An efficient adaptive procedure for psychophysical discrimination experiments

We present an adaptive procedure to conduct psychophysical discrimination experiments. In a discrimination experiment, an observer senses (sees, hears, feels, etc.) two stimuli (separated in space or time) and is asked to order these stimuli with respect to a particular parameter (say,s). Under the usual assumption of a locally linear internal representation ofs, perturbed by additive Gaussian noise, the probabilityP(s ₂)—of judging test stimuluss ₂ “larger” than a reference stimuluss ₁—is an error function (a cumulative normal distribution). Such an error function,Erf [(s ₂μ)/σ], is parametrized by two parameters: μand σ. The parameter μ is the value for whichP(s ₂) = 50% and is related to possible bias effects in the internal representation of the observer. The parameter σ is √2 times the standard deviation of the noise distribution and is generally called thediscrimination threshold. In this paper, we present (1) an algorithm to estimate μ and σ given the data generated by such an observer, (2) an analysis of the efficiency of a stimulus presentation with respect to the estimation of μ and σ , and (3) a method that controls the specific choice of stimulus values during an experiment so that an optimal estimation of μ and σ is obtained.     

On Some Categories of Involutive Centered Residuated Lattices

Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K ^• relating integral residuated lattices with 0 (IRL₀) with certain involutive residuated lattices. Our work is also based on the results obtained by Cignoli about an adjunction between Heyting and Nelson algebras, which is an enrichment of the basic adjunction between lattices and Kleene algebras. The lifting of the functor to the category of residuated lattices leads us to study other adjunctions and equivalences. For example, we treat the functor C whose domain is cuRL, the category of involutive residuated lattices M whose unit is fixed by the involution and has a Boolean complement c (the underlying set of C M is the set of elements greater or equal than c). If we restrict to the full subcategory NRL of cuRL of those objects that have a nilpotent c, then C is an equivalence. In fact, C M is isomorphic to C _e M, and C _e is adjoint to , where assigns to an object A of IRL₀ the product A × A ⁰ which is an object of NRL.     

A probabilistic multidimensional scaling with unique axes1

Abstract: A probabilistic multidimensional scaling model is proposed. The model assumes that the coordinates of each stimulus are normally distributed with variance Σ_i = diag(σ²₁, … σ²_Ri). The advantage of this model is that axes are determined uniquely. The distribution of the distance between two stimuli is obtained by polar coordinates transformation. The method of maximum likelihood estimation for means and variances using the EM algorithm is discussed. Further, simulated annealing is suggested as a means of obtaining initial values in order to avoid local maxima. A simulation study shows that the estimates are accurate, and a numerical example concerning the location of Japanese cities shows that natural axes can be obtained without introducing individual parameters.     

Microstructural characterization of the M23C6 carbide in a long-term aged Ni-based superalloy

The microstructural features of M₂₃C₆ carbide in a long-term aged heat- and corrosion-resistant Ni-based superalloy have been investigated in detail using various kinds of transmission electron microscope (TEM) techniques. It is found that TEM contrast, which is related to structural and chemical inhomogeneities inside the grains, always exists in the interior of grains in the alloy. The structure of these inhomogeneous regions has been determined to be the same as that of the γ′ and t-M₂₃C₆ phases, where t-M₂₃C₆ indicates a transitional and metastable phase. Although possessing the same structure as the M₂₃C₆ phase, the chemical composition of the t-M₂₃C₆ is different from that of the M₂₃C₆ phase. Compared with M₂₃C₆, t-M₂₃C₆ is richer in Ni, Co, Al and Ti but poorer in W, Mo and Cr. This phenomenon of structural and chemical inhomogeneity demonstrates that pristine M₂₃C₆ carbide (p-M₂₃C₆) precipitated in standard heat-treated samples is unstable. Therefore, upon long-term ageing treatment, Ni, Co, Al and Ti may locally enrich inside the p-M₂₃C₆ phase, finally forming the γ′ phase, which can be described by the decomposition reaction p-M₂₃C₆ → M₂₃C₆ + γ′.     

Comparing score tests and other local dependence diagnostics for the graded response model

Score tests for identifying locally dependent item pairs have been proposed for binary item response models. In this article, both the bifactor and the threshold shift score tests are generalized to the graded response model. For the bifactor test, the generalization is straightforward; it adds one secondary dimension associated only with one pair of items. For the threshold shift test, however, multiple generalizations are possible: in particular, conditional, uniform, and linear shift tests are discussed in this article. Simulation studies show that all of the score tests have accurate Type I error rates given large enough samples, although their small‐sample behaviour is not as good as that of Pearson's Χ² and M₂ as proposed in other studies for the purpose of local dependence (LD) detection. All score tests have the highest power to detect the LD which is consistent with their parametric form, and in this case they are uniformly more powerful than Χ² and M₂; even wrongly specified score tests are more powerful than Χ² and M₂ in most conditions. An example using empirical data is provided for illustration.     

The closure factors related to other cognitive processes

Twenty-five group tests, assembled with certain hypotheses concerning the first and second closure factors in mind, were administered to 154 subjects, mostly graduate students. The intercorrelations were analyzed factorially, yielding eight factors that were rotated to an oblique simple structure. The factors were interpreted as: speed of closure, C₁; flexibility of closure, C₂; verbal closure, C₃; word fluency, W; reasoning, R; perceptual speed, P; the first space factor, S₁; and speed of handwriting, H. Four second-order factors were tentatively described as analytical ability, synthetic ability, speed of perception, and word fluency. Three of the reasoning tests had their highest loadings on C₂ and one on C₃, which seems to be evidence that flexibility of closure generalizes in the cognitive domain and is associated with analytical ability.This paper summarizes part of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the University of Chicago. The writer is deeply indebted to Dr. L. L. Thurstone for his generous advice and guidance. The complete study is obtainable on microfilm, from the University of Chicago library, Film No. T1279 (price $2.15). It includes reproductions of the tests used, score distributions, and plots of the obliqueV-matrices.     

Early attrition among suicidal clients

The study aimed to identify the level of suicidal ideation in early attrition clients and their reasons for the early termination of their therapy. The cross-sectional design involved early attrition clients (C_A) who withdrew from therapy before their second session (n?=?61), and continuing clients who (C_C) progressed beyond their second session (n?=?73). All completed the Suicidal Behaviours Questionnaire-Revised scale, and the C_A group also completed the Reasons for Terminating Therapy Scale. Clients were significantly more likely to disengage if they were self-referred, had no health-care support or had lower suicidal ideation. The study identifies the significant role of suicidal ideation and referral source in therapy retention and the implications this has for therapists and counsellors.     

Characterization of the discriminative stimulus effects of lorcaserin in rats

Lorcaserin is approved by the Food and Drug Administration for treating obesity and is under consideration for treating substance use disorders; it has agonist properties at serotonin (5‐HT)_2C receptors and might also have agonist properties at other 5‐HT receptor subtypes. This study used drug discrimination to investigate the mechanism(s) of action of lorcaserin. Male Sprague–Dawley rats discriminated 0.56 mg/kg i.p. lorcaserin from saline while responding under a fixed‐ratio 5 schedule for food. Lorcaserin (0.178‐1.0 mg/kg) dose‐dependently increased lorcaserin‐lever responding. The 5‐HT_2C receptor agonist mCPP and the 5‐HT_2A receptor agonist DOM each occasioned greater than 90% lorcaserin‐lever responding in seven of eight rats. The 5‐HT_1A receptor agonist 8‐OH‐DPAT occasioned greater than 90% lorcaserin‐lever responding in four of seven rats. The 5‐HT_2C receptor selective antagonist SB 242084 attenuated lorcaserin‐lever responding in all eight rats and the 5‐HT_2A receptor selective antagonist MDL 100907 attenuated lorcaserin‐lever responding in six of seven rats. These results suggest that, in addition to agonist properties at 5‐HT_2C receptors, lorcaserin also has agonist properties at 5‐HT_2A and 5‐HT_1A receptors. Because some drugs with 5‐HT_2A receptor agonist properties are abused, it is important to fully characterize the behavioral effects of lorcaserin while considering its potential for treating substance use disorders.     

Depth relevance of some paraconsistent logics

The paper essentially shows that the paraconsistent logicDR satisfies the depth relevance condition. The systemDR is an extension of the systemDK of [7] and the non-triviality of a dialectical set theory based onDR has been shown in [3]. The depth relevance condition is a strengthened relevance condition, taking the form: If _DR- AB thenA andB share a variable at the same depth, where the depth of an occurrence of a subformulaB in a formulaA is roughly the number of nested 's required to reach the occurrence ofB inA. The method of proof is to show that a model structureM consisting of {M ₀ , M₁, ..., M}, where theM _i s are all characterized by Meyer's 6-valued matrices (c. f, [2]), satisfies the depth relevance condition. Then, it is shown thatM is a model structure for the systemDR.     

Replacement in Logic

We study a range of issues connected with the idea of replacing one formula by another in a fixed (linguistic) context. The replacement core of a consequence relation ? is the relation holding between a set of formulas {A ₁, ..., A _m , ...} and a formula B when for every context C(·), we have C(A ₁), ..., C(A _m ), ...???C(B). Section 1 looks at some differences between which inferences are lost on passing to the replacement cores of the classical and intuitionistic consequence relations. For example, we find that while the inference from A and B to $A \land B$ , sanctioned by both these initial consequence relations, is retained on passage to the replacement core in the classical case, it is lost in the intuitionistic case. Further discussion of these two (and some other) logics occupies Sections 3 and 4. Section 2 looks at the m?=?1 case, describing A as replaceable by B according to ? when B is a consequence of A by the replacement core of ?, and inquiring as to which choices of ? render this induced replaceability relation symmetric. Section 5 investigates further conceptual refinements— such as a contrast between horizontal and vertical replaceability—suggested by some work of R. B. Angell and R. Harrop (and a comment on the latter by T. J. Smiley) in the 1950s and 1960s. Appendix 1 examines a related aspect of term-for-term replacement in connection with identity in predicate logic. Appendix 2 is a repository for proofs which would otherwise clutter up Section 3.     

Atomic imaging of the interface between M23C6-type carbide and matrix in a long-term ageing polycrystalline Ni-based superalloy

Besides the well-known cube-on-cube orientation relationship (OR) between M₂₃C₆ carbide and matrix, we have determined a new OR named as the twin-related OR in a long-term ageing Ni-based superalloy on the basis of the extensive and detailed electron diffraction analyses. Furthermore, by means of atomic-resolution high angle annular dark-field imaging technique which is implemented in the aberration-corrected scanning transmission electron microscope, we elucidated the interfacial characteristics between M₂₃C₆ and matrix for above two types of ORs. Taking into account of the interfacial characteristics, we propose that the twin-related OR possesses a higher total interfacial energy. Thus, its frequency of occurrence is lower than that of the cube-on-cube OR though both ORs are usually seen in the long-term ageing samples.     

A positional coding mechanism in pigeons after learning multiple three-item lists

Pigeons were trained on three three-item lists (List 1: A₁ → B₁ → C_1; List 2: A₂ → B₂ → C_2; List 3: A₃ → B₃ → C₃). After sessions in which any one of the three lists could be presented on a trial, derived-maintained list and derived-changed list probe trials were introduced. The derived list probe trials were composed of three items, one drawn from each of the training lists. On derived-maintained probe trials, each item was in the same ordinal position it occupied during training (e.g., A₃ → B₁ → C₂). On derived-changed probe trials, items that occupied the second and third position during training were exchanged (e.g., A₂ → C₃ → B₁). The performance of subjects on derived-maintained probe trials was significantly above chance and no different to that observed on the training lists. In contrast, subjects’ performance on derived-changed probe trials was significantly below chance. To our knowledge, this is the first study that has demonstrated pigeons are able to learn and retain multiple three-item lists. In addition, subjects’ performance on the derived-maintained probe trials suggests that they acquire knowledge of each list item’s ordinal position when learning multiple lists.     

A syntactical approach to modality

Conclusion The systems T _N and T _M show that necessity can be consistently construed as a predicate of syntactical objects, if the expressive/deductive power of the system is deliberately engineered to reflect the power of the original object language operator. The system T _N relies on salient limitations on the expressive power of the language L _N through the construction of a quotational hierarchy, while the system T _Mrelies on limiting the scope of the modal axioms schemas to the sublanguage L _infM ⁺, which corresponds exactly with the restrictive hierarchy of L _N. The fact that L _infM ⁺ is identical to the image of the metalinguistic mapping C ⁺ from the normal operator system into L _M reveals that iterated operator modality is implicitly hierarchical, and that inconsistency is produced by applying the principles of the modal logic to formulas which have no natural analogues in the operator development. Thus the contradiction discovered by Montague can be diagnosed as the result of instantiating the axiom schemas with modally ungrounded formulas, and thereby adding radically new modal axioms to the predicate system.The predicate treatment of necessity differs significantly from that of the operator in that the cumulative models for the predicate system are strictly first-order. Possible worlds are not used as model-theoretic primitives, but rather alternate models are appealed to in order to specify the extension of N, which is semantically construed as a first-order predicate. In this manner, the intensional aspects of modality are built into the mode of specifying the particular set of objects which the denotation function assigns to N, rather than in the specification of the basic truth conditions for modal formulas. Intensional phenomena are thereby localised to the special requirements for determining the extension of a particular predicate, and this does not constitute a structural modification of the first-order models, but rather limits the relevant class of models to those which possess an appropriate denotation function.     

Differential luminance sensitivity of the human visual system

In this paper the differential sensitivity of the visual system is investigated by means of two simultaneously presented stimuli in a yes-no procedure. The sensitivity measure σ_I appears to be proportional to stimulus intensity (i.e., Weber’s law). The curve displaying Weber’s law is little affected by variation of the background intensity or of the adaptation level. An increment threshold experiment using only one stimulus yields a proportionality of σ_I with the square root of the background intensity. An additional experiment shows that the sensitivity measure σ_I for two flashes decreases first, from dark up to a particular background intensity, and increases when the background tends to mask the flashes. So, in general, two background levels exist with the same differential sensitivity. The results cannot easily be explained by the simple quantum fluctuation concept. A model based partially on electrophysiological data from the literature is proposed which encounters a particular adaptation mechanism, a transducer with a limited dynamical range, and a range setting mechanism.     

Testing for selectivity in the dependence of random variables on external factors

Random variables A and B, whose joint distribution depends on factors (x,y), are selectively influenced by x and y, respectively, if A and B can be represented as functions of, respectively, (x,S_A,C) and (y,S_B,C), where S_A,S_B,C are stochastically independent and do not depend on (x,y). Selective influence implies selective dependence of marginal distributions on the respective factors: thus no parameter of A may depend on y. But parameters characterizing stochastic interdependence of A and B, such as their mixed moments, are generally functions of both x and y. We derive two simple necessary conditions for selective dependence of (A,B) on (x,y), which can be used to conduct a potential infinity of selectiveness tests. One condition is that, for any factor values x,x^′ and y,y^′,

s_xy≤s_xy^′+s_x^′y^′+s_x^′y,     

Supracompact inference operations

When a proposition is cumulatively entailed by a finite setA of premisses, there exists, trivially, a finite subsetB ofA such thatB B entails for all finite subsetsB that are entailed byA. This property is no longer valid whenA is taken to be an arbitrary infinite set, even when the considered inference operation is supposed to be compact. This leads to a refinement of the classical definition of compactness. We call supracompact the inference operations that satisfy the non-finitary analogue of the above property. We show that for any arbitrary cumulative operationC, there exists a supracompact cumulative operationK(C) that is smaller thenC and agrees withC on finite sets. Moreover,K(C) inherits most of the properties thatC may enjoy, like monotonicity, distributivity or disjunctive rationality. The main part of the paper concerns distributive supracompact operations. These operations satisfy a simple functional equation, and there exists a representation theorem that provides a semantic characterization for this family of operations. We examine finally the case of rational operations and show that they can be represented by a specific kind of model particularly easy to handle.     

Changes in absolute detection threshold and in subjective intensity of suprathreshold stimuli during olfactory adaptation and recovery

Olfactory adaptation and recovery to methyl isobutyl ketone at a concentration 10 times the absolute detection threshold (I_{t o}) was intensively studied in two human Ss. A combined psychophysical procedure was used that allowed comparisons of changes in threshold (I_t) with changes in the subjective intensity of suprathreshold stimuli. Information was also obtained on the effect of the adapting stimulus on the psychophysical power function for this odorant. A threshold detection procedure was used to estimate changes in I_t; an unstructured magnitude-estimation procedure was used to monitor changes in the subjective intensity of suprathreshold stimuli and the psychophysical power function. The data provided additional information on the behavioral course of olfactory adaptation and recovery and suggested that this combined method can be used profitably for further investigations of this kind. Complementary to the work of Cain and Engen (1969), the results suggested an increase in the exponent of the power function with increasing adaptation.     

From Wittgenstein’s N-operator to a New Notation for Some Decidable Modal Logics

Wittgenstein’s N-operator is a ‘primitive sign’ which shows every complex proposition is the result of the truth-functional combination of a finite number of component propositions, and thus provides a mechanical method to determine logical truth. The N-operator can be interpreted as a generalized Sheffer stroke. In this paper, I introduce a new ‘primitive sign’ that is a hybrid of generalized Sheffer stroke and modality, and give a uniform expression for modal formulas. The general form of modal formula in the new notation is [A₀···A_n?1; B₀···B_m?1], which is semantically equivalent to ¬A₀∨···∨¬ A_n?1∨? (¬B₀∨···∨¬B_m?1). Based on this new notation, I propose several analytic axiomatic systems for some decidable modal logics. Every axiom of these analytic systems is an ‘Atomic-Sheffer’, which is the result of the combination of a finite number of component propositions. The inferential rules are analytic in that the set of elementary propositions that are combined in the premiss overlaps the set of elementary propositions combined in the conclusion, in virtue of which every complex proposition can be reduced to an ‘Atomic-Sheffer’ at the ultimate level. The analytic modal systems have the same classical inferential rules. Different modal systems can be built by adding special modal inferential rules. In an analytic system for modal logic L, valid formulas on L-models can be proved by a purely mechanical method.