24,618 research outputs found

    Complementary algorithms for graphs and percolation

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    A pair of complementary algorithms are presented. One of the pair is a fast method for connecting graphs with an edge. The other is a fast method for removing edges from a graph. Both algorithms employ the same tree based graph representation and so, in concert, can arbitrarily modify any graph. Since the clusters of a percolation model may be described as simple connected graphs, an efficient Monte Carlo scheme can be constructed that uses the algorithms to sweep the occupation probability back and forth between two turning points. This approach concentrates computational sampling time within a region of interest. A high precision value of pc = 0.59274603(9) was thus obtained, by Mersenne twister, for the two dimensional square site percolation threshold.Comment: 5 pages, 3 figures, poster version presented at statphys23 (2007

    Stochastic Forecasts of the Social Security Trust Fund

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    We present stochastic forecasts of the Social Security trust fund by modeling key demographic and economic variables as historical time series, and using the fitted models to generate computer simulations of future fund performance. We evaluate several plans for achieving long-term solvency by raising the normal retirement age (NRA), increasing taxes, or investing some portion of the fund in the stock market. Stochastic population trajectories by age and sex are generated using the Lee-Carter and Lee- Tuljapurkar mortality and fertility models. Interest rates, wage growth and equities returns are modeled as vector autoregressive processes. With the exception of mortality, central tendencies are constrained to the Intermediate assumptions of the 2002 Trustees Report. Combining population forecasts with forecasted per-capita tax and benefit profiles by age and sex, we obtain inflows to and outflows from the fund over time, resulting in stochastic fund trajectories and distributions. Under current legislation, we estimate the chance of insolvency by 2038 to be 50%, although the expected fund balance stays positive until 2041. An immediate 2% increase in the payroll tax rate from 12.4% to 14.4% sustains a positive expected fund balance until 2078, with a 50% chance of solvency through 2064. Investing 60% of the fund in the S&P 500 by 2015 keeps the expected fund balance positive until 2060, with a 50% chance of solvency through 2042. An increase in the NRA to age 69 by 2024 keeps the expected fund balance positive until 2047, with a 50% chance of solvency through 2041. A combination of raising the payroll tax to 13.4%, increasing the NRA to 69 by 2024, and investing 25% of the fund in equities by 2015 keeps the expected fund balance positive past 2101 with a 50% chance of solvency through 2077.

    Effect of a repeated reading and utility value intervention on the fluency of an 8th grade student with a learning disability

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    An intervention focused on teacher assisted guided reading, repeated reading, and a reading motivation technique was implemented to increase the fluency of a special education student with a Learning Disability (LD) in an 8th grade mid-western school. Previous research has indicated that both repeated readings and reading motivation techniques increase academic achievement (Hawkins, Hale, Sheeley, and Ling, 2011; Hulleman and Harackiewicz, 2009), but few investigations have integrated these interventions. This research used a utility value technique along with texts of gradually increasing difficulty, facilitated by oral reading and feedback provided by an individual educator, to increase a student\u27s reading speed and accuracy. An analysis of pretest and posttest results, as measured by the Pearson Qualitative Reading Inventory (QRI-5; Leslie & Caldwell, 2011) and Adolescent Motivation to Read profile (Pitcher et al., 2007), indicated small but notable improvements in value attributed to reading, as well as increased performance on word lists, correct words per minute, and accuracy
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