The Bayesian explanation of transmission failure

Even if our justified beliefs are closed under known entailment, there may still be instances of transmission failure. Transmission failure occurs when P entails Q, but a subject cannot acquire a justified belief that Q by deducing it from P. Paradigm cases of transmission failure involve inferences from mundane beliefs (e.g., that the wall in front of you is red) to the denials of skeptical hypotheses relative to those beliefs (e.g., that the wall in front of you is not white and lit by red lights). According to the Bayesian explanation, transmission failure occurs when (i) the subject’s belief that P is based on E, and (ii) P(Q|E) < P(Q). But there are compelling cases of transmission failure where P(Q|E) > P(Q). No modifications of the Bayesian explanation are capable of accommodating such cases, so the explanation must be rejected as inadequate. Alternative explanations employing simple subjunctive conditionals are fully capable of capturing all of the paradigm cases, as well as those missed by the Bayesian explanation.     

A note on ROC analysis and non-parametric estimate of sensitivity

In the signal detection paradigm, the non-parametric index of sensitivity A′, as first introduced by Pollack and Norman (1964), is a popular alternative to the more traditional d′ measure of sensitivity. Smith (1995) clarified a confusion about the interpretation of A′ in relation to the area beneath proper receiver operating characteristic (ROC) curves, and provided a formula (which he called A′′) for this commonly held interpretation. However, he made an error in his calculations. Here, we rectify this error by providing the correct formula (which we call A) and compare the discrepancy that would have resulted. The corresponding measure for bias b is also provided. Since all such calculations apply to “proper” ROC curves with non-decreasing slopes, we also prove, as a separate result, the slope-monotonicity of ROC curves generated by likelihood-ratio criterion.This revised article was published online in August 2005 with the PDF paginated correctly.     

Making the Quantum of Relevance

Summary  The two Heisenberg Uncertainties (UR) entail an incompatibility between the two pairs of conjugated variables E, t and p, q. But incompatibility comes in two kinds, exclusive of one another. There is incompatibility defineable as: (p → − q) & (q→ − p) or defineable as [(p →− q) & (q →− p)] ↔ r. The former kind is unconditional, the latter conditional. The former, in accordance, is fact independent, and thus a matter of logic, the latter fact dependent, and thus a matter of fact. The two types are therefore diametrically opposed.In spite of this, however, the existing derivations of the Uncertainties are shown here to entail both types of incompatibility simultaneously. Δ E Δ t ≥ h is known to derive from the quantum relation E = hν plus the Fourier relation Δ ν Δ t ≥ 1. And the Fourier relation assigns a logical incompatibility between Δ ν = 0, Δ t = 0. (Defining a repetitive phenomenon at an instant t → 0 is a self contradictory notion.) An incompatibility, therefore, which is fact independent and unconditional. How can one reconcile this with the fact that Δ EΔ t exists if and only if h > 0, which latter supposition is a factual truth, entailing that a Δ E = 0, Δ t = 0 incompatibility should itself be fact dependent? Are we to say that E and t are unconditionally incompatible (via Δ ν Δ t ≥ 1) on condition that E = hν is at all true? Hence, as presently standing, the UR express a self-contradicting type of incompatibility.To circumvent this undesirable result, I reinterpret E = hν as relating the energy with a period. Though only one such period. And not with frequency literally. (It is false that E = ν . It is true that E = ν times the quantum.) In this way, the literal concept of frequency does not enter as before, rendering Δ ν Δ t ≥ 1 inapplicable. So the above noted contradiction disappears. Nevertheless, the Uncertainties are derived. If energy is only to be defined over a period, momentum only over a distance (formerly a wavelength) resulting during such period, thus yielding quantized action of dimensions Et = pq, then energies will become indefinite at instants, momenta indefinite at points, leading, as demanded, to (symmetric!) Δ E Δ t = Δ p Δ q ≥ h’s.     

Association of prenatal attachment and early childhood emotional,behavioral, and developmental characteristics: A longitudinal study

This study examines the associations between prenatal attachment and child development, socioemotional behavioral problems, and competence at early childhood. It also inquires whether maternal depression and anxiety at the prenatal period and at early childhood are associated with child outcomes. The study consisted of 83 mothers and their children. Data regarding the prenatal attachment, depression, and anxiety were collected during Weeks 28 to 40 of gestation. When the children were 21 to 31 months old, the Brief Infant and Toddler Social Emotional Assessment (BITSEA) and the Ankara Developmental Screening Inventory (ADSI) were applied to children along with Beck Depression Inventory (BDI) and the Beck Anxiety Inventory (BAI) administered to mothers. Results showed that prenatal attachment scores significantly correlated with BITSEA-Competency subscale scores and ADSI total scores at early childhood, r(83) = 0.246, P = .025, and r(82) = 0.316, P = .004, respectively. Prenatal attachment levels were found to be the predictors of both behavioral and emotional competence and development at early childhood, b = 0.081, t(83) = 2.273, P = .014, and b = 0.281, t(83) = 3.225, P = .002, respectively. In addition, prenatal attachment was shown to be even a stronger predictor of development than was worsening maternal depression at early childhood, b = −0.319, t(83) = 2.140, P = .035. Our results indicate that fostering prenatal attachment may be beneficial for better infant outcomes at early childhood.     

Frames and MV-algebras

We describe a class of MV-algebras which is a natural generalization of the class of “algebras of continuous functions”. More specifically, we're interested in the algebra of frame maps Hom (Ω(A), K) in the category T of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame. Given a topological space X and a topological MV-algebra A, we have the algebra C (X, A) of continuous functions from X to A. We can look at this from a frame point of view. Among others we have the result: if K is spatial, then C(pt(K), A), pt(K) the points of K, embeds into Hom (Ω(A), K) analogous to the case of C (X, A) embedding into Hom (Ω(A), Ω (X)). 1991 Mathematics Subject Classification: 06F20, 06F25, 06D30 Presented by Ewa Orlowska     

Distribution of the midgap density of states and their capture cross-sections in hydrogenated amorphous silicon deduced from space-charge-limited conduction in the dark and under illumination

Space-charge-limited current measurements in the dark and under illumination offer the means of obtaining the density of states N(E) and their capture cross-sections s(E) in a range of energy E above the equilibrium Fermi level in hydrogenated amorphous silicon (a-Si:H) n⁺–i–n⁺ structures. N(E) and s(E) have been measured in the energy region from 0.65 to 0.5?eV below the conduction-band edge E _c. The decrease on s(E) observed as the energy E increases agrees with recent observations and is attributed to the coexistence of two types of defect having different capture cross-sections. This is confirmed by light soaking of a-Si:H which makes the defects with high s(E) predominant.     

Repeated measurements analysis of variance when the correlations have a certain pattern

Consider a repeated measurements study in which a single observation is taken at each oft(t > 2) equally spaced time points for each ofn subjects. This paper uses a result of Box to find the appropriate multiplicative correction term for the degrees of freedom in the analysis of variance table for the case when there is equal variability per time point, and when the correlation between observationsu time units apart is equal to ^u . For large values oft, the multiplicative correction has a lower bound approximately equal to 2.5/(t – 1).Dr. Fleiss is also with the Biometrics Research Unit of the New York State Psychiatric Institute. This work was supported in part by grant DE 04068 from the National Institute of Dental Research.     

Reformulation of the hidden variable problem using entropic measure of uncertainty

Using a recently introduced entropy-like measure of uncertainty of quantum mechanical states, the problem of hidden variables is redefined in operator algebraic framework of quantum mechanics in the following way: if A, , E(A), E() are von Neumann algebras and their state spaces respectively, (, E()) is said to be an entropic hidden theory of (A, E(A)) via a positive map L from onto A if for all states E(A) the composite state ° L E() can be obtained as an average over states in E() that have smaller entropic uncertainty than the entropic uncertainty of . It is shown that if L is a Jordan homomorphism then (, E()) is not an entropic hidden theory of (A, E(A)) via L.     

Resolution time and the coding of arithmetic relations on supraliminally different visual extents

Comparison time for pairs of vertical-line stimuli, sufficiently different that they can be errorlessly discriminated with respect to visual extent, was examined as a function of arithmetic relations (physical ratio and difference) on members of the pair. Arithmetic relations are coded very precisely by judgment time: Responses slow as stimulus ratios approach one with difference fixed, and as stimulus differences approach zero with ratio fixed. Most models which assume a simple (Difference or Ratio) resolution rule operating on independent sensations require judgment time to depend on either ratios or on differences but not on both. Further tests showed both an index based on median judgment times and a confusion index based on pairs of observed judgment times, satisfied the requirements for a Positive Difference Structure. One representation of these data, which remains acceptable through all analyses, is a Difference resolution rule operating on sensations determined by a power psychophysical function with β < 1. Specifically, L(x, y) = F{ψ(x) ? ψ(y)} + R, where L(x, y) is the judgment time with the stimulus pair x and y, ψ(x) = Ax^β + C, R is a positive constant, and F is a continuous monotone decreasing function.     

Reaction-anticipation transitions in human perception-action patterns

We investigated the hypothesis that reaction and anticipation in human perceptual-motor performance are two coordinative modes of a single pattern-forming dynamical system, rather than separate behaviors. Subjects coordinated the onset of finger flexions with visual metronome flashes in each of three patterns: reactive, synchronized, or syncopated. The stimulus frequency was progressively increased (0.125–1.375 Hz) or decreased (1.375-0.125 Hz) in small steps (0.125 Hz) every 10 cycles. We observed qualitative transitions in both the time interval between stimulus and corresponding action (Δt) and their relative phase (ø) at critical values of the stimulus frequency, corresponding to changes from ‘reactive-to-anticipatory’ and ‘anticipatory-to-reactive’ performance. Such transitions provide evidence of a single, multifunctional system, which can be adequately described by the dynamics of collective variables characterizing the respective perception-action patterns.     

Constructing a covariance matrix that yields a specified minimizer and a specified minimum discrepancy function value

A method is presented for constructing a covariance matrix Σ*₀ that is the sum of a matrix Σ(γ₀) that satisfies a specified model and a perturbation matrix,E, such that Σ*₀=Σ(γ0) +E. The perturbation matrix is chosen in such a manner that a class of discrepancy functionsF(Σ*₀, Σ(γ₀)), which includes normal theory maximum likelihood as a special case, has the prespecified parameter value γ₀ as minimizer and a prespecified minimum δ A matrix constructed in this way seems particularly valuable for Monte Carlo experiments as the covariance matrix for a population in which the model does not hold exactly. This may be a more realistic conceptualization in many instances. An example is presented in which this procedure is employed to generate a covariance matrix among nonnormal, ordered categorical variables which is then used to study the performance of a factor analysis estimator. We are grateful to Alexander Shapiro for suggesting the proof of the solution in section 2.     

Utility of extension of functional equations—when possible

Jean-Claude Falmagne observed in 1981 [On a recurrent misuse of classical functional equation result. Journal of Mathematical Psychology, 23, 190-193] that, even under regularity assumptions, not all solutions of the functional equation k(s+t)=k(s)+k(t), important in many fields, also in the theory of choice, are of the form k(s)=Cs. This is certainly so when the domain of the equation (the set of (s,t) for which the equation is satisfied) is finite. We mention an example showing that this can happen even on some infinite, open, connected sets (open regions). The more general equations k(s+t)=?(s)+n(t) and k(s+t)=m(s)n(t), called Pexider equations, have been completely solved on R². In case they are assumed valid only on an open region, they have been extended to R² and solved that way (the latter if k is not constant). In this paper their common generalization

k(s+t)=?(s)+m(s)n(t)     

Higher chronic psychological stress is associated with blunted affective responses to strenuous resistance exercise: RPE,pleasure, pain

The aim of this study was to determine whether mental stress moderates perceptions of muscular pain, exertion, pleasure and arousal during a bout of strenuous resistance exercise. Two hundred and ten undergraduate students recruited from resistance exercise classes were screened with the Perceived Stress Scale (PSS). Fifty-seven individuals (age = 20.1 ± 1.2 y) were invited to complete the Undergraduate Stress Questionnaire (USQ), a measure of life event stress, and fitness testing. They later performed a two-phase, acute heavy-resistance exercise protocol: first phase: 10-repetition maximum (RM) leg press test; second phase: six sets at 80–100% of 10-RM. During exercise, participants responded to the Feeling Scale (pleasure), Felt Arousal Scale, Omni-RPE and the Pain Intensity Scale. Affective responses and heart rate were analyzed with a hierarchical linear modeling (HLM) growth curve analysis. USQ moderated the trajectories of affective responses and heart rate during exercise. Higher stress (USQ) levels were significantly related to lower rise in RPE (time², p = .002; time³, p < .001) and heart rate (time², p < .001; time³, p < .001). USQ had a main effect on pleasure and arousal (p values < .001), in which higher levels of stress were related to less affect. Models using the PSS scale produced similar results. PSS, but not USQ, interacted with time to predict pain (time², p = .048; time³, p = .024). Relationships held even after adjusting for covariates, such as depression. Future research should determine if differential responses to exercise by stress have implications for behavioral interventions and mental health outcomes.     

Against Probabilistic Measures of Coherence

It is shown that the probabilistic theories of coherence proposed up to now produce a number of counter-intuitive results. The last section provides some reasons for believing that no probabilistic measure will ever be able to adequately capture coherence. First, there can be no function whose arguments are nothing but tuples of probabilities, and which assigns different values to pairs of propositions {A, B} and {A, C} if A implies both B and C, or their negations, and if P(B)=P(C). But such sets may indeed differ in their degree of coherence. Second, coherence is sensitive to explanatory relations between the propositions in question. Explanation, however, can hardly be captured solely in terms of probability.     

The Poznań school methodology of idealization and concretization from the point of view of a revised structuralist theory conception

My thesis is that some methodological ideas of the Pozna school, i.e., the principles of idealization and concretization (factualization), and the correspondence principle can be represented rather successfully using the relations of theoretization and specialization of revised structuralism.Let <n(i), t(j)> (i=1,...m, j=1,...k) denote the conceptual apparatus of a theory T, and a class M={} (i=1,...m, j=1,...k) the models of T. The n-components refer to the values of dependent variables and t-components to the values of independent variables of the theory. The n- and t-components in turn represent appropriate concepts. Consider T ^* as a conceptual enrichment of T with concepts <n(i ^*), t(j ^*)> (i<i ^* or j<j ^*) and models M ^*={<D ^*, n(i ^*), t(j ^*)>}. If the classes M and M ^* are suitably related, then the situation illustrates both the case of the theoretization-relation of (revised) structuralism and of the factualization-principle of the Pozna school.Assume now that the concepts n(i), t(j) of T for some i, j are operationalized using some special assumptions generating appropriate empirical values n and t for these concepts. Let M denote the class {<D,...n,...t,...>} which is formed by substituting n and t for values of concepts n(i), t(j) in the elements of M. If the classes M and M are related in a suitable way then the situation is an example of both the specialization-relation of (revised) structuralism and the concretization-principle of the Pozna school. The correspondence principle in turn can be represented as a limiting case of the theoretization-relation of (revised) structuralism.Many thanks to my anonymous referees for critical and fruitful comments and special thanks to Dr. Carol Norris for correcting the language of this paper.     

PERSONALITY AND BEHAVIOURAL MEASURES: GENDER,AGE, AND RACE CONTRASTS IN AN AUSTRALIAN SETTING*

As a complement to previous comparative studies focusing on cognition, this study compares a number of personality and behavioural traits of Australian Anglocelt and Aboriginal children. The personality scales are Extraversion (E), Neuroticism (N), Psychoticism (P), Lie (L), Impulsiveness (Imp), Venturesomeness (Vent), and Empathy (Emp); and the behavioural scales are Relating (R), Asserting (A), Investing (I). and Coping (C). The personality scales were administered to 113 and 42 sixth- and ninth-grade children, respectively. The teachers of the children completed a behavioural rating scale for each child. Thirty-three sixth-graders and 16 ninth-grader were Aboriginal. Sixth-grade males had higher means on P and Vent, while sixth-grade females averaged higher on L, Emp, R, I, and C. Aboriginal sixth-graders averaged higher on P, while Aboriginals overall averaged higher on E, R, A, I, and C than Anglocelts. Ninth-grade males averaged significantly higher on E, Imp, and Vent, and lower on L. The only significant difference for ninth-graders was that Aboriginals averaged higher on L. These results indicate cultural influences bearing upon contact, and support previous informal judgements that Aboriginal children tend to be more reserved in response to formal situations than Anglocelts. Implications are inferred for educational policy.     

The adequacy of the theories of deductive systems with respect to sentential calculi

Summary The sentential calculiR, under discussion, are axiomatizable and implication is among their primitive terms. The modus ponens and the rule of substitution are their primitive rules. ByS _r is denoted the set of sentences obtained from the formulae of the calculusR by substituting sentences of a given language for all variables. The variablesx, y, z ... represent the elements of the setS _r , the variablesX, Y, Z ... represent the subsets ofS _R . The formulacxy designates an implication withx as its antecedent andy as its consequent,cxy is always an element ofS _R δ(X) means, thatX is closed with respect to the modus ponens rule.A _R designates the class of allS _R -substitutions of the axioms of the sentential calculusR.