Chaos in music: historical developments and applications to music theory and composition

The Doctoral Dissertation submitted by Jonathan R. Salter, in partial fulfillment of the requirements for the degree Doctor of Musical Arts at the University of North Carolina at Greensboro comprises the following: 1. Doctoral Recital I, March 24, 2007: Chausson, Andante et Allegro; Tomasi, Concerto for Clarinet; Bartok, Contrasts; Fitkin, Gate. 2. Doctoral Recital II, December 2, 2007: Benjamin, Le Tombeau de Ravel ; Mandat, Folk Songs; Bolcom, Concerto for Clarinet; Kovacs, Sholem-alekhem, rov Fiedman! 3. Doctoral Recital III, May 3, 2009: Kalliwoda, Morceau du Salon; Shostakovich, Sonata, op. 94 (transcription by Kennan); Tailleferre, Arabesque; Schoen eld, Trio for Clarinet, Violin, and Piano. 4. Dissertation Document: Chaos in Music: Historical Developments and Applications to Music Theory and Composition. Chaos theory, the study of nonlinear dynamical systems, has proven useful in a wide-range of applications to scienti c study. Here, I analyze the application of these systems in the analysis and creation of music, and take a historical view of the musical developments of the 20th century and how they relate to similar developments in science. I analyze several 20th century works through the lens of chaos theory, and discuss how acoustical issues and our interpretation of music relate to the theory. The application of nonlinear functions to aspects of music including organization, acoustics and harmonics, and the role of chance procedures is also examined toward suggesting future possibilities in incorporating chaos theory in the act of composition. Original compositions are included, in both sheet music and recorded form

Simulation of Abnormal/Normal Brain States Using the KIV Model

Recent studies have focused on the phenomena of abnormal electrical brain activity which may transition into a debilitating seizure state through the entrainment of large populations of neurons.Starting from the initial epileptogenisis of a small population of abnormally firing neurons, to the mobilization of mesoscopic neuron populations behaving in a synchronous manner, a model has been formulated that captures the initial epileptogenisis to the semi-periodic entrainment of distant neuron populations.The normal non-linear dynamic signal captured through EEG, moves into a semi-periodic state, which can be quantified as the seizure state.Capturing the asynchronous/synchronous behavior of the normal/pathological brain state will be discussed.This model will also demonstrate how electrical stimulation applied to the limbic system restores the seizure state of the brain back to its original normal condition.Human brain states are modeled using a biologically inspired neural network, the KIV model.The KIV model exhibits the noisy, chaotic attributes found in the limbic system of brains of higher forms of organisms, and in its normal basal state, represents the homogeneous activity of millions of neuron activations.The KIV can exhibit the ’unbalanced state’ of neural activity, whereas when a small cluster of abnormal firing neurons starts to exhibit periodic neural firings that eventually entrain all the neurons within the limbic system, the network has moved into the ‘seizure’ state.These attributes have been found in human EEG recordings and have been duplicated in this model of the brain.The discussion in this dissertation covers the attributes found in human EEG data and models these attributes.Additionally, this model proposes a methodology to restore the modeled ‘seizure’ state, and by doing so, proposes a manner for external electrical titration to restore the abnormal seizure state back to a normal chaotic EEG signal state.Quantification measurements of normal, abnormal, and restoration to normal brain states will be exhibited using the following approaches:Analysis of human EEG dataQuantification measurements of brain states.Development of models of the different brain states, i.e. fit parameters of the model on individual personal data/history.Implementation of quantitative measurements on “restored” simulated seizure state

Order out of Randomness : Self-Organization Processes in Astrophysics

Self-organization is a property of dissipative nonlinear processes that are governed by an internal driver and a positive feedback mechanism, which creates regular geometric and/or temporal patterns and decreases the entropy, in contrast to random processes. Here we investigate for the first time a comprehensive number of 16 self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous {\sl order out of chaos}, during the evolution from an initially disordered system to an ordered stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical resonances, or gyromagnetic resonances. The internal driver can be gravity, rotation, thermal pressure, or acceleration of nonthermal particles, while the positive feedback mechanism is often an instability, such as the magneto-rotational instability, the Rayleigh-B\'enard convection instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or loss-cone instability. Physical models of astrophysical self-organization processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra equation systems.Comment: 61 pages, 38 Figure

Decentralising resource management in operating systems

This dissertation explores operating system mechanisms to allow resource-aware applications to be involved in the process of managing resources under the premise that these applications (1) potentially have some (implicit) notion of their future resource demands and (2) can adapt their resource demands. The general idea is to provide feedback to resource-aware applications so that they can proactively participate in the management of resources. This approach has the benefit that resource management policies can be removed from central entities and the operating system has only to provide mechanism. Furthermore, in contrast to centralised approaches, application specific features can be more easily exploited. To achieve this aim, I propose to deploy a microeconomic theory, namely congestion or shadow pricing, which has recently received attention for managing congestion in communication networks. Applications are charged based on the potential "damage" they cause to other consumers by using resources. Consumers interpret these congestion charges as feedback signals which they use to adjust their resource consumption. It can be shown theoretically that such a system with consumers merely acting in their own self-interest will converge to a social optimum. This dissertation focuses on the operating system mechanisms required to decentralise resource management this way. In particular it identifies four mechanisms: pricing & charging, credit accounting, resource usage accounting, and multiplexing. While the latter two are mechanisms generally required for the accurate management of resources, pricing & charging and credit accounting present novel mechanisms. It is argued that congestion prices are the correct economic model in this context and provide appropriate feedback to applications. The credit accounting mechanism is necessary to ensure the overall stability of the system by assigning value to credits

Discrimination and control in stochastic neuron models

Major topics of great interest in neuroscience involve understanding the brain function in stimuli coding, perceptive discrimination, and movement control through neuronal activities. Many researchers are designing biophysical and psychological experiments to study the activities of neurons in the presence of various stimuli. People have also been trying to link the neural responses to human perceptual and behavioral level. In addition, mathematical models and neural networks have been developed to investigate how neurons respond and communicate with each other. In this thesis, my aim is to understand how the central nervous system performs discrimination tasks and achieves precise control of movement, using noisy neural signals. I have studied, both through experimental and modelling approaches, how neurons respond to external stimuli. I worked in three aspects in details. The first is the neuronal coding mechanism of input stimuli with different temporal frequencies. Intracellular recordings of single neurons were performed with patch-clamp techniques to study the neural activities in rats somatosensory cortices in vitro, and the simplest possible neural model—integrate-and-fire model—was used to simulate the observations. The results obtained from the simulation were very consistent with that in the experiments. Another focus of this work is the link between the psychophysical response and its simultaneous neural discharges. I derived that under a widely accepted psychophysical law (Weber’s law), the neural activities were less variable than a Poisson process (which is often used to describe the neuron spiking process). My work shows how psychophysical behaviour reflects intrinsic neural activities quantitatively. Finally, the focus is on the control of movements by neural signals. A generalized approach to solve optimal movement control problems is proposed in my work, where pulses are used as neural signals to achieve a precise control. The simulation results clearly illustrate the advantage of this generalized control. In this thesis, I have raised novel, insightful yet simple approaches to study and explain the underlying mechanism behind the complexity of neural system, from three examples on sensory discrimination and neural movement control

Predicting multibody assembly of proteins

textThis thesis addresses the multi-body assembly (MBA) problem in the context of protein assemblies. [...] In this thesis, we chose the protein assembly domain because accurate and reliable computational modeling, simulation and prediction of such assemblies would clearly accelerate discoveries in understanding of the complexities of metabolic pathways, identifying the molecular basis for normal health and diseases, and in the designing of new drugs and other therapeutics. [...] [We developed] F²Dock (Fast Fourier Docking) which includes a multi-term function which includes both a statistical thermodynamic approximation of molecular free energy as well as several of knowledge-based terms. Parameters of the scoring model were learned based on a large set of positive/negative examples, and when tested on 176 protein complexes of various types, showed excellent accuracy in ranking correct configurations higher (F² Dock ranks the correcti solution as the top ranked one in 22/176 cases, which is better than other unsupervised prediction software on the same benchmark). Most of the protein-protein interaction scoring terms can be expressed as integrals over the occupied volume, boundary, or a set of discrete points (atom locations), of distance dependent decaying kernels. We developed a dynamic adaptive grid (DAG) data structure which computes smooth surface and volumetric representations of a protein complex in O(m log m) time, where m is the number of atoms assuming that the smallest feature size h is [theta](r[subscript max]) where r[subscript max] is the radius of the largest atom; updates in O(log m) time; and uses O(m)memory. We also developed the dynamic packing grids (DPG) data structure which supports quasi-constant time updates (O(log w)) and spherical neighborhood queries (O(log log w)), where w is the word-size in the RAM. DPG and DAG together results in O(k) time approximation of scoring terms where k << m is the size of the contact region between proteins. [...] [W]e consider the symmetric spherical shell assembly case, where multiple copies of identical proteins tile the surface of a sphere. Though this is a restricted subclass of MBA, it is an important one since it would accelerate development of drugs and antibodies to prevent viruses from forming capsids, which have such spherical symmetry in nature. We proved that it is possible to characterize the space of possible symmetric spherical layouts using a small number of representative local arrangements (called tiles), and their global configurations (tiling). We further show that the tilings, and the mapping of proteins to tilings on arbitrary sized shells is parameterized by 3 discrete parameters and 6 continuous degrees of freedom; and the 3 discrete DOF can be restricted to a constant number of cases if the size of the shell is known (in terms of the number of protein n). We also consider the case where a coarse model of the whole complex of proteins are available. We show that even when such coarse models do not show atomic positions, they can be sufficient to identify a general location for each protein and its neighbors, and thereby restricts the configurational space. We developed an iterative refinement search protocol that leverages such multi-resolution structural data to predict accurate high resolution model of protein complexes, and successfully applied the protocol to model gp120, a protein on the spike of HIV and currently the most feasible target for anti-HIV drug design.Computer Science

Discrimination and control in stochastic neuron models

Major topics of great interest in neuroscience involve understanding the brain function in stimuli coding, perceptive discrimination, and movement control through neuronal activities. Many researchers are designing biophysical and psychological experiments to study the activities of neurons in the presence of various stimuli. People have also been trying to link the neural responses to human perceptual and behavioral level. In addition, mathematical models and neural networks have been developed to investigate how neurons respond and communicate with each other. In this thesis, my aim is to understand how the central nervous system performs discrimination tasks and achieves precise control of movement, using noisy neural signals. I have studied, both through experimental and modelling approaches, how neurons respond to external stimuli. I worked in three aspects in details. The first is the neuronal coding mechanism of input stimuli with different temporal frequencies. Intracellular recordings of single neurons were performed with patch-clamp techniques to study the neural activities in rats somatosensory cortices in vitro, and the simplest possible neural model—integrate-and-fire model—was used to simulate the observations. The results obtained from the simulation were very consistent with that in the experiments. Another focus of this work is the link between the psychophysical response and its simultaneous neural discharges. I derived that under a widely accepted psychophysical law (Weber’s law), the neural activities were less variable than a Poisson process (which is often used to describe the neuron spiking process). My work shows how psychophysical behaviour reflects intrinsic neural activities quantitatively. Finally, the focus is on the control of movements by neural signals. A generalized approach to solve optimal movement control problems is proposed in my work, where pulses are used as neural signals to achieve a precise control. The simulation results clearly illustrate the advantage of this generalized control. In this thesis, I have raised novel, insightful yet simple approaches to study and explain the underlying mechanism behind the complexity of neural system, from three examples on sensory discrimination and neural movement control.EThOS - Electronic Theses Online ServiceUniversity of Warwick (UoW)GBUnited Kingdo

Tailoring the structure-function relationship in wheat gluten

Gluten proteins ranging in size from 30 000 to several million daltons form one of the largest and most complex polymers in nature. The giant molecular nature and intricate network of the over 100 types of proteins in gluten make structural studies rather challenging. This thesis examines the molecular crosslinking and structural properties of variously sourced gluten and its gliadin and glutenin protein fractions, both as unprocessed proteins and in films and foams. Protein modification through chemical additives, separation procedure and genotype (G) and environmental (E) interactions had an impact on protein polymerization, nano-structure morphology, secondary structures and the mechanical properties of films. The extent of denaturation in the starting material for film formation was of relevance for the development of specific nano-scale morphology and improved mechanical properties of films. When molded into films, non-aggregated starting material such as gliadin with additives and mildly separated gluten indicated both hydrogen- and disulfide-bonded protein network, with some non-reducible covalent crosslinks. These films also showed bi-structural morphology at nano scale. The gliadin films revealed hexagonal structures and additional not previously observed structural units. The films from mildly separated gluten also showed hexagonal and lamellar structural morphology. The films from glutenin and industrially sourced gluten proteins showed a high content of non-reducible covalent crosslinks and unorganized morphology at nano scale. The G and E interactions were associated with strong and weak gluten, resulting in films with various structural and mechanical properties. The mechanical properties of films were found to be influenced by protein structure development. Structural attributes such as relatively high number of disulfide crosslinks compared with non-reducible crosslinks, high β-sheet content and specific nano-scale morphology also led to high mechanical performance of films

Data-Driven Classification of Spectral Profiles Reveals Brain Region-Specific Plasticity in Blindness

Congenital blindness has been shown to result in behavioral adaptation and neuronal reorganization, but the underlying neuronal mechanisms are largely unknown. Brain rhythms are characteristic for anatomically defined brain regions and provide a putative mechanistic link to cognitive processes. In a novel approach, using magnetoencephalography resting state data of congenitally blind and sighted humans, deprivation-related changes in spectral profiles were mapped to the cortex using clustering and classification procedures. Altered spectral profiles in visual areas suggest changes in visual alpha-gamma band inhibitory-excitatory circuits. Remarkably, spectral profiles were also altered in auditory and right frontal areas showing increased power in theta-to-beta frequency bands in blind compared with sighted individuals, possibly related to adaptive auditory and higher cognitive processing. Moreover, occipital alpha correlated with microstructural white matter properties extending bilaterally across posterior parts of the brain. We provide evidence that visual deprivation selectively modulates spectral profiles, possibly reflecting structural and functional adaptation

Cortico-muscular coherence in sensorimotor synchronisation

This thesis sets out to investigate the neuro-muscular control mechanisms underlying the ubiquitous phenomenon of sensorimotor synchronisation (SMS). SMS is the coordination of movement to external rhythms, and is commonly observed in everyday life. A large body of research addresses the processes underlying SMS at the levels of behaviour and brain. Comparatively, little is known about the coupling between neural and behavioural processes, i.e. neuro-muscular processes. Here, the neuro-muscular processes underlying SMS were investigated in the form of cortico-muscular coherence measured based on Electroencephalography (EEG) and Electromyography (EMG) recorded in human healthy participants. These neuro-muscular processes were investigated at three levels of engagement: passive listening and observation of rhythms in the environment, imagined SMS, and executed SMS, which resulted in the testing of three hypotheses: (i) Rhythms in the environment, such as music, spontaneously modulate cortico-muscular coupling, (ii) Movement intention modulates cortico-muscular coupling, and (iii) Cortico-muscular coupling is dynamically modulated during SMS time-locked to the stimulus rhythm. These three hypotheses were tested through two studies that used Electroencephalography (EEG) and Electromyography (EMG) recordings to measure Cortico-muscular coherence (CMC). First, CMC was tested during passive music listening, to test whether temporal and spectral properties of music stimuli known to induce groove, i.e., the subjective experience of wanting to move, can spontaneously modulate the overall strength of the communication between the brain and the muscles. Second, imagined and executed movement synchronisation was used to investigate the role of movement intention and dynamics on CMC. The two studies indicate that both top-down, and somatosensory and/or proprioceptive processes modulate CMC during SMS tasks. Although CMC dynamics might be linked to movement dynamics, no direct correlation between movement performance and CMC was found. Furthermore, purely passive auditory or visual rhythmic stimulation did not affect CMC. Together, these findings thus indicate that movement intention and active engagement with rhythms in the environment might be critical in modulating CMC. Further investigations of the mechanisms and function of CMC are necessary, as they could have important implications for clinical and elderly populations, as well as athletes, where optimisation of motor control is necessary to compensate for impaired movement or to achieve elite performance