Partial primary reinforcement as a parameter of secondary reinforcement

Thesis (Ph.D.)--Boston UniversityThe problem of this paper is to investigate partial primary reinforcement as a possible parameter of secondary reinforcement. Although partial primary reinforcement is known to be important in many learning situations, there appears to be little systematic knowledge of its relationship to secondary reinforcement. An experiment was performed in which (1) a neutral stimulus was present on every training trial, (2) a primary reinforcer was present on only some of these trials, (3) after training was completed, a test was made for the secondary reinforcing properties of the neutral stimulus. Six independent groups of albino rats were trained in a simple runway with food as the primary reinforcer and goal box brightness as the neutral stimulus. Each group received a different number of primary reinforcements, namely, 100%, 90%, 80%, 60%, 40%, and 20%, out of one-hundred-twenty training trials. Half of the subjects were trained on a white goal box and half on a black goal box. When training was completed, the alleyway was converted to a T maze with black and white goal boxes. Neither goal box was visible to the subjects until after entrance. The animals were given twenty trials in the T maze, and the number of times they entered each goal box was tabulated. Analysis of the data revealed that the lower the percentage of reinforcement given during training, the greater were the number of entries into the training box during the test. Some characteristics of the function were: between 100% and 90% the strength of secondary reinforcement did not increase, between 90% and 80% there was a large increase, from 80% to 40% there was a further increase, and from 40% to 20% there was some decrease. It was also revealed that some subjects in the lower percentage of reinforcement groups went either to the training box or to the novel box on every test trial. Other aspects of the data were also analyzed. From this data a number of conclusions were drawn: 1. Partial primary reinforcement is a parameter of secondary reinforcement. Decrease in partial reinforcement results in an increase in secondary reinforcement various characteristics of this relationship were discussed. It was pointed out that the obtained function might be derived from two separate functions: the relationship of secondary reinforcement to the number of reinforced trials, and the relationship of secondary reinforcement to the number of non-reinforced trials. 2. The fact that some subjects went to the same box on every test trial was explained in terms of the development of strong secondary reinforcement, in the case of subjects who went to the training box, and in terms of the development of strong generalized secondary reinforcement, in the case of subjects who went to the novel box. 3. It has often been reported in the experimental literature that partially reinforced subjects show greater resistance to extinction than continuously reinforced subjects. Our findings can be applied to this phenomenon. Stimuli present during partial reinforcement are apt to acquire greater secondary reinforcing properties than those present during continuous reinforcement, and, hence, the presence of the former during extinction are able to maintain a higher frequency of responding than the presence of the latter. This hypothesis was distinguished from others offered in the literature which purport to explain the greater resistance to extinction in terms of secondary reinforcement. 4. It was pointed out that this experiment revealed a significant variable, secondary reinforcement, which might develop in studies whose training set up resembles ours. 5. Minor findings of the experiment were discussed

Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary

Vapour bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^½ where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ=10^6cm^2/sec^2 ≈ 1 atm/density of water the jet had a speed of about 130m/sec in the first case and 170m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapour are not important

Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary

Vapor bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. The method uses finite time steps and features an iterative technique for applying the boundary conditions at infinity directly to the liquid at a finite distance from the free surface. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^1/2 where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ = 10^6 (cm/sec)^2 ~ 1 atm./density of water the jet had a speed of about 130 m/sec in the first case and 170 m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapor are not important

High frequency homogenization for travelling waves in periodic media

We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schr{\"o}dinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wave vector \Bk and frequency $\omega_1$ plus a modulated Bloch carrier wave having crystal wave vector \Bm and frequency $\omega_2$. We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless $\omega_1=\omega_2$ and (\Bk-\Bm)\odot\Lambda \in 2\pi \mathbb Z^d, where $\Lambda=(\lambda_1\lambda_2\dots\lambda_d)$ is the periodicity cell of the medium and for any two vectors $a=(a_1,a_2,\dots,a_d), b=(b_1,b_2,\dots,b_d)\in\mathbb R^d,$ the product $a\odot b$ is defined to be the vector $(a_1b_1,a_2b_2,\dots,a_db_d).$ This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigor as that of Allaire and coworkers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.Comment: 30 pages, Proceedings of the Royal Society A, 201

Application of discrete distributions in quality control

M.S.Douglas C. Montgomer

A study on load transfer of model friction piles

Previous investigations concerned with disturbance of soft clay by driving displacement piles are summarized. The initiation of excess pore water pressures due to pile driving, and mechanisms of load transfer are also described, along with the applicapability of model pile testing in analysis of the various phenomena. Load tests were conducted on assorted sizes of model friction piles embedded in sedimented soil samples with consisted of a silt and clay mixture. Pilot holes of various diameters were cut in the samples. A theoretical load distribution curve was used to calculate the load transferred to the soil as a function of pile embedment. Laboratory vane shear test results were compared to the load transferred to the soil by the pile. Results of the research program indicate that: 1) The ratio of the load transferred to the soil to the undrained strength of the soil changes with depth in the sample, and with the ratio of the pilot hole diameter to the pile diameter, 2) an optimum pilot hole size exists for each pile which offers a balance between low soil disturbance and high load carrying capacity, 3) the soil sample size should be four to five times the pile size to achieve valid load test results, and 4) the ultimate load that a friction pile can support increases with time after pile insertion and with increased rates of penetration --Abstract, page ii

Exploring how the social model of disability can be re-invigorated: in response to Jonathan Levitt.

Levitt argues the social model of disability needs to be re-invigorated, potentially by adapting the tool for separate countries. The social model has been successfully applied for some disabled groups in the United Kingdom. However, the social model is not implemented for neurodivergent labels such as autism, through negative language of autism, causing severe problems for autistic individuals’ daily lives. The social model can be re-invigorated for autism, removing social barriers by; changing non-autistic people’s attitudes towards autism through ensuring positive language of autism, preventing the categorisation of autism and fully enacting The Autism Act 2009 and The Equality 2010