Summation and configuration between and within sensory modalities in classical conditioning of the rabbit

Three experiments examined “atomistic” and “configurai” processes in stimulus compounding using the rabbit’s conditioned nictitating membrane response. Two conditioned stimuli (CSs) were trained separately and then tested together in a compound. Animals trained with CSs from different modalities—namely, tone and light—showed summation in both acquisition and extinction. That is, the probability of a response to the compound could be predicted by the statistical sum of responding to the CSs. In contrast, animals trained with CSs from the auditory modality, tone and noise, showed a level of responding to the tone + noise compound that was the same as that of the CSs, well under the level predicted by the statistical sum of responding to the CSs. In conclusion, atomistic processes appear to predominate in cross-modal compounding. Configurai processes may occur during compounding within the auditory modality, but atomistic alternatives—namely, common elements and selective attention hypotheses—may be able to explain the results.     

Temporal specificity in patterning of the rabbit nictitating membrane response

Rabbits were trained in either positive patterning (AX+, A−, X−) or negative patterning (A+, X+, AX−) using one of four intervals between the onset of A and the onset of X on AX trials. These intervals were 0, 800, 2,400, and 5,600 msec. In each task, all groups acquired an appropriate pattern of discriminative responding. Following acquisition, all rabbits were tested with the four different A-X intervals. All positive patterning groups showed an excitatory gradient, in which the highest level of responding occurred at the interval used in training. Conversely, all but one of the negative patterning groups showed an inhibitory gradient, in which the lowest level of responding occurred at the interval used in training. The one exception was the negative patterning group trained with simultaneous AX stimuli (0 msec), which showed a low, broad gradient, indicating transfer of inhibition across all the intervals. The results are discussed with respect to temporal encoding mechanisms and accounts of conditional discriminations.     

Summation and overexpectation with qualitatively different outcomes

In five experiments, a Pavlovian appetitive conditioning preparation was used with rats to explore the interaction of associations with different, but equivalently valued, outcomes. Experiment 1 demonstrated summation in magazine responding when two stimuli previously associated with different outcomes were combined. Experiments 2A and 2B found that pairing that stimulus compound with one of the outcomes led to a decrease in performance (overexpectation) for both of the stimulus elements. Experiments 3A and 3B confirmed that result but demonstrated the continued presence of the original stimulus-outcome associations. The results are consonant with a view in which replacing one outcome with another leads to an associative structure containing both stimulus-outcome associations and an outcome-independent depressive process.     

An analysis of “signaled double-alternation patterning” in the rat

Rats given training with double alternation of rewards and nonrewards in which the first reward or nonreward of each pair occurred in a black runway and the second in a white runway developed fast running on rewarded trials in both runways and slow running on nonrewarded trials in both runways—signaled double alternation patterning. A subsequent shift in the reinforcement schedule produced a period of reversed patterning—slow on rewarded trials and fast on nonrewarded trials. The results are consistent with a compound stimulus discrimination interpretation of signaled double-alternation patterning rather than with a selective memory-retrieval explanation.     

The influence of cue type and configuration upon radial-maze performance in the rat

The influence of cue type and cue configuration on radial-maze performance in rats was examined in two experiments. In the first experiment, it was found that rats provided with both salient intramaze and extramaze cues acquired the task faster than rats given only one set of cues. No difference in acquisition was found between a group trained with intramaze cues alone and a group trained with extramaze cues alone. In a cue-preference test, it was found that groups that had been trained with extramaze cues, intramaze cues, or both sets of cues relied on extra-maze cues to avoid visited arms when given both types of cues concurrently. When all groups were transferred to intramaze-cue-alone trials, only the group that had been originally trained with extramaze cues alone showed any disruption. Also, during the second half of the intramaze-cue-alone trials, the arrangement of these cues was randomly changed on each trial. This disruption in cue configuration did not deleteriously affect performance in any of the three groups; all remained above chance performance, although the performance of the group originally trained with extramaze cues alone was inferior to that of the other two groups. In Experiment 2, groups of rats were trained on daily alternating trials under intramaze-cue-alone and extramaze-cue-alone conditions. For one group, the configuration of intramaze cues was altered randomly on each trial; the other group had intramaze cues always presented in the same configuration over trials. It was found that acquisition was more rapid on intramaze trials in the group given static configurations. Also, acquisition of the extramaze task was faster than the intramaze task in the group given variable intramaze cue configurations. No difference was found between the intramaze and extramaze conditions in the group given static intramaze cue configurations. These data suggest that a static cue configuration may influence radial maze performance, but is not a necessary condition for such performance.     

两个数列命题及其在若干和式不等式证明中的应用

文章建立了两个数列命题,并运用于证明若干和式不等式。     

函数的差分与数列求和

在研究数列时,求数列的和是比较重要的,本文提供一种用函数的差分求数列和的方法。     

例说无穷递缩等比数列求和公式的解题功能

对于无穷递缩等比数列{a1q^（n-1）}（0〈｜q｜〈1）的求和公式：     

一类幂级数求和方法及其应用

文章给出一类幂级数求和的方法,并用此解决了此类级数求和的问题。     

计算复杂度中的底等差幂数列求和

为了解决复杂度计算过程中求指数相同底数呈等差递增的数列和问题,从一个简单问题入手,给出求解底等差幂数列和问题的三种方法,即升次展开错位相减求和方法,裂项叠加抵消求和方法和待定系数法,并将三种求解方法推广到了一般情形。     

自然数列幂求和的类比激活新策略

贮存在人脑中的命题的活动水平是不同的,大量的命题处于静止状态,只有少量命题处于激活状态,那些处于激活状态的命题是我们正在思考着的命题．一些命题激活以后,它的活动可以扩散到与它相关联的命题。     

浅析求和问题的解题思想方法

数学解题思想就是对数学形式的认识,这是变换形式的全过程,方法就是变形.解决求和问题的思想方法需要从不同角度去思考,如:巧用化归思想求和、巧借数表求和、巧用分类讨论思想求和、作差分求和.     

Fourier部分和算子及Valle’e-Poussin算子的逼近

讨论了具有高斯测度的Sobolev空间上的Fourier部分和算子及Valle’e-Poussin算子逼近的问题．获得了在平均框架和Lq（1≤q〈∞）空间尺度下Fourier部分和算子及Valle’e-Poussin算子逼近的平均误差估计的渐近阶．     

Development of preference and spontaneous recovery in choice behavior with concurrent variable-interval schedules

Pigeons pecked on two response keys that delivered reinforcers on a variable-interval schedule. The proportion of reinforcers delivered by one key was constant for a few sessions and then changed, and subjects’ choice responses were recorded during these periods of transition. In Experiment 1, response proportions approached a new asymptote slightly more slowly when the switch in reinforcement proportions was more extreme. In Experiment 2, slightly faster transitions were found with higher overall rates of reinforcement. The results from the first session, after a switch in the reinforcement proportions, were generally consistent with a mathematical model that assumes that the strength of each response is increased by reinforcement and decreased by nonreinforcement. However, neither this model nor other similar models predicted the “spontaneous recovery” observed in later sessions: At the start of these sessions, response proportions reverted toward their preswitch levels. Computer simulations could mimic the spontaneous recovery by assuming that subjects store separate representations of response strength for each session, which are averaged at the start of each new session.     

Temporal comparator rules and responding in multiple schedules

Three response rules for explaining the role of temporal factors in the control of responding were examined. These were the cycle-to-trial comparator rule from scalar expectancy theory (SET; Gibbon & Balsam, 1981), the “deletion” comparator rule proposed by Cooper, Aronson, Balsam, and Gibbon (1990), and a “bad/good” comparator rule—a type of ITI-to-trial comparator. Two of these rules were designed to explain the acquisition of responding in simple associative learning paradigms (i.e., autoshaping). Here, their generality as predictors of response levels in response-dependent multiple schedules was examined. SET’s overall cycle-to-trial comparator rule was the best predictor of the pattern of responding. Contrary to previous findings regarding contrast in multiple schedules, which show greater contrast with shorter component durations, there was no effect of absolute component duration. As predicted by SET, relative, not absolute, component durations controlled response levels.     

Nap schedules and sleep practices in infant-toddler groups

This article describes and analyzes sleep-wake schedules and nap times in multiage infant-toddler groups through three case studies based on ethnographic research conducted in two Finnish day care centers. The study asks how day care centers and homes in collaboration can protect children’s biological sleep-wake rhythms and the physiological effectiveness of sleep. Data were derived through participant-observation in the groups, taped interviews with staff and parents, and sleep diaries kept by the parents. Findings show some of the complex interactions among family daily patterns, day care patterns, and sleep disturbances in very young children. The findings further show that major differences exist in day care practices regarding the quality of sleep and its physiological effectiveness. These differences are related to three issues: (1) whether the timing of naps in the multiage group is simultaneous or staggered in an age-appropriate and individually appropriate manner; (2) how efficiently the home/day care personnel communicate with one another; and (3) what is the awareness level of the day care staff about the significance of the sleep environment. The article further discusses the team aspect of protective practices, differences between caregivers and their differences in organizing work, as well as implications for further research and for caregiver training.     

Response strength and temporal control in fixed-interval schedules

Pigeons responded in a two-component peak procedure in which the components differed in terms of reinforcement magnitude (Experiment 1), immediacy (Experiment 2), or probability (Experiment 3). The prediction of behavioral momentum theory that responding in the relatively richer component should be more resistant to change was tested by (1) presenting response-independent food in the intervals between components according to a variable-time (VT) schedule, (2) prefeeding, and (3) extinction. In all the experiments, peak location in baseline occurred earlier, relative to the schedule value in the richer component. Peak response rate was more resistant to change in the richer component during the VT and prefeeding tests, and change in peak rate was more sensitive to differential reinforcement than change in overall response rate. Changes in measures of performance on peak trials during the disruptor tests were partially consistent with predictions of the behavioral theory of timing. The results suggest that peak response rate provides a more sensitive index of resistance to change for fixed-interval schedules than does overall response rate and that reinforcement strengthens both peak responding and temporal control.     

考研数学中的幂级数求和一题多解

幂级数求和是考研数学中的一个重要内容,也是学生学习中普遍感觉比较困难的知识点。文章以近几年数学考研试题中的幂级数求和问题为例,采用一题多解的形式,介绍了求幂级数和函数的三种常用方法。     

Optimization of project payment schedules with Nash equilibrium model and genetic algorithm

To minimize the deviations of the net present values of project payment for both the owner and the client and optimize project payment schedules, a Nash equilibrium model based on game theory was set up and a genetic algorithm was developed to work out the Nash equilibrium solution with a two-stage backward inductive approach that requires the client responds to the owner’s payment schedule with an activity schedule so as to maximize the client’s net present value of cash flows. A case study demonstrated that a payment schedule at the Nash equilibrium position enables both the owner and the client to gain their desirable interests, thus is a win-win solution for both parties. Despite the computation time of the proposed algrithm in need of improving, combining Nash equilibrium and genetic algorithm into a complete-information dynamic-game model is a promising method for project management optimization.