 chipset in which sequences are added in solution at known concentrations. The spike-in set contains sequences of bacterial, human and artificial origin. Our analysis is based on a recently introduced molecular-based model [E. Carlon and T. Heim, Physica A 362, 433 (2006)] which takes into account both probe-target hybridization and target-target partial hybridization in solution. The hybridization free energies are obtained from the nearest-neighbor model with experimentally determined parameters. The molecular-based model suggests a rescaling that should result in a "collapse" of the data at different concentrations into a single universal curve. We indeed find such a collapse, with the same parameters as obtained before for the older HGU95 chip set. The quality of the collapse varies according to the probe set considered. Artificial sequences, chosen by Affymetrix to be as different as possible from any other human genome sequence, generally show a much better collapse and thus a better agreement with the model than all other sequences. This suggests that the observed deviations from the predicted collapse are related to the choice of probes or have a biological origin, rather than being a problem with the proposed model.Comment: 11 pages, 10 figure

Universality in the pair contact process with diffusion

The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time or of system length and extrapolate asymptotically towards values consistent with the directed percolation universality class. We argue that an intermediate regime exists where the effective critical dynamics resembles that of a parity conserving process.Comment: 8 Pages, 9 figures, final version as publishe

Equilibrium shapes and faceting for ionic crystals of body-centered-cubic type

A mean field theory is developed for the calculation of the surface free energy of the staggered BCSOS, (or six vertex) model as function of the surface orientation and of temperature. The model approximately describes surfaces of crystals with nearest neighbor attractions and next nearest neighbor repulsions. The mean field free energy is calculated by expressing the model in terms of interacting directed walks on a lattice. The resulting equilibrium shape is very rich with facet boundaries and boundaries between reconstructed and unreconstructed regions which can be either sharp (first order) or smooth (continuous). In addition there are tricritical points where a smooth boundary changes into a sharp one and triple points where three sharp boundaries meet. Finally our numerical results strongly suggest the existence of conical points, at which tangent planes of a finite range of orientations all intersect each other. The thermal evolution of the equilibrium shape in this model shows strong similarity to that seen experimentally for ionic crystals.Comment: 14 Pages, Revtex and 10 PostScript figures include

Crossover from reptation to Rouse dynamics in a one-dimensional model

A simple one-dimensional model is constructed for polymer motion. It exhibits the crossover from reptation to Rouse dynamics through gradually allowing hernia creation and annihilation. The model is treated by the density matrix technique which permits an accurate finite-size-scaling analysis of the behavior of long polymers.Comment: 5 Pages RevTeX and 5 PostScript figures included (to appear in Physical Review E

Fixed Point of the Finite System DMRG

The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system algorithm, that uses the block structure B**B. This is because the tensors are not improved directly. We overcome this problem by using the simpler block structure B*B for the final several sweeps in the finite iteration process. It is possible to increase the numerical precision of the finite system algorithm without increasing the computational effort.Comment: 6 pages, 4 figure

Elastic Lattice Polymers

We study a model of "elastic" lattice polymer in which a fixed number of monomers $m$ is hosted by a self-avoiding walk with fluctuating length $l$. We show that the stored length density $\rho_m = 1 - /m$ scales asymptotically for large $m$ as $\rho_m=\rho_\infty(1-\theta/m + ...)$, where $\theta$ is the polymer entropic exponent, so that $\theta$ can be determined from the analysis of $\rho_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $\rho_m$. The resulting estimates support the hypothesis that the exponent $\theta$ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.Comment: 10 page

The generalized contact process with n absorbing states

We investigate the critical properties of a one dimensional stochastic lattice model with n (permutation symmetric) absorbing states. We analyze the cases with $n \leq 4$ by means of the non-hermitian density matrix renormalization group. For n=1 and n=2 we find that the model is respectively in the directed percolation and parity conserving universality class, consistent with previous studies. For n=3 and n=4, the model is in the active phase in the whole parameter space and the critical point is shifted to the limit of one infinite reaction rate. We show that in this limit the dynamics of the model can be mapped onto that of a zero temperature n-state Potts model. On the basis of our numerical and analytical results we conjecture that the model is in the same universality class for all $n \geq 3$ with exponents $z = \nu_\|/\nu_\perp = 2$, $\nu_\perp = 1$ and $\beta = 1$. These exponents coincide with those of the multispecies (bosonic) branching annihilating random walks. For n=3 we also show that, upon breaking the symmetry to a lower one ($Z_2$), one gets a transition either in the directed percolation, or in the parity conserving class, depending on the choice of parameters.Comment: 10 pages, RevTeX, and 10 PostScript figures include

Crossover from Reptation to Rouse dynamics in the Cage Model

The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the Density Matrix Method as a solver of the Master Equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.Comment: RevTeX, 11 PostScript figures include

Effective affinities in microarray data

In the past couple of years several studies have shown that hybridization in Affymetrix DNA microarrays can be rather well understood on the basis of simple models of physical chemistry. In the majority of the cases a Langmuir isotherm was used to fit experimental data. Although there is a general consensus about this approach, some discrepancies between different studies are evident. For instance, some authors have fitted the hybridization affinities from the microarray fluorescent intensities, while others used affinities obtained from melting experiments in solution. The former approach yields fitted affinities that at first sight are only partially consistent with solution values. In this paper we show that this discrepancy exists only superficially: a sufficiently complete model provides effective affinities which are fully consistent with those fitted to experimental data. This link provides new insight on the relevant processes underlying the functioning of DNA microarrays.Comment: 8 pages, 6 figure