ON COUNTING SEQUENCES AND SOME RESEARCH QUESTIONS

A counting sequence is a list of all binary words of the same length. Counting sequences of any fixed odd Hamming distance between successive words (codewords) are discussed. Gray codes are examples of counting sequences having a single-bit change between neighboring codewords. We describe some results on Gray codes and highlight some research questions. The spectrum of bit changes or transition counts for individual variables for some uniform counting sequences is considered. We show some recent minor findings and pose remaining open questions

An econometric analysis of multimedia advertising effects on consumers\u27 purchase decisions at the supermarket level using scanner-derived data

Because of the shrinking market share, due in part to the distribution of the shopper\u27s dollar for various kinds of variable weight items which has been changing and the competitive nature of the supermarket industry, retail firms are looking for appropriate strategies to reverse the decline. To deal with the eroding market share, part of the response has been increased interest in recent years to identify how food shoppers respond to weekly advertising effects. However, existing studies on the responsiveness of food shoppers to advertising effects has tended to focus on a singular influence of media and/or single dimension advertising measures. For the retail firms, a strategic and beneficial approach may be to examine shoppers\u27 responses to weekly multimedia advertising effects and to the measures of their various dimensions. Also, the limited shelf-life of variable weight items and their significant contributions to sales total revenue, point to the need for accurate analysis and prediction of consumer purchasing decisions to achieve cost reductions and higher profits. If accurate econometric models can he built, the hurdles to effective planning and decision-making may be surmounted, thus permitting better customer service, smaller inventory levels, and less product spoilage. Further, retail firms will be able to anticipate sales more accurately and identify for producers, processors, distributors and/or suppliers some of the factors that can lead to variations in weekly sales. So, there is a need for a broader research effort on consumer demand for fresh meats at the retail level, because it holds potential for assisting supermarkets and suppliers. Inaccurate prediction of sales can lead to short-run surpluses or shortages in supply. Thus, knowledge of weekly demand elasticities would enable retail firms and their suppliers to handle these situations. The results based on the econometric analysis of weekly scan data from May 14,1988 through January 1,1994) for both unrestricted and restricted multimedia LA/AIDS models indicate that (1) own-newspaper advertising impacts are important for fresh ground, roast, and steak categories; (2) Own-electronic media advertising effects appear to he important only for ground and roast categories; (3) Own-price effects appear to be important for ground and steak items; and cross-price effects appear to be important for all the foods; (4) spring and summer seasons have positive influences on steak purchases, while July 4 is important for roast; (5) trend and consumption habits have positive effects on both roast and steak; (6) newspaper advertising intensity has a positive influence on the expenditure elasticity for steak; (7) newspaper advertising has a positive on own-price elasticities for ground and steak, while electronic media advertising has positive impact on own-price elasticity for ground, that is, these advertising modes tend to make own-price elasticities more inelastic for the food items; and (8) newspaper advertising has a positive effects on own-newspaper advertising elasticities for all the three beef categories, while electronic media advertising has positive influences on own electronic media advertising elasticities for both ground and roast. Overall, elasticity estimates reveal the sensitivity of shoppers\u27 purchases to price changes and advertising efforts. This study has demonstrated the applicability of scanner-derived data in modifying and/or developing econometric models to analyze and obtain new estimates of food shoppers\u27 responses to traditional and nontraditional factors at the supermarket level

Permutational labeling of constant weight Gray codes.

We prove that for positive integers n and r satisfying 1 \u3c r \u3c n, with the single exception of n = 4 and r = 2, there exists a constant weight Gray code of r-sets of Xn = {1,2,... ,n} that admits an orthogonal labelling by distinct partitions, with each subsequent partition obtained from the previous one by an application of a permutation of the underlying set. Specifically, an r-set A and a partition •K of Xn are said to be orthogonal if every class of n meets A in exactly one element. We prove that for all n and r as stated, and i = 1,2,..., I J taken modulo [ J, there exists a list Ai, A2,..., A(n\ of the distinct r-sets of Xn with \A\ n Aj+1| = r - 1 and a list of distinct partitions TTI, 7T2,..., irin\ such that TTJ is orthogonal to both Ai and Ai+i, and 7Tj+i = TTiAj for a suitable permutation A* of Xn

Efficient coding of spectrotemporal binaural sounds leads to emergence of the auditory space representation

To date a number of studies have shown that receptive field shapes of early sensory neurons can be reproduced by optimizing coding efficiency of natural stimulus ensembles. A still unresolved question is whether the efficient coding hypothesis explains formation of neurons which explicitly represent environmental features of different functional importance. This paper proposes that the spatial selectivity of higher auditory neurons emerges as a direct consequence of learning efficient codes for natural binaural sounds. Firstly, it is demonstrated that a linear efficient coding transform - Independent Component Analysis (ICA) trained on spectrograms of naturalistic simulated binaural sounds extracts spatial information present in the signal. A simple hierarchical ICA extension allowing for decoding of sound position is proposed. Furthermore, it is shown that units revealing spatial selectivity can be learned from a binaural recording of a natural auditory scene. In both cases a relatively small subpopulation of learned spectrogram features suffices to perform accurate sound localization. Representation of the auditory space is therefore learned in a purely unsupervised way by maximizing the coding efficiency and without any task-specific constraints. This results imply that efficient coding is a useful strategy for learning structures which allow for making behaviorally vital inferences about the environment.Comment: 22 pages, 9 figure

Processing bimodal stimuli: integrality/separability of color and orientation

We examined how two distinct stimulus features, orientation and color, interact as contributions to global stimulus dissimilarity. Five subjects rated dissimilarity between pairs of bars (N = 30) varying in color (four cardinal hues, plus white) and orientation (six angles at 30° intervals). An exploratory analysis with individual-differences multidimensional scaling (MDS) resulted in a 5D solution, with two dimensions required to accommodate the circular sequence of the angular attribute, and red-green, blue-yellow and achromatic axes for the color attribute. Weights of the orientation subspace relative to the color subspace varied among the subjects, from a 0.32:0.61 ratio to 0.53:0.44, emphasis shifting between color and orientation. In addition to Euclidean metric, we modeled the interaction of color and orientation using Minkowski power metrics across a range of Minkowski exponents p, including the city-block (p = 1), Euclidean (p = 2) and Dominance metric (p → ∞) as special cases. For averaged data, p ~ 1.3 provided the best fit, i.e., intermediate between separable and integral features. For individual subjects, however, the metric exponent varied significantly from p = 0.7 to p = 3.1, indicating a subject-specific rule for combining color and orientation, as in Tversky and Gati's variable-weights model. No relationship was apparent between dimensional weights and individual p exponents. Factors affecting dimensional integrality are discussed, including possible underlying neural mechanisms where the interaction of the low-level vision attributes orientation and color might shift between uncorrelated (p = 1) or correlated (p ≥ 2) forms