Multidimensional scaling in riemannian space

A metric which is a function of position is proposed for the analysis of the intrinsic geometry involved in preference or similarity judgments. Variation in the distance function or metric is characteristic of the Riemannian spaces and may be interpreted as curvature, stress or distortion in distance estimates and thus in the subjective perceptual space. It is possible to find the coefficients in the distance function at selected points by fitting a least-squares Riemannian surface to the Euclidean plane. The functional form of the distance can then be obtained by an application of the Laplace equation. Several examples are worked out for the two-dimensional solution but extension to higher spaces appears to be quite feasible.     

Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts

ABSTRACT

In this paper, a mode-III crack in one-dimensional (1D) hexagonal quasicrystals subjected to anti-plane impact loading is analyzed. The elasto-hydrodynamics of quasicrystals is adopted, where the phonon field obeys wave equation, and the phason field obeys diffusion equation. By introducing a new auxiliary function, the coupled wave-diffusion equations are converted to a single higher-order partial differential equation. With the aid of the Laplace transform, an associated mixed initial-boundary value problem is reduced to two sets of dual integral equations, and then transformed into two coupled Fredholm integral equations of the second kind. Numerical results of transient phonon and phason stress intensity factors and crack-centre displacement jump are obtained through the numerical inversion of the Laplace transform and are presented graphically to show the influences of the phason.     

空间距离与产品属性对消费者选择偏好的影响*

通过两个实验检验空间距离如何影响消费者选择偏好。实验一中,产品与消费者之间的空间距离不影响他们对不可匹配属性更优产品的偏好。实验二中,两种产品之间的空间距离与产品属性交互作用影响了消费者的选择偏好,使他们在两产品之间空间距离远时比近时更偏好不可匹配属性更优产品。两种不同类型的空间距离对消费者选择偏好的影响是不同的。强调两产品之间的空间距离远,会影响消费者在选择过程中对不可匹配属性的使用。     

An analytical solution to the nonlinear evolutionary equations for nucleation and growth of particles

ABSTRACT

In this paper, we consider a mathematical model for the growing crystals in supersaturated or supercooled systems. An integro-differential equation of the Fokker-Planck type is analytically solved using the saddle point method for the Laplace integral. The solution describes an intermediate stage of the phase transition process with allowance for the power law of the growth rate of spherical particles and the nucleation mechanisms known as the Meirs and Weber-Volmer-Frenkel-Zeldovich kinetics. A dynamical dependencies for the supersaturation/supercooling and the distribution function of crystals by their size are obtained. The novelty of the theory is the use of a power law for the growth rate of crystals, which leads to new analytical solutions of the problem.     

Intelligent vector field visualization based on line integral convolution

In order to reflect the internal motion characteristics of entire vector fields, texture visualization methods based on line integral convolution are usually adopted. However, the visualization results obtained in this way have low image quality. To solve this problem, this paper suggests using line integral convolution to optimize two specific aspects - texture enhancement and color enhancement – to provide an enhanced vector field visualization model. Existing texture enhancement algorithms can create texture aliasing. Based on an analysis of the relationship between vector angles, sampling distance and texture aliasing, the paper puts forward a texture enhancement algorithm that uses the vector angle to adjust the sampling distance of a high-pass filter. This greatly reduces the presence of texture aliasing. For color enhancement, a linear algorithm is usually used that adds vector size information to the vector field. However, the resulting image has a problem of color concentration. In view of this, the distribution characteristics of the vector field are analyzed using a histogram and a dynamic nonlinear color enhancement algorithm is proposed. This noticeably improves the color distribution of the resulting image and improves the overall visual quality of the result.     

A distance judgment function based on space perception mechanisms: revisiting Gilinsky's (1951) equation

In her seminal article in Psychological Review, A. S. Gilinsky (1951) successfully described the relationship between physical distance (D) and perceived distance (d) with the equation d = DA/(A + D), where A = constant. To understand its theoretical underpinning, the authors of the current article capitalized on space perception mechanisms based on the ground surface to derive the distance equation d = Hcosalpha/sin(alpha + eta), where H is the observer's eye height, alpha is the angular declination below the horizon, and eta is the slant error in representing the ground surface. Their equation predicts that (a) perceived distance is affected by the slant error in representing the ground surface; (b) when the slant error is small, the ground-based equation takes the same form as Gilinsky's equation; and (c) the parameter A in Gilinsky's equation represents the ratio of the observer's eye height to the sine of the slant error. These predictions were empirically confirmed, thus bestowing a theoretical foundation on Gilinsky's equation.     

An illusion of eccentricity

The illusion investigated here is that two concentric arcs, drawn in different (though possibly overlapping) circular sectors and having the same angular extent, appear to be eccentric. Three possible explanations of the illusion are tested. The first hypothesis is that concentricity judgments are made by elongating the arcs to see if they intersect, the illusion being due to the tendency, when elongating a curve, to follow the end-tangent. The second hypothesis is that concentricity judgments are based on a test of coincidence of centers, the illusion being due to the overestimation of the radius of short arcs. The third hypothesis is that both of these factors contribute in equal measure. These hypotheses make different predictions about the effect (on the magnitude of the illusion) of the following variables: (1) the angular distance between the arcs; (2) the radial distance between the arcs; (3) the degree of curvature of the arcs; and (4) the angular extent of the arcs. The observed values of the illusion angle (obtained by the method of limits) in relation to these variables did not uniformly support any of the hypotheses. A more complex model that is consistent with the observed results is therefore proposed.     

Matching as a multivariate power law: Frequency of behavior versus frequency and magnitude of reinforcement

Two groups of food-deprived rats responded for access to liquid reinforcers on a wide range of concurrent variable-interval schedules. During the first part of the experiment, one group chose between two different sucrose solutions; for a second group, the choice involved a sucrose solution and a solution of condensed milk. In the latter part of the experiment, the two groups chose between identical sucrose solutions. A variety of multivariate equations were applied to data obtained from both conditions. The best-fitting equation proved to be a multivariate power function, which is an extension of Herrnstein's basic matching law.     

Ontogeny of behavioral arousal: the role of environmental stimuli

During the course of ontogenesis the developing rat has been reported to pass through a transient period of intense behavioral arousal which peaks at 15 days of age, a phenomenon that has been interpreted to reflect a sequential caudal to rostral development of excitatory and inhibitory systems in the mammalian brain. In a series of four experiments it was shown (a) that this period of intense hyperactivity occurs only when the animal is tested alone in an unfamiliar environment, that the degree of arousal is proportional to the dissimilarity between the home cage and the test environment, and that isolation per se is insufficient to elicit the arousal response; (b) that environmental temperature has a minimal influence on the degree of behavioral arousal seen in either familiar of unfamiliar environments; (c) that unlearned responses to pheromonal or other naturally occurring nest odors do not suppress the high levels of locomotor activity evoked by unfamiliar environments in the 15-day old rat pup; and (d) that it is fear or distress evoked by the unfamiliar environment rather than curiosity that underlies this developmental phenomenon. It is concluded that the sequential increase and decrease in locomotor activity that occurs during ontogenesis cannot be used to support the principle of caudal to rostral development of excitatory and inhibitory centers in the central nervous system.     

Reevaluating the two-representation model of numerical magnitude processing

One debate in mathematical cognition centers on the single-representation model versus the two-representation model. Using an improved number Stroop paradigm (i.e., systematically manipulating physical size distance), in the present study we tested the predictions of the two models for number magnitude processing. The results supported the single-representation model and, more importantly, explained how a design problem (failure to manipulate physical size distance) and an analytical problem (failure to consider the interaction between congruity and task-irrelevant numerical distance) might have contributed to the evidence used to support the two-representation model. This study, therefore, can help settle the debate between the single-representation and two-representation models.     

COMMUNICATION FACTORS RELATED TO CLOSER INTERNATIONAL TIES

The question of what promotes closer ties between nations has long been central to the study of intercultural communication. This research develops and tests a model that specifies three factors drawn from social distance and systems perspectives that are posited to have an influence on the desire for closer ties between the U.S. and Mexico. Each of the factors, perceptions of homophily, shared interests, and threats, have previously been identified as occupying central positions in the development of international relationships. The sample used to test the model was drawn from eight elite occupational groups within Mexican urban centers (N = 800). The results were supportive of the model, with quite acceptable goodness of fit measures, with a high level of variance accounted for in the dependent variable, and with support for the paths between exogenous and endogenous variables as predicted in the model.     

Stimulus-response with reciprocal kernels: The rise and fall of sensation

The paper presents a theory for constructing response scales based on the reciprocal property of paired comparisons of stimuli from the same sensory continuum. Reciprocal paired comparisons define the pair estimator function K(s, t), the kernel of a Fredholm integral equation of the second kind. The solution of this equation yields a response scale of the form s^αe^−βs, where s is the stimulus scale. The response scale provides a basis for a theory to describe how images and sensation patterns are formed from stimuli.     

Inhibitory control and empathy-related personality traits: sex-linked associations

We here report two studies exploring associations between inhibitory control (measured with the Sustained Attention to Response Task, SART) on the one hand, and self-reports of trait cooperativeness and empathy on the other. A coherent picture was obtained in women whose inhibitory control proficiency predicted higher scores on the Temperament and Character Inventory Cooperativeness and a higher Empathy Quotient. Individual differences in working memory did not predict self-reported empathy. In men, the association between SART performance and empathy was less clear: Good performance on the inhibitory task predicted lower scores on Cooperativeness and was unrelated to the Empathy Quotient. In both studies, women outperformed men on the SART. The results in women may reflect how individual differences in elemental neuro-cognitive operations such as inhibitory control influence more complex functions such as social cognition.     

负性情绪在冲突适应中的作用机制：分离与整合视角

负性情绪如何影响冲突适应一直以来受到领域内研究者们的广泛关注。根据负性情绪产生的源头(冲突外部操纵vs.冲突内部固有), 对于该问题的论述可以分别从认知与情绪的分离与整合视角展开。分离视角下, 操纵于冲突之外的负性情绪(外部负性情绪)独立于冲突加工过程, 通过情绪加工系统或个体自身的动机/唤醒水平影响冲突适应。近些年来的研究发现冲突加工自动产生负性情绪(固有负性情绪), 寓示着认知冲突与负性情绪间的内在关联, 固有负性情绪因此可被视作诱发冲突适应的另一个有效来源。整合视角下, 操纵于冲突内部的(固有)负性情绪高度整合于冲突加工过程, 其功能与冲突信息类似, 通过内在地促进目标导向行为直接诱发冲突适应。对这一主题的论述加深了我们对负性情绪如何作用于冲突适应过程的理解, 也为探索认知与情绪系统的整合过程及作用机制提供了一个全新的视角, 在此基础上, 我们也提出一些未来可行的研究方向。     

Attention and learning processes in the identification and categorization of integral stimuli

The relationship between subjects' identification and categorization learning of integral-dimension stimuli was studied within the framework of an exemplar-based generalization model. The model was used to predict subjects' learning in six different categorization conditions on the basis of data obtained in a single identification learning condition. A crucial assumption in the model is that because of selective attention to component dimensions, similarity relations may change in systematic ways across different experimental contexts. The theoretical analysis provided evidence that, at least under unspeeded conditions, selective attention may play a critical role in determining the identification-categorization relationship for integral stimuli. Evidence was also provided that similarity among exemplars decreased as a function of identification learning. Various alternative classification models, including prototype, multiple-prototype, average distance, and "value-on-dimensions" models, were unable to account for the results.     

Laterally induced impedance effects in vision

A linear integral equation for a system of mutually impeding points is developed and solved explicitly. Particular solutions are shown to be subharmonic functions for a large class of stimuli. Specialized forms of the general equation presented in this paper occur within a number of mathematical models of Mach bands. In addition to these known spatial properties, our results also show that the time course of this basic equation may be useful in developing models of transient neural activity as well as of temporal psychophysical phenomena, such as the Broca-Sulzer effect. Further, a spatial transfer function much like the low-frequency cutoff of empirically derived modulation transfer functions follows directly from our basic integral equation if the additional assumption of spatial homogeneity is imposed.     

Multidimensional scaling: I. Theory and method

Multidimensional scaling can be considered as involving three basic steps. In the first step, a scale of comparative distances between all pairs of stimuli is obtained. This scale is analogous to the scale of stimuli obtained in the traditional paired comparisons methods. In this scale, however, instead of locating each stimulus-object on a given continuum, the distances between each pair of stimuli are located on a distance continuum. As in paired comparisons, the procedures for obtaining a scale of comparative distances leave the true zero point undetermined. Hence, a comparative distance is not a distance in the usual sense of the term, but is a distance minus an unknown constant. The second step involves estimating this unknown constant. When the unknown constant is obtained, the comparative distances can be converted into absolute distances. In the third step, the dimensionality of the psychological space necessary to account for these absolute distances is determined, and the projections of stimuli on axes of this space are obtained. A set of analytical procedures was developed for each of the three steps given above, including a least-squares solution for obtaining comparative distances by the complete method of triads, two practical methods for estimating the additive constant, and an extension of Young and Householder's Euclidean model to include procedures for obtaining the projections of stimuli on axes from fallible absolute distances.This study was carried out while the author was an Educational Testing Service Psychometric Fellow at Princeton University. The author expresses his appreciation to his thesis adviser, Dr. H. Gulliksen, for his guidance throughout the study and to Dr. B. F. Green, Jr., for valuable assistance on several of the derivations.     

Interaction between consecutive learnings: inhibitory avoidance and habituation

Rats were submitted to step-down inhibitory avoidance training and to habituation of a rearing response to a tone with a 2-h interval between the two tasks, and were tested for retention of both tasks on the next day. When animals were trained first in inhibitory avoidance and then in habituation, retention of the avoidance behavior was impaired. When the animals were trained first in the habituation task and then in the avoidance task, retention of the two tasks was normal. The same results were obtained regardless of the order in which the two tasks were presented on the day of testing. This asymmetrical influence of habituation training on inhibitory avoidance retention could be due either to cognitive or, more likely, to task-specific neurochemical interactions.     

Sensitivity analysis of structural equation models

The main purpose of this paper is to investigate the sensitivity analysis of structural equation model when minor perturbation is introduced. Some influence measure that based on the general case weight perturbation is derived for the generalized least squares estimation. An influence measure that related to the Cook's distance is also developed for the special case deletion perturbation scheme. Using the proposed methodology, the influential observation in a data set can be detected. Moreover, the general theory can be applied to detect the influential parameters in a model. Finally, some illustrative artificial and real examples are presented. The research of the first author was supported by a Hong Kong UPGC grant. The authors are greatly indebted to two reviewers for some very valuable comments for improvement of the paper.