The behavioral effects of partial reinforcement as a function of the stimulus similarity of the intertrial interval

Although Pavlov (1927) and Skinner (1938) had published articles dealing with the effects of less than 100% reinforcement upon acquisition and extinction, it was not until the Humphrey\u27s investigation (1939) that partial reinforcement became an enigma for leaning theorists. Hull\u27s theory came under the sharpest criticism because with a decrease in the number of reinforcement in acquisition there was not a corresponding decrease in habit strength as measured by resistance to extinction. Despite much criticism, Hull did not deet it necessary to consider the problem of partial reinforcement in his Principles of Behavior (1943). Humphreys, on the other hand, proposed an expectancy principle as an alternative theory, In his theory, conditioned responses are the consequences of the Ss expectation that reinforcement will appear. After reinforcement on every trail during acquisition, the extinction responses dissipate because the sudden shift from uniform reinforcement to uniform nonreinforcement makes it easy to change an expectation of uniform nonreinforcement. In extinction after partial reinforcement, however, the S continues to expect that reinforcement will be periodic as it was during acquisition, thus extinction is prolonged by his expectation that reinforcement will be re-introduced

Resources in Europe of interest to mathematics teachers,

Thesis (M.A.)--Boston University. This thesis was written in conjunction with Dennis J. Roberts, Mary Lee McLaughlin and Robert F. Pierce.Statement of the problem: It is the purpose of this thesis to formulate plans for a guided tour throughout Western Europe for secondary-school teachers with emphasis on present and past mathematical and allied science contributions. This study will serve as an answer to four fundamental questions: 1. What are the resources available in Europe of value to mathematics teachers? 2. From the standpoint of marginal utility, which of these would be the most important? 3. where are they to be found? 4. How long would it take to see each of them profitably in a limited amount of time? [TRUNCATED

Real-time ensemble control with reduced-order modeling

The control of spatially distributed systems is often complicated by significant uncertainty about system inputs, both time-varying exogenous inputs and time-invariant parameters. Spatial variations of uncertain parameters can be particularly problematic in geoscience applications, making it difficult to forecast the impact of proposed controls. One of the most effective ways to deal with uncertainties in control problems is to incorporate periodic measurements of the system’s states into the control process. Stochastic control provides a convenient way to do this, by integrating uncertainty, monitoring, forecasting, and control in a consistent analytical framework. This paper describes an ensemble-based approach to closed-loop stochastic control that relies on a computationally efficient reduced-order model. The use of ensembles of uncertain parameters and states makes it possible to consider a range of probabilistic performance objectives and to derive real-time controls that explicitly account for uncertainty. The process divides naturally into measurement updating, control, and forecasting steps carried out recursively and initialized with a prior ensemble that describes parameter uncertainty. The performance of the ensemble controller is investigated here with a numerical experiment based on a solute transport control problem. This experiment evaluates the performance of open and closed-loop controllers with full and reduced-order models as well as the performance obtained with a controller based on perfect knowledge of the system and the nominal performance obtained with no control. The experimental results show that a closed-loop controller that relies on measurements consistently performs better than an open loop controller that does not. They also show that a reduced-order forecasting model based on offline simulations gives nearly the same performance as a significantly more computationally demanding full order model. Finally, the experiment indicates that a moderate penalty on the variance of control cost yields a robust control strategy that reduces uncertainty about system performance with little or no increase in average cost. Taken together, these results confirm that reduced-order ensemble closed-loop control is a flexible and efficient control option for uncertain spatially distributed systems.Shell Oil Compan

Real-time ensemble control with reduced-order modeling

The control of spatially distributed systems is often complicated by significant uncertainty about system inputs, both time-varying exogenous inputs and time-invariant parameters. Spatial variations of uncertain parameters can be particularly problematic in geoscience applications, making it difficult to forecast the impact of proposed controls. One of the most effective ways to deal with uncertainties in control problems is to incorporate periodic measurements of the system’s states into the control process. Stochastic control provides a convenient way to do this, by integrating uncertainty, monitoring, forecasting, and control in a consistent analytical framework. This paper describes an ensemble-based approach to closed-loop stochastic control that relies on a computationally efficient reduced-order model. The use of ensembles of uncertain parameters and states makes it possible to consider a range of probabilistic performance objectives and to derive real-time controls that explicitly account for uncertainty. The process divides naturally into measurement updating, control, and forecasting steps carried out recursively and initialized with a prior ensemble that describes parameter uncertainty. The performance of the ensemble controller is investigated here with a numerical experiment based on a solute transport control problem. This experiment evaluates the performance of open and closed-loop controllers with full and reduced-order models as well as the performance obtained with a controller based on perfect knowledge of the system and the nominal performance obtained with no control. The experimental results show that a closed-loop controller that relies on measurements consistently performs better than an open loop controller that does not. They also show that a reduced-order forecasting model based on offline simulations gives nearly the same performance as a significantly more computationally demanding full order model. Finally, the experiment indicates that a moderate penalty on the variance of control cost yields a robust control strategy that reduces uncertainty about system performance with little or no increase in average cost. Taken together, these results confirm that reduced-order ensemble closed-loop control is a flexible and efficient control option for uncertain spatially distributed systems.Shell Oil Compan

Why Is a CCP failure very unlikely?

Central counterparties (CCPs) are designed to be robust enough to withstand generally at least the simultaneous default of their largest two clearing members in extreme but plausible market conditions. This is called a 'cover 2' CCP. However, the extreme-and-implausible case cannot be excluded i.e. where the CCP would exhaust all funded financial resources (i.e. skin-in-the-game and the default fund D) to cover the default losses and would need to resort to unfunded recovery tools. The aim of this paper is to consider the resilience of a CCP for both default losses and non-default losses. For the former case, it is shown under plausible assumptions that the assessment (or cash call) for the surviving members is sufficient to recover a cover 1 CCP provided that the total assessment powers under the CCP Rulebook equals 2D. Given the extreme scenario we also take into account that some surviving clearing members might decide to leave the CCP. Some intuitive results for the cover 2 CCP case are provided as well. For the latter case, it is demonstrated that under plausible assumptions, the likelihood that a non-default loss is larger than the CCP's capital including one year of profits, is equivalent to an AAA risk. These observations together provide substantiation for the very low likelihood of a CCP's failure

The role of model dynamics in ensemble Kalman filter performance for chaotic systems

The ensemble Kalman filter (EnKF) is susceptible to losing track of observations, or ‘diverging’, when applied to large chaotic systems such as atmospheric and ocean models. Past studies have demonstrated the adverse impact of sampling error during the filter’s update step. We examine how system dynamics affect EnKF performance, and whether the absence of certain dynamic features in the ensemble may lead to divergence. The EnKF is applied to a simple chaotic model, and ensembles are checked against singular vectors of the tangent linear model, corresponding to short-term growth and Lyapunov vectors, corresponding to long-term growth. Results show that the ensemble strongly aligns itself with the subspace spanned by unstable Lyapunov vectors. Furthermore, the filter avoids divergence only if the full linearized long-term unstable subspace is spanned. However, short-term dynamics also become important as nonlinearity in the system increases. Non-linear movement prevents errors in the long-term stable subspace from decaying indefinitely. If these errors then undergo linear intermittent growth, a small ensemble may fail to properly represent all important modes, causing filter divergence. A combination of long and short-term growth dynamics are thus critical to EnKF performance. These findings can help in developing practical robust filters based on model dynamics.National Science Foundation (U.S.) (CMF Program Grant 0530851)National Science Foundation (U.S.) (DDAS Program Grant 0540259)National Science Foundation (U.S.) (ITR/AP Program Grant 0121182

Evaluation of Long-Term SSM/I-Based Precipitation Records over Land

The record of global precipitation mapping using Special Sensor Microwave Imager (SSM/I) measurements now extends over two decades. Similar measurements, albeit with different retrieval algorithms, are to be used in the Global Precipitation Measurement (GPM) mission as part of a constellation to map global precipitation with a more frequent data refresh rate. Remotely sensed precipitation retrievals are prone to both magnitude (precipitation intensity) and phase (position) errors. In this study, the ground-based radar precipitation product from the Next Generation Weather Radar stage-IV (NEXRAD-IV) product is used to evaluate a new metric of error in the long-term SSM/I-based precipitation records. The new metric quantifies the proximity of two multidimensional datasets. Evaluation of the metric across the years shows marked seasonality and precipitation intensity dependence. Drifts and changes in the instrument suite are also evident. Additionally, the precipitation retrieval errors conditional on an estimate of background surface soil moisture are estimated. The dynamic soil moisture can produce temporal variability in surface emissivity, which is a source of error in retrievals. Proper filtering has been applied in the analysis to differentiate between the detection error and the retrieval error. The identification of the different types of errors and their dependence on season, intensity, instrument, and surface conditions provide guidance to the development of improved retrieval algorithms for use in GPM constellation-based precipitation data products

Hybrid Proofs of the \u3cem\u3eq\u3c/em\u3e-Binomial Theorem and Other Identities

We give hybrid proofs of the q-binomial theorem and other identities. The proofs are hybrid in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities due to Ramanujan. Finally, we use these new summation formulae to give new partition interpretations of the Rogers-Ramanujan identities and the Rogers-Selberg identities

Highlights of Aeroacoustics Research in the U.S. 1998

Highlights of aeroacoustics research in the United States of America during 1998 are reported in a summary compiled from information provided by members of the Aeroacoustics Technical Committee of the American Institute of Aeronautics and Astronautics (AIAA) and other leading research groups in industry, national laboratories, and academia. The past few years have seen significant progress in aeroacoustics. Research has steadily progressed toward enhanced safety, noise benefits, and lower costs. Since industrial progress is generally not published in the archival literature, it is particularly important to highlight these accomplishments. This year we chose to report on five topics of great interest to the aerospace industry including a synopsis of fundamental research at universities and national laboratories. The topics chosen are: (1) Advanced Subsonic Technology (AST), (2) High Speed Research (HSR), (3) Rotorcraft, (4) Weapons bay aeroacoustics control and (5) Academic research including Computational AeroAcoustics (CAA). Although the information presented in this review is not all encompassing we hope that the topics covered will provide some insights into aeroacoustics activity in the U.S

On the Scaling of Small, Heat Simulated Jet Noise Measurements to Moderate Size Exhaust Jets

Modern military aircraft jet engines are designed with variable geometry nozzles to provide optimum thrust in different operating conditions, depending on the flight envelope. However, the acoustic measurements for such nozzles are scarce, due to the cost involved in making full scale measurements and the lack of details about the exact geometry of these nozzles. Thus the present effort at The Pennsylvania State University and the NASA Glenn Research Center- in partnership with GE Aviation is aiming to study and characterize the acoustic field produced by supersonic jets issuing from converging-diverging military style nozzles. An equally important objective is to validate methodology for using data obtained from small and moderate scale experiments to reliably predict the most important components of full scale engine noise. The experimental results presented show reasonable agreement between small scale and moderate scale jet acoustic data, as well as between heated jets and heat-simulated ones. Unresolved issues however are identified that are currently receiving our attention, in particular the effect of the small bypass ratio airflow. Future activities will identify and test promising noise reduction techniques in an effort to predict how well such concepts will work with full scale engines in flight conditions