Hybrids of the -translation for

In [W. Burr, Functional interpretation of Aczel's constructive set theory, Annals of Pure and Applied Logic 104 (2000) 31–73] Wolfgang Burr presents a functional interpretation of constructive set theory in all finite types, , in a theory of constructive set functionals. is a subtheory of , containing bounded quantifiers only. His interpretation theorem reduces the consistency problem of (and certain extensions thereof) to the consistency problem of .We want to study admissible rules in , i.e. rules under which is closed. To do so, we study a Troelstra-style q-hybrid of, in fact, a modification ^× of Burr's translation. We introduce this modification in order to close a minor gap in Burr's proof of the functional interpretation of the schema of (Strong Collection).First of all, but surely after a short introduction, we analyse the less complex translation of modified realisation ^mr and its hybrids ^mq and ^mrt.     

A kinematic and dynamic comparison of surface and underwater displacement in high level monofin swimming

Fin swimming performance can be divided into underwater and surface water races. World records are about 10% faster for underwater swimming vs. surface swimming, but little is known about the advantage of underwater swimming for monofin swimming. Some authors reported that the air–water interface influences the kinematics and leads to a narrow vertical amplitude of the fin. On the one hand, surface swimming is expected to affect drag parameters (cross-sectional area (S) and active drag (AD)) when compared to underwater swimming. On the other hand, the surface swimming technique may also affect efficiency (η_F). The aim of this study is therefore to evaluate and compare drag parameters and efficiency during underwater and surface swimming. To this end, 12 international level monofin swimmers were measured during both underwater and surface swimming. Kinematic parameters (both dimensional and non-dimensional), η_F (calculated according to the Elongated-Body Theory), and AD (computed with Velocity Perturbation Method) were calculated for an underwater and a surface fin swimming trial, performed at maximal speed. As expected, results showed significantly lower velocities during surface swimming vs. underwater  = 2.5 m s⁻¹ vs.  = 2.36 m s⁻¹, p < .01). Velocities during underwater and surface swimming were strongly correlated (r = .97, p < .01). Underwater swimming was also associated with higher vertical amplitudes of the fin compared to surface swimming ( = 0.55 m vs. ) = 0.46 m, p < .01). Length-specific amplitudes (A_under/L_b) were in the order of 20% during underwater swimming as for undulating fish, and significantly higher than during surface swimming (A_surf/L_b = 17%, p < .01). Efficiency for surface swimming was about 6% lower than for underwater swimming ( = 0.79 vs.  = 0.74, p < .01). This decrease could be associated with an increase in swimming frequency for surface swimming ( = 2.15 Hz vs.  = 2.08 Hz, p < .01). Active drag during surface swimming was about 7% higher than for underwater swimming ( = 78.9 N vs.  = 84.7 N, p < .01). A significantly smaller cross-sectional area for surface swimming ( = 0.053 m² vs.  = 0.044 m², p < .01) and higher drag coefficient for surface swimming ( = 0.47 vs.  = 0.69, p < .01) were measured. Finally, correlation between cross-sectional area and vertical amplitude of the fin was reported for both underwater and surface swimming. These results suggest that the performance improvement during underwater swimming is not only linked to a wave drag reduction effect but also to a specific swimming technique due to the free surface.     

On the consistency problem for the calculus

In this paper, we further investigate the consistency problem for the qualitative temporal calculus introduced by Pujari et al. [A.K. Pujari, G.V. Kumari, A. Sattar, INDU: An interval and duration network, in: Australian Joint Conference on Artificial Intelligence, 1999, pp. 291–303]. We prove the intractability of the consistency problem for the subset of pre-convex relations, and the tractability of strongly pre-convex relations. Furthermore, we also define another interesting set of relations for which the consistency problem can be decided by the -closure method, a method similar to the usual path-consistency method. Finally, we prove that the -closure method is also complete for the set of atomic relations of implying that the intervals have the same duration.     

-Cycloserine: Effects on Long-Term Retention of a Conditioned Response and on Memory for Contextual Attributes

-Cycloserine (DCS), a partial agonist of the glycine recognition site of the N-methyl -aspartate receptor, has beneficial effects on learning and memory. In order to investigate its potential to influence learning and memory of both the response and the stimulus attributes of training, male Sprague-Dawley albino rats were trained in a one-trial inhibitory avoidance task following an acute intraperitoneal injection of DCS (3 mg/kg) or an equal volume of saline. In order to measure memory for stimulus attributes, testing involved a context shift paradigm, in which subjects are tested in either the environment of training or a different one. Good memory for the contextual attributes of training is indicated by poor performance in the alternate context. Retention was assessed either 1, 7, or 14 days after training. At 1 day, Saline subjects were affected by a change in context, while DCS subjects were not. In subjects tested 1 week following training, Saline subjects were no longer affected by a change in context, in that they performed the avoidance response in both contexts. This indicates the forgetting of stimulus attributes in Saline subjects. DCS subjects did show the context shift effect at 1 week, indicating the retention of stimulus attributes. Finally, Saline subjects demonstrated the context shift rebound at 14 days, while DCS subjects performed equivalently in both contexts. Taken together, these data suggest that DCS may enhance retention of fear and slow the forgetting of stimulus attributes.     

On the provenance of judgments of conditional probability

In standard treatments of probability, is defined as the ratio of to , provided that . This account of conditional probability suggests a psychological question, namely, whether estimates of arise in the mind via implicit calculation of . We tested this hypothesis (Experiment 1) by presenting brief visual scenes composed of forms, and collecting estimates of relevant probabilities. Direct estimates of conditional probability were not well predicted by . Direct estimates were also closer to the objective probabilities defined by the stimuli, compared to estimates computed from the foregoing ratio. The hypothesis that arises from the ratio fared better (Experiment 2). In a third experiment, the same hypotheses were evaluated in the context of subjective estimates of the chance of future events.     

Social networks and web minorities

The conception of appropriate models of information retrieval is a crucial step for the actual growth and development of the web. In addition to traditional information retrieval techniques, nowadays search engines have adopted methods for taking into account the social network deriving from the pattern of interconnections. Using different arguments, it has been shown that this is very effective in practice. In this paper we subscribe that point of view, but state also that social networks based ranking schemes operating on the whole web, like Google’s , prevent small communities to become visible on the Web, regardless of the quality of the information. Hence, we strongly advocate the development of new cognitive models of the whole process of information retrieval which are capable of facing this problem. We give a picture of distributed architectures which incorporates topic-based intelligent agents and personal agents for capturing the user’s profile.     

Using information criteria to determine the number of regimes in threshold autoregressive models

Threshold autoregressive models can be used to study processes that are characterized by recurrent switches between two or more regimes, where switching is triggered by a manifest threshold variable. In this paper the performance of diverse information criteria for selecting the number of regimes in small to moderate sample sizes (i.e., n=50,100,200) is investigated. In addition it is investigated whether these information criteria can be used to determine whether the residual variances are identical across the regimes. It is concluded that for small sample sizes should be preferred, while for larger sample sizes either BIC or should be considered: The latter is the only information criterion that includes a penalty for the unknown threshold parameters.     

Thurstonian-type representations for “same-different” discriminations: Deterministic decisions and independent images

A discrimination probability function obtained in the “same-different” paradigm assigns to every ordered pair of stimuli the probability with which they are judged to be different. This function is said to possess the regular minimality property if, for any stimulus pair ,

     

LSD response in Eysenckian trait types identified by polypredictive CFA

The four personality type combinations derived from high and low extraversion () and high and low neuroticism () have been related to response patterns composed of three symptoms (affective disturbances, thinking disturbances, and blackouts) scored as present (+) or absent (−) after a single oral dose of the hallucinogenic drug LSD-25. Hypotheses for expected response patterns for each personality group were derived from a data set obtained by Kohnen and Lienert (1987). Significance of associations was tested by two strategies of polyprediction configural frequency analysis (CFA): multiple uniprediction and biprediction CFA. Both strategies yielded a significant hyperpresentation of all three symptoms present in E+N+ (hysterics), merely thinking disorders in dysthymics (E−N+), merely affective symptoms in E+N− (stable extraverts), and merely blackouts in N−E− (stable introverts). Authors tried to relate these symptoms to Kretschmer's temperament types and could afterwards show by a chessboard modification of prediction CFA, that by applying two combined hypotheses for two personality types each, the significance of the predicted associations could be increased.     

Thurstonian-type representations for “same-different” discriminations: Probabilistic decisions and interdependent images

A general Thurstonian-type representation (with stochastically interdependent images and probabilistic decisions) for a “same-different” discrimination probability function is a model in which the two stimuli are mapped into two generally interdependent random images and taking on their values in some “perceptual” space; and the realizations of these two random images in a given trial determine the probability with which and in this trial are judged to be different. While stochastically interdependent, and are selectively attributed to (influenced by), respectively, and , which is understood as the possibility of conditioning and on some random variable R that renders them stochastically independent, with their conditional distributions selectively depending on, respectively, and . A general Thurstonian-type representation is considered “well-behaved” if the conditional probability with which and , given a value of the conditioning random variable R, fall within two given subsets of the perceptual space, possess appropriately defined bounded directional derivatives with respect to and . It is shown that no such well-behaved Thurstonian-type representation can account for possessing two basic properties: regular minimality and nonconstant self-similarity. At the same time, an alternative to Thurstonian-type modeling (a model employing “uncertainty blobs” in stimulus spaces instead of random variables in perceptual spaces) is readily available that predicts these two properties “automatically”.     

Dissimilarity cumulation theory in arc-connected spaces

This paper continues the development of the Dissimilarity Cumulation theory and its main psychological application, Universal Fechnerian Scaling [Dzhafarov, E.N and Colonius, H. (2007). Dissimilarity Cumulation theory and subjective metrics. Journal of Mathematical Psychology, 51, 290-304]. In arc-connected spaces the notion of a chain length (the sum of the dissimilarities between the chain’s successive elements) can be used to define the notion of a path length, as the limit inferior of the lengths of chains converging to the path in some well-defined sense. The class of converging chains is broader than that of converging inscribed chains. Most of the fundamental results of the metric-based path length theory (additivity, lower semicontinuity, etc.) turn out to hold in the general dissimilarity-based path length theory. This shows that the triangle inequality and symmetry are not essential for these results, provided one goes beyond the traditional scheme of approximating paths by inscribed chains. We introduce the notion of a space with intermediate points which generalizes (and specializes to when the dissimilarity is a metric) the notion of a convex space in the sense of Menger. A space is with intermediate points if for any distinct there is a different point such that (where D is dissimilarity). In such spaces the metric G induced by D is intrinsic: coincides with the infimum of lengths of all arcs connecting to In Universal Fechnerian Scaling D stands for either of the two canonical psychometric increments and (ψ denoting discrimination probability). The choice between the two makes no difference for the notions of arc-connectedness, convergence of chains and paths, intermediate points, and other notions of the Dissimilarity Cumulation theory.     

Sequential learning using temporal context

The temporal context model (TCM) has been extensively applied to recall phenomena from episodic memory. Here we use the same formulation of temporal context to construct a sequential learning model called the predictive temporal context model (pTCM) to extract the generating function of a language from sequentially-presented words. In pTCM, temporal context is used to generate a prediction vector at each step of learning and these prediction vectors are in turn used to construct semantic representations of words on the fly. The semantic representation of a word is defined as the superposition of prediction vectors that occur prior to the presentation of the word in the sequence. Here we create a formal framework for pTCM and prove several useful results. We explore the effect of manipulating the parameters of the model on learning a sequence of words generated by a bi-gram generating function. In this simple case, we demonstrate that feeding back the constructed semantic representation into the temporal context during learning improves the performance of the model when trained with a finite training sequence from a language with equivalence classes among some words. We also describe , a variant of the model that is identical to pTCM at steady state. has significant computational advantages over pTCM and can improve the quality of its prediction for some training sequences.     

You’ll see what you mean: Students encode equations based on their knowledge of arithmetic

This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., ) and mathematical equivalence problems (e.g., or ). Next, they completed an encoding task in which they reconstructed addition and equivalence problems after viewing each for 5 s. Equivalence problems of the form overlap with a perceptual pattern found in traditional arithmetic problems (i.e., answer blank in final position), and students’ encoding was poorest on problems of this type. Individual differences in encoding the equivalence problems were related to variations in strategy use. Some students solved blank-final equivalence problems using the standard arithmetic strategy of performing all given operations on all given numbers. These students made more errors in encoding problem structure, but fewer errors in encoding the numbers, than did students who solved the problems using correct or other incorrect strategies. Moreover, students who expressed many strategies for solving the blank-final equivalence problems made fewer errors in encoding problem structure, but more errors in encoding the numbers, than did students who expressed only a single strategy. Results highlight that encoding is intended to guide action and that prior experience can simultaneously facilitate and interfere with accurate encoding.     

Generalized Pexider equation on a restricted domain

Let X be a normed space and D be a nonempty, open and connected subset of X×X. Inspired by a problem of J. Aczél, we study the functional equation

     

Analytical methods in the theory of psychophysical discrimination I: Inequalities, convexity and integration of just noticeable differences

We re-examine the theoretical status of Fechner's Mathematical Auxiliary Principle [Fechner, G. T. (1889). Elemente der psychophysik. Leipzig: Breitkopf und Härtel] which underlies Fechner's method of constructing a sensory scale by integrating just noticeable differences (jnds). That “Principle” has been roundly criticized [Luce, R. D., & Edwards, W. (1958). The derivation of subjective scales from just noticeable differences. Psychological Review, 65, 227-237] as being inconsistent with the very basis of Fechner's psychophysical theory, and indeed this is the case. In important papers Pfanzagl [(1962). Über die stochastische Fundierung des psychophysischen Gesetzes (On the stochastic foundations of the psychophysical law). Biometrische Zeitschrift, 4, 1-14] and Krantz [(1971). Integration of just noticeable differences. Journal of Mathematical Psychology, 8, 591-599] resurrected Fechner's method; their analysis showed that the sensory scale could be written as the limit of a sequence of integrals, each of the form suggested by the auxiliary principle. In this work, we investigate the properties of a typical member of the Krantz-Pfanzagl sequence of integrals; we do so with the view to obtaining useful approximations to the true scale. Weber's inequality [Falmagne, J.-Cl. (1977). Note: Weber's inequality and Fechner's problem. Journal of Mathematical Psychology, 16, 267-271] plays an important role in our developments. That inequality, and other inequalities of a similar nature, allows us to place bounds on the error incurred by approximating a true scale u by an integral of jnds. Under appropriate conditions these bounds are sufficiently tight that the relative error is very small over the entire stimulus domain. We illustrate our theoretical results with a number of examples.     

Functional equations arising in a theory of rank dependence and homogeneous joint receipts

This paper focuses on a class of utility representations of uncertain alternatives with two possible consequences (binary gambles) when they are linked via a distributivity property called segregation to an operation of joint receipt, which may be non-commutative. The assumption that the gambling structure and the joint receipt operation both have homogeneous representations that are order preserving leads to a functional equation that has too many solutions to be useful for characterizing a reasonably specific utility representation. A plausible restriction on the form of the utility of gambles leads to the functional equation