Detection of tones in noise and the "severe departure" from Weber's law

Thresholds were measured for the detection of 20-ms sinusoids, with frequencies 500, 4000, or 6500 Hz, presented in bursts of bandpass noise of the same duration and centered around the signal frequency. A range of noise levels from 35 to 80 dB SPL was used. Noise at different center frequencies was equated in terms of the total noise power in an assumed auditory filter centered on the signal frequency. Thresholds were expressed as the signal levels, relative to these noise levels, necessary for subjects to achieve 71% correct. For 500-Hz signals, thresholds were about 5 dB regardless of noise level. For 6500-Hz signals, thresholds reached a maximum of 14 dB at intermediate noise levels of 55-65 dB SPL. For 4000-Hz signals, a maximum threshold of 10 dB was observed for noise levels of 45-55 dB SPL. When the bandpass noises were presented continuously, however, thresholds for 6500-Hz, 20-ms signals remained low (about 1 dB) and constant across level. These results are similar to those obtained for the intensity discrimination of brief tones in bandstop noise [R. P. Carlyon and B. C. J. Moore, J. Acoust. Soc. Am. 76, 1369-1376 (1984); R. P. Carlyon and B. C. J. Moore, J. Acoust. Soc. Am. 79, 453-460 (1986)].     

Auditory profile analysis: frequency, phase, and Weber's law

This paper reports three separate experiments on different aspects of performance in auditory profile analysis. The first experiment deals with the effects of the frequency and position of an increment in a single component of a multitonal complex. The general results indicate that detection of the signal is easier for components in the mid-frequency range (around 1000 Hz) independent of signal position within the complex. The second experiment investigates the effects of relative phase of the individual components of the complex. Regardless of the number of components, our results indicate that phase has very little effect, even when different phases are selected for each presentation. The third experiment compares the detection of an increment in intensity of a single component, the traditional Weber fraction experiment, and conditions where additional components are present, a profile experiment. The detection of the increment is measured as a function of the level of the standard. The single-tone condition shows the usual near miss to Weber's law whereas the multitone condition does not. In addition, threshold for the increment is better for the multitone condition than for the single tone condition for levels of the standard up to 70 dB SPL. This last result is investigated for ten observers, five of whom were experienced in profile tasks and five of whom were not. Using a low level standard, the five experienced observers replicate the results described above. The inexperienced observers show the opposite result. On average, they are better able to detect the increment in the single-component condition.     

Invariant power law distribution of langevin systems with colored multiplicative noise

The random multiplicative process is studied for the case of a colored multiplicative noise with exponentially decreasing autocorrelation function. We observe the power law exponent of probability distribution in a statistically steady state numerically to clarify the effect of finite correlation time. The renormalization procedure is applied to derive the power law exponent theoretically. The power law exponent is inversely proportional to the autocorrelation time of the multiplicative noise.     

Perception of suprathreshold amplitude modulation and intensity increments: Weber's law revisited

The perceived strength of intensity fluctuations evoked by suprathreshold sinusoidal amplitude modulation (AM) and the perceived size of intensity increments were compared across levels of a wideband noise and a 1-kHz tone. For the 1-kHz tone, the comparisons were made in quiet and in a high-pass noise. The data indicate that suprathreshold modulation depths and intensity increments, perceived as equivalent across levels, follow a pattern resembling Weber's law for noise and the "near miss" to Weber's law for a tone. The effect of a high-pass noise was largely consistent with that observed for AM and increment detection. The data suggest that Weber's law is not a direct consequence of the dependence of internal noise on stimulus level, as suggested by multiplicative internal noise models. Equal loudness ratios and equal loudness differences (computed using loudness for the stationary portions before and after the increment) accounted for the increment-matching data for noise and for the tone, respectively, but neither measure predicted the results for both types of stimuli. Predictions based on log-transformed excitation patterns and predictions using an equal number of intensity just-noticeable differences were in qualitative, but not quantitative, agreement with the data.     

Continuous versus gated pedestals and the "severe departure" from Weber's law

Thresholds were compared for the detection of 20-ms sinusoidal signals presented with either continuous or gated sinusoidal pedestals of the same frequency (500 or 6500 Hz). Pedestal levels ranged from 35-80 dB SPL. For 500-Hz signals, thresholds were lower in the continuous-pedestal condition than in the gated-pedestal condition, for all pedestal levels above 35 dB SPL. When the pedestal level was 35 dB, thresholds were higher in the continuous-pedestal condition than in the gated-pedestal condition. This was also true at all pedestal levels when bandstop noise centered around the pedestal frequency was added to the pedestal. For 6500-Hz signals, a deterioration in performance at intermediate levels, similar to that reported by Carlyon and Moore [J. Acoust. Soc. Am. 76, 1369-1376 (1984)], was found in the gated-pedestal condition. No such deterioration occurred in the continuous-pedestal condition. However, masking signal onsets and offsets by bursts of bandpass noise produced a midlevel deterioration in the continuous-pedestal condition. This was true when bandstop noise was absent, and when it was gated on and off in each observation interval. When continuous bandstop noise was present, no midlevel deterioration was observed, even when onsets and offsets were masked. The results suggest that in the continuous-pedestal condition subjects may normally maintain performance across level at 6500 Hz by attending to a transient response to signal onsets. Presenting bursts of bandpass noise disrupts the detection of such a response. The absence of a midlevel deterioration when continuous bandstop noise was present may be related to the adaptation to the sinusoidal pedestal that was caused by the bandstop noise.     

Weber's law for biological responses in autocatalytic networks of chemical reactions

Biological responses often obey Weber's law, according to which the magnitude of the response depends only on the fold change in the external input. In this study, we demonstrate that a system involving a simple autocatalytic reaction shows such a response when a chemical is slowly synthesized by the reaction from a faster influx process. We also show that an autocatalytic reaction process occurring in series or in parallel can obey Weber's law with an oscillatory adaptive response. Considering the simplicity and ubiquity of the autocatalytic process, our proposed mechanism is thought to be commonly observed in biological reactions.     

Cold plasma oscillations according to Weber's law. An unphysical result

Applying Weber's law to particle interactions in a uniform infinite cold plasma, a dispersion relation for longitudinal plasma oscillations is found. The classical result of plasma frequency oscillations is recovered for small wavelengths. Depending on the wavelength, the phase and group velocities may be singular. This unphysical result is due to the absence of transverse interaction in Weber's law.     

Linear power filtration of nonsteady, doubly-stochastic, Gaussian noise

Optimal linear filtration of the dispersion of a nonsteady Gaussian noise, the dispersion of which is a function of an unobservable Markov control process, is considered. Discrete and continuous, first-order, autoregression models are considered, and a limiting transition is made. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 15–22, April, 1998.     

Weber's force and Maxwell's equations

We explore the mathematical connection that exists between Weber's force and Maxwell's equations. The Weber force is shown to be compatible with Maxwell's equations when expressed in relative coordinates with the time dependence determined by the source motion.     

Unified scaling law in the coherent noise model

The waiting time distribution between successive events and the unified scaling law is studied using the coherent noise model. It is shown that, although this model generates uncorrelated event sizes and does not exhibit criticality, it still provides the unified scaling law. We argue the role of characteristic kink observed in the unified scaling law and the meaning of the parameter C$C$ used to fix the peak of the kink to unity. Our results indicate that the parameter C$C$ is indeed a physical quantity localizing the end of the linear tendency in the scaling law, which corresponds to the completion of the dominance of correlated events in time.     

External and internal noise surveys of London primary schools

Internal and external noise surveys have been carried out around schools in London, UK, to provide information on typical levels and sources to which children are exposed while at school. Noise levels were measured outside 142 schools, in areas away from flight paths into major airports. Here 86% of the schools surveyed were exposed to noise from road traffic, the average external noise level outside a school being 57 dB L(Aeq). Detailed internal noise surveys have been carried out in 140 classrooms in 16 schools, together with classroom observations. It was found that noise levels inside classrooms depend upon the activities in which the children are engaged, with a difference of 20 dB L(Aeq) between the "quietest" and "noisiest" activities. The average background noise level in classrooms exceeds the level recommended in current standards. The number of children in the classroom was found to affect noise levels. External noise influenced internal noise levels only when children were engaged in the quietest classroom activities. The effects of the age of the school buildings and types of window upon internal noise were examined but results were inconclusive.     

Frequency power law of material damping

The experimental studies often show that the damping in various solid materials increases with frequency over a finite bandwidth, and the increase is weak if the damping is low. A frequency power law is suggested and discussed in this paper to describe this damping behaviour with special respect to the low loss resilient materials used for sound and vibration control. The dynamic modulus as a function of frequency is determined from the loss modulus through the Kramers-Kronig dispersion relations to satisfy the causality requirement. It is proved that the dynamic modulus obeys the frequency power law of the same type as the loss modulus. In addition, it is proved that the weak frequency dependences of damping properties are inevitably associated with the low loss factor. Examples of fitting the frequency power law to experimental data on some materials of acoustical purposes are presented.     

Studies on modified power law inflation

In this study, we evaluate power law inflation (PLI) with a monomial potential and obtain a novel exact solution. It is well known that the conventional PLI with an exponential potential is inconsistent with the Planck data. Unlike the standard PLI, the present model does not encounter the graceful exit problem, and the results agree fairly well with recent observations. In our analysis, we calculate the spectral index and the tensor-to-scalar ratio, both of which agree very well with recent observational data and are comparable with those of other modified inflationary models. The employed technique reveals that the large cosmological constant decreases with the expansion of the universe in the case of the PLI. The coupling of the inflaton with gravitation is the primary factor in this technique. The basic assumption here is that the two metric tensors in the gravitational and inflaton parts correspond to different conformal frames, which contradicts with the conventional PLI, where the inflaton is directly coupled with the background metric tensor. This fact has direct applications to different dark energy models and the assisted quintessence theory.     

Fractal power law in literary English

We present in this paper a numerical investigation of literary texts by various well-known English writers, covering the first half of the twentieth century, based upon the results obtained through corpus analysis of the texts. A fractal power law is obtained for the lexical wealth defined as the ratio between the number of different words and the total number of words of a given text. By considering as a signature of each author the exponent and the amplitude of the power law, and the standard deviation of the lexical wealth, it is possible to discriminate works of different genres and writers and show that each writer has a very distinct signature, either considered among other literary writers or compared with writers of non-literary texts. It is also shown that, for a given author, the signature is able to discriminate between short stories and novels.     

Punctuated equilibrium and power law in economic dynamics

This work is primarily based on a recently proposed toy model by Thurner et al. (2010) [3] on Schumpeterian economic dynamics (inspired by the idea of economist Joseph Schumpeter [9]). Interestingly, punctuated equilibrium has been shown to emerge from the dynamics. The punctuated equilibrium and Power law are known to be associated with similar kinds of biologically relevant evolutionary models proposed in the past. The occurrence of the Power law is a signature of Self-Organised Criticality (SOC). In our view, power laws can be obtained by controlling the dynamics through incorporating the idea of feedback into the algorithm in some way. The so-called ‘feedback’ was achieved by introducing the idea of fitness and selection processes in the biological evolutionary models. Therefore, we examine the possible emergence of a power law by invoking the concepts of ‘fitness’ and ‘selection’ in the present model of economic evolution.     

Criticality, the area law, and the computational power of projected entangled pair states

The projected entangled pair state (PEPS) representation of quantum states on two-dimensional lattices induces an entanglement based hierarchy in state space. We show that the lowest levels of this hierarchy exhibit a very rich structure including states with critical and topological properties. We prove, in particular, that coherent versions of thermal states of any local 2D classical spin model correspond to such PEPS, which are in turn ground states of local 2D quantum Hamiltonians. This correspondence maps thermal onto quantum fluctuations, and it allows us to analytically construct critical quantum models exhibiting a strict area law scaling of the entanglement entropy in the face of power law decaying correlations. Moreover, it enables us to show that there exist PEPS which can serve as computational resources for the solution of NP-hard problems.