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This chapter gives an introduction to the distinctive structural features of aperiodic crystals, including incommensurately modulated crystals, composite crystals, and quasicrystals. Atomic structures are discussed in relation to the structures of periodic crystals, while it is shown that translational symmetry is lost. Diffraction by incommensurately modulated structures is shown to give rise to Bragg reflections that can be indexed by four or more integers. The modulation wave vector is introduced as the vector defining the periodicity of the modulation functions, as well as being the reciprocal vector employed in the indexing of Bragg reflections.

This chapter provides an overview of the methods of structure solution of incommensurately modulated crystals and composite crystals. Assuming the periodic average structure is known, it is shown that modulation functions can often be determined by trial and error, employing structure refinements starting with randomly chosen but small values for the structural parameters. The presentation of systematic methods of structure determination includes Patterson function methods, direct methods, and the method of charge flipping.

This chapter considers the properties of the generalized electron density as it can be displayed in superspace. Fourier maps and difference Fourier maps allow the visual inspection of various structural features, including the positions of the atoms, the shapes and amplitudes of modulation functions, and possible advanced properties of the modulations, like modulation of the anisotropic displacement parameters (ADPs) and the presence anharmonic displacements. The maximum entropy method (MEM) is introduced as a model-independent method that provides a more accurate picture of the electron density than is provided by Fourier maps. The MEM can be used to determine the precise shapes of modulation functions and to study the electron density in the chemical bond.

This chapter develops the relation between crystal structures of aperiodic crystals and superstructures. Superstructures are described as commensurately modulated structures, and it is shown that superspace methods can be applied to this particular kind of periodic crystals. Alternatively, superstructures are obtained as the commensurate approximation to incommensurately modulated crystals and composite crystals. Relations are derived between modulation functions and superspace groups of the modulated-structure description, and atomic coordinates and supercell space groups of the superstructure description.

Hearing loss implies more than just a loss of sensitivity as expressed in the audiogram. Yet, this is not always appreciated. As in aging, auditory pathology that is not reflected in increased hearing thresholds may add to temporal processing deficits. Animal experiments have shown that non-traumatic noise exposure at a young age may cause degeneration of auditory nerve fibers in old age. The pathology reflects changes in inner hair cell ribbon synapses as a result of lifelong exposure to non-traumatic noise. These fibers are likely the ones with high threshold and their loss therefore is not reflected in the audiogram. Animal auditory cortex studies have also shown that noise-induced hearing loss leads to deterioration in gap detection and voice-onset-time representation. Changes also occurred in the temporal modulation transfer functions, namely a slight reduction in the upper repetition rate limit of coding for click trains. In contrast, and surprisingly a considerable enhancement in the upper limit of modulation frequency representation as well as the strength of the tMTFs for amplitude modulated noise. The latter can be explained by a homeostatic increase in central synaptic efficacy as a result of the hearing loss. However, even in auditory nerve fibers the strength of envelope coding was enhanced after noise exposure. In human imaging studies it was found that even moderate declines in peripheral auditory acuity may lead to a systematic downregulation of neural activity during the processing of higher-level aspects of speech, and may also contribute to loss of gray matter volume in primary auditory cortex.

Temporal auditory processing disorders are typically arrived at by comparison with age-match control groups. Both during maturation and aging temporal processing capabilities change. Roughly speaking a mature auditory system starts around age 18, whereas temporal processing declines have already been reported for middle age, even in the absence of loss in hearing sensitivity. One of the evidences for the late maturation comes from auditory evoked potentials; the N1 component only emerges around age 9 and the N2 component is not yet mature at age 16. It is undeniable that cognitive aspects, including attention and memory, also affect performance in both children and the elderly. Nevertheless there is ample evidence from animal experiments that central auditory processing deficits, even after hearing sensitivity is taken info account, likely underlie the observed decrease in perceptual functions in the elderly. Characteristic of temporal processing deficits, gap detection and temporal modulation transfer functions are affected in aging animals and humans. Elderly listeners show gap thresholds that are about twice as large as those reported for young listeners. Electrophysiological evidence in humans can already be obtained at the level of the brainstem, but also in the responses to 40 Hz amplitude modulated stimuli, and the long latency cortical responses to gap-in-noise stimuli. Comparing mismatch negativity responses with behavioral gap detection suggests that processing of basic temporal stimulus features in elderly subjects is considerably more reduced for passive listening (as indicated by MMN), than when attention is directed to the task (as indicated by the psychoacoustic results).

Treating an imaging system as a linear system and use llinear system properties to d iscuss both coherent and incoherent imaging. Use a one dimensional pin hole camera to study the theory of incoherent imaging. Two different criteria, Rayleigh and Sparrow, are used to define the resolution limits of the camera. From the simple theory define the optical transfer function and the modulation transfer function as appropriate characterizations of complex imaging systems. A review of the human imaging system emphasizes tits idfferences with man made cameras. Coherent imaging is based on Abbe’s theory of microscopy. A simple 4f imaging system can be used to understand how spatial resolution is limited by the optical aperture and by controlling the aperture, we can enhance the edges of an image or remove noise intensity noise on a plane wave. Apodizing the aperture allows astronomers to locate planents orbiting distant stars.

Auditory neuropathy occurs frequently and is responsible for approximately 8% of newly diagnosed cases of hearing loss in children per year. Hyperbilirubinemia and hypoxia represent major risk factors, whereas generalized neuropathic disorders, or a genetic substrate involving the otoferlin (OTOF) gene, are responsible for the phenotype of auditory neuropathy in certain cases. Auditory nerve myelinopathy and/or desynchrony of neural discharges, and disordered function of the inner hair cell ribbon synapses are the most probable underlying pathophysiological mechanisms. There is no or very little hearing threshold loss. The disrupted neural activity did not affect intensity-related perception, however, significantly impaired timing-related perception, such as pitch discrimination at low frequencies, temporal integration, gap detection, temporal modulation detection, backward and forward masking, signal detection in noise, binaural beats, and sound localization using interaural time differences. There was a close association between gap detection thresholds measured psychoacoustically and electrophysiologically (N1 and P2 long-latency components) in auditory neuropathy subjects. Whereas auditory neuropathy is a purely peripheral disorder, multiple sclerosis (MS) is an inflammatory disease in which the fatty myelin sheaths around the axons of the central nervous system are damaged, leading to demyelination and scarring as well as a broad spectrum of signs and symptoms. MS affects the ability of nerve cells in the brain and spinal cord to communicate with each other effectively. Audiograms are generally normal for age. Abnormal auditory brainstem responses showed prolonged inter-wave latencies reflecting conduction delays along the brainstem. Reduced mismatch negativity and white matter changes correlate with cognitive deficits.

Accurate representation of the dynamic aspects of sound in the auditory nervous system are crucial in understanding speech, enjoying music, being able to localize a sound source, and make it possible to communicate in noisy environments. Stationary sounds are represented in the auditory system in a way that onsets and offsets produce more activity than the parts in between. This is called perstimulatory adaptation of firing rate. The mechanisms underlying it also play a role in the masking effects of other sounds on the ones of interest, and determine our sensitivity to periodically time varying sounds. Stimulus-specific adaptation also may be largely determined by this mechanism. The first five chapters in the book describe the role of adaptation mechanisms from auditory nerve to auditory cortex. Chapter 6 describes a simple phenomenological model that links together perstimulatory adaptation and recovery therefrom with forward masking and temporal modulation transfer functions. Neural synchronization and its role in brain rhythms and perception are elucidated. Based on this, the role of temporal processing in periodicity pitch, sound localization, stream segregation and scene analysis are reviewed. Temporal processing ability of the nervous system is affected by maturation as well as aging, and on top of that by hearing loss. Less clear is the role of temporal processing deficits in dyslexia, specific language impairment and auditory processing disorders, potentially because of the confounding role of maturation and aging. Various neurological disorders such as auditory neuropathy, multiple sclerosis, schizophrenia, autism and epilepsy present itself with temporal processing deficits. These deficits are often multimodal in nature and this is reflected on in the final chapter.

Cochlear adaptation is postulated to arise in the haircell-first auditory neuron junction due to steady-state reactions between transmitter quanta and receptor sites, thus forming transmitter-receptor complexes that are destroyed enzymatically. The striking resemblance between this mechanism and the occupation and liberation of lines in telephone exchanges led us to apply a well-established stochastic theory for the latter to the adaptation phenomena in the peripheral hearing organ. The theory is evaluated by comparison with experimental data from forward-masking experiments using the compound action potential as a sensor and also with single-nerve fiber data from the literature. The model is with minor adaptations also applicable to gap detection and temporal modulation transfer functions (tMTF) in primary auditory cortex. In both cases one needs to introduce the effects of after-hyperpolarization and non-linearity in the spike generation mechanism, to explain the abrupt decrease as function of the early gap duration or number of modulation periods in the tMTF.

Synchronization of oscillatory responses in the beta- and gamma-band is involved in a variety of cognitive functions, such as perceptual grouping, attention-dependent stimulus selection, working memory, and perceptual awareness. Here, we review evidence that autism (ASD), schizophrenia and epilepsy show temporal processing deficits that are associated with abnormal neural synchronization. There are close correlations between abnormalities in neuronal synchronization and cognitive dysfunctions, emphasizing the importance of temporal coordination. ASD is a developmental disability that affects social behavior and language acquisition. Current theories and experimental data converge on the notion that dysfunctional integrative mechanisms in autism may be the result of reduced neural synchronization. There is also consistent evidence that neural synchrony in the β‎- and γ‎-frequency ranges is impaired in patients with schizophrenia. The cognitive abnormalities in schizophrenic patients include fragmented perception, erroneous binding of features, deficits in attention, impaired working memory, delusions, and hallucinations. Synchronization of oscillatory activity in the beta- and gamma-band frequency range is associated with cognitive functions that are disturbed in schizophrenia patients. Epilepsy is a common and diverse set of chronic neurological disorders characterized by seizures. Seizures may not only be a consequence of heightened neuronal excitability such as results from an imbalance between excitatory and inhibitory mechanisms. Alterations of the mechanisms that support the oscillatory patterning and the synchronization of neuronal activity appear to be equally important. Both the reduced synchronization preceding some forms of epileptic activity and the enhanced synchronization associated with seizures proper go along with the disturbance of cognitive functions. There are suggestive genetic links between schizophrenia and epilepsy, between schizophrenia and dyslexia via magnocellular deficits, and between autism and SLI through impaired language.