Improving the estimation of psychometric functions in 2AFC discrimination tasks.

Ulrich and Vorberg (2009) presented a method that fits distinct functions for each order of presentation of standard and test stimuli in a two-alternative forced-choice (2AFC) discrimination task, which removes the contaminating influence of order effects from estimates of the difference limen. The two functions are fitted simultaneously under the constraint that their average evaluates to 0.5 when test and standard have the same magnitude, which was regarded as a general property of 2AFC tasks. This constraint implies that physical identity produces indistinguishability, which is valid when test and standard are identical except for magnitude along the dimension of comparison. However, indistinguishability does not occur at physical identity when test and standard differ on dimensions other than that along which they are compared (e.g., vertical and horizontal lines of the same length are not perceived to have the same length). In these cases, the method of Ulrich and Vorberg cannot be used. We propose a generalization of their method for use in such cases and illustrate it with data from a 2AFC experiment involving length discrimination of horizontal and vertical lines. The resultant data could be fitted with our generalization but not with the method of Ulrich and Vorberg. Further extensions of this method are discussed.

Efficient numerical methods for the random-field Ising model: Finite-size scaling, reweighting extrapolation, and computation of response functions

It was recently shown [Phys. Rev. Lett. 110, 227201 (2013)] that the critical behavior of the random-field Ising model in three dimensions is ruled by a single universality class. This conclusion was reached only after a proper taming of the large scaling corrections of the model by applying a combined approach of various techniques, coming from the zero-and positive-temperature toolboxes of statistical physics. In the present contribution we provide a detailed description of this combined scheme, explaining in detail the zero-temperature numerical scheme and developing the generalized fluctuation-dissipation formula that allowed us to compute connected and disconnected correlation functions of the model. We discuss the error evolution of our method and we illustrate the infinite limit-size extrapolation of several observables within phenomenological renormalization. We present an extension of the quotients method that allows us to obtain estimates of the critical exponent a of the specific heat of the model via the scaling of the bond energy and we discuss the self-averaging properties of the system and the algorithmic aspects of the maximum-flow algorithm used.

On the uniform approximation of Cauchy continuous functions

In the context of real-valued functions defined on metric spaces, it is known that the locally Lipschitz functions are uniformly dense in the continuous functions and that the Lipschitz in the small functions - the locally Lipschitz functions where both the local Lipschitz constant and the size of the neighborhood can be chosen independent of the point - are uniformly dense in the uniformly continuous functions. Between these two basic classes of continuous functions lies the class of Cauchy continuous functions, i.e., the functions that map Cauchy sequences in the domain to Cauchy sequences in the target space. Here, we exhibit an intermediate class of Cauchy continuous locally Lipschitz functions that is uniformly dense in the real-valued Cauchy continuous functions. In fact, our result is valid when our target space is an arbitrary Banach space.

Effects of the environment on the electric conductivity of double-stranded DNA molecules

We present a theoretical analysis of the effects of the environment on charge transport in double-stranded synthetic poly(G)-poly(C) DNA molecules attached to two ideal leads. Coupling of the DNA to the environment results in two effects: (i) localization of carrier functions due to static disorder and (ii) phonon-induced scattering of the carriers between the localized states, resulting in hopping conductivity. A nonlinear Pauli master equation for populations of localized states is used to describe the hopping transport and calculate the electric current as a function of the applied bias. We demonstrate that, although the electronic gap in the density of states shrinks as the disorder increases, the voltage gap in the I-V characteristics becomes wider. A simple physical explanation of this effect is provided.

Fitting model-based psychometric functions to simultaneity and temporal-order judgment data: MATLAB and R routines

Research on temporal-order perception uses temporal-order judgment (TOJ) tasks or synchrony judgment (SJ) tasks in their binary SJ2 or ternary SJ3 variants. In all cases, two stimuli are presented with some temporal delay, and observers judge the order of presentation. Arbitrary psychometric functions are typically fitted to obtain performance measures such as sensitivity or the point of subjective simultaneity, but the parameters of these functions are uninterpretable. We describe routines in MATLAB and R that fit model-based functions whose parameters are interpretable in terms of the processes underlying temporal-order and simultaneity judgments and responses. These functions arise from an independent-channels model assuming arrival latencies with exponential distributions and a trichotomous decision space. Different routines fit data separately for SJ2, SJ3, and TOJ tasks, jointly for any two tasks, or also jointly for the three tasks (for common cases in which two or even the three tasks were used with the same stimuli and participants). Additional routines provide bootstrap p-values and confidence intervals for estimated parameters. A further routine is included that obtains performance measures from the fitted functions. An R package for Windows and source code of the MATLAB and R routines are available as Supplementary Files.

Psychometric functions for detection and discrimination with and without flankers.

Recent studies have reported that flanking stimuli broaden the psychometric function and lower detection thresholds. In the present study, we measured psychometric functions for detection and discrimination with and without flankers to investigate whether these effects occur throughout the contrast continuum. Our results confirm that lower detection thresholds with flankers are accompanied by broader psychometric functions. Psychometric functions for discrimination reveal that discrimination thresholds with and without flankers are similar across standard levels, and that the broadening of psychometric functions with flankers disappears as standard contrast increases, to the point that psychometric functions at high standard levels are virtually identical with or without flankers. Threshold-versus-contrast (TvC) curves with flankers only differ from TvC curves without flankers in occasional shallower dippers and lower branches on the left of the dipper, but they run virtually superimposed at high standard levels. We discuss differences between our results and other results in the literature, and how they are likely attributed to the differential vulnerability of alternative psychophysical procedures to the effects of presentation order. We show that different models of flanker facilitation can fit the data equally well, which stresses that succeeding at fitting a model does not validate it in any sense.

On the metallicity dependence of the 24 μm luminosity as a star formation tracer

We investigate the use of the rest-frame 24 μm luminosity as an indicator of the star formation rate (SFR) in galaxies with different metallicities by comparing it to the (extinction-corrected) Hα luminosity. We carry out this analysis in two steps: First, we compare the emission from H (II) regions in different galaxies with metallicities between 12 + and 8.9. We find that the 24 μm and the extinction-corrected Hα luminosities from individual H (II) log (O/H) = 8.1 regions follow the same correlation for all galaxies, independent of their metallicity. Second, the role of metallicity is explored further for the integrated luminosity in a sample of galaxies with metallicities in the range of 12 +. For this sample we compare the 24 μm and Hα luminosities integrated over the entire galaxies log (O/ H) = 7.2-9.1 and find a lack of the 24 μm emission for a given Hα luminosity for low-metallicity objects, likely reflecting a low dust content. These results suggest that the 24 μm luminosity is a good metallicity-independent tracer for the SFR in individual H (II) regions. On the other hand, metallicity has to be taken into account when using the 24 μm luminosity as a tracer for the SFR of entire galaxies.

Holomorphic functions on non-Runge domains and related problems.

Let U be a domain in CN that is not a Runge domain. We study the topological and algebraic properties of the family of holomorphic functions on U which cannot be approximated by polynomials.