scholarly journals Measurement invariance explains the universal law of generalization for psychological perception

2018 ◽  
Author(s):  
Steven A. Frank

The universal law of generalization describes how animals discriminate between alternative sensory stimuli. On an appropriate perceptual scale, the probability that an organism perceives two stimuli as similar typically declines exponentially with the difference on the perceptual scale. Exceptions often follow a Gaussian probability pattern rather than an exponential pattern. Previous explanations have been based on underlying theoretical frameworks such as information theory, Kolmogorov complexity, or empirical multidimensional scaling. This article shows that the few inevitable invariances that must apply to any reasonable perceptual scale provide a sufficient explanation for the universal exponential law of generalization. In particular, reasonable measurement scales of perception must be invariant to shift by a constant value, which by itself leads to the exponential form. Similarly, reasonable measurement scales of perception must be invariant to multiplication, or stretch, by a constant value, which leads to the conservation of the slope of discrimination with perceptual difference. In some cases, an additional assumption about exchangeability or rotation of underlying perceptual dimensions leads to a Gaussian pattern of discrimination, which can be understood as a special case of the more general exponential form. The three measurement invariances of shift, stretch, and rotation provide a sufficient explanation for the universally observed patterns of perceptual generalization. All of the additional assumptions and language associated with information, complexity, and empirical scaling are superfluous with regard to the broad patterns of perception.

2018 ◽  
Vol 115 (39) ◽  
pp. 9803-9806 ◽  
Author(s):  
Steven A. Frank

The universal law of generalization describes how animals discriminate between alternative sensory stimuli. On an appropriate perceptual scale, the probability that an organism perceives two stimuli as similar typically declines exponentially with the difference on the perceptual scale. Exceptions often follow a Gaussian probability pattern rather than an exponential pattern. Previous explanations have been based on underlying theoretical frameworks such as information theory, Kolmogorov complexity, or empirical multidimensional scaling. This article shows that the few inevitable invariances that must apply to any reasonable perceptual scale provide a sufficient explanation for the universal exponential law of generalization. In particular, reasonable measurement scales of perception must be invariant to shift by a constant value, which by itself leads to the exponential form. Similarly, reasonable measurement scales of perception must be invariant to multiplication, or stretch, by a constant value, which leads to the conservation of the slope of discrimination with perceptual difference. In some cases, an additional assumption about exchangeability or rotation of underlying perceptual dimensions leads to a Gaussian pattern of discrimination, which can be understood as a special case of the more general exponential form. The three measurement invariances of shift, stretch, and rotation provide a sufficient explanation for the universally observed patterns of perceptual generalization. All of the additional assumptions and language associated with information, complexity, and empirical scaling are superfluous with regard to the broad patterns of perception.


Methodology ◽  
2011 ◽  
Vol 7 (3) ◽  
pp. 88-95 ◽  
Author(s):  
Jose A. Martínez ◽  
Manuel Ruiz Marín

The aim of this study is to improve measurement in marketing research by constructing a new, simple, nonparametric, consistent, and powerful test to study scale invariance. The test is called D-test. D-test is constructed using symbolic dynamics and symbolic entropy as a measure of the difference between the response patterns which comes from two measurement scales. We also give a standard asymptotic distribution of our statistic. Given that the test is based on entropy measures, it avoids smoothed nonparametric estimation. We applied D-test to a real marketing research to study if scale invariance holds when measuring service quality in a sports service. We considered a free-scale as a reference scale and then we compared it with three widely used rating scales: Likert-type scale from 1 to 5 and from 1 to 7, and semantic-differential scale from −3 to +3. Scale invariance holds for the two latter scales. This test overcomes the shortcomings of other procedures for analyzing scale invariance; and it provides researchers a tool to decide the appropriate rating scale to study specific marketing problems, and how the results of prior studies can be questioned.


2020 ◽  
Vol 13 (1) ◽  
pp. 9-14
Author(s):  
Golamreza Bahoush ◽  
Maryam Vafapour ◽  
Roxana Kariminejad

About 2–5% of acute lymphoblastic leukemia (ALL) cases in pediatric patients are infants with an unfavorable prognosis because of high relapse probability. Early detection of the disease is, therefore, very important. Despite the fact that leukemia in twins occurs rarely, more attention has been paid to it in genetic studies. In the present study, through cytogenetic testing, a special case of concordant ALL in monozygotic twins was presented with different outcomes. In spite of an acceptable initial consequence to medical treatment in twins, in another brother (Twin B), early relapse was observed. In the cytogenetic study, both twins expressed t (4; 11) (q21; q23) while twin A expressed t (2; 7) (p10; q10). No cases have previously reported this mutation. Whether this translocation has a protective role for leukemia with mixed-lineage leukemia (MLL) gene rearrangement is still unclear. The difference in the translocation identified in the identical twins is also subject to further investigations.


1979 ◽  
Vol 16 (1) ◽  
pp. 117-128 ◽  
Author(s):  
E. H. Lloyd ◽  
S. D. Saleem

Weighted sums defined on a Markov chain (MC) are important in applications (e.g. to reservoir storage theory). The rather intractable theory of such sums simplifies to some extent when the transition p.d.f. of the chain {Xt} has a Laplace transform (LT) L(Xt+1; θ |Χ t=x) of the ‘exponential' form H(θ) exp{ – G(θ)x}. An algorithm is derived for the computation of the LT of Σat,Χ t for this class, and for a seasonal generalization of it.A special case of this desirable exponential type of transition LT for a continuous-state discrete-time MC is identified by comparison with the LT of the Bessel distribution. This is made the basis for a new derivation of a gamma-distributed MC proposed by Lampard (1968).A seasonal version of this process is developed, valid for any number of seasons.Reference is made to related chains with three-parameter gamma-like distributions (of the Kritskii–Menkel family) that may be generated from the above by a simple power transformation.


10.29007/xqpk ◽  
2020 ◽  
Author(s):  
Van On Vo

In this paper, we investigate the linear perturbation of the material density of the universe in f(R) modified gravity of polynomial exponential form on the scale of distance below the cosmic horizon (sub-horizon). The results show that the model for the evolutionary aspects of the universe is slightly different from that in the standard cosmological model of ΛCDM. They can be used to show the difference between this modified gravitational model with the standard cosmological model of ΛCMD and other cosmological models. We also investigate the ration Ψ/ Φ and Geff / GN in the model and show that they are within allowable limits of experiments.


2008 ◽  
Vol 60 (3) ◽  
pp. 556-571 ◽  
Author(s):  
Jan Draisma ◽  
Gregor Kemper ◽  
David Wehlau

AbstractWe prove a characteristic free version of Weyl’s theorem on polarization. Our result is an exact analogue ofWeyl’s theorem, the difference being that our statement is about separating invariants rather than generating invariants. For the special case of finite group actions we introduce the concept of cheap polarization, and show that it is enough to take cheap polarizations of invariants of just one copy of a representation to obtain separating vector invariants for any number of copies. This leads to upper bounds on the number and degrees of separating vector invariants of finite groups.


Author(s):  
E. A. Milne

In a recent paper in these Proceedings, Dr G. C. McVittie has published some criticisms of kinematical relativity. These criticisms are to a large extent based on his formula (4.10), namely,It must be stated at the outset that McVittie's interpretation of his derivation of (1) as a derivation of “Milne's formula for the acceleration of a ‘free particle moving in the presence of a substratum,’ for the special case of one spatial co-ordinate only” is wrong. McVittie does not derive the result, as he claims, from what he calls the “axioms of kinematical relativity” alone; he deduces it from these axioms together with an additional assumption, which is equivalent to begging the answer to the whole problem it was my object to solve. Instead of considering a free particle, as I did—that is, a particle whose motion we do not a priori know—he prescribes a priori the motion of his particle as being constrained to obey the rule, in his notation,


Author(s):  
Kantaro Shimomura ◽  
Kazushi Ikeda

The covariance matrix of signals is one of the most essential information in multivariate analysis and other signal processing techniques. The estimation accuracy of a covariance matrix is degraded when some eigenvalues of the matrix are almost duplicated. Although the degradation is theoretically analyzed in the asymptotic case of infinite variables and observations, the degradation in finite cases are still open. This paper tackles the problem using the Bayesian approach, where the learning coefficient represents the generalization error. The learning coefficient is derived in a special case, i.e., the covariance matrix is spiked (all eigenvalues take the same value except one) and a shrinkage estimation method is employed. Our theoretical analysis shows a non-monotonic property that the learning coefficient increases as the difference of eigenvalues increases until a critical point and then decreases from the point and converged to the distinct case. The result is validated by numerical experiments.


2014 ◽  
Vol 8 (2) ◽  
Author(s):  
Simone Elisabeth Lang

AbstractIn describing the position of the narrator, research in literary studies generally follows Gérard Genette’s pioneering theory of narrative in distinguishing between the homo- and heterodiegetic type of narrator. This categorization is not sufficient to allow the position of the narrator to be described properly. The different ways in which the terms are used in literary studies reveal a shortcoming in the distinction behind them. Even in Genette’s work, there is a contradiction between the definition and the names of the two categories: Genette defines homo- and heterodiegesis with reference to the narrator’s presence in the narrated story, whereas he elsewhere states that the diegesis (in the sense of FrenchThe present article aims to do just that, starting from a theoretical standpoint. Thus, the different types of narrator that are possible are sketched in outline, and then explained with the help of examples.I begin by exposing the problems that result from using the terms in Genette’s manner (1), in order then to develop a list of possible narratorial standpoints based on the one hand on the involvement of the narratorial instance in the narrated world and on the other on its involvement in the story. By establishing separation of the two aspects as a ground rule in this way, a number of misunderstandings that are due to the varied ways in which the terminology has been used to date can be overcome.There follows a description of those cases that are unambiguously hetero- and homodiegetic (2), after which the problematic cases are considered (3), yielding the different types of homodiegetic narration that are possible. This latter set of distinctions will, like the others, shed light on the contours of the different narratorial positions and thus be capable of being put profitably into practice in textual interpretation. Accordingly, what is suggested is a way of using the terms that is first unambiguous and second beneficial to the interpretation of works, thus doing justice to the heuristic importance of narratology (see Kindt/Müller 2003; Stanzel 2002, 19).Thus, whereas the concept of diegesis provides the foundation for a distinction based on an ontological criterion that divides homo- and heterodiegesis from each other, the relationship between story and narrator is used to describe various types of homodiegetic narration. In the process, there come to light two types that are distinguished from each other by involvement in events (›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ narrators). If the narrator is not involved in events, the question arises of whether it would in principle have been possible for him to be involved in events, which is the norm with ›homodiegetic, not in the story‹ narrators, or whether a physical impossibility is the reason for his lack of involvement in the story. A special case of the ›homodiegetic, not in the story‹ narrator can be derived from this: peridiegetic narration: whereas narratorial instances of the ›homodiegetic, in the story‹ and ›homodiegetic, not in the story‹ types could in principle have been involved in the action and those of the ›homodiegetic, in the story‹ type actually were, peridiegetic narrators are marked by the fact that they cannot have been involved in the events.In summary, it will be shown that the concept of homodiegesis – in particular in the form in which it has previously been used, where links with the action and appearance in the story were not kept distinct – is in effect an umbrella term that brings together a number of possible forms. There is a prominent distinction between the ›homodiegetic, in the story‹ and the ›homodiegetic, not in the story‹ types of narrator (these types are represented in the present article by the old lawyer in Leo Perutz’s »The Beaming Moon« and the narrator who is a friend of Nathanael in E. T. A. Hoffmann’s »Sandman« respectively). The different degrees of homodiegetic narrator, which have often been mentioned in previous research and are defined by the strength of the character’s presence in the narrated world (from an uninvolved witness to an autodiegetic protagonist), are also to be situated between these two poles.It will also be shown in the process that the case of the narrator who is, for reasons of physical difference, not involved in events (the peridiegetic narrator) should be treated as a form of homodiegesis (for instance the schoolmaster in Theodor Storm’s


1968 ◽  
Vol 23 (10) ◽  
pp. 1569-1582 ◽  
Author(s):  
L. Reimer ◽  
K.H. Sommer

Electron transmission experiments under electron microscope conditions were done with C-, Ge- and Pt-films to get information about the influence of electron energy and objective aperture. One gets an exponential law of transmission for small mass thicknesses x of the objects and can calculate the “contrast thickness” xk (in T = exp(— x/xk)). Using the Lenz theory, two constants Xa and ϑ0 are determined, for each element and electron energy, from the measurements of xk at four different objective apertures. xa is related to the total elastic scattering cross section and ϑ0 is the half width of the atomic scattering amplitude ƒ(ϑ). The variation of xa and ϑ0 with electron energy is not in agreement with the theory using the first Born approximation and a simple screened atomic potential. But using these two experimentally determined constants in a plural scattering theory of LENZ, good agreement between calculated and experimental deviations from the exponential law of transmission up to mass thicknesses of 300 µg · cm-2 is obtained.To get better theoretical values of xk, the complex atomic scattering amplitudes were calculated quantum theoretically with the WKB-method and Hartree potentials. The values agree with the experimental results for Ge- and Pt-films. For carbon there is a large contribution by inelastic scattering making a direct comparison with experimental results difficult.The energy dependence of xa shows saturation for high voltages, as expected by theory. At high voltages the difference in the xk-values for films with different atomic numbers is larger, resulting in lower xk-values for platinum. But at very low voltages the xk-values of carbon are lower than those of platinum. Some measurements of xk at 60 keV on targets of noble gases confirm the absence of a large difference in contrast between atoms in the gaseous and condensed amorphous state.


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