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Due to the mildness of initial injury, many athletes with recurrent mild traumatic brain injury (mTBI) are misdiagnosed with other neuropsychiatric illnesses. This study was designed as a proof-of-principle feasibility trial for athletic trainers at a sports facility to generate electroencephalograms (EEGs) from student athletes for discriminating (mTBI) associated EEGs from uninjured ones. A total of forty-seven EEGs were generated, with thirty athletes recruited at baseline (BL) pre-season, after a concussive injury (IN), and post season (PS). Outcomes included: 1) Visual analyses of EEGs by a neurologist, 2) Support vector machine (SVM) classification for inferences about whether particular groups belonged to the three subgroups of BL, IN, or PS, 3) Analyses of EEG synchronies including Phase locking value (PLV) computed between pairs of distinct electrodes. All EEGs were visually interpreted as normal. SVM classification showed that BL and IN could be discriminated with 81% accuracy using features of EEG synchronies combined. Frontal inter-hemispheric phase synchronization measured by PLV was significantly lower in the IN group. It is feasible for athletic trainers, to record high quality EEGs from student athletes. Also, spatially localized metrics of EEG synchrony can discriminate mTBI associated EEGs from control EEGs.

BACKGROUND Video games can be a valuable tool for surgery training. Individuals who interact or play video games, tend to have a better visuospatial ability when compared to non-gamers. Numerous studies suggest that video game experience is associated with faster acquisition, greater sharpening, and longer retention of laparoscopic skills. Given the neurocognitive complexity of surgery skill, multimodal approaches are required to understand how video game playing enhances laparoscopy skill. METHODS Data from thirteen surgeons with varying levels of laparoscopy experience and no video game experience, and 27 students with no laparoscopy experience and varying levels of video game experience performed standard laparoscopic training tasks. Their performance, subjective cognitive loading, and prefrontal cortical activity were recorded and analyzed. RESULTS The surgeons performed the tasks significantly faster, had significantly lower cognitive load as well as less left prefrontal activation, relative to the non-gamer novices. In gamer novices, the task completion time decreased significantly with increasing game experience. The cognitive load decreased significantly with increasing gaming experience in gamer novices and with laparoscopy experience in surgeons. CONCLUSION Our results suggest that along the dimensions of performance, cognitive load, and brain activity, the effects of video gaming experience on novice laparoscopy trainees are similar to those of real-world laparoscopy experience on surgeons. We believe that the neural underpinnings of surgery skill and its links with gaming experience need to be investigated further using wearable functional brain imaging.

Aim Measuring cognitive load is important for surgical education and patient safety. Traditional approaches of measuring cognitive load of surgeons utilise behavioural metrics to measure performance and surveys and questionnaires to collect reports of subjective experience. There is a need for more automated, more accurate and objective evaluation methods. Method Functional neuroimaging data was collected using wireless NIRS device from sixteen surgeons (11 attending surgeons and 5 surgery resident) and 17 students while they performed two laparoscopic tasks (Peg transfer and String pass). Participant’s subjective mental load was assessed using NASA-TLX survey. Machine learning approaches were used for predicting the subjective experience and skill levels. Results The Prefrontal cortex (PFC) activations were greater in students who reported higher-than-median task load, as measured by the NASA-TLX survey. However, in the case of attending surgeons the opposite tendency was observed, namely higher activations in lower v higher task loaded subjects. We found response was greater in the left PFC of students particularly near dorso- and ventrolateral areas. We quantified the ability of PFC activation to predict differences in skill and task load using machine learning while focusing on the effects of NIRS channel separation distance on the results. Our results showed that the classification of skill level and subjective task load could be predicted based on PFC activation with an accuracy of nearly 90%. Conclusions The high accuracy of results is encouraging and suggest the integration of the strategy developed in this study as a promising approach to design automated, more accurate and objective evaluation methods.

Mental workload and its effects on surgical performance are underexplored topics, despite their importance for operating room (OR) efficiency and patient safety. We developed a multimodal platform that can simultaneously collect data from EEG, heart rate and breathing rate, tool handle pressure, and eye tracker from mobile subjects. We performed experiments using the Fundamentals of Laparoscopic Surgery model, with 22 subjects of varying skill levels ranging from nonsurgeon to expert. The results indicated significant modulations of the measurements depending on pupil size, heart rate variability, P300 response, tool pressure, task difficulty, time-on-task, and skill level. These provide evidence that physiology based metrics can be used in automated classification of fine gradations of skill, the assessment and certification of surgery trainees, developing real-time flags and warnings for the OR, and validating new OR technology.

The reliability of normal gel-based electrode electroencephalogram (EEG) for measuring pain has been validated. To date, however, few documented trials have used dry EEG for pain quantification. The primary goal of this study was to objectively quantify pain using dry EEG in conjunction with a support vector machine (SVM). SVMs have been proven accurate for classifying pain intensity. The authors believe that EEG combined with an SVM could increase the statistical power of pain assessment. Currently, clinicians primarily rely on verbal (i.e., subjective) reports for assessing pain; therefore, the research described here could offer a method to objectively monitor pain, eliminate observer error, and individualize treatment.

Objective: Concurrent scalp electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS), which we refer to as EEG+fNIRS, promises greater accuracy than the individual modalities while remaining nearly as convenient as EEG. We sought to quantify the hybrid system's ability to decode mental states and compare it with unimodal systems.\ud \ud Approach: We recorded from healthy volunteers taking the category fluency test and applied machine learning techniques to the data.\ud \ud Main results: EEG+fNIRS's decoding accuracy was greater than that of its subsystems, partly due to the new type of neurovascular features made available by hybrid data.\ud \ud Significance: Availability of an accurate and practical decoding method has potential implications for medical diagnosis, brain-computer interface design, and neuroergonomics .

We investigated the use of a multimodal functional neuroimaging system in quantifying mental workload of healthy human volunteers. We recorded behavioral performance measures as well as electroencephalography (EEG) and functional near-infrared spectroscopy (fNIRS) simultaneously from subjects performing n-back tasks. The EEG and fNIRS signals were used in feature generation and classification offline using support vector machines. We examined the classification accuracy of three distinct systems: EEG based; fNIRS based; and Hybrid, which contained features from the first two systems as based on their interactions. The classification accuracy of the Hybrid system was observed to be greater than that of either system, indicating the synergistic role played by multimodal signals and by neurovascular coupling in quantifying mental workload.

Measuring the diagnostic accuracy (DA) of an EEG device is unconventional and complicated by imperfect interrater reliability. We sought to compare the DA of a miniature, wireless, battery-powered EEG device ("microEEG") to a reference EEG machine in emergency department (ED) patients with altered mental status (AMS). Two hundred twenty-five ED patients with AMS underwent 3 EEGs. Two EEGs, EEG1 (Nicolet Monitor, "reference") and EEG2 (microEEG) were recorded simultaneously with EEG cup electrodes using a signal splitter. The remaining study, EEG3, was recorded with microEEG using an electrode cap immediately before or after EEG1/EEG2. The official EEG1 interpretation was considered the gold standard (EEG1-GS). EEG1, 2, and 3 were de-identified and blindly interpreted by two independent readers. A generalized mixed linear model was used to estimate the sensitivity and specificity of these interpretations relative to EEG1-GS and to compute a diagnostic odds ratio (DOR). Seventy-nine percent of EEG1-GS were abnormal. Neither the DOR nor the κf representing interrater reliabilities differed significantly between EEG1, EEG2, and EEG3. The mean setup time was 27 min for EEG1/EEG2 and 12 min for EEG3. The mean electrode impedance of EEG3 recordings was 12.6 kΩ (SD: 31.9 kΩ). The diagnostic accuracy of microEEG was comparable to that of the reference system and was not reduced when the EEG electrodes had high and unbalanced impedances. A common practice with many scientific instruments, measurement of EEG device DA provides an independent and quantitative assessment of device performance.

Objectives Altered mental status (AMS) is a common presentation in the emergency department (ED). A previous study revealed 78% electroencephalogram (EEG) abnormalities, including nonconvulsive seizure (NCS; 5%), in ED patients with AMS. The objective of this study was to assess the impact of EEG on clinical management and outcomes of ED patients with AMS. Methods This was a randomized controlled trial at two urban teaching hospitals. Adult patients (≥18 years old) with AMS were included. Excluded patients had immediately correctable AMS (e.g., hypoglycemia) or were admitted before enrollment. Patients were randomized to routine care (control) or routine care plus EEG (intervention). Research assistants used a scalp electrode set with a miniature, wireless EEG device (microEEG) to record standard 30-minute EEGs at presentation, and results were reported to the ED attending physician by an off-site epileptologist within 30 minutes. Primary outcomes included changes in ED management (differential diagnosis, diagnostic work-up, and treatment plan from enrollment to disposition) as determined by surveying the treating physicians. Secondary outcomes were length of ED and hospital stay, intensive care unit (ICU) requirement, and in-hospital mortality. Results A total of 149 patients were enrolled (76 control and 73 intervention). Patients in the two groups were comparable at baseline. EEG in the intervention group revealed abnormal findings in 93% (95% confidence interval [CI] = 85% to 97%), including NCS in 5% (95% CI = 2% to 13%). Using microEEG was associated with change in diagnostic work-up in 49% (95% CI = 38% to 60%) of cases and therapeutic plan in 42% (95% CI = 31% to 53%) of cases immediately after the release of EEG results. Changes in probabilities of differential diagnoses and the secondary outcomes were not statistically significant between the groups. Conclusions An EEG can be obtained in the ED with minimal resources and can affect clinical management of AMS patients. Resumen Objetivos La alteracion del nivel de consciencia (ANC) es un motivo de consulta frecuente en el servicio de urgencias (SU). Un estudio previo revelo un 78% de alteraciones en el electroencefalograma (EEG), que incluian un 5% de crisis no convulsivas en los pacientes con ANC en el SU. El objetivo de este estudio fue evaluar el impacto del EEG en el manejo clinico y en los resultados en los pacientes con ANC. Metodologia Ensayo clinico controlado y aleatorizado en dos hospitales universitarios urbanos. Se incluyeron pacientes adultos (>18 anos) con ANC. Se excluyeron los pacientes que tuvieron ANC inmediatamente corregible (ej: hipoglucemia) asi como algun ingreso anterior a la inclusion. Los pacientes se aleatorizaron a atencion rutinaria (control), o atencion rutinaria mas EEG (intervencion). Los investigadores usaron un conjunto de electrodos en el cuero cabelludo con, un dispositivo de EEG en miniatyra conectado de forma inalambrica (microEEG) para la grabacion estandar del EEG durante los 30 minutos desde la llegada, y los resultados fueron informados al medico del SU por un neurofisiologo en los primeros 30 minutos. Los resultados principales incluyeron cambios en el manejo en el SU (diagnostico diferencial, proceso diagnostico, plan terapeutico desde la inclusion hasta la ubicacion) los cuales se determinaron mediante una encuesta a los medicos responsables de la atencion. Los resultados secundarios fueron el tiempo de estancia en el SU y en el hospital, la necesidad de cuidados intensivos y la mortalidad intrahospitalaria. Resultados Se incluyeron 149 pacientes (76 controles y 73 grupo intervencion). Los pacientes de los dos grupos fueron comparables en la visita basal. El EEG revelo en el grupo de intervencion hallazgos anormales en un 93% (IC 95% = 85% a 97%), que incluyeron crisis no convulsivas en un 5% (IC 95% = 2% a 13%). El uso de microEEG se asocio con un cambio en el proceso diagnostico en un 49% (IC 95% = 38% a 60%) de los casos y en el plan terapeutico en un 42% (IC 95% = 31% a 53%) de los casos, inmediatamente tras los resultados del EEG. Los cambios en probabilidades del diagnostico diferencial y de los resultados secundarios no fueron estadisticamente significativos entre los grupos. Conclusiones Un EEG puede ser obtenido en el SU con recursos minimos y puede impactar en el manejo clinico de los pacientes con ANC.

The intrarater and interrater reliability (I&IR) of EEG interpretation has significant implications for the value of EEG as a diagnostic tool. We measured both the intrarater reliability and the interrater reliability of EEG interpretation based on the interpretation of complete EEGs into standard diagnostic categories and rater confidence in their interpretations and investigated sources of variance in EEG interpretations. During two distinct time intervals, six board-certified clinical neurophysiologists classified 300 EEGs into one or more of seven diagnostic categories and assigned a subjective confidence to their interpretations. Each EEG was read by three readers. Each reader interpreted 150 unique studies, and 50 studies were re-interpreted to generate intrarater data. A generalizability study assessed the contribution of subjects, readers, and the interaction between subjects and readers to interpretation variance. Five of the six readers had a median confidence of ≥99%, and the upper quartile of confidence values was 100% for all six readers. Intrarater Cohen's kappa (κc) ranged from 0.33 to 0.73 with an aggregated value of 0.59. Cohen's kappa ranged from 0.29 to 0.62 for the 15 reader pairs, with an aggregated Fleiss kappa of 0.44 for interrater agreement. Cohen's kappa was not significantly different across rater pairs (chi-square=17.3, df=14, p=0.24). Variance due to subjects (i.e., EEGs) was 65.3%, due to readers was 3.9%, and due to the interaction between readers and subjects was 30.8%. Experienced epileptologists have very high confidence in their EEG interpretations and low to moderate I&IR, a common paradox in clinical medicine. A necessary, but insufficient, condition to improve EEG interpretation accuracy is to increase intrarater and interrater reliability. This goal could be accomplished, for instance, with an automated online application integrated into a continuing medical education module that measures and reports EEG I&IR to individual users.

Four to ten percent of patients evaluated in emergency departments (ED) present with altered mental status (AMS). The prevalence of non-convulsive seizure (NCS) and other electroencephalographic (EEG) abnormalities in this population is unknown. Objectives To identify the prevalence of NCS and other EEG abnormalities in ED patients with AMS. Methods A prospective observational study at 2 urban ED. Inclusion: patients ≥13 years old with AMS. Exclusion: An easily correctable cause of AMS (e.g. hypoglycemia). A 30-minute standard 21-electrode EEG was performed on each subject upon presentation. Outcome: prevalence of EEG abnormalities interpreted by a board-certified epileptologist. EEGs were later reviewed by 2 blinded epileptologists. Inter-rater agreement (IRA) of the blinded EEG interpretations is summarized with κ . A multiple logistic regression model was constructed to identify variables that could predict the outcome. Results Two hundred fifty-nine patients were enrolled (median age: 60, 54% female). Overall, 202/259 of EEGs were interpreted as abnormal (78%, 95% confidence interval [CI], 73-83%). The most common abnormality was background slowing (58%, 95% CI, 52-68%) indicating underlying encephalopathy. NCS (including non-convulsive status epilepticus [NCSE]) was detected in 5% (95% CI, 3-8%) of patients. The regression analysis predicting EEG abnormality showed a highly significant effect of age ( P κ : 0.45, 95% CI, 0.36-0.54). Conclusions The prevalence of EEG abnormalities in ED patients with undifferentiated AMS is significant. ED physicians should consider EEG in the evaluation of patients with AMS and a high suspicion of NCS/NCSE.

The brains of awake, resting human subjects display spontaneously occurring neural activity patterns whose magnitude is typically many times greater than those triggered by cognitive or perceptual performance. Such resting state (RS) activity is thought to reflect the functional organization of the brain. In addition, both evoked and RS activation affect local cerebral hemodynamic properties through processes collectively referred to as neurovascular coupling. This is a major topic of interest due to its relationship with pathological conditions that include hypertension, stroke, subarachnoid hemorrhage, and traumatic brain injury. Its investigation calls for an ability to track both the neural and vascular aspects of brain function. We used scalp electroenc ephalography (EEG) which provided a measure of the electrical potentials generated by cortical postsynaptic currents. Simultaneously we utilized functional near-infrared spectroscopy (NIRS) to continuously monitor hemoglobin concentration changes in superficial cortical layers. The multi-modal signal from 18 healthy adult subjects allowed us to investigate the association of neural activity in a range of frequencies over the whole-head to local changes in hemoglobin concentrations. Our results verified the delayed alpha (8-16 Hz) modulation of hemodynamics in posterior areas known from the literature. They also indicated strong beta (16-32 Hz) modulation of hemodynamics. Analysis revealed, however, that beta modulation was likely generated by the alpha-beta coupling in EEG. Signals from the inferior electrode sites were dominated by scalp muscle related activity. Our study aimed to characterize the phenomena related to neurovascular coupling observable by practical, cost-effective, and non-invasive multi-modal techniques.

Non-invasive Brain-Computer Interfaces (BCI) have demonstrated great promise for neuroprosthetics and assistive devices. Here we aim to investigate methods to combine Electroencephalography (EEG) and functional Near-Infrared Spectroscopy (fNIRS) in an asynchronous Sensory Motor rhythm (SMR)-based BCI. We attempted to classify 4 different executed movements, namely, Right-Arm—Left-Arm—Right-Hand—Left-Hand tasks. Previous studies demonstrated the benefit of EEG-fNIRS combination. However, since normally fNIRS hemodynamic response shows a long delay, we investigated new features, involving slope indicators, in order to immediately detect changes in the signals. Moreover, Common Spatial Patterns (CSPs) have been applied to both EEG and fNIRS signals. 15 healthy subjects took part in the experiments and since 25 trials per class were available, CSPs have been regularized with information from the entire population of participants and optimized using genetic algorithms. The different features have been compared in terms of performance and the dynamic accuracy over trials shows that the introduced methods diminish the fNIRS delay in the detection of changes.

We introduce a method of accurately and efficiently modeling a large population of participants in a financial market. Each participant is modeled as having an internal preference state affected by the continual arrival of exogenous information and by the behavior of others. In order to describe a community of traders, we introduce a population equation that is derived rigorously from the underlying single-agent model. The population equation is used to investigate collective behavior with mimetic interactions. We observe and study the sharp transitions in parameter space from a stable time-independent regime to instability where the demand and supply diverge sharply.

The response of a noninteracting population of identical neurons to a step change in steady synaptic input can be analytically calculated exactly from the dynamical equation that describes the population's evolution in time. Here, for model integrate-and-fire neurons that undergo a fixed finite upward shift in voltage in response to each synaptic event, we compare the theoretical prediction with the result of a direct simulation of 90,000 model neurons. The degree of agreement supports the applicability of the population dynamics equation. The theoretical prediction is in the form of a series. Convergence is rapid, so that the full result is well approximated by a few terms.

The behavior of an aggregate of neurons is followed by means of a population equation which describes the probability density of neurons as a function of membrane potential. The model is based on integrate-and-fire membrane dynamics and a synaptic dynamics which produce a fixed potential jump in response to stimulation. In spite of the simplicity of the model, it gives rise to a rich variety of behaviors. Here only the equilibrium problem is considered in detail. Expressions for the population density and firing rate over a range of parameters are obtained and compared with like forms obtained from the diffusion approximation. The introduction of the jump response to stimulation produces a delay term in the equations, which in turn leads to analytical challenges. A variety of asymptotic techniques render the problem solvable. The asymptotic resultsshow excellent agreement with direct numerical simulations.

The dynamics of large populations of interacting neurons is investigated. Redundancy present in subpopulations of cortical networks is exploited through the introduction of a probabilistic description. A derivation of the kinetic equations for such subpopulations, under general transmembrane dynamics, is presented. The particular case of integrate-and-fire membrane dynamics is considered in detail. A variety of direct simulations of neuronal populations, under varying conditions and with as many as O(10(5)) neurons, is reported. Comparison is made with analogous kinetic equations under the same conditions. Excellent agreement, down to fine detail, is obtained. It is emphasized that no free parameters enter in the comparisons that are made.

Background We describe and characterize the performance of microEEG compared to that of a commercially available and widely used clinical EEG machine. microEEG is a portable, battery-operated, wireless EEG device, developed by Bio-Signal Group to overcome the obstacles to routine use of EEG in emergency departments (EDs). Methods The microEEG was used to obtain EEGs from healthy volunteers in the EEG laboratory and ED. The standard system was used to obtain EEGs from healthy volunteers in the EEG laboratory, and studies recorded from patients in the ED or ICU were also used for comparison. In one experiment, a signal splitter was used to record simultaneous microEEG and standard EEG from the same electrodes. Results EEG signal analysis techniques indicated good agreement between microEEG and the standard system in 66 EEGs recorded in the EEG laboratory and the ED. In the simultaneous recording the microEEG and standard system signals differed only in a smaller amount of 60 Hz noise in the microEEG signal. In a blinded review by a board-certified clinical neurophysiologist, differences in technical quality or interpretability were insignificant between standard recordings in the EEG laboratory and microEEG recordings from standard or electrode cap electrodes in the ED or EEG laboratory. The microEEG data recording characteristics such as analog-to-digital conversion resolution (16 bits), input impedance (>100MΩ), and common-mode rejection ratio (85 dB) are similar to those of commercially available systems, although the microEEG is many times smaller (88 g and 9.4 × 4.4 × 3.8 cm). Conclusions Our results suggest that the technical qualities of microEEG are non-inferior to a standard commercially available EEG recording device. EEG in the ED is an unmet medical need due to space and time constraints, high levels of ambient electrical noise, and the cost of 24/7 EEG technologist availability. This study suggests that using microEEG with an electrode cap that can be applied easily and quickly can surmount these obstacles without compromising technical quality.

We use high-order approximation schemes for the space derivatives in the nonlinear cable equation and investigate the behavior of numerical solution errors by using exact solutions, where available, and grid convergence. The space derivatives are numerically approximated by means of differentiation matrices. Nonlinearity in the equation arises from the Hodgkin-Huxley dynamics of the gating variables for ion channels. We have investigated in particular the effects of synaptic current distribution and compared the accuracy of the spectral solutions with that of finite differencing. A flexible form for the injected current is used that can be adjusted smoothly from a very broad to a narrow peak, which furthermore leads, for the passive cable, to a simple, exact solution. We have used three distinct approaches to assess the numerical solutions: comparison with exact solutions in an unbranched passive cable, the convergence of solutions with progressive refinement of the grid in an active cable, and the simulation of spike initiation in a biophysically realistic single-neuron model. The spectral method provides good numerical solutions for passive cables comparable in accuracy to those from the second-order finite difference method and far greater accuracy in the case of a simulated system driven by inputs that are smoothly distributed in space. It provides faster convergence in active cables and in a realistic neuron model due to better approximation of propagating spikes.

The scale of large neuronal network simulations is memory limited due to the need to store connectivity information: connectivity storage grows as the square of neuron number up to anatomically relevant limits. Using the NEURON simulator as a discrete-event simulator (no integration), we explored the consequences of avoiding the space costs of connectivity through regenerating connectivity parameters when needed: just in time after a presynaptic cell fires. We explored various strategies for automated generation of one or more of the basic static connectivity parameters: delays, postsynaptic cell identities, and weights, as well as run-time connectivity state: the event queue. Comparison of the JitCon implementation to NEURON's standard NetCon connectivity method showed substantial space savings, with associated run-time penalty. Although JitCon saved space by eliminating connectivity parameters, larger simulations were still memory limited due to growth of the synaptic event queue. We therefore designed a JitEvent algorithm that added items to the queue only when required: instead of alerting multiple postsynaptic cells, a spiking presynaptic cell posted a callback event at the shortest synaptic delay time. At the time of the callback, this same presynaptic cell directly notified the first postsynaptic cell and generated another self-callback for the next delay time. The JitEvent implementation yielded substantial additional time and space savings. We conclude that just-in-time strategies are necessary for very large network simulations but that a variety of alternative strategies should be considered whose optimality will depend on the characteristics of the simulation to be run.

Network simulations can help identify underlying mechanisms of epileptic activity which are hard to isolate in biological preparations. To be useful, simulations must be suffciently realistic to make possible biological and clinical prediction. This requirement for large networks of sufficiently detailed neurons raises challenges both with regard to computational load and the difficulty of obtaining insights with large numbers of free parameters and the large amounts of generated data. We have addressed these problems by simulating computationally managable networks of moderate size consisting of 1000-3000 neurons with multiple intrinsic and synaptic properties. Experiments on these simulations demonstrated the presence of epileptiform behavior in the form of repeatitive high-intensity population events (clonic behavior) or latch-up with near maximal activity (tonic behavior). We found that intrinsic neuronal excitability is not always a predictor of network epileptiform activity but may paradoxically produce anti-epileptic effects, depending on the settings of other parameters. We noted in several simulations the importance of random coincident inputs to shift a network from a low-activation to a high-activation epileptiform state. Finally, we explored the effects of a simulated anticonvulsant acting on excitability, noting that this tended to preferentially decrease tonic activity.

A population formulation of neuronal activity is employed to study an excitatory network of (spiking) neurons receiving external input as well as recurrent feedback. At relatively low levels of feedback, the network exhibits time stationary asynchronous behavior. A stability analysis of this time stationary state leads to an analytical criterion for the critical gain at which time asynchronous behavior becomes unstable. At instability the dynamics can undergo a supercritical Hopf bifurcation and the population passes to a synchronous state. Under different conditions it can pass to synchrony through a subcritical Hopf bifurcation. And at high gain a network can reach a runaway state, in finite time, after which the network no longer supports bounded solutions. The introduction of time delayed feedback leads to a rich range of phenomena. For example, for a given external input, increasing gain produces transition from asynchrony, to synchrony, to asynchrony and finally can lead to divergence. Time delay is also shown to strongly mollify the amplitude of synchronous oscillations. Perhaps, of general importance, is the result that synchronous behavior can exist only for a narrow range of time delays, which range is an order of magnitude smaller than periods of oscillation.

It is shown in the context of the periodically driven eccentric annular system that small rigid spherical particles advected in a time‐periodic bounded flow can be represented by a dissipative dynamical system with simple or strange attractors. The behavior of such particles differs significantly from the patterns in the fluid flow driving the dynamical system. This may have implications for transport, mixing, and separation in multiphase flows as well as in predicting the dispersion of trace substances in natural fluid media. Numerical results suggest that the sensitivity of the limit sets to parameter values may be used to separate species of particles differing slightly in the value of some physical property.

Any realistic model of the neuronal pathway from the retina to the visual cortex (V1) must account for the burstingbehavior of neurons in the lateral geniculate nucleus (LGN). A robust but minimal model, the integrate- and-fire-or-burst (IFB) model, has recently been proposed for individual LGN neurons. Based on this, we derive a dynamic population model and study a population of such LGN cells. This population model, the first simulation of its kind evolving in a two-dimensional phase space, is used to study the behavior of bursting populations in response to diverse stimulus conditions.

We investigate a sequence of low-dimensional models of turbulent channel flows. These models are based on the extraction of the Karhunen–Loeve (KL) eigenfunctions from a large-scale simulation in a wide channel with R *=180 (based on the friction velocity). KL eigenfunctions provide an optimal coordinate system in which to represent the dynamics of the turbulent flow. The hierarchy of KL modes identifies the most energetic independent phenomena in the system. A series of Galerkin projections is then used to derive a dynamical approximation to flows. In order to capture essential aspects of the flow in a low-dimensional system, a careful selection of modes is carried out. The resulting models satisfy momentum and energy conservation as well as yielding the amount of viscous dissipation found in the exact system. Their dynamics includes modes which characterize the flux, rolls, and propagating waves. Unlike previous treatments the instantaneous streamwise flow is time dependent and represented by KL flux modes. The rolls correspond to the streaks observed in experiments in the viscous sublayer. Propagating waves which first appear in the model flow at low Reynolds number (R *∼ 60) persist through the chaotic regime that appears as the Reynolds number is increased. Statistical measures of the chaotic flows which have been generated by the models compare favorably with those found in full-scale simulations.