Quantitative measures of discrimination with application to appointment processes.

Bias and discrimination in appointment processes such as hiring decisions (and analogous selection procedures for performance evaluations, promotions, scholarships, and awards), are quantified statistically via the binomial distribution. These statistical measures are described and an easily used webapp for calculating them is provided. The measures considered include the likelihood that a given number of appointments arose from a fair process and the likelihood that an existing process would give rise to a fair outcome if it were repeated. These methods are illustrated by applying them to sex (including gender) discrimination and racial discrimination in senior appointments in the Australian university sector; both conscious and unconscious biases are included. Significant sex discrimination is found to have existed in the appointments of university chief executives (Vice Chancellors) who were in office in 2018, but with a moderate chance that current processes will yield fair outcomes in the future. However, there is no evidence of strong sex discrimination in the country's eight main research universities for senior appointments (i.e., Faculty Deans and members of their governing Boards or Senates) for those in office as of 2021. However, at the same dates, extreme racial discrimination was implicit in the selection procedures for both Vice Chancellors and senior appointments in all these universities. The University of Sydney's senior appointments were found to have had the most racially biased outcomes among the country's eight main research universities. Significantly, there is negligible statistical likelihood of achieving racially unbiased outcomes in the future in any of the contexts considered, unless the selection procedures are significantly modified.

Method for quantifying arousal and consciousness in healthy states and severe brain injury via EEG-based measures of corticothalamic physiology.

BACKGROUND: Characterization of normal arousal states has been achieved by fitting predictions of corticothalamic neural field theory (NFT) to electroencephalographic (EEG) spectra to yield relevant physiological parameters. NEW METHOD: A prior fitting method is extended to distinguish conscious and unconscious states in healthy and brain injured subjects by identifying additional parameters and clusters in parameter space. RESULTS: Fits of NFT predictions to EEG spectra are used to estimate neurophysiological parameters in healthy and brain injured subjects. Spectra are used from healthy subjects in wake and sleep and from patients with unresponsive wakefulness syndrome, in a minimally conscious state (MCS), and emerged from MCS. Subjects cluster into three groups in parameter space: conscious healthy (wake and REM), sleep, and brain injured. These are distinguished by the difference X-Y between corticocortical (X) and corticothalamic (Y) feedbacks, and by mean neural response rates α and ß to incoming spikes. X-Y tracks consciousness in healthy individuals, with smaller values in wake/REM than sleep, but cannot distinguish between brain injuries. Parameters α and ß differentiate deep sleep from wake/REM and brain injury. COMPARISON WITH EXISTING METHODS: Other methods typically rely on laborious clinical assessment, manual EEG scoring, or evaluation of measures like Φ from integrated information theory, for which no efficient method exists. In contrast, the present method can be automated on a personal computer. CONCLUSION: The method provides a means to quantify consciousness and arousal in healthy and brain injured subjects, but does not distinguish subtypes of brain injury.

Mutual consistency of multiple visual feature maps constrains combined map topology.

The primary visual cortex (V1) is the first cortical area that processes visual information relayed from the thalamus. The topologies permitted in joint ocular dominance (OD), orientation preference (OP), and direction preference (DP) maps in V1 are considered, with the aim of finding a maximally symmetric periodic case that can serve as the basis for perturbations toward natural realizations. It is shown that mutual consistency of the maps selects just two possible such lattice structures, and that one of these is much closer to experiment than the other. This comprises a hexagonal lattice of alternating positive and negative OP singularities, with each unit cell or hypercolumn containing four such singularities, each of which radiates three DP discontinuities that follow OP contours and end at OP singularities of opposite sign. Other DP discontinuities emanate at 90 degrees to the midpoints of the ones that link OP singularities, and cross OP contours perpendicularly. These features explain experimentally observed relationships between DP discontinuities and OP contours, including sudden approximately 90-degree changes of direction in the former.

Spatiotemporal evolution of urban populations and housing: A dynamic utility-driven market-mediated model.

A model of the spatiotemporal evolution of urban areas is developed that simultaneously includes the effects on household utility of geography, population density, income distribution, and household preference for characteristics of dwellings and neighbors. The result is a utility function whose structure is similar to that of the energy of interacting spin systems in external fields. Spatiotemporal housing market evolution then results via transactions driven by increases in utility and changes in numbers of households and dwellings. It is shown that the model successfully predicts formation of monocentric and polycentric urban areas, stratification by wealth, segregation due to preferences for housing or neighbors, and the balance of supply and demand. These results go well beyond those of prior models that each dealt with subsets of these phenomena, and do so within a single, unified framework. Potential generalizations are discussed and further applications are suggested.

Ten rules for effective modeling.

Modeling a natural system such as the brain aims to deepen understanding and to help to explain and link multiple phenomena into a coherent picture. In any specific case, this requires a clear view of the aims of each modeling project, followed by coordinated selection of the model's style and components; theoretical, numerical, and statistical analysis methods; distillation and presentation of results; and resulting well supported conclusions. The ten rules presented here apply to modeling of the brain and other systems and are designed to assist in carrying out integrated modeling with valid and well-supported outcomes that effectively achieve the modeling aims; referees can also use them when assessing the validity of modeling in submitted manuscripts.

Cortical waste clearance in normal and restricted sleep with potential runaway tau buildup in Alzheimer's disease.

Accumulation of waste in cortical tissue and glymphatic waste clearance via extracellular voids partly drives the sleep-wake cycle and modeling has reproduced much of its dynamics. Here, new modeling incorporates higher void volume and clearance in sleep, multiple waste compounds, and clearance obstruction by waste. This model reproduces normal sleep-wake cycles, sleep deprivation effects, and performance decreases under chronic sleep restriction (CSR). Once fitted to calibration data, it successfully predicts dynamics in further experiments on sleep deprivation, intermittent CSR, and recovery after restricted sleep. The results imply a central role for waste products with lifetimes similar to tau protein. Strong tau buildup is predicted if pathologically enhanced production or impaired clearance occur, with runaway buildup above a critical threshold. Predicted tau accumulation has timescales consistent with the development of Alzheimer's disease. The model unifies a wide sweep of phenomena, clarifying the role of glymphatic clearance and targets for interventions against waste buildup.

Generalized neural field theory of cortical plasticity illustrated by an application to the linear phase of ocular dominance column formation in primary visual cortex.

Physiologically based neural field theory (NFT) is extended to encompass cortical plasticity dynamics. An illustrative application is provided which treats the evolution of the connectivity of left- and right-eye visual stimuli to neuronal populations in the primary visual cortex (V1), and the initial, linear phase of formation of approximately one-dimensional (1D) ocular dominance columns (ODCs) that sets their transverse spatial scale. This links V1 activity, structure, and physiology within a single theory that already accounts for a range of other brain activity and connectivity phenomena, thereby enabling ODC formation and many other phenomena to be interrelated and cortical parameters to be constrained across multiple domains. The results accord with experimental ODC widths for realistic cortical parameters and are based directly on a unified description of the neuronal populations involved, their connection strengths, and the neuronal activity they support. Other key results include simple analytic approximations for ODC widths and the parameters of maximum growth rate, constraints on cortical excitatory and inhibitory gains, elucidation of the roles of specific poles of the V1 response function, and the fact that ODCs are not formed when input stimuli are fully correlated between eyes. This work provides a basis for further generalization of NFT to model other plasticity phenomena, thereby linking them to the range multiscale phenomena accounted for by NFT.

Integrals and series related to propagators of neural and haemodynamic waves.

The propagator, or Green function, of a class of neural activity fields and of haemodynamic waves is evaluated exactly. The results enable a number of related integrals to be evaluated, along with series expansions of key results in terms of Bessel functions of the second kind. Connections to other related equations are also noted.

Discrete spectral eigenmode-resonance network of brain dynamics and connectivity.

The problem of finding a compact natural representation of brain dynamics and connectivity is addressed using an expansion in terms of physical spatial eigenmodes and their frequency resonances. It is demonstrated that this discrete expansion via the system transfer function enables linear and nonlinear dynamics to be analyzed in compact form in terms of natural dynamic "atoms," each of which is a frequency resonance of an eigenmode. Because these modal resonances are determined by the system dynamics, not the investigator, they are privileged over widely used phenomenological patterns, and obviate the need for artificial discretizations and thresholding in coordinate space. It is shown that modal resonances participate as nodes of a discrete spectral network, are noninteracting in the linear regime, but are linked nonlinearly by wave-wave coalescence and decay processes. The modal resonance formulation is shown to be capable of speeding numerical calculations of strongly nonlinear interactions. Recent work in brain dynamics, especially based on neural field theory (NFT) approaches, allows eigenmodes and their resonances to be estimated from data without assuming a specific brain model. This means that dynamic equations can be inferred using system identification methods from control theory, rather than being assumed, and resonances can be interpreted as control-systems data filters. The results link brain activity and connectivity with control-systems functions such as prediction and attention via gain control and can also be linked to specific NFT predictions if desired, thereby providing a convenient bridge between physiologically based theories and experiment. Amplitudes of modes and resonances can also be tracked to provide a more direct and temporally localized representation of the dynamics than correlations and covariances, which are widely used in the field. By synthesizing many different lines of research, this work provides a way to link quantitative electrophysiological and imaging measurements, connectivity, brain dynamics, and function. This underlines the need to move between coordinate and spectral representations as required. Moreover, standard theoretical-physics approaches and mathematical methods can be used in place of ad hoc statistical measures such as those based on graph theory of artificially discretized and decimated networks, which are highly prone to selection effects and artifacts.

Neural field theory of neural avalanche exponents.

The power-law exponents of observed size and lifetime distributions of near-critical neural avalanches are calculated from neural field theory using diagrammatic methods. This brings neural avalanches within the ambit of neural field theory, which has also previously explained near-critical 1/f spectra and many other observed features of neural activity. This strengthens the case for near-criticality of the brain and opens the way for these other phenomena to be interrelated with avalanches and their dynamics.

Relationships between lognormal distributions of neural properties, activity, criticality, and connectivity.

Relationships between convergence of inputs onto neurons, divergence of outputs from them, synaptic strengths, nonlinear firing response properties, and randomness of axonal ranges are systematically explored by interrelating means and variances of synaptic strengths, firing rates, and soma voltages. When self-consistency is imposed, it is found that broad distributions of synaptic strength are a necessary concomitant of the known massive convergence of inputs to individual neurons, and observed widths of lognormal distributions of synaptic strength and firing rate are explained provided the brain is in a near-critical state, consistent with independent observations. The strongest individual synapses are shown to have an effect on soma voltage comparable to the effect of all others combined, which supports suggestions that they may have a key role in neural communication. Remarkably, inclusion of moderate randomness in characteristic axonal ranges is shown to account for the observed [Formula: see text]-fold variability in two-point connectivity at a given separation and [Formula: see text]-fold overall when the known mean exponential fall-off is included, consistent with observed near-lognormal distributions. Inferred axonal deviations from straight-line paths are also consistent with independent estimates.

Importance of self-connections for brain connectivity and spectral connectomics.

Spectral analysis and neural field theory are used to investigate the role of local connections in brain connectivity matrices (CMs) that quantify connectivity between pairs of discretized brain regions. This work investigates how the common procedure of omitting such self-connections (i.e., the diagonal elements of CMs) in published studies of brain connectivity affects the properties of functional CMs (fCMs) and the mutually consistent effective CMs (eCMs) that correspond to them. It is shown that retention of self-connections in the fCM calculated from two-point activity covariances is essential for the fCM to be a true covariance matrix, to enable correct inference of the direct total eCMs from the fCM, and to ensure their compatibility with it; the deCM and teCM represent the strengths of direct connections and all connections between points, respectively. When self-connections are retained, inferred eCMs are found to have net inhibitory self-connections that represent the local inhibition needed to balance excitation via white matter fibers at longer ranges. This inference of spatially unresolved connectivity exemplifies the power of spectral connectivity methods, which also enable transformation of CMs to compact diagonal forms that allow accurate approximation of the fCM and total eCM in terms of just a few modes, rather than the full [Formula: see text] CM entries for connections between N brain regions. It is found that omission of fCM self-connections affects both local and long-range connections in eCMs, so they cannot be omitted even when studying the large-scale. Moreover, retention of local connections enables inference of subgrid short-range inhibitory connectivity. The results are verified and illustrated using the NKI-Rockland dataset from the University of Southern California Multimodal Connectivity Database. Deletion of self-connections is common in the field; this does not affect case-control studies but the present results imply that such fCMs must have self-connections restored before eCMs can be inferred from them.

Effects of parcellation and threshold on brainconnectivity measures.

It is shown that the statistical properties of connections between regions of the brain and their dependence on coarse-graining and thresholding in published data can be reproduced by a simple distance-based physical connectivity model. This allows studies with differing parcellation and thresholding to be interrelated objectively, and for the results of future studies on more finely grained or differently thresholded networks to be predicted. As examples of the implications, it is shown that the dependences of network measures on thresholding and parcellation imply that chosen brain regions can appear to form a small world network, even though the network at finer scales, or ultimately of individual neurons, may not be small world networks themselves.

Nonlinear wave-wave interactions in the brain.

Neural field theory of the corticothalamic system is used to analyze nonlinear wave-wave interactions in steady state visual evoked potential responses. The nonlinear power spectrum is analytically calculated by convolving the linear power spectrum with itself and other factors. Periodic sine and square wave stimuli are used to generate steady state visual evoked potential responses and to study stimulus-driven nonlinear corticothalamic dynamic interactions. Moreover, we use dual sine drives to analyze the driven dynamics. Numerical analysis shows that the nonlinear power spectrum embodies key nonlinear features, including harmonic and subharmonic generation, entrainment of the alpha rhythm to periodic stimuli at the drive frequency, sum and difference frequencies due to wave-wave coalescence and decay. Further, the scaling properties of the key phenomena observed in nonlinear interactions are studied, verifying some of the theoretical predictions for these being generated by three-wave processes.

Gamma-band correlations in the primary visual cortex.

This paper generalizes and extends previous work on using neural field theory to quantitatively analyze the two-dimensional (2D) spatiotemporal correlation properties of gamma-band (30-70 Hz) oscillations evoked by stimuli arriving at the primary visual cortex, and modulated by patchy connectivities that depend on orientation preference (OP). Correlation functions are derived analytically for general stimulus and measurement conditions. The theoretical results reproduce a range of published experimental results. These include (i) the existence of two-point oscillatory temporal cross correlations with zero time lag between neurons with similar OP; (ii) the influence of spatial separation of neurons on the strength of the correlations; and (iii) the effects of differing stimulus orientations. They go beyond prior work by incorporating experimentally observed patchy projection patterns to predict the 2D correlation structure including both OP and ocular dominance effects, thereby relaxing assumptions of translational invariance implicit in prior one-dimensional analysis.

Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures.

The temporal and spectral characteristics of tonic-clonic seizures are investigated using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into ∼ 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs. In this study, the spectral and temporal characteristics of tonic-clonic seizures are explored as functions of the relevant properties of physiological connection strengths, such as maximum strength, time above threshold, and the ramp rate at which the strength increases or decreases. Analysis shows that the seizure onset time decreases with the maximum connection strength and time above threshold, but increases with the ramp rate. Seizure duration and offset time increase with maximum connection strength, time above threshold, and rate of change. Spectral analysis reveals that the power of nonlinear harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. A secondary limit cycle at ∼ 18 Hz, termed a saddle-cycle, is also seen during seizure onset and becomes more prominent and robust with increasing ramp rate. If the time above the threshold is too small, the system does not reach the 10 Hz limit cycle, and only exhibits 18 Hz saddle-cycle oscillations. It is also seen that the time to reach the saturated large amplitude limit-cycle seizure oscillation from both the instability threshold and from the end of the saddle-cycle oscillations is inversely proportional to the square root of the ramp rate.

Evoked response activity eigenmode analysis in a convoluted cortex via neural field theory.

Neural field theory of the corticothalamic system is used to explore evoked response potentials (ERPs) caused by spatially localized impulse stimuli on the convoluted cortex and on a spherical cortex. Eigenfunctions are calculated analytically on the spherical cortex and numerically on the convoluted cortex via eigenfunction expansions. Eigenmodes on a convoluted cortex are similar to those of the spherical cortex, and a few such modes are found to be sufficient to reproduce the main ERP features. It is found that the ERP peak is stronger in spherical cortex than convoluted cortex, but in both cases the peak decreases monotonically with increasing distance from the stimulus point. In the convoluted case, cortical folding causes ERPs to differ between locations at the same distance from the stimulus point and spherical symmetries are only approximately preserved.

Unified dynamics of interictal events and absence seizures.

The dynamics of interictal events between absence seizures and their relationship to seizures themselves are investigated by employing a neural field model of the corticothalamic system. Interictal events are modeled as being due to transient parameter excursions beyond the seizure threshold, in the present case by sufficiently temporally varying the connection strength between the cerebral cortex and the thalamus. Increasing connection strength drives the system into ∼3-Hz seizure oscillations via a supercritical Hopf bifurcation once the linear instability threshold is passed. Depending on the time course of the excursion above threshold, different interictal activity event dynamics are seen in the time series of corticothalamic fields. These resemble experimental interictal time series observed via electroencephalography. It is found that the morphology of these events depends on the magnitude and duration of the excursion above threshold. For a large-amplitude excursion of short duration, events resemble interictal spikes, where one large spike is seen, followed by small damped oscillations. For a short excursion with long duration, events like observed interictal periodic sharp waves are seen. When both amplitude and duration above threshold are large, seizure oscillations are seen. Using these outcomes, proximity to seizure can be estimated and tracked.

Power spectrum of resting-state blood-oxygen-level-dependent signal.

Hemodynamic modeling is used to explore the origin, predict, and analyze the power spectrum of the resting-state blood-oxygen-level-dependent (BOLD) signal measured by functional magnetic resonance imaging (fMRI), which has been reported to have a power-law form, i.e., P(f)∝f^{-s}, where P(f) is the power, f is the frequency, and s>0 is the power-law exponent. However, current fMRI experimental paradigms have limited acquisition durations, affecting the spectral resolution of fMRI data at the low-frequency regime. Here, the claimed power-law spectrum is investigated by using a recent hemodynamic model to analytically derive the BOLD power spectrum, with parameters that are related to neurophysiology. The theoretical results show that, for all realistic parameter combinations, the BOLD power spectrum is flat at f≲0.01Hz, has a weak resonance originating from intrinsic oscillations of vasodilatory response, and becomes a power law for high frequencies, all of which is in agreement with an empirical data set that describes the spectrum of one subject and brain region. However, the results are contrary to studies reporting a pure power-law spectrum at f≲0.2Hz. The discrepancy is attributed largely to data averaging employed by current approaches that averages together important properties of the BOLD power spectrum, such as its resonance, that biases the spectrum to only show a power law. Data averaging also reduces the high-frequency power-law exponent relative to individual cases. Overall, this work demonstrates how the model can reproduce BOLD dynamics and further analyze its low-frequency behavior. Moreover, it also uses the model to explain the impact of procedures, such as data averaging, on the reported features of the BOLD power spectrum.

Unified analysis of global and focal aspects of absence epilepsy via neural field theory of the corticothalamic system.

Absence epilepsy is characterized by a sudden paroxysmal loss of consciousness accompanied by oscillatory activity propagating over many brain areas. Although primary generalized absence seizures are supported by the global corticothalamic system, converging experimental evidence supports a focal theory of absence epilepsy. Here a physiology-based corticothalamic model is investigated with spatial heterogeneity due to focal epilepsy to unify global and focal aspects of absence epilepsy. Numeric and analytic calculations are employed to investigate the emergent spatiotemporal dynamics as well as their underlying dynamical mechanisms. They can be categorized into three scenarios: suppressed epilepsy, focal seizures, or generalized seizures, as summarized from a phase diagram vs focal width and characteristic axon range. The corresponding temporal frequencies and spatial extents of cortical waves in generalized seizures and focal seizures agree well with experimental observations of global and focal aspects of absence epilepsy, respectively. The emergence of the spatiotemporal dynamics corresponding to focal seizures provides a biophysical explanation of the temporally higher frequency but spatially more localized cortical waves observed in genetic rat models that display characteristics of human absence epilepsy. Predictions are also presented for further experimental test.