Search

Most consumer choices are repeat choices driven by habits. Psychological accounts of habits have generally emphasized the driving role of external factors, especially contextual cues, in habit performance. The present research investigates the influence of an individual-difference variable that reflects a more internal driver of habits. Three studies reveal a negative relationship between people’s tendency to generate relatively uncommon word responses in free-association tasks and their tendency to repeat choice behavior across different consumer contexts. These results implicate free associations as having a role in habit performance and inform practical research on predictors of consumers’ repeat choices.

A conceptual analysis of measurement can properly begin by formulating the two fundamental problems of any measurement procedure. The first problem is that of representation, justifying the assignment of numbers to objects or phenomena. We cannot literally take a number in our hands and ’apply’ it to a physical object. What we can show is that the structure of a set of phenomena under certain empirical operations and relations is the same as the structure of some set of numbers under corresponding arithmetical operations and relations. Solution of the representation problem for a theory of measurement does not completely lay bare the structure of the theory, for there is often a formal difference between the kind of assignment of numbers arising from different procedures of measurement. This is the second fundamental problem, determining the scale type of a given procedure. Counting is an example of an absolute scale. The number of members of a given collection of objects is determined uniquely. In contrast, the measurement of mass or weight is an example of a ratio scale. An empirical procedure for measuring mass does not determine the unit of mass. The measurement of temperature is an example of an interval scale. The empirical procedure of measuring temperature by use of a thermometer determines neither a unit nor an origin. In this sort of measurement the ratio of any two intervals is independent of the unit and zero point of measurement. Still another type of scale is one which is arbitrary except for order. Moh’s hardness scale, according to which minerals are ranked in regard to hardness as determined by a scratch test, and the Beaufort wind scale, whereby the strength of a wind is classified as calm, light air, light breeze, and so on, are examples of ordinal scales. A distinction is made between those scales of measurement which are fundamental and those which are derived. A derived scale presupposes and uses the numerical results of at least one other scale. In contrast, a fundamental scale does not depend on others. Another common distinction is that between extensive and intensive quantities or scales. For extensive quantities like mass or distance an empirical operation of combination can be given which has the structural properties of the numerical operation of addition. Intensive quantities do not have such an operation; typical examples are temperature and cardinal utility. A widespread complaint about this classical foundation of measurement is that it takes too little account of the analysis of variability in the quantity measured. One important source is systematic variability in the empirical properties of the object being measured. Another source lies not in the object but in the procedures of measurement being used. There are also random errors which can arise from variability in the object, the procedures or the conditions surrounding the observations.

Although the concept of uncertainty is as old as Epicurus's writings, and an excellent quantitative theory, with entropy as the measure of uncertainty having been developed in recent times, there has been little exploration of the qualitative theory. The purpose of the present paper is to give a qualitative axiomatization of uncertainty, in the spirit of the many studies of qualitative comparative probability. The qualitative axioms are fundamentally about the uncertainty of a partition of the probability space of events. Of course, it is common to speak of the uncertainty, or randomness, of a random variable, but only the partition defined by the values of the random variable enter into the definition of uncertainty, not the actual values. It is straightforward to add axioms for decision making following the general line of Savage from the 1950s. Indeed, in the spirit of Epicurus, it is really our intuitive feeling about the uncertainty of the future that motivates much of our thinking about decisions. Here, the distinction between the concepts of probability and uncertainty can be made by citing many familiar examples. Without spelling out the technical details, the axiomatization of qualitative probability with uncertainty as the most important primitive concept, it is possible to raise a different kind of question about bounded rationality. This new question is whether or not one should bound the uncertainty in thinking and investigating any detailed framework of decision making. Discussion of this point is certainly different from the question of bounding rationality by not maximizing expected utility. In practice, we naturally bound uncertainty in our analysis of decision-making problems. As in the case of formulating an alternative for maximizing expected utility, so is the case of rational alternatives to maximizing uncertainty. There are several issues to consider. In the spirit of my other work in qualitative probability, I explore alternatives rather than attempt to give a definitive argument for one single solution.

Tracking the coordinated activity of cellular events through volumes of intact tissue is a major challenge in biology that has inspired significant technological innovation. Yet scanless measurement of the high-speed activity of individual neurons across three dimensions in scattering mammalian tissue remains an open problem. Here we develop and validate a computational imaging approach (SWIFT) that integrates high-dimensional, structured statistics with light field microscopy to allow the synchronous acquisition of single-neuron resolution activity throughout intact tissue volumes as fast as a camera can capture images (currently up to 100 Hz at full camera resolution), attaining rates needed to keep pace with emerging fast calcium and voltage sensors. We demonstrate that this large field-of-view, single-snapshot volume acquisition method—which requires only a simple and inexpensive modification to a standard fluorescence microscope—enables scanless capture of coordinated activity patterns throughout mammalian neural volumes. Further, the volumetric nature of SWIFT also allows fast in vivo imaging, motion correction, and cell identification throughout curved subcortical structures like the dorsal hippocampus, where cellular-resolution dynamics spanning hippocampal subfields can be simultaneously observed during a virtual context learning task in a behaving animal. SWIFT’s ability to rapidly and easily record from volumes of many cells across layers opens the door to widespread identification of dynamical motifs and timing dependencies among coordinated cell assemblies during adaptive, modulated, or maladaptive physiological processes in neural systems.

First, Padoa’s principle is used to prove the non-definability of the fundamental qualitative concepts of comparative probability, independence and comparative uncertainty in terms of each other. Second, the qualitative axioms of uncertainty leading to an entropy representation are new. Third, a qualitative random-variable axiomatization of these concepts is given, but the random variables are restricted to generalized indicator functions, their products and their iterates. A new axiom of independence in terms of such indicator functions is used in this axiomatization. Fourth, a standard extensive-quantity representation is then proved for comparative probability, and the new axiom of independence provides the basis for proving the desired absolute invariance theorem for the constructed probability measure.

Stanford University's Education Program for Gifted Youth (EPGY) conducted a randomized-treatment experiment during the 2006–2007 school year to test the efficacy, for Title I students, of the technological and individualized EPGY Kindergarten through Grade 5 Mathematics Course Sequence, modified for the Title I schools. Restricting attention to students who were in the top half of the distribution of correct first-exercise attempts (a measure of work and engagement), we found substantial and statistically significant improvements in the 2007 California Standard Math Tests (CST07) scores compared to those of matched control students. Gains in second grade were larger than those in Grades 3 to 5. Less able students, as measured by their 2006 CST mathematics scores, also had, on average, larger gains.

The source of human applications of mathematics to natural phenomena is very likely to be found in the perceptual processes necessary for most animals to survive, either as prey, predator, or forager. Much of the resources of the brain are used to transform the patterns of energy that impinge on sensory nerve endings into representations more or less isomorphic to the structure of some portion of the world. It is one of the intellectual triumphs of Ancient Greek thought, especially by Aristotle, to have recognized for the first time systematically the centrality of such isomorphisms for perception. The move from visual perception to intuitive geometry, and then to systematic Euclidean geometry seems psychologically natural. The Greek application of this geometric viewpoint to the motion of the heavens constitutes the first great work in mathematical physics. The progress from the Stone Age to Ptolemy is surely a very much bigger step than the move from Ptolemy to Newton and Einstein.

The idea that synchronized oscillations are important in cognitive tasks is receiving significant attention. In this view, single neurons are no longer elementary computational units. Rather, coherent oscillating groups of neurons are seen as nodes of networks performing cognitive tasks. From this assumption, we develop a model of stimulus-pattern learning and recognition. The three most salient features of our model are: 1) a new definition of synchronization; 2) demonstrated robustness in the presence of noise; and 3) pattern learning.

The idea of a hierarchical structure of language constituents of phonemes, syllables, words, and sentences is robust and widely accepted. Empirical similarity differences at every level of this hierarchy have been analyzed in the form of confusion matrices for many years. By normalizing such data so that differences are represented by conditional probabilities, semiorders of similarity differences can be constructed. The intersection of two such orderings is an invariant partial ordering with respect to the two given orders. These invariant partial orderings, especially between perceptual and brain representations, but also for comparison of brain images of words generated by auditory or visual presentations, are the focus of this letter. Data from four experiments are analyzed, with some success in finding conceptually significant invariants.