Recent Applications in Graph Theory

Graph theory, being a rigorously investigated field of combinatorial mathematics, is adopted by a wide variety of disciplines addressing a plethora of real-world applications. Advances in graph algorithms and software implementations have made graph theory accessible to a larger community of interest. Ever-increasing interest in machine learning and model deployments for network data demands a coherent selection of topics rewarding a fresh, up-to-date summary of the theory and fruitful applications to probe further. This volume is a small yet unique contribution to graph theory applications and modeling with graphs. The subjects discussed include information hiding using graphs, dynamic graph-based systems to model and control cyber-physical systems, graph reconstruction, average distance neighborhood graphs, and pure and mixed-integer linear programming formulations to cluster networks

Brain-Computer Interface

Brain-computer interfacing (BCI) with the use of advanced artificial intelligence identification is a rapidly growing new technology that allows a silently commanding brain to manipulate devices ranging from smartphones to advanced articulated robotic arms when physical control is not possible. BCI can be viewed as a collaboration between the brain and a device via the direct passage of electrical signals from neurons to an external system. The book provides a comprehensive summary of conventional and novel methods for processing brain signals. The chapters cover a range of topics including noninvasive and invasive signal acquisition, signal processing methods, deep learning approaches, and implementation of BCI in experimental problems

Analysis of the structure of time-frequency information in electromagnetic brain signals

This thesis encompasses methodological developments and experimental work aimed at revealing information contained in time, frequency, and time–frequency representations of electromagnetic, specifically magnetoencephalographic, brain signals. The work can be divided into six endeavors. First, it was shown that sound slopes increasing in intensity from undetectable to audible elicit event-related responses (ERRs) that predict behavioral sound detection. This provides an opportunity to use non-invasive brain measures in hearing assessment. Second, the actively debated generation mechanism of ERRs was examined using novel analysis techniques, which showed that auditory stimulation did not result in phase reorganization of ongoing neural oscillations, and that processes additive to the oscillations accounted for the generation of ERRs. Third, the prerequisites for the use of continuous wavelet transform in the interrogation of event-related brain processes were established. Subsequently, it was found that auditory stimulation resulted in an intermittent dampening of ongoing oscillations. Fourth, information on the time–frequency structure of ERRs was used to reveal that, depending on measurement condition, amplitude differences in averaged ERRs were due to changes in temporal alignment or in amplitudes of the single-trial ERRs. Fifth, a method that exploits mutual information of spectral estimates obtained with several window lengths was introduced. It allows the removal of frequency-dependent noise slopes and the accentuation of spectral peaks. Finally, a two-dimensional statistical data representation was developed, wherein all frequency components of a signal are made directly comparable according to spectral distribution of their envelope modulations by using the fractal property of the wavelet transform. This representation reveals noise buried processes and describes their envelope behavior. These examinations provide for two general conjectures. The stability of structures, or the level of stationarity, in a signal determines the appropriate analysis method and can be used as a measure to reveal processes that may not be observable with other available analysis approaches. The results also indicate that transient neural activity, reflected in ERRs, is a viable means of representing information in the human brain.reviewe

Change blindness: eradication of gestalt strategies

Arrays of eight, texture-defined rectangles were used as stimuli in a one-shot change blindness (CB) task where there was a 50% chance that one rectangle would change orientation between two successive presentations separated by an interval. CB was eliminated by cueing the target rectangle in the first stimulus, reduced by cueing in the interval and unaffected by cueing in the second presentation. This supports the idea that a representation was formed that persisted through the interval before being 'overwritten' by the second presentation (Landman et al, 2003 Vision Research 43149–164]. Another possibility is that participants used some kind of grouping or Gestalt strategy. To test this we changed the spatial position of the rectangles in the second presentation by shifting them along imaginary spokes (by ±1 degree) emanating from the central fixation point. There was no significant difference seen in performance between this and the standard task [F(1,4)=2.565, p=0.185]. This may suggest two things: (i) Gestalt grouping is not used as a strategy in these tasks, and (ii) it gives further weight to the argument that objects may be stored and retrieved from a pre-attentional store during this task

Statistical Inference in Auditory Perception

The human auditory system effortlessly parses complex sensory inputs despite the ever-present randomness and uncertainty in real-world scenes. To achieve this, the brain tracks sounds as they evolve in time, collecting contextual information to construct an internal model of the external world for predicting future events. Previous work has shown the brain is sensitive to many predictable (and often complex) patterns in sequential sounds. However, real-world environments exhibit a broader spectrum of predictability, and moreover, the level of predictability is constantly in flux. How does the brain build robust internal representations of such stochastic and dynamic acoustic environments? This question is addressed through the lens of a computational model based in statistical inference. Embodying theories from Bayesian perception and predictive coding, the model posits the brain collects statistical estimates from sounds and maintains multiple hypotheses for the degree of context to include in predictive processes. As a potential computational solution for perception of complex and dynamic sounds, this model is used to connect sensory inputs with listeners' responses in a series of human behavioral and electroencephalography (EEG) experiments incorporating uncertainty. Experimental results point toward the underlying sufficient statistics collected by the brain, and the extension of these statistical representations to multiple dimensions is examined along spectral and spatial dimensions. The computational model guides interpretation of behavioral and neural responses, revealing multiplexed responses in the brain corresponding to different levels of predictive processing. In addition, the model is used to explain individual differences across listeners highlighted by uncertainty. The proposed computational model was developed based on first principles, and its usefulness is not limited to the experiments presented here. The model was used to replicate a range of previous findings in the literature, unifying them under a single framework. Moving forward, this general and flexible model can be used as a broad-ranging tool for studying the statistical inference processes behind auditory perception, overcoming the need to minimize uncertainty in perceptual experiments and pushing what was previously considered feasible for study in the laboratory towards what is typically encountered in the "messy" environments of everyday listening

From locomotion to dance and back : exploring rhythmic sensorimotor synchronization

Le rythme est un aspect important du mouvement et de la perception de l’environnement. Lorsque l’on danse, la pulsation musicale induit une activité neurale oscillatoire qui permet au système nerveux d’anticiper les évènements musicaux à venir. Le système moteur peut alors s’y synchroniser. Cette thèse développe de nouvelles techniques d’investigation des rythmes neuraux non strictement périodiques, tels que ceux qui régulent le tempo naturellement variable de la marche ou la perception rythmes musicaux. Elle étudie des réponses neurales reflétant la discordance entre ce que le système nerveux anticipe et ce qu’il perçoit, et qui sont nécessaire pour adapter la synchronisation de mouvements à un environnement variable. Elle montre aussi comment l’activité neurale évoquée par un rythme musical complexe est renforcée par les mouvements qui y sont synchronisés. Enfin, elle s’intéresse à ces rythmes neuraux chez des patients ayant des troubles de la marche ou de la conscience.Rhythms are central in human behaviours spanning from locomotion to music performance. In dance, self-sustaining and dynamically adapting neural oscillations entrain to the regular auditory inputs that is the musical beat. This entrainment leads to anticipation of forthcoming sensory events, which in turn allows synchronization of movements to the perceived environment. This dissertation develops novel technical approaches to investigate neural rhythms that are not strictly periodic, such as naturally tempo-varying locomotion movements and rhythms of music. It studies neural responses reflecting the discordance between what the nervous system anticipates and the actual timing of events, and that are critical for synchronizing movements to a changing environment. It also shows how the neural activity elicited by a musical rhythm is shaped by how we move. Finally, it investigates such neural rhythms in patient with gait or consciousness disorders

Modality-specific tracking of attention and sensory statistics in the human electrophysiological spectral exponent

A hallmark of electrophysiological brain activity is its 1/f-like spectrum – power decreases with increasing frequency. The steepness of this ‘roll-off’ is approximated by the spectral exponent, which in invasively recorded neural populations reflects the balance of excitatory to inhibitory neural activity (E:I balance). Here, we first establish that the spectral exponent of non-invasive electroencephalography (EEG) recordings is highly sensitive to general (i.e., anaesthesia-driven) changes in E:I balance. Building on the EEG spectral exponent as a viable marker of E:I, we then demonstrate its sensitivity to the focus of selective attention in an EEG experiment during which participants detected targets in simultaneous audio-visual noise. In addition to these endogenous changes in E:I balance, EEG spectral exponents over auditory and visual sensory cortices also tracked auditory and visual stimulus spectral exponents, respectively. Individuals’ degree of this selective stimulus–brain coupling in spectral exponents predicted behavioural performance. Our results highlight the rich information contained in 1/f-like neural activity, providing a window into diverse neural processes previously thought to be inaccessible in non-invasive human recordings

How musical rhythms entrain the human brain : clarifying the neural mechanisms of sensory-motor entrainment to rhythms

When listening to music, people across cultures tend to spontaneously perceive and move the body along a periodic pulse-like meter. Increasing evidence suggests that this ability is supported by neural mechanisms that selectively amplify periodicities corresponding to the perceived metric pulses. However, the nature of these neural mechanisms, i.e., the endogenous or exogenous factors that may selectively enhance meter periodicities in brain responses to rhythm, remains largely unknown. This question was investigated in a series of studies in which the electroencephalogram (EEG) of healthy participants was recorded while they listened to musical rhythm. From this EEG, selective contrast at meter periodicities in the elicited neural activity was captured using frequency-tagging, a method allowing direct comparison of this contrast between the sensory input, EEG response, biologically-plausible models of auditory subcortical processing, and behavioral output. The results show that the selective amplification of meter periodicities is shaped by a continuously updated combination of factors including sound spectral content, long-term training and recent context, irrespective of attentional focus and beyond auditory subcortical nonlinear processing. Together, these observations demonstrate that perception of rhythm involves a number of processes that transform the sensory input via fixed low-level nonlinearities, but also through flexible mappings shaped by prior experience at different timescales. These higher-level neural mechanisms could represent a neurobiological basis for the remarkable flexibility and stability of meter perception relative to the acoustic input, which is commonly observed within and across individuals. Fundamentally, the current results add to the evidence that evolution has endowed the human brain with an extraordinary capacity to organize, transform, and interact with rhythmic signals, to achieve adaptive behavior in a complex dynamic environment