Generalization to anomalous diffusion of Budó's treatment of polar molecules containing interacting rotating groups.

A fractional Smoluchowski equation for the orientational distribution of dipoles incorporating interactions with continuous time random walk Ansatz for the collision term is obtained. This equation is written via the non-inertial Langevin equations for the evolution of the Eulerian angles and their associated Smoluchowski equation. These equations govern the normal rotational diffusion of an assembly of non-interacting dipolar molecules with similar internal interacting polar groups hindering their rotation owing to their mutual potential energy. The resulting fractional Smoluchowski equation is then solved in the frequency domain using scalar continued fractions yielding the linear dielectric response as a function of the fractional parameter for extensive ranges of the interaction parameter and friction ratios. The complex susceptibility comprises a multimode Cole-Cole-like low frequency band with width dependent on the fractional parameter and is analogous to the discrete set of Debye mechanisms of the normal diffusion. The results, in general, comprise an extension of Budó's treatment [A. Budó, J. Chem. Phys. 17, 686 (1949)] of the dynamics of complex molecules with internal hindered rotation to anomalous diffusion.

Anomalous diffusion of a dipole interacting with its surroundings.

A fractional Fokker-Planck equation based on the continuous time random walk Ansatz is written via the Langevin equations for the dynamics of a dipole interacting with its surroundings, as represented by a cage of dipolar molecules. This equation is solved in the frequency domain using matrix continued fractions, thus yielding the linear dielectric response for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio, and hence the complex susceptibility. The latter comprises a low frequency band with width depending on the anomalous parameter and a far infrared (THz) band with a comb-like structure of peaks. Several physical consequences of the model relevant to anomalous diffusion in the presence of interactions are discussed. The entire calculation may be regarded as an extension of the cage model interpretation of the dynamics of polar molecules to anomalous diffusion, taking into account inertial effects.

Cage model of polar fluids: Finite cage inertia generalization.

The itinerant oscillator model describing rotation of a dipole about a fixed axis inside a cage formed by its surrounding polar molecules is revisited in the context of modeling the dielectric relaxation of a polar fluid via the Langevin equation. The dynamical properties of the model are studied by averaging the Langevin equations describing the complex orientational dynamics of two bodies (molecule-cage) over their realizations in phase space so that the problem reduces to solving a system of three index linear differential-recurrence relations for the statistical moments. These are then solved in the frequency domain using matrix continued fractions. The linear dielectric response is then evaluated for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio and along with the usual inertia corrected microwave Debye absorption gives rise to significant far-infrared absorption with a comb-like structure of harmonic peaks. The model may be also regarded as an extension of Budó's [J. Chem. Phys. 17, 686 (1949)] treatment of molecules containing rotating polar groups to include inertial effects.

Anomalous diffusion of molecules with rotating polar groups: The joint role played by inertia and dipole coupling in microwave and far-infrared absorption.

Budó's generalization [A. Budó, J. Chem. Phys. 17, 686 (1949)10.1063/1.1747370] of the Debye rotational diffusion model of dielectric relaxation of polar molecules to an assembly with internal interacting polar groups is extended to inertial anomalous diffusion. Thus, the theory can be applied both in the GHz and the THz regions, accounting for anomalous behavior as well as the necessary return to optical transparency at very high frequencies. The linking of both dispersion regions in a single model including anomalous effects is accomplished via a fractional Fokker-Planck equation in phase space based on the continuous time random walk ansatz. The latter is written via the Langevin equations for the stochastic dynamics of pairs of interacting heavy polar groups embedded in the frame of reference of a particular molecule or molecular dimer rotating about a space-fixed axis. The fractional Fokker-Planck equation is then converted to a three-term matrix differential recurrence equation for the statistical moments. This is solved in the frequency domain for the linear dielectric response using matrix continued fractions. Thus, one has the complex susceptibility χ(ω) for extensive ranges of damping, group dipole moment ratio, and friction. The susceptibility, as inferred from the small oscillation limit, inherently comprises a low frequency (GHz) band with width depending on the anomalous parameter and a far-infrared (THz) or Poley peak of resonant character with a comblike structure of harmonic peaks. This behavior is due to the double transcendental nature of the after-effect function.

Recognition of transposed melodies: a key-distance effect in developmental perspective.

Four experiments examined the possibility of a key-distance effect in a transposition detection task. Subjects heard standard melodies followed by comparison melodies presented in the same key, a musically near key or a musically far key. The task was to recognize comparisons that were exact transpositions of the standards, rejecting nontranspositions. Results suggested a largely invariant key-distance effect with nontransposition comparisons (lures); same- and near-key lures evoked more false alarms than far-key lures. The variables of musical experience, age of subject, and familiarity of melody affected the level of transposition-recognition performance but did not consistently affect the size of the key-distance effect. The results support the psychological reality of key distance and are consistent with both musical and nonmusical-auditory theories of its effects. The key-distance effect was not found with transposition comparisons (targets), a result with implications for the separability of key and interval information in short-term memory for melodies.

The hierarchical nature of perceiving direction of motion in depth from optic flow.

Monocular adaptation to flow fields of optic expansion and contraction juxtaposed on either side of fixation influenced subsequently perceived rotation direction of a figure rotating in depth (kinetic depth effect) about its vertical axis with a normally ambiguous direction. This influence was shown to be asymmetric since adapting to optic expansion produced significantly more aftereffects of translation in depth than did adapting to perceived rotation in depth when viewing a neutral test stimulus. The results are evidence for a hierarchical processing model for the perception of motion in depth from optic flow. Serendipitously, we discovered a new aftereffect from viewing kinetic depth rotation with direction specified by proximity-luminance covariation (PLC). The results and other research are discussed in terms of neural network models with synergistic interactions between levels.

Aging and experience in the recognition of musical transpositions.

The authors examined the effects of age, musical experience, and characteristics of musical stimuli on a melodic short-term memory task in which participants had to recognize whether a tune was an exact transposition of another tune recently presented. Participants were musicians and nonmusicians between ages 18 and 30 or 60 and 80. In 4 experiments, the authors found that age and experience affected different aspects of the task, with experience becoming more influential when interference was provided during the task. Age and experience interacted only weakly, and neither age nor experience influenced the superiority of tonal over atonal materials. Recognition memory for the sequences did not reflect the same pattern of results as the transposition task. The implications of these results for theories of aging, experience, and music cognition are discussed.

Effects of aging and musical experience on the representation of tonal hierarchies.

Two experiments explored the representation of the tonal hierarchy in Western music among older (aged 60 to 80) and younger (aged 15 to 22) musicians and nonmusicians. A probe tone technique was used: 4 notes from the major triad were presented, followed by 1 note chosen from the 12 notes of the chromatic scale. Whereas musicians had a better sense of the tonal hierarchy than nonmusicians, older adults were no worse than younger adults in differentiating the notes according to musical principles. However, older adults were more prone than younger adults to classify the notes by frequency proximity (pitch height) when proximity was made more salient, as were nonmusicians compared with musicians. With notes having ambiguous pitch height, pitch height effects disappeared among older adults but not nonmusicians. Older adults seem to have internalized tonal structure, but they sometimes fail to inhibit less musically relevant information.

Identification of speeded and slowed familiar melodies by younger, middle-aged, and older musicians and nonmusicians.

There is a range of tempos within which listeners can identify familiar tunes (around 0.8 to 6.0 notes/s). Faster and slower tunes are difficult to identify. The authors assessed fast and slow melody-identification thresholds for 80 listeners ages 17-79 years with expertise varying from musically untrained to professional. On fast-to-slow (FS) trials the tune started at a very fast tempo and slowed until the listener identified it. Slow-to-fast (SF) trials started slow and accelerated. Tunes either retained their natural rhythms or were stylized isochronous versions. Increased expertise led to better performance for both FS and SF thresholds (r = .45). Performance declined uniformly across the 62-year age range in the FS condition (r = .27). SF performance was unaffected by age. Although early encoding processes may slow with age, expertise has a greater effect. Musical expertise involves perceptual learning with melodies at a wide range of tempos.

Tonal expectations influence pitch perception.

In this study, we investigated the influence of tonal relatedness on pitch perception in melodies. Tonal expectations for target tones were manipulated in melodic contexts while controlling sensory expectations, thus allowing us to assess specifically the influence oftonal expectations on pitch perception. Three experimentsprovided converging evidence that tonal relatedness modulates pitch perception in nonmusician listeners. Experiment 1 showed, with a rating task, the influence of the tonal relatedness of a target tone on listeners' judgments of tuning/mistuning. Experiment 2 showed, with a priming task, that pitch processing of in-tune tones was faster for tonally related targets than for less related targets. Experiment 3 showed, with a comparison task, that discrimination performance for small mistunings was better when the to-be-compared tones were tonally related to the melodic context. Findings are discussed in relation to psychoacoustic research on contextual pitch perception and to studies showing facilitation of early processing steps via knowledge- and attention-related processes.

Tonal strength and melody recognition after long and short delays.

In a continuous-running-memory task, subjects heard novel seven-note melodies that were tested after delays of 11 sec (empty) or 39 sec (filled). Test items were transposed to new pitch levels (to moderately distant keys in the musical sense) and included exact transpositions (targets), same-contour lures with altered pitch intervals, and new-contour lures. Melodies differed in tonal strength (degree of conformity to a musical key) and were tonally strong, tonally weak, or atonal. False alarms to same-contour lures decreased over the longer delay period, but only for tonal stimuli. In agreement with previous studies, discrimination of detailed changes in pitch intervals improved with increased delay, whereas discrimination of more global contour information declined, again only for tonal stimuli. These results suggest that poor short-delay performance in rejecting same-contour lures arises from confusion that is based on the similarity of tonality between standard stimuli and lures. If a test item has the same contour and a similar tonality to a just-presented item, subjects tend to accept it. After a delay filled with melodies in other tonalities, the salience of key information recedes, and subjects base their judgments on more detailed pattern information (namely, exact pitch intervals). The fact that tonality affects judgments of melodic contour indicates that contour is not an entirely separable feature of melodies but rather that a melody with its contour constitutes an integrated perceptual whole.

The time course of recognition of novel melodies.

Seven experiments explored the time course of recognition of brief novel melodies. In a continuous-running-memory task, subjects recognized melodic transpositions following delays up to 2.0 min. The delays were either empty or filled with other melodies. Test items included exact transpositions (T), same-contour lures (SC) with altered pitch intervals, and different-contour lures (DC); DCs differed from Ts in the pattern of ups and downs of pitch. With this design, we assessed subjects' discrimination of detailed changes in pitch intervals (T/SC discrimination) as well as their discrimination of contour changes (T/DC). We used both artificial and "real" melodies. Artificial melodies differed in conformity to a musical key, being tonal or atonal. After empty delays, T/DC discrimination was superior to T/SC discrimination. Surprisingly, after filled delays, T/SC discrimination was superior to T/DC. When only filled delays were tested, T/SC discrimination did not decline over the longest delays. T/DC performance declined more than did T/SC performance across both empty and filled delays. Tonality was an important factor only for T/SC discrimination after filled delays. T/DC performance was better with rhythmically intact folk melodies than with artificial isochronous melodies. Although T/SC performance improved over filled delays, it did not overtake T/DC performance. These results suggest that (1) contour and pitch-interval information make different contributions to recognition, with contour dominating performance after brief empty delays and pitch intervals dominating after longer filled delays; (2) a coherent tonality facilitates the encoding of pitch-interval patterns of melodies; and (3) the rich melodic-rhythmic contours of real melodies facilitate T/DC discrimination. These results are discussed in terms of automatic and controlled processing of melodic information.

Recognition of familiar and unfamiliar melodies in normal aging and Alzheimer's disease.

We tested normal young and elderly adults and elderly Alzheimer's disease (AD) patients on recognition memory for tunes. In Experiment 1, AD patients and age-matched controls received a study list and an old/new recognition test of highly familiar, traditional tunes, followed by a study list and test of novel tunes. The controls performed better than did the AD patients. The controls showed the "mirror effect" of increased hits and reduced false alarms for traditional versus novel tunes, whereas the patients false-alarmed as often to traditional tunes as to novel tunes. Experiment 2 compared young adults and healthy elderly persons using a similar design. Performance was lower in the elderly group, but both younger and older subjects showed the mirror effect. Experiment 3 produced confusion between preexperimental familiarity and intraexperimental familiarity by mixing traditional and novel tunes in the study lists and tests. Here, the subjects in both age groups resembled the patients of Experiment 1 in failing to show the mirror effect. Older subjects again performed more poorly, and they differed qualitatively from younger subjects in setting stricter criteria for more nameable tunes. Distinguishing different sources of global familiarity is a factor in tune recognition, and the data suggest that this type of source monitoring is impaired in AD and involves different strategies in younger and older adults.

Benign giant adrenal cyst and parathyroid adenoma: a case report.

An unusual case of a benign adrenal cyst and a parathyroid adenoma occurring in a 59-year-old man with hypercalcemia is reported. Excretory urography, ultrasound, renal aortography, computerized axial tomography and selective thyroid venous sampling were used to establish a diagnosis. Left adrenalectomy was done because of a suspicion of malignancy, which was followed by excision of a retrolaryngeal parathyroid adenoma.