Papers by Geoffrey Iverson
Geometric Representations of Perceptual Phenomena
Geometric Representations of Perceptual Phenomena, 1995
Contents: R.D. Luce, Preface. T. Indow, Psychophysical Scaling: Scientific and Practical Applicat... more Contents: R.D. Luce, Preface. T. Indow, Psychophysical Scaling: Scientific and Practical Applications. Appendix: T. Indow, A Brief Biography and a Bibliography of His Papers in English. Part I: Space. D. Hoffman, Introduction. P. Suppes, Some Foundational Problems in the Theory of Visual Space. D.I.A. MacLeod, J.D. Willen, Is There a Visual Space? V. Lakshminarayanan, T.S. Santhanam, Representation of Rigid Transformations by Cortical Activity Patterns. J. Drosler, The Invariances of Weber's and Other Laws as Determinants of Psychophysical Structures. M.K. Albert, D. Hoffman, Genericity in Spatial Vision. E.N. Dzhafarov, Empirical Meaningfulness, Measurement-Dependent Constants, and Dimensional Analysis. Part II: Color. M. D'Zmura, G. Iverson, Introduction. L.T. Maloney, S.M. Wuerger, J. Krauskopf, A Method for Testing Euclidean Representations of Proximity Judgments in Linear Psychological Spaces. C. Izmailov, Spherical Model of Discrimination of Self-Luminous and Surface Colors. G. Iverson, M. D'Zmura, Color Constancy: Spectral Recovery Using Trichromatic Bilinear Models. M. D'Zmura, G. Iverson, B. Singer, Probabilistic Color Constancy. Part III: Scaling. A.K. Romney, Introduction. L.E. Marks, Intermodel Similarity and Cross-Modality Matching: Coding Perceptual Dimensions. J.C. Baird, Judgment Windows in Psychophysical Scaling. H. Eisler, The Psychophyscial Function for Time Perception: Interpreting Their Parameters. A.K. Romney, W.H. Batchelder, T. Brazill, Scaling Semantic Domains. J.D. Carroll, A. Chaturvedi, A General Approach to Clustering and Multidimensional Scaling of Two-Way, Three-Way, or Higher-Way Data. K.C. Klauer, J.D. Carroll, Network Models for Scaling Proximity Data.
Fundamental Interactions in Physics and Astrophysics
Physical review, Nov 15, 1970
Among the unitary irreducible representations of the Poincare group classi6ed by Wigner, there oc... more Among the unitary irreducible representations of the Poincare group classi6ed by Wigner, there occurs a class of mass-zero representations 0+'(p) which has not hitherto been used for the description of known elementary particles. For historical reasons, these are called "continuous-spin" representations. They are labeled by values of the Poincare invariants P'=0, W lV = -p~, with p)0. We propose to assign one or both neutrinos p"v" to such a representation. A corresponding neutrino can exist in a denumerable set of helicity states X, with X assuming all half-odd-integer values 'A= +~, ~z, .. .. We present a theory of weak interactions with such continuous-spin neutrinos. It di6'ers from the conventional V-A theory with two- component neutrinos in the form of the leptonic current. The predictions of the latter are approached as a limit when p -+ 0. Explicit expressions for the matrix elements of the new leptonic current are derived. Lepton numbers are conserved if all the neutrinos and antineutrinos are distinct particles. It is, however, also possible in this theory, and consistent with present experimental evidence, to identify either v, =v, or p, -= v". Lepton-number-nonconserving processes are then allowed, though suppressed if p is small.
Fundamental interactions in physics and astrophysics. Conference held at Coral Gables, Florida, January 19--21, 1972
Characterization Of Periodic Functions By Higher Order Spectra
... References 1. H. Bartelt, A. W. Lohmann, & B. Wirtnitzer (1984) “Phase and amplitude reco... more ... References 1. H. Bartelt, A. W. Lohmann, & B. Wirtnitzer (1984) “Phase and amplitude recovery from bispectra”, Applied optics, Vol. 23, pp 3121-3129. 2. J. I. Yellott and G. Iverson (1991). ... 90-24, University of California, Irvine. 3. S. A. Klein and C. W. Tyler (1986). ...
Conditions under which affine representations are also Fechnerian under the power law of similarity on the Weber sensitivities
Journal of Mathematical Psychology, Dec 1, 2016
Abstract In a recent paper, Hsu, Iverson, and Doble (2010) examined some properties of a (weakly ... more Abstract In a recent paper, Hsu, Iverson, and Doble (2010) examined some properties of a (weakly balanced) affine representation for choices, Ψ ( x , y ) = F ( u ( x ) − u ( y ) σ ( y ) ) , and showed that using the Fechner method of integrating jnds, one can reconstruct the scales u and σ from the behavior of (Weber) sensitivities ξ s ( x ) = x + Δ s ( x ) (where s = F − 1 ( π ) and Δ s is the jnd) in a neighborhood of s = 0 . Following Iverson (2006b), in this article we impose a power law of similarity on the sensitivities, ξ s ( λ x ) = λ ι ( s ) ξ η ( λ , s ) ( x ) , and study its impact on u and σ in the affine representation. Especially, we specify the conditions for the first- and second-order derivatives of ξ s ( x ) with respect to s (and evaluated at s → 0 ) under which the affine representation degenerates to a Fechnerian one. We also link the results to the solutions in Iverson (2006b), which was worked out within the Fechnerian framework.
Probabilistic Measurement Theory
Recent research in psychology, 1991
Measurement theories formulated in algebraic terms are usually unsuitable for direct confrontatio... more Measurement theories formulated in algebraic terms are usually unsuitable for direct confrontation with empirical data. Probabilistic measurement theory involves a recasting of measurement models in a form better suited to empirical testing. Interestingly, the statistical models which arise in this way have received little attention in the statistical literature. To fill this gap we suggest a likelihood ratio procedure, and illustrate it for the probabilistic measurement axiom known as weak stochastic transitivity.
A group-theoretical interpretation of complex angular momentum
Il Nuovo Cimento A (1965-1970), Sep 1, 1967
Summary Group properties of complex angular momentum are investigated from the point of view of ... more Summary Group properties of complex angular momentum are investigated from the point of view of the Schrödinger equation and representation theory of the complex orthogonal groupO 3,c and its subgroups. Analytic functions corresponding to arbitrary values ofl are constructed on the complex sphere; these functions carry irreducible representations of a subgroupL⊂O 3,c . An expansion formula for analytic functions defined on
Affine representations in psychophysics and the near-miss to Weber’s law
Journal of Mathematical Psychology, Apr 1, 2010
A theoretical account for the near-miss to Weber’s law in the form of a power function, with a sp... more A theoretical account for the near-miss to Weber’s law in the form of a power function, with a special emphasis on the interpretation of the exponent, was proposed by Falmagne [Falmagne, J.-C. (1985). Elements of psychophysical theory. New York: Oxford University Press] within the framework of a subtractive representation, P(x,y)=F(u(x)−g(y)). In this paper, we examine a more general affine representation,
E2¯−Parametrization of <i>SL</i>(2, <i>C</i>)
Journal of Mathematical Physics, May 1, 1970
We consider the E2¯−parametrization of unimodular 2 × 2 matrices A ∈ SL(2, C), which is of the fo... more We consider the E2¯−parametrization of unimodular 2 × 2 matrices A ∈ SL(2, C), which is of the form A=E1e−12aσ3VE2, with V=e12iπσ2 and E=(e−12iφ0ze12iφ)∈E2¯. E2¯ is a covering of the group of Euclidean motions in the plane. We compute the correspondingly factorized matrix elements of the unitary representations of SL(2, C) in an E2¯−basis the result is given in Eq. (6). As a fringe benefit we obtain an integral transform which amounts to expansion in terms of Meijer G-functions and which generalizes the familiar Hankel transform. The results of this paper are useful, e.g., for computing vertex functions in the theory of massless particles with continuous spin.
Uniqueness of results for multiple correlations of periodic functions
Journal of the Optical Society of America, Jul 1, 1993
Page 1. Vol. 10, No. 7/July 1993/J. Opt. Soc. Am. A 1517 Uniqueness of results for multiple corre... more Page 1. Vol. 10, No. 7/July 1993/J. Opt. Soc. Am. A 1517 Uniqueness of results for multiple correlations of periodic functions Ramakrishna Kakarala Department of Electrical and Electronic Engineering, University of Auckland, Private Bag 92019, Auckland, New Zealand ...
Conjoint Weber laws and additivity
Journal of Mathematical Psychology, Oct 1, 1979
ABSTRACT
Psychonomic Bulletin & Review, Apr 1, 2009
The probability of "replication, " p rep , has been proposed as a means of identifying replicable... more The probability of "replication, " p rep , has been proposed as a means of identifying replicable and reliable effects in the psychological sciences. We conduct a basic test of p rep that reveals that it misestimates the true probability of replication, especially for small effects. We show how these general problems with p rep play out in practice, when it is applied to predict the replicability of observed effects over a series of experiments. Our results show that, over any plausible series of experiments, the true probabilities of replication will be very different from those predicted by p rep . We discuss some basic problems in the formulation of p rep that are responsible for its poor performance, and conclude that p rep is not a useful statistic for psychological science.
The Invariances of Weber's and Other Laws as Determinants of Psychophysical Structures
Color Constancy: Spectral Recovery Using Trichromatic Bilinear Models
Thurstonian psychophysics: Case III
Journal of Mathematical Psychology, Sep 1, 1987
... Two random variables X, Y are said to be of the same type iff for some real constants a 0, b.... more ... Two random variables X, Y are said to be of the same type iff for some real constants a 0, b. Here and throughout we ... processes Ux, but in terms of "random comparisons" or "comparative processes" A, which play the role of Thurstone's discriminal differences UYUY, and which ...
Statistical issues in measurement
Mathematical Social Sciences, Oct 1, 1985
ABSTRACT
Uniqueness of higher-order autocorrelation functions
Optical Society of America Annual Meeting, 1991
The kth order autocorrelation function (ACF) of an image is formed by integrating the product of ... more The kth order autocorrelation function (ACF) of an image is formed by integrating the product of the image and k independently shifted copies of itself: the case k = 1 is the ordinary autocorrelation; k = 2 is the triple correlation. Bartelt et al.1 have shown that every image of finite size is uniquely determined up to translation by its triple correlation function. We point out that this is not true in general for images of infinite size, e.g., frequency band-limited images. Examples are given of pairs of simple band-limited periodic images, and pairs of band-limited aperiodic images, that are not translations of one another but that have identical triple correlations. Further examples show that for every k there are distinct band-limited images that have identical kth order ACFs. However certain natural subclasses of infinite images are uniquely determined up to translation by their triple correlations. We develop two general types of criterion for the triple correlation to have an inverse image that is unique up to translation, one based on the zeros of the image spectrum, the other on image moments.
Journal of the Optical Society of America, Jul 1, 1994
We examine conditions under which the spectral properties of lights and surfaces may be recovered... more We examine conditions under which the spectral properties of lights and surfaces may be recovered by a trichromatic visual system that uses bilinear models. We derive criteria for perfect recovery, formulated in terms of invariant properties of model matrices, for situations in which either two or three lights are shone sequentially on a set of surfaces.
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Papers by Geoffrey Iverson