An optimization approach for mapping and measuring the divergence and correspondence between paths

Many domains of empirical research produce or analyze spatial paths as a measure of behavior. Previously, approaches for measuring the similarity or deviation between two paths have either required timing information or have used ad hoc or manual coding schemes. In this paper, we describe an optimization approach for robustly measuring the area-based deviation between two paths we call ALCAMP (Algorithm for finding the Least-Cost Areal Mapping between Paths). ALCAMP measures the deviation between two paths and produces a mapping between corresponding points on the two paths. The method is robust to a number of aspects in real path data, such as crossovers, self-intersections, differences in path segmentation, and partial or incomplete paths. Unlike similar algorithms that produce distance metrics between trajectories (i.e., paths that include timing information), this algorithm uses only the order of observed path segments to determine the mapping. We describe the algorithm and show its results on a number of sample problems and data sets, and demonstrate its effectiveness for assessing human memory for paths. We also describe available software code written in the R statistical computing language that implements the algorithm to enable data analysis.     

认知诊断中的Q矩阵及其作用

Q矩阵作为连接认知和测量的桥梁,在认知诊断中起重要作用。本文梳理了应用Q矩阵解决认知诊断相关问题的理论与方法。首先整理Q矩阵的相关概念、算法、性质及其在认知诊断中的作用;并根据Q矩阵可计算理论构念效度、可以构成格等,指出Q矩阵是特殊的关联矩阵;接着介绍Q矩阵理论研究方面的几个近期发展;并对Q矩阵未来的应用研究作出展望。期望本文能为测量工作者更灵活地利用Q矩阵提供参考和帮助。     

认知诊断中的Q矩阵及其作用

Q矩阵作为连接认知和测量的桥梁，在认知诊断中起重要作用。本文梳理了应用Q矩阵解决认知诊断相关问题的理论与方法。首先整理Q矩阵的相关概念、算法、性质及其在认知诊断中的作用；并根据Q矩阵可计算理论构念效度、可以构成格等，指出Q矩阵是特殊的关联矩阵；接着介绍Q矩阵理论研究方面的几个近期发展；并对Q矩阵未来的应用研究作出展望。期望本文能为测量工作者更灵活地利用Q矩阵提供参考和帮助。     

Visual detection in relation to display size and redundancy of critical elements I

Visual detection was studied in relation to displays of discrete elements, randomly selected consonant letters, distributed in random subsets of cells of a matrix, the S being required on each trial to indicate only which member of a predesignated pair of critical elements was present in a given display. Experimental variables were number of elements per display and number of redundant critical elements per display. Estimates of the number of elements effectively processed by a S during a 50 ms. exposure increased with display size, but not in the manner that would be expected if the S sampled a fixed proportion of the elements present in a display of given area. Test-retest data indicated substantial correlations over long intervals of time in the particular elements sampled by a S from a particular display. Efficiencies of detection with redundant critical elements were very close to those expected on the hypothesis of constant sample size over trials for any given display size and were relatively invariant with respect to distance between critical elements.     

Should information be redundantly distributed among group members? Effective use of group memory in collaborative problem solving

This study examined the relation between the redundancy in task assignment and group performance. It was predicted that assigning items to group members too redundantly would undermine group problem‐solving performance. To test this prediction, dyads and triads engaged in a problem‐solving task. A logic puzzle solvable with seven clues was employed as the task. Participants were asked to memorize the clues before engaging in group problem solving. In the shared condition, all seven clues were assigned to each group member. In the unshared condition, a portion of the seven clues was assigned to each member. Unshared triads whose members were assigned the smallest number of clues were most likely to return the correct solution. This result suggests that less redundant item assignment led to successful problem solving via information pooling among group members. Copyright © 2005 John Wiley & Sons, Ltd.     

Fusion prevents the redundant signals effect: evidence from stereoscopically presented stimuli

In a simple reaction time (RT) experiment, visual stimuli were stereoscopically presented either to one eye (single stimulation) or to both eyes (redundant stimulation), with brightness matched for single and redundant stimulations. Redundant stimulation resulted in two separate percepts when noncorresponding retinal areas were stimulated, whereas it resulted in a single fused percept when corresponding areas were stimulated. With stimulation of noncorresponding areas, mean RT was shorter to redundant than to single stimulation, replicating the redundant signals effect (RSE) commonly found with visual stimuli. With stimulation of corresponding areas, however, no RSE was observed. This suggests that the RSE is driven by the number of percepts rather than by the number of stimulated receptors or sensory organs. These results are consistent with previous findings in the auditory modality and have implications for models of the RSE.     

A family of chance-corrected association coefficients for metric scales

A chance-corrected version of the family of association coefficients for metric scales proposed by Zegers and ten Berge is presented. It is shown that a matrix with chance-corrected coefficients between a number of variables is Gramian. The members of the chance-corrected family are shown to be partially ordered. The author is obliged to Jos ten Berge for helpful comments.     

Minimum Muscle-Tension Change Trajectories Predicted by Using a 17-Muscle Model of the Monkey's Arm

Four computational problems to be solved for visually guided reaching movements, hand path, and trajectory formations, coordinate transformation, and calculations of muscle tensions are ill-posed in redundant biological control systems. These problems are ill-posed in the sense that there exist an infinite number of possible solutions. In this article, it is shown that the nervous system can solve those problems simultaneously by imposing a single global constraint: finding the smoothest muscle- tension trajectory that satisfies the desired final hand position, velocity, and acceleration. Horizontal trajectories were simulated by using a l7-muscle model of the monkey's arm as the controlled object. The simulations predicted gently curved hand paths for lateral hand movements and for movements from the side of the body to the front, and a roughly straight hand path for anterioposterior movements. The tangential hand velocities were roughly bell shaped. The simulated results were in agreement with the actual biological movements.     

Studies in spatial learning. I. Orientation and the short-cut. 1946.

1. The original rough formulation of the expectancy theory is difficult to distinguish from the alternative stimulus-response doctrines. Part of this difficulty results from the fact that implicit in this rough formulation, is a definition of the matrix "x expects a goal at location L," which makes it equivalent to the matrix "x runs down the practiced path," when certain conditions are fulfilled. Because of this difficulty, we have rejected this definition. 2. We have suggested instead a definition of the matrix "x expects a goal at location L" which makes it equivalent to the matrix "x runs down the path which points directly to the location L," when certain conditions are fulfilled. 3. To determine whether rats will run down such a path, whenever the original path is blocked, we have run 56 female rats in a situation which conformed to these conditions. 4. Thirty-six percent of the rats chose the path which pointed directly towards the location of the goal. The remaining rats were distributed over the other paths in a chance fashion. 5. We have concluded (1) that rats do learn to expect goals in specific locations, (2) that there are important similarities between this behavior and human symbolic behavior, and (3) that these similarities justify our using the word 'expectation' as a name for the disposition to short-cut when the original patch is blocked.     

Matrix operations and the properties of networks and directed graphs

Matrix multiplication is frequently used to derive properties and quantitative features of directed graphs and networks from their adjacency or value matrices. In many cases, a “modified” matrix multiplication is employed, where other binary operations replace ordinary addition and multiplication. In this paper, a set of conditions for permissible value domains, “addition” and “multiplication” operations, and value matrices is developed under which generalized matrix multiplication directly yields properties of a digraph or network. An additional condition ensures that the properties are related to paths of the structure rather than sequences in general. Finally, a number of applications of generalized matrix multiplication are discussed.     

The number of paths and cycles in a digraph

An algorithm is presented for constructing from the adjacency matrix of a digraph the matrix of its simplen-sequences. In this matrix, thei, j entry,i j, gives the number of paths of lengthn from a pointv _i to a pointv _j ; the diagonal entryi, i gives the number of cycles of lengthn containingv _i . The method is then generalized to networks—that is, digraphs in which some value is assigned to each line. With this generalized algorithm it is possible, for a variety of value systems, to calculate the values of the paths and cycles of lengthn in a network and to construct its value matrix of simplen-sequences. The procedures for obtaining the two algorithms make use of properties of a line digraph—that is, a derived digraph whose points and lines represent the lines and adjacency of lines of the given digraph.The research reported here was supported by Grant NSF-G-17771 from the National Science Foundation. We wish to thank Professor Frank Harary for suggesting certain ways of improving an earlier draft of this paper.     

Hierarchical control in redundant and non-redundant postural tasks

Prior studies of postural coordination have shown inconsistencies between hip-ankle coordination in redundant and non-redundant coordination tasks as well as predictions of the HKB model. These inconsistencies were investigated by testing the hypothesis that there are different hierarchical control structures for redundant (multiple potential task solutions) and non-redundant (a single task solution) coordination tasks (Bernstein, 1996). The transfer between a non-redundant postural tracking task and a redundant scanning task consisting of 16 hip-ankle relative phase patterns from 0° to 337.5° was investigated. The results showed that the transfer between the tasks was transitory, negative and occurred only from the non-redundant to the redundant task. This finding supports the hypothesis that inconsistencies between redundant and non-redundant coordination dynamics may be due to a hierarchical relation between control structures for the performance of these types of tasks.     

Pattern redundancy and detection in very short-term memory

A tachistoscopically presented target letter is detected better in a background of redundant items than in nonredundant material. The present experiment extended this finding by showing that detection rate increased systematically across three levels of background letter redundancy. A conclusion based on the earlier findings was that a serial process of letters in memory could not account for the effects of background redundancy on detection accuracy. Contrary to this conclusion, the present analysis showed that detection for semiredundant displays was successfully predicted by two variants of a serial process model. One model assumed that the scan of a letter is faster when the letter is the same as any prior letter scanned in the matrix. The other model assumes that nonredundant letters are processed serially and that redundant letters are processed all at once, i.e., in parallel.     

Cross-Lagged Relationships Between Insomnia and Posttraumatic Stress Disorder in Treatment-Receiving Veterans

Insomnia is a risk factor for the development of posttraumatic stress disorder (PTSD) while it is also plausible that PTSD symptoms can maintain insomnia symptoms. The present study examined longitudinal bidirectional relationships between insomnia and PTSD symptoms in treatment-seeking veterans. Participants were 693 ex-serving members of the Australian Defence Force who participated in an accredited, hospital-based outpatient PTSD program. Participants completed self-reported assessments of PTSD and insomnia symptoms at four time points: intake, discharge, 3-month, and 9-months posttreatment follow-up.Cross-lagged pathway analyses indicated significant bi-directional pathways between insomnia symptoms and PTSD symptoms at most time points. A final cross-lagged model between insomnia symptoms and the PTSD symptom clusters indicated that the PTSD symptom paths on insomnia symptoms, between intake and discharge, were attributable to reexperiencing PTSD symptoms. In contrast, across posttreatment follow-up time points there were significant paths of insomnia symptoms on all PTSD symptom clusters except from insomnia at 3-months to avoidance symptom at 9-months. PTSD symptoms and insomnia symptoms have bidirectional associations over time that may lead to the mutual maintenance or exacerbation of each condition following PTSD treatment. Where residual insomnia symptoms are present post-treatment, a sleep-focussed intervention is indicated and a sequenced approach to treatment recommended.     

Semantic Holism is seriously false

Semantic Holism is the claim that any semantic path from inferential semantics (the indeterminate semantics forced by the classical inference rules of PC) reaches all the way to classical semantics if it is even one step long. In our joint paper Semantic Holism, Belnap and I showed that some such semantic paths are two steps long, but we left open a number of questions about the lengths of semantic paths. Here I answer the most important of these questions by showing that there are infinitely long semantic paths that begin at inferential semantics but that do not even reach classical semantics. I do this by showing how to construct such an infinite semantic path from the members of the family of (n–1)-out-of-n-disjunction connectives.     

Informed horses are influential in group movements,but they may avoid leading

In species that move in cohesive groups, animals generally reach decisions through socially distributed processes, and individual knowledge is expected to influence collective decision making. Pooling of information should not be considered a general rule, however, since conflicts of interest may occur between group members. When resources are limited or highly attractive, higher-ranking individuals can prevent others from accessing food, and subordinates may have an interest in withholding information about its location. We investigated the role individual knowledge may play in recruitment processes in four groups of horses (Equus caballus). Animals were repeatedly released in a food search situation, in which one individual had been informed about the location of a preferred food, while another was a naïve control subject. Horses that were informed about the location of the feeding site were seen to approach the food source more steadily and were followed by a higher number of group members than their uninformed counterparts. Recruitment processes appeared mostly passive. Among the informed subjects, lower-ranking individuals were overall less followed than the higher-ranking ones. Most lower-ranking horses arrived alone at the feeding site. Non-followed informed subjects spent less time in active walk and used direct paths less frequently than followed animals, and they were joined by fewer partners at the attractive food source and spent more time feeding alone. This indicates that the influence of informed individuals on the behavior of other group members was a mixed process. Some horses brought nutritional benefits to their conspecifics by leading them to food supplies, whereas the behavior of others might be functionally deceptive.     

The race model inequality: interpreting a geometric measure of the amount of violation

An inequality by J. O. Miller (1982) has become the standard tool to test the race model for redundant signals reaction times (RTs), as an alternative to a neural summation mechanism. It stipulates that the RT distribution function to redundant stimuli is never larger than the sum of the distribution functions for 2 single stimuli. When many different experimental conditions are to be compared, a numerical index of violation is very desirable. Widespread practice is to take a certain area with contours defined by the distribution functions for single and redundant stimuli. Here this area is shown to equal the difference between 2 mean RT values. This result provides an intuitive interpretation of the index and makes it amenable to simple statistical testing. An extension of this approach to 3 redundant signals is presented.     

How to Assess a Model's Testability and Identifiability

Formal definitions are given of the following intuitive concepts: (a) A model is quantitatively testable if its predictions are highly precise and narrow. (b) A model is identifiable if the values of its parameters can be ascertained from empirical observations. (c) A model is redundant if the values of some parameters can be deduced from others or if the values of some observables can be deduced from others. Various rules of thumb for nonredundant models are examined. The Counting Rule states that a model is quantitatively testable if and only if it has fewer parameters than observables. This rule can be safely applied only to identifiable models. If a model is unidentifiable, one must apply a generalization of the Counting Rule known as the Jacobian Rule. This rule states that a model is quantitatively testable if and only if the maximum rank (i.e., the number of linearly independent columns) of its Jacobian matrix (i.e., the matrix of partial derivatives of the function that maps parameter values to the predicted values of observables) is smaller than the number of observables. The Identifiability Rule states that a model is identifiable if and only if the maximum rank of its Jacobian matrix equals the number of parameters. The conclusions provided by these rules are only presumptive. To reach definitive conclusions, additional analyses must be performed. To illustrate the foregoing, the quantitative testability and identifiability of linear models and of discrete-state models are analyzed. Copyright 2000 Academic Press.     

The relation between results obtainable with raw and corrected correlation coefficients in multiple factor analysis

This paper presents three theorems concerning the relation between results with obtained and corrected correlation coefficients in the Thurstone method of multiple factor analysis. (1) The rank of the correlational matrix, and thus the number of factors involved, is unaffected by correcting the obtained coefficients for attenuation. (2) The communality of a variable when the obtained coefficients have been corrected for attenuation is equal to the communality with obtained coefficients divided by the reliability coefficient of the variable. (3) The relationship is shown between the factorial matrix of a correlational matrix of raw correlation coefficients and the factorial matrix of a correlational matrix of corrected correlation coefficients, and a method of obtaining either of these factorial matrices from the other is indicated.     

Variables underlying the recognition of random shapes

Speed of sorting decks of 32 cards with two alternative stimuli was measured. The stimuli were pairs of dots with attributes of distance between dots, angle of orientation of the pair, and position of the pair to the right or left of center. The attributes varied in relative discriminability and were used in all possible pair- and triple-correlated (redundant) combinations. Results showed an increase in speed of sorting with either an increase in discriminability or an increase in number of redundant attributes. It is argued that the increased speed with addition of redundant attributes is due both to a selective serial processing of attributes (requiring attribute separability) and to an increased discriminability with combined attributes (requiring attribute integrality).