Analysis of variance with Fourier analysis of coherent data

Like orthogonal polynomials, the sine and cosine components used in Fourier analysis are orthogonal under summation over equally spaced points. Therefore, they can be used in the same way as orthogonal polynomials are used with analysis of variance. They are usually used on records consisting of sequences of observations taken equally spaced in time. Analysis of variance can be performed on replicated records. The most straightforward cases occur under the following conditions: (1) The phenomenon is periodic, (2) the phenomenon is coherent (synchronized) over the various replicates, (3) the record length is an integral multiple of the fundamental period, and (4) the phenomenon is not buried too deeply in noise. Two numerical examples are examined that satisfy these conditions. Planning is illustrated for a case that violates Conditions 3 and 4.     

Transformation-induced elastic strain effect on the precipitation kinetics of ordered intermetallics

Abstract

A transformation-induced elastic strain effect on the decomposition kinetics of a disordered phase into a mixture of ordered and disordered phases was investigated for a prototype binary alloy in two dimensions (2-D) by using a computer simulation technique. The simulation technique not only described simultaneously different processes, such as atomic ordering, clustering, disordering and coarsening, but also produced automatically ordered structures and alloy morphologies. It was found that irrespective of the degree of the crystal lattice mismatch between precipitates and the matrix, the alloy morphologies, developed during the congruent ordering stage which preceded the decomposition, showed no alignment in any of the crystallographic directions. Alignment developed during subbequent decomposition of the congruently ordered single phase, which resulted in the appearance of an equilibrium disordered phase preferentially along the antiphase domain boundaries. It became increasingly pronounced as the time of alloy aging increased. The aligned morphology finally formed the modulated structure found in many alloys. This mechanism of modulated structure formation is new since almost all previous experimentally observed modulated structures were interpreted as a result of a homogeneous spinodal decomposition. The predicted kinetics was found to be in excellent agreement with recent experimental results in a Fe-Si system and should be expected in most two-phase alloys with an ordered intermetallic precipitate whose stress-free lattice constant is significantly different from that of the disordered matrix.     

A Coalgebraic Perspective on Logical Interpretations

In Computer Science stepwise refinement of algebraic specifications is a well-known formal methodology for rigorous program development. This paper illustrates how techniques from Algebraic Logic, in particular that of interpretation, understood as a multifunction that preserves and reflects logical consequence, capture a number of relevant transformations in the context of software design, reuse, and adaptation, difficult to deal with in classical approaches. Examples include data encapsulation and the decomposition of operations into atomic transactions. But if interpretations open such a new research avenue in program refinement, (conceptual) tools are needed to reason about them. In this line, the paper’s main contribution is a study of the correspondence between logical interpretations and morphisms of a particular kind of coalgebras. This opens way to the use of coalgebraic constructions, such as simulation and bisimulation, in the study of interpretations between (abstract) logics.     

Mystery,abstraction, and narrative psychotherapy

Abstract

The rhythm of life involves the creation and resolution of mysteries. In the social realm, such mysteries are usually solved by the process of abstraction—linguistic devices are invented and used to coordinate patterns of communal action. Although such devices are necessary and useful, they also tend to entrap a person in a social cocoon of shared explanatory fictions. Narrative psychotherapy helps clients break free of the spell woven by the abstractions to which they have become adapted. This occurs through the process Maturana (1988) called “orthogonal interaction,” in which the therapist assists the client in stepping outside the “club rules” and seeing things anew. This process is discussed, contrasted with other interpretations of narrative work, and illustrated with a brief clinical vignette.     

Eponymous verb phrases and ambiguity resolution

To understand eponymous verb phrases such as "do a John Travolta," readers cannot merely select a sense out of a mental lexicon (sense selection). They must create new senses (sense creation) by retrieving salient information from memory. We conducted two experiments to test the hypothesis that these processes of memory retrieval parallel those used for ordinary lexical ambiguities. To prepare for Experiment 1, we gathered readers' interpretations of eponymous verb phrases like "do a John Travolta" to establish dominant and subordinate interpretations. We then wrote story contexts that biased comprehension toward one or the other interpretation. In Experiment 1, paraphrase judgment times were used to demonstrate that dominant meanings are privileged in the sense that they are accessible even when the story creates a subordinate bias. In Experiment 2, this privilege faded somewhat when there was a delay before the paraphrase judgment. We discuss the results with respect to the distinction between sense selection and sense creation.     

The Implicit Representation of Characters in Dallas

Current research on the psychological effects of television viewing emphasizes the mediating role played by viewers’ interpretations of the characters and events portrayed. Three studies used multidimensional scaling to discover the main themes by which views represent the characters in Dallas. In Study I, a two-dimensional space captured viewers’ representations of the characters. Study II replicated this space using a different method. Study III tested competing theoretical interpretations of the space derived from implicit personality theory, gender schema theory, and cultural studies. The first and major dimension of the semantic space was morality. This was semantically close to warmth and family values. The properties hard, dominant, active, values power, and business oriented clustered together and were orthogonal to morality. Implications for the role of socio-cognitive and textual determinants of viewers’ representations of television characters are discussed.     

Interpretation and Justification

Whenever understanding is sought we are obliged to justify our interpretations – to demonstrate that they furnish an adequate understanding of the world and its objects. The problem is to know whether this is possible – that what we take to be conclusive justifications do not covertly appeal to other favoured interpretations or systems of explanation, thus obviating the possibility of a neutral justification. By exploring the nature of interpretation, I argue that neutral justifications of interpretations about works of art are indeed possible and that such interpretations can be shown to be true or false.     

Thermodynamic fluctuations in magnetic states: Fe3Pt as a prototype

To understand the Invar anomalies, such as negative thermal expansion and spontaneous magnetization, we have applied our recently developed thermodynamic framework for a system with itinerant-electron magnetism to the ordered Fe₃Pt. The framework has coherently predicted the finite temperature intermixing between the fully ferromagnetic (FM) configuration and the spin-flipping configurations (SFCs). We have also discovered a tri-critical point at which a high-temperature second-order phase transition, between the fully ordered FM phase and the paramagnetic phase which is disordered due to SFCs, becomes first order at low temperatures.     

Analysis of Multiple Partially Ordered Responses to Belief Items with Don’t Know Option

Understanding beliefs, values, and preferences of patients is a tenet of contemporary health sciences. This application was motivated by the analysis of multiple partially ordered set (poset) responses from an inventory on layman beliefs about diabetes. The partially ordered set arises because of two features in the data—first, the response options contain a Don’t Know (DK) option, and second, there were two consecutive occasions of measurement. As predicted by the common sense model of illness, beliefs about diabetes were not necessarily stable across the two measurement occasions. Instead of analyzing the two occasions separately, we studied the joint responses across the occasions as a poset response. Few analytic methods exist for data structures other than ordered or nominal categories. Poset responses are routinely collapsed and then analyzed as either rank ordered or nominal data, leading to the loss of nuanced information that might be present within poset categories. In this paper we developed a general class of item response models for analyzing the poset data collected from the Common Sense Model of Diabetes Inventory. The inferential object of interest is the latent trait that indicates congruence of belief with the biomedical model. To apply an item response model to the poset diabetes inventory, we proved that a simple coding algorithm circumvents the requirement of writing new codes such that standard IRT software could be directly used for the purpose of item estimation and individual scoring. Simulation experiments were used to examine parameter recovery for the proposed poset model.     

Interpretation bias and depressive symptoms: The role of self-relevance

Cognitive theories of depression emphasize negatively biased interpretations as an important target of therapy. Much of the research on interpretation bias in depression has focused on selection, or deciding which of several interpretations is likely. However, depressive biases may also exist in the generation of possible interpretations, or the ability to think of positive alternatives. If biases exist for generation as well as selection, therapeutic techniques to encourage the generation of more positive interpretations would be warranted. Asking therapy clients to consider someone else in a similar situation is a commonly used therapy strategy but has not been sufficiently examined empirically. In the current studies, we examine interpretation generation and selection in dysphoric and nondysphoric individuals, and contrast interpretations made for the self to interpretations made for two types of “other.” Our studies reveal depressive biases in both interpretation generation and selection, and indicate that interpretation valence is highly sensitive to the type of other considered. All participants generated and selected significantly more positive interpretations for friends than for themselves, but generated significantly more negative interpretations for hypothetical others than for themselves. Our results suggest that encouraging dysphoric individuals to imagine others can be beneficial, but the type of “other” used is critically important, with instructions to consider a close friend most likely to be effective in decreasing negativity in interpretation.     

The circle as a model for the interpersonal domain of Swedish trait terms

Swedish interpersonal traits were assumed to have the structure demonstrated by Wiggins for the Interpersonal Adjective Scales in English. Positive and negative interpersonal trait terms were rated for accuracy when describing people. The ratings were used to construct 16 eight-item scales which were ordered relative to two principal components and labelled A to P. The evaluative meaning of each scale item was rated by a second group. The ranks of the mean ratings for the scales followed expectations. The 16 scales were combined into eight scales PA, BC, DE, etc., to NO. From a new group of subjects (N = 159) self-ratings were obtained. The correlations between the eight scales were used to obtain maximum-likelihood estimates of population coefficients of a hypothetical circulant matrix. A circumplex model fitted the data well and the two equally large orthogonal components ordered the PA to NO variables within a circular semantic space. The model was interpreted as a structural representation of basic-level categories for interpersonal attributes of personality in the natural language.     

A test of the minimum principle requires a perceptual coding system

The minimum principle states that a perceiver will see the simplest possible interpretation of a pattern. Some theorists of human perception take this principle as a core explanatory concept. Others, especially Rock and Hochberg, hold the view that a perceptual minimum principle is untenable. Rock presents a great number of demonstrations which, in his opinion, rule out the minimum principle. Hochberg states that 'impossible' figures especially present a difficulty for this principle. It is argued here that, in order to test the minimum principle, a method is needed to describe interpretations of patterns in such a way that they can be ordered according to simplicity. To achieve this, Leeuwenberg's coding system was used. The analyses reported here of the patterns which Rock produces as evidence against the principle show that, contrary to Rock's claim, the way these patterns are preferentially perceived provides strong support for the minimum principle. Next, it is demonstrated that interpreting certain patterns as 'impossible' figures is not incompatible with the principle. Finally, it is argued that a test of the minimum principle is necessarily conflated with two other hypotheses, one concerning the metric of simplicity and one concerning the task conception of the experimental subjects.     

Mathematical foundations of consciousness

We employ the Zermelo–Fränkel Axioms that characterize sets as mathematical primitives. The Anti-foundation Axiom plays a significant role in our development, since among other of its features, its replacement for the Axiom of Foundation in the Zermelo–Fränkel Axioms motivates Platonic interpretations. These interpretations also depend on such allied notions for sets as pictures, graphs, decorations, labelings and various mappings that we use. A syntax and semantics of operators acting on sets is developed. Such features enable construction of a theory of non-well-founded sets that we use to frame mathematical foundations of consciousness. To do this we introduce a supplementary axiomatic system that characterizes experience and consciousness as primitives. The new axioms proceed through characterization of so-called consciousness operators. The Russell operator plays a central role and is shown to be one example of a consciousness operator. Neural networks supply striking examples of non-well-founded graphs the decorations of which generate associated sets, each with a Platonic aspect. Employing our foundations, we show how the supervening of consciousness on its neural correlates in the brain enables the framing of a theory of consciousness by applying appropriate consciousness operators to the generated sets in question.     

The fruits of irony: gaining insight into how we make meaning of the world

Many philosophers of education emphasise the impossibility to really ‘solve’ philosophical—and with that, educational—problems these days. Philosophers have been trying to give philosophy a new, constructive turn in the face of this insolvability. This paper focuses on irony-based approaches that try to exploit the very uncertainty of philosophical issues to further philosophical understanding. We will first briefly discuss a few highlights of historical uses of irony as a philosophical tool. Then we concentrate on two different interpretations of irony, formulated by Bransen and Rorty, that aim at gaining insight into how we make meaning of the world, while at the same time recognising that such an understanding would be impossible. After discussing some problematic aspects of these interpretations a third interpretation of irony is developed, based on a third view of the nature of meaning-making. Following these three interpretations, we will discuss their philosophical merits and the different kinds of insight they can produce for philosophy of education.     

Disambiguation by community membership

To interpret utterances in conversations, listeners must often make reference to the common ground they share with speakers. For example, when faced with an utterance such as "That game was a disaster," listeners must decide whether they share common assumptions about what outcome would be disastrous. In our experiments, we examine how common ground, as encoded in community membership, is used to constrain judgments about the interpretations of ambiguous utterances. In Experiment 1, subjects were sensitive to community membership when they were asked to evaluate the interpretations at a leisurely pace. Experiment 2 replicated this result with greater time pressure. Experiment 3 demonstrated that judgments based on assessments of community membership were equivalent to those based on certain knowledge, except when the judgements were challenged. The results suggest that models of memory retrieval during language comprehension should make mention of access to common ground.     

Behind the Pencil/Paper Measurement of Sexual Coercion: Interview-Based Clarification of Men's Interpretations of Sexual Experiences Survey Items1

The ubiquity of self-report pencil and paper surveys in sexual coercion research is matched only by the lack of attention to respondents' individual interpretations of survey items. Our purpose in this study was to examine men's interpretations of four apparently ambiguous items from a commonly used sexual coercion research instrument, the original Sexual Experiences Survey (SES; Koss & Oros, 1982). After completing the SES, college men (N = 102) were immediately interviewed about their interpretations of 4 of the SES items. Across the interviews, the men reported a variety of interpretations of each item. Ignoring SES item interpretations when forming research conclusions has significant implications for sexual coercion research. Based on the results of this investigation, we urge caution in interpreting results of studies based on self-administered measures of coercive sexual behavior.     

Semantic memory and the granularity of semantic relations: Evidence from speed-accuracy decomposition

In the present study we examined whether semantic relations are atomistic unitary associations, or are complex concepts consisting of a number of relational elements. The complexity of the ownership relation was assessed by combining a relation verification task (“Many people own [cars/ comets]”) with the speed-accuracy decomposition procedure (Meyer, Irwin, Osman, & Kounios, 1988). The latter permits one to determine whether subjects achieve their final state of response accuracy in a single, discrete all-or-none transition, or whether the relevant processes yield partial information representing intermediate states of knowledge. The rationale was that the retrieval of a unitary relational link from a classical associative network should be an all-or-none affair. In contrast, a set of relational elements need not be processed as a unitary bundle, thereby allowing partial response-information states. In two experiments, we found evidence of such partial information (i.e., sensitivity in units ofd′), lending support to the notion that relations are complex. Furthermore, the results suggest that the accumulation of guessing sensitivity was linear over time, weighing against alternate theoretical interpretations.     

A Happiness Study Using Age-Period-Cohort Framework

Age effects and birth cohort effects have not been differentiated in happiness studies. In this paper, age-period-cohort decomposition is applied to happiness data in the US. Since the relationship is linear, such as age = period ? cohort, it is not possible to identify the three effects. This paper considers four identification models: the polynomial age-effect model, the proxy-variable model, the orthogonal period-effect model, and the principal component model. Happiness data are obtained from the General Social Survey for 1972–2008. Except for the polynomial age-effect model, three alternative models provide similar results. In particular, there is little difference between the decomposition results obtained by the orthogonal period-effect model and by the principal component model. The age effect shows downward movements for 18–55 and for 80–89, an upward movement for 56–69, and an almost flat movement for 70–79. The period effect shows cyclical movements slightly similar to unemployment rates fluctuations. The cohort effect shows a downward movement for the birth cohorts of 1894–1936, a dip for 1945–1958 (baby boomers), an upward movement for 1959–1969, and an almost flat movement for 1970–1987.     

An Investigation of Counselor Interpretations in Client-Centered Therapy

Preliminary findings by the McGill Psychotherapy Process Research Team indicate that not only are interpretations used in client-centered therapy, but they are also efficient in producing in-session client change. Using the Hill Counsellor Verbal Response Category System—Revised (Friedlander, 1982) as a guide to locate interpretations, we investigated the qualitative differences between interpretations leading to different in-session client change events in six sessions conducted by Carl Rogers. The occurrence of in-session therapeutic phenomena were assessed using the Experiencing Scale (Klein, Mathieu, Gendlin, & Keisler, 1970) and the Category System of Good Moments (Mahrer & Nadler, 1986). Results indicate that significant in-session therapeutic phenomena are preceded by interpretations and that qualitative differences exist between interpretations that precede change events and those that do not. Implications for psychotherapy theory, research, and practice are discussed.     

Estimating Dynamical Systems: Derivative Estimation Hints From Sir Ronald A. Fisher

The fitting of dynamical systems to psychological data offers the promise of addressing new and innovative questions about how people change over time. One method of fitting dynamical systems is to estimate the derivatives of a time series and then examine the relationships between derivatives using a differential equation model. One common approach for estimating derivatives, Local Linear Approximation (LLA), produces estimates with correlated errors. Depending on the specific differential equation model used, such correlated errors can lead to severely biased estimates of differential equation model parameters. This article shows that the fitting of dynamical systems can be improved by estimating derivatives in a manner similar to that used to fit orthogonal polynomials. Two applications using simulated data compare the proposed method and a generalized form of LLA when used to estimate derivatives and when used to estimate differential equation model parameters. A third application estimates the frequency of oscillation in observations of the monthly deaths from bronchitis, emphysema, and asthma in the United Kingdom. These data are publicly available in the statistical program R, and functions in R for the method presented are provided.