An Umm an‐Nar culture stone bas‐relief from Al‐Qutainah,Sultanate of Oman

The Al‐Qutainah stone with its bas‐relief decoration was found in a secondary position, reused through time. The object is clearly a facing stone, originally part of an Umm an‐Nar period tomb, and was subsequently repeatedly reused for making new engravings. While working out the sequence of images it became clear that the very first image was a pair of human figures. This artwork is associated to grave architecture and therefore dates to the Umm an‐Nar period. Two models of interpretation can be suggested, the image of a human pair or the image of a supplicant and deity. Changes in the original meaning of the image indicate conceptual changes in subsequent periods, most probably alterations in the underlying social structure. The importance of the Qutainah stone is not solely due to rare monumental human figurative expression of the period in Oman; furthermore, the find spot in the Adam region is at a distance from the central location of Umm an‐Nar culture that has so far emerged.     

Housing Choice in a Regulated Market: A Nested Multinomial Logit Analysis

The paper integrates several important elements of the institutionalized and regulated nature of the housing market and analyzes the relationship between household type and housing choice in Vienna within a nested multinomial logit framework. In particular, the concept of household specific choice sets is used to account for institutional, informational and income-based constraints of the choice process. Government subsidies (such as housing and rent allowances, non-interest-bearing state loans) are explicitly taken into account in the definition of variables. Housing choice is considered in three stages: the choice of a dwelling unit given dwelling type and residential zone, the choice of a dwelling type given residential zone, and the marginal choice of a residential zone. The coefficients are derived by means of a sequential ML-procedure. The empirical results clearly indicate that demographic variables have significant impacts on housing choice behavior. Income as a single explanatory variable as well as its interacting with size measures and the quality of the house are found to be important criteria for dwelling unit choice, as housing cost variables for dwelling type choice behavior. The dwelling unit and dwelling type choice submodels fit reasonably well, whereas the residential zone model is less successful.     

Bibliographischer hinweis zu s. 146, anm. 74

Ohne Zusammenfassung     

Gedanken zum namen Himālaya

Ohne ZusammenfassungWilhelm Brandenstein zum 60. Geburtstag gewidmet.     

Optimization in an Error Backpropagation Neural Network Environment with a Performance Test on a Spectral Pattern Classification Problem

This paper attempts to develop a mathematically rigid framework for minimizing the cross-entropy function in an error backpropagating framework. In doing so, we derive the backpropagation formulae for evaluating the partial derivatives in a computationally efficient way. Various techniques of optimizing the multiple-class cross-entropy error function to train single hidden layer neural network classifiers with softmax output transfer functions are investigated on a real-world multispectral pixel-by-pixel classification problem that is of fundamental importance in remote sensing. These techniques include epoch-based and batch versions of backpropagation of gradient descent, PR-conjugate gradient, and BPGS quasi-Newton errors. The method of choice depends upon the nature of the learning task and whether one wants to optimize learning for speed or classification performance. It was found that, comparatively considered, gradient descent error backpropagation provided the best and most stable out-of-sample performance results across batch and epoch-based modes of operation. If the goal is to maximize learning speed and a sacrifice in classification accuracy is acceptable, then PR-conjugate gradient error backpropagation tends to be superior. If the training set is very large, stochastic epoch-based versions of local optimizers should be chosen utilizing a larger rather than a smaller epoch size to avoid unacceptable instabilities in the classification results.     

A Methodology for Neural Spatial Interaction Modeling

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modeling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete‐valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilize a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation, and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained neural network model versions in terms of generalization performance measured by Kullback and Leibler's information criterion.