This article examines the transformation of the sacred landscape in the cities of Syria and Palestine from late antiquity to early Islam. This phase of urban and architectural history, often obscured by the changes brought in during the medieval period, is investigated through a close comparison of textual and material evidence related to the main urban religious complexes. It is suggested that the new Friday mosques were frequently built contiguous to Christian great churches, creating a sort of shared sacred area within the cities. Legal issues related to the Islamic conquest and the status of minorities are considered in order to explain the rationale behind such a choice by Muslims.

Let x denote a vector of length q consisting of 0s and 1s. It can be interpreted as an ‘opinion’ comprised of a particular set of responses to a questionnaire consisting of q questions, each having {0, 1}-valued answers. Suppose that the questionnaire is answered by n individuals, thus providing n ‘opinions’. Probabilities of the answer 1 to each question can be, basically, arbitrary and different for different questions. Out of the 2q different opinions, what number, μn , would one expect to see in the sample? How many of these opinions, μn (k), will occur exactly k times? In this paper we give an asymptotic expression for μn / 2q and the limit for the ratios μn (k)/μn , when the number of questions q increases along with the sample size n so that n = λ2q , where λ is a constant. Let p(x ) denote the probability of opinion x . The key step in proving the asymptotic results as indicated is the asymptotic analysis of the joint behaviour of the intensities np(x ). For example, one of our results states that, under certain natural conditions, for any z > 0, ∑1 {np( x) > z} = d n z −u ,d n = o(2q ).

The view that learning is governed by positive and negative consequences has dominated theory and application throughout this century. In some systems stimulus-response connections are stamped in or stamped out by the consequences of action, in others, cognitive expectancies are formed by experience with past consequences. The evidence from early experiments with rats and pigeons and the feedback principles of early servomechanisms seemed to offer both hard evidence and a plausible model for the law of effect in either its behaviorist or its cognitive form.

A large body of evidence demonstrates that the results of operant conditioning appear regardless of and often in spite of response-contingent consequences. Experiments designed to measure a residual effect of consequences exhibit an inevitable ex post facto error that vitiates all possible versions of this experimental design. Experiments designed to measure the effect of predictive contingency in Pavlovian conditioning exhibit a corresponding error. There appears to be a fundamental logical defect in all contingency models of the learning process.

Meanwhile, modern developments in ethology and computer science provide a unified feedforward model of the learning of adaptive and maladaptive behavior under both laboratory and field conditions. Because the feedforward model is more parsimonious, it is also more compatible with Darwinian principles of biological economy. Research on teaching new and challenging tasks to freeliving, well-fed subjects such as children and cross-fostered chimpanzees illustrates the wide applicability and practical effectiveness of feedforward.

Effective conditioning requires a correlation between the experimenter's definition of a response and an organism's, but an animal's perception of its behavior differs from ours. These experiments explore various definitions of the response, using the slopes of learning curves to infer which comes closest to the organism's definition. The resulting exponentially weighted moving average provides a model of memory that is used to ground a quantitative theory of reinforcement. The theory assumes that: incentives excite behavior and focus the excitement on responses that are contemporaneous in memory. The correlation between the organism's memory and the behavior measured by the experimenter is given by coupling coefficients, which are derived for various schedules of reinforcement. The coupling coefficients for simple schedules may be concatenated to predict the effects of complex schedules. The coefficients are inserted into a generic model of arousal and temporal constraint to predict response rates under any scheduling arrangement. The theory posits a response-indexed decay of memory, not a time-indexed one. It requires that incentives displace memory for the responses that occur before them, and may truncate the representation of the response that brings them about. As a contiguity-weighted correlation model, it bridges opposing views of the reinforcement process. By placing the short-term memory of behavior in so central a role, it provides a behavioral account of a key cognitive process.

This paper deals with the likelihood ratio test (LRT) for testing hypotheseson the mixing measure in mixture models with or without structural parameter. The main result gives the asymptotic distribution of the LRTstatisticsunder some conditions that are proved to be almost necessary.A detailed solution is given for two testing problems: thetest of a single distribution against any mixture, with application to Gaussian, Poisson andbinomial distributions; the test of the number of populations in afinite mixture with or without structural parameter.

Conditions are given for the family of distributions of a stationary, discrete-time, Gaussian, vector-valued time-series with covariance structure given up to a finite number of parameters to satisfy the asymptotic differentiability conditions introduced by Le Cam (1969).