John Milton

William R. Kenan Jr. Professor of Computational Neuroscience
Professor of Biology

Email: jmilton@kecksci.claremont.edu
Office: Keck Science Center 105
Phone: 909-607-0024
Web Site: https://faculty.jsd.claremont.edu/jmilton

Educational Background

BSc, McGill University
Ph.D., McGill University
MDCM, McGill University

Research Interests

Mathematical and experimental investigation of neural feedback control mechanisms

Selected Publications
(note – a number of PDF reprints that need to be downloaded, then uploaded to WP server)

1. J. G. Milton, T. Insperger, W. Cook, D. M. Harris and G. Stepan. (2018). Microchaos in human postural balance: Sensory deadzones and sampled time-delayed feedback. Physical Review E  98: 022223.
   Abstract – Models for the stabilization of an inverted pendulum figure prominently in studies of human balance control. Surprisingly, fluctuations in measures related to the vertical displacement angle for quietly standing adults with eye closed exhibit chaos. Here we show that small amplitude chaotic fluctuations (“microchaos”) can be generated by the interplay between three essential components of human neural balance control, namely, time-delayed feedback, a sensory dead zone and frequency-dependent encoding of force. When the sampling frequency of the force encoding is decreased, the sensitivity of the balance control to changes in the initial conditions increases. The sampled, time-delayed nature of the balance control may provide insights into why falls are more common in the very young and the elderly.
   Article – https://journals.aps.org/pre/abstract/10.1103/PhysRevE.98.022223
2. G. Stepan, J. Milton and T. Insperger. (2017). Quanization improves stabilization of dynamical systems with delayed feedback. Chaos   27: 114306.
   Abstract – We show that an unstable scalar dynamical system with time-delayed feedback can be stabilized by quantizing the feedback. The discrete time model corresponds to a previously unrecognized case of the microchaotic map in which the fixed point is both locally and globally repelling. In the continuous-time model, stabilization by quantization is possible when the fixed point in the absence of feedback is an unstable node, and in the presence of feedback it is an unstable focus (spiral). The results are illustrated with numerical simulation of the unstable Hayes equation. The solutions of the quantized Hayes equation take the form of oscillations in which the amplitude is a function of the size of the quantization step. If the quantization step is sufficiently small, the amplitude of the oscillations can be small enough to practically approximate the dynamics around a stable fixed point.
3. J. Milton, J. Wu, S. A. Campbell and J. Belair. (2017). Outgrowing neurological diseases: Microcircuits, conduction delay and dynamic diseases. Computational Neurology – Computational Psychiatry: Why and how (P. Erdi, S. Bhattacharya and A. Cochran, eds) Springer : 11-47.
   Abstract – The study of familial disorders characterized by recurring changes in neurodynamics, such as epileptic seizures, paralysis and headaches, provide opportunities to identify the mechanisms for dynamic changes in the nervous system. Many of these diseases are channelopathies. The computational challenge is to understand how a constantly present molecular defect in an ion channel can give rise to paroxysmal changes in neurodynamics. The most common of these channelopathies is childhood absence epilepsy (CAE). Here we review the dynamical properties of three neural microcircuits thought to be important in epilepsy: counter inhibition, recurrent inhibition and recurrent excitation. Time delays, r, are an intrinsic property of these microcircuits since the time for a signal to travel between two neurons depends on the distance between them and the axonal conduction velocity. It is shown that all of these microcircuits can generate multistability provided that r is large enough. The term ‘multistability” means that there can be the co-existence of two or more attractors. Attention is drawn to the transient dynamics which can be associated with transitions between attractors, such as delay-induced transient oscillations. In this way, we link the paroxysmal nature of seizure recurrences in CAE with time-delayed multistable dynamical systems. The tendency of children with CAE to outgrow their epilepsy is linked to developmental changes in axonal myelination which decreases.
4. J. A. Nessler, S. Heredia, J. Belair and J. Milton. (2017). Walking on a vertically oscillating treadmill: Phase synchronization and gait kinematics. PLoS ONE   12: e0169924.
   Abstract – Sensory motor synchronization can be used to alter gait behavior. This type of therapy may be useful in a rehabilitative setting, though several questions remain regarding the most effective way to promote and sustain synchronization. The purpose of this study was to describe a new technique for using synchronization to influence a person’s gait and to compare walking behavior under this paradigm with that of side by side walking. Thirty-one subjects walked on a motorized treadmill that was placed on a platform that oscillated vertically at various frequencies and amplitudes. Synchronization with the platform and stride kinematics were recorded during these walking trials and compared with previously reported data from side by side walking. The results indicated that vertical oscillation of the treadmill surface at frequencies that matched the subject’s preferred stride or step frequency resulted in greater unintentional synchronization when compared with side by side walking data (up to 78.6 +\- 8.3% of the trial vs 59.2 +\- 17.4%). While intermittent phase locking was observed in all cases, periods of synchronization occurred more frequently and lasted longer while walking on the oscillating treadmill (mean length of phase locking 11.85 steps vs 5.18 steps). Further, stride length, height and duration were alerted by changing the frequency of treadmill oscillation. These results suggest that synchronization to a haptic signal may hold implications for use in a clinical setting.
5. T. Insperger and J. Milton. (2017). Stick balancing with feedback delay, sensory dead zone and jerk limitation. Procedia IUTAM   22: 59-66.
   Abstract – A simplified model of stick balancing on the fingertip subjected to predictor feedback is investigated, which accounts for three important modeling issues: (1) feedback delay; (2) the sensory dead zone; and (3) limitation of the control force corresponding to the maximum acceleration and the maximum jerk of human hand movement. Eight different cases ( +/- sensory dead zone, +/- acceleration limitation, +/- jerk limitation) are compared for estimating the maximum balance time out of five time-domain simulations with different initial conditions. It is shown that the region of linear stability in the plane of control parameters is reduced by the presence of the dead zone, not affected by limitations on hand acceleration, but is increased by limitations on the jerk.
6. D. Hajdu, J. Milton and T. Insperger. (2016). Extension of stability radius to neuromechanical systems with structured real perturbations. IEEE Trans. Neural Sys. Rehab. Eng.
   Abstract – The ability of humans to maintain balance about an unstable position in a continuously changing environment attests to the robustness of their balance control mechanisms to perturbations. A mathematical tool to analyze robust stabilization of unstable equilibria is the stability radius. Based on the pseudospectra, the stability radius gives a measure to the maximum change of the system parameters without resulting loss of stability. Here we compare stability radii for a model for human frontal plane balance controlled by a delayed proportional-derivative feedback to two types of perturbations: unstructured complex and weighted structured real. It is shown that 1) narrow stance widths are more robust to parameter variation; 2) stability is maintained for larger structured real perturbations than for unstructured complex perturbations; and 3) the most robust derivative gain to weighted structured real perturbations is located near the stability boundary. It is argued that stability radii can effectively be used to compare different control concepts associated with human motor control.
7. J. Milton, R. Meyer, M. Zhvanetsky, S. Ridge and T. Insperger. (2016). Control at stability’s edge minimizes energetic costs: expert stick balancing. Journal of the Royal Society Interface 13: 20160212.
   Abstract – Stick balancing on the fingertip is a complex voluntary motor task that requires the stabilization of an unstable system. For seated expert stick balancers, the time delay is 0.23 s, the shortest stick that can be balanced for 240 s is 0.32 m and there is a 0.88 degree dead zone for the estimation of the vertical displacement angle in the sagittal plane. These observations motivate a switching-type, pendulum-cart model for balance control which uses an internal model to compensate for the time delay by predicting the sensory consequences of the stick’s movements. Numerical simulations using the semi-discretization method suggest that the feedback gains are tuned near the edge of stability. For these choices of the feedback gains, the cost function which takes into account the position of the fingertip and the corrective forces is minimized. Thus, expert stick balancers optimize control with a combination of quick maneuverability and minimum energy expenditures.
   Article – https://faculty.jsd.claremont.edu/jmilton/reprints/2016_Interface_mv.pdf
8. T. Insperger, J. Milton and G. Stepan. (2015). Semi-discretization and the time-delayed PDA feedback control of human balance. 12th IFAC Workshop on time delay systems  : 93-98.
   Abstract – An important question for human balance control concerns how the differential equations for the neural control of balance should be formulated. In this paper, we consider a discrete-time and a continuous-time delayed proportional-derivative-acceleration controller and establish the transition between them by means of the semi-discretization. We show that the critical delay, which limits stabilizability of the system, is about the same for the continuous-time systems and its semi-discrete counterparts.
   Article – https://faculty.jsd.claremont.edu/jmilton/reprints/tamas_PDA_deadzone.pdf
9. J. G. Milton. (2015). Time delays and the control of biological systems: An overview. 12th IFAC Workshop on time delay systems : 87-92.
   Abstract – This special session provides an introduction for engineers to the applications of delay differential equations to biological control. Topics include the regulation of populations of organisms and neurons, the stabilization of unstable states and the design of drug delivery systems.
   Article – https://faculty.jsd.claremont.edu/jmilton/reprints/milton_overview_delay.pdf
10. J. Milton, G. Stepan and T. Insperger. (2015). Sensory dead zones and time delays in neural feedback control. 17th Yale Workshop on Adaptive and Learning Systems  Yale University.
    Abstract – Sensory dead zones are intrinsic components of the neural control of human balancing. Numerical and analytical studies of the resulting time-delayed switching models for balance control suggest that transient stabilizations of an inverted pendulum are possible. In other words, falls can be an intrinsic property of the same mechanisms designed to prevent them! These observations raise the possibility that the increased risks of falling in the elderly may be a consequence of age-dependent changes in the size of sensory dead zones.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/yale_milton_final.pdf
11. J. A. Nessler, T. Spargo, A Craig-Jones and J. Milton. (2015). Phase resetting behavior is influenced by treadmill walking speed. Gait & Posture  43: 187-191.
    Abstract – Gait is often modeled as a limit cycle oscillator. When perturbed, this type of system will reset its output in a stereotypical manner, which may be shifted in time with respect to its original trajectory. In contrast to other biological oscillators, relatively little is known regarding the phase resetting properties for human gait. Because humans must often reset their gait in response to perturbation, an improved understanding of this behavior may have implications for reducing the risk of fall. The purpose of this study was to further evaluate phase resetting behaviors in human gait with particular emphasis on (1) variance of the phase resetting response among healthy individuals and (2) the sensitivity of this response to walking speed. Seventeen healthy subjects walked on a treadmill at 2.0mph, 2.5mph, and 3.0mph while their right limb was perturbed randomly every 12-20 strides. Discrete, mechanical perturbations were applied by a rope that was attached to each subject’s ankle and actuated by a motorized arm. Perturbations were applied once during a select stride, always at a different point in the swing phase, and the amount of phase shift that occurred on the subsequent stride was recorded. A subset of 8 subjects also walked at their preferred walking speed for 3 additional trials on a separate day in order to provide an estimate of within-subjects variability. The results suggested that phase resetting behavior is relatively consistent among subjects, but that minor variations in phase resetting behavior are attributable to walking at different treadmill speeds.
12. J. Milton, T. Insperger and G. Stepan. (2015). Human balance control: Dead zones, intermittency and micro-chaos. Mathematical approaches to biological systems: Networks, oscillations and collective phenomena T. Ohira and T. Ozawa Springer, New York: 1-28.
    Abstract – The development of strategies to minimize the risk of falling in the elderly represents a major challenge for aging in industrialized societies. The corrective movements made by humans to maintain balance are small amplitude, intermittent and ballistic. Small-amplitude, complex oscillations (“micro-chaos”) frequently arise in industrial settings when a time-delayed digital processor attempts to stabilize an unstable equilibrium. Taken together, these observations motivate considerations of the effects of a sensory threshold on the stabilization of an inverted pendulum by time-delayed feedback. In the resulting switching-type delay differential equations, the sensory threshold is a strong small-scale nonlinearity which has no effect on large-scale stabilization but may produce complex, small-amplitude dynamics including limit cycle oscillations and micro-chaos. A close mathematical relationship exists between a scalar model for balance control and the micro-chaotic map that arises in some models of digitally controlled machines. Surprisingly, transient, time-dependent, bounded solutions (“transient stabilization”) can arise even for parameter ranges where the equilibrium is asymptotically unstable. In other words, the combination of a sensory threshold with a time-delayed sampled feedback can increase the range of parameter values for which balance can be maintained, at least transiently. Neurobiological observations suggest that sensory thresholds can be manipulated either passively by changing posture or actively using efferent feedback. Thus it may be possible to minimize the risk of falling by means of strategies that manipulate sensory thresholds by using physiotherapy and appropriate exercises.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/Milton_2015_switch.pdf
13. T. Insperger, J. Milton and G. Stepan. (2015). Semidiscretization for time-delayed neural balance control. SIAM J. Appl. Dyn. Sys. 14: 1258-1277.
    Abstract – The observation that time-delayed feedback can stabilize an inverted pendulum motivates the formulation of models of human balance control in terms of delay differential equations (DDEs). Recently the intermittent, digital-like nature of the neural feedback control of balance has become evident. Here, semi-discretization methods for DDEs are used to investigate an unstable dynamic system subject due to digital controller in the context of a switching model for postural control. In addition to limit cycle and chaotic (“micro-chaos”) oscillations, transiently stabilized balance states are possible even though the equilibrium is asymptotically unstable. The possibility that falls can be an intrinsic component of neural control of balance may provide new insights into how the risk of falling in the elderly can be minimized.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/SIADS_2015.pdf
14. J. Milton and T. Ohira. (2014). Mathematics as a laboratory tool: Dynamics, delays and noise.  Springer, New York.
    Abstract – The importance of mathematics in the undergraduate biology curriculum is ever increasing, as is the importance of biology within the undergraduate applied mathematics curriculum. This ambitious forward thinking book strives to make concrete connections between the two fields at the undergraduate level, bringing in a wide variety of mathematical methods such as signal processing, systems identification, and stochastic differential equations to an undergraduate audience interested in biological dynamics. The presentation stresses a practical hands-on approach: important concepts are introduced using linear first- or second-order differential equations that can be solved using “pencil and paper”; next, these are extended to “real world” applications through the use of computer algorithms written in Scientific Python or similar software.
15. T. Insperger and J. Milton. (2014). Sensory uncertainty and stick balancing at the fingertip. Biological Cybernetics   108: 85-101.
    Abstract – The effects of sensory input uncertainty, ε, on the stability of time-delayed human motor control are investigated by calculating the minimum stick length, crit, that can be stabilized in the inverted position for a given time delay, τ . Five control strategies often discussed in the context of human motor control are examined: three time invariant controllers [proportional–derivative, proportional–derivative–acceleration (PDA), model predictive (MP) controllers] and two time-varying controllers [act-and-wait (AAW) and intermittent predictive controllers]. The uncertainties of the sensory input are modeled as a multiplicative term in the system output. Estimates based on the variability of neural spike trains and neural population responses suggest that ε ≈ 7–13%. It is found that for this range of uncertainty, a tapped delay-line type of MP controller is the most robust controller. In particular, this controller can stabilize inverted sticks of the length balanced by expert stick balancers (0.25–0.5 m when τ ≈ 0.08 s). However, a PDA controller becomes more effective when ε > 15 %. A comparison between crit for human stick balancing at the fingertip and balancing on the rubberized surface of a table tennis racket suggest that friction likely plays a role in balance control. Measurements of crit, τ , and a variability of the fluctuations in the vertical displacement angle, an estimate of ε, may make it possible to study the changes in control strategy as motor skill develops.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/Biol_Cybern_2014.pdf
16. T. Insperger, J. Milton and G. Stepan. (2013). Acceleration feedback improves balancing against reflex delay. J. Roy. Soc. Interface 10: 20120763.
    Abstract – A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (PDA feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative (PD) controller in the sense that the PDA controller can stabilize systems with approximately 40% larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are typical feature of human postural sway.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/interface_2012.pdf
17. P. J. Marin, A. J. Herrero, J. Milton, T. J. Hazell and D. Garcia-Lopez. (2013). Whole-body vibration applied during upper body exercise improves performance. Journal of Strength and Conditioning Research  27: 1807-1812.
    Abstract – Whole-body vibration training has exercises perform static and dynamic resistance training exercises on a ground-based platform. Exposure to WBV exposure has demonstrated benefits and no effect on lower body strength, power, and performance. The aim of this study was determine if WBV exposure (50 Hz, 2.51 mm) has any potentiating effects post-exercise by measuring the kinematic variables of a set of upper body elbow extensor exercise (70% one-repetition maximum [1RM]) to volitional exhaustion. Sixteen recreationally active students (12 males and 4 females) performed three different experimental conditions on separate days. Each condition has subject’s perform on set of elbow-extension exercise to fatigue with one of three WBV treatments: WBV simultaneously during the set (AE); 60s after application of WBV for 30s (RE); and no WBV (CTRL). Kinematic parameters of each repition were monitored by linking a rotary encoder to the highest load plate. Mean velocity and acceleration throughout the set, as well as perceived exertion was analyzed. A significant increase (p<0.05) was observed in the mean velocity for the whole set in AE condition versus the CTRL condition. The mean acceleration was significantly higher (p < 0.05) in AE condition in comparison to RE (increased by 45.3%) and CTRL (increased by 50.4%) conditions. The positive effect indued by WBV on upper limb performance is only achieved when the stimulus is applied during the exercise. However, WBV aplpied 60s prior to the upper body exercise results in no benefit.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/marin_2013.pdf
18. J G Milton, A. Fuerte, C. Belair, J. Lippai, A. Kamimura and T. Ohira. (2013). Delayed pursuit-escape as a model for virtual stick balancing. Nonlinear Theory and Its Applications, IEICE   4: 129-137.
    Abstract – The process of pursuit and escape underlies many biological phenomena ranging from predator-prey interactions, combat and sporting activities. Time delays arise as a consequence of the time taken to identify the opponent, formulate a strategy, and then act upon it. Here we consider virtual stick balancing (VSB) as a delayed pursuit–escape task. The movements of the target in VSB are programmed to resemble those of balancing a stick at the fingertip. A model of delayed pursuit–escape is developed by assuming that the target movements are governed by a simple random walk that is under the control of the computer mouse through a delayed random walk biased towards the target when the time delay is zero. When the time delay is present movements can become transiently biased away from the target. Under conditions where the model reproduces the oscillatory dynamics and statistical properties of VSB, similar transient behaviors are observed immediately preceding escape of the target off the computer screen. The presence of a signature, or trigger, for impending escape suggests the possibility that escapes can be predicted before they occur.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/nolta_2013.pdf
19. J Milton. (2012). Neuronal avalanches, epileptic quakes and other transient forms of neurodynamics. European Journal of Neuroscience   36: 2156-2163.
    Abstract – Power law behaviors in brain activity in healthy animals, in the form of neuronal avalanches, potentially benefit the computational activities of the brain, including information storage, transmission and processing. In contrast, power law behaviors associated with seizures, in the form of epileptic quakes; potentially interfere with the brain’s computational activities. This review draws attention to the potential roles played by homeostatic mechanisms and multistable time-delayed recurrent inhibitory loops in the generation of power law phenomena. Moreover, it is suggested that distinctions between health and disease are scale-dependent. In other words, it is not the propagation of neural activity that is abnormal, but the propagation of activity in a neural population that is large enough to interfere with the normal activities of the brain that defines disease. From this point of view, epilepsy is a disease that results from a failure of mechanisms, possibly located in part in the cortex itself or in the deep brain nuclei and brainstem, which truncate, or otherwise confine, the spatiotemporal scales of these power law phenomena.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/EJN_avalanches.pdf
20.  J. L. Cabrera and J. G. Milton. (2012). Stick balancing, falls and Dragon Kings. European Physics Journal Special Topics   205: 231-241.
    Abstract – The extent to which the occurrence of falls, the dominant feature of human attempts to balance a stick at their fingertip, can be predicted is examined in the context of the “Dragon King” hypothesis. For skilled stick balancers, fluctuations in the controlled variable, namely the vertical displacement angle $\theta$, exhibit power law behaviors. When stick balancing is made less stable by either decreasing the length of the stick or by requiring the subject to balance the stick on the surface of a table tennis racket, systematic departures from the power law behaviors are observed in the range of large $\theta$. This observation raises the possibility that the presence of departures from the power law in the large length scale region, possibly Dragon Kings, may identify situations in which the occurrence of a fall is more imminent. However, whether or not Dragon Kings are observed, there is a Weibull-type survival function for stick falling. The possibility that increased risk of falling can, at least to some extent, be predicted from fluctuations in the controlled variable before the event occurs has important implications for the development of preventative strategies for the management of phenomena ranging from earthquakes to epileptic seizures to falls in the elderly.
    [Article – not found on jsd server]
21. J. G. Milton. (2012). Intermittent motor control: The “drift-and-act” hypothesis. Progress in Motor Control: Neural, computational and dynamic approaches M. J. Richardson, M. Riley and K. Shockley, eds Springer, New York: 169-193.
    Abstract – A characteristic of living organisms is the intermittency of their movement patterns. Here we discuss a mechanism for intermittent control in the context of human stick balancing at the fingertip. It is suggested that corrective movements are made only when deviations of the vertical displacement angle, and possibly the speed at which this angle changes, exceed certain thresholds. This ‘drift and act’ control strategy is facilitated by interplay between noise and delay which makes this balancing task easier to control. It is suggested that noise and delay are not part of the balance control problem, but rather, part of the solution used by the nervous system to control this complex voluntary motor task.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/chapter_motor_control.pdf
22. J. Milton, J. Lippai, R. Bellow, A. Blomberg, A. Kamimura and T. Ohira. (2011). Visuomotor tracking tasks with delayed pursuit and escape (DETC2011-47312). 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control  4: 419-425.
    Abstract – Virtual stick balancing (VSB) is a manual visuomotor tracking task that involves interplay between a human and a computer in which the movements are programmed to resemble those of balancing a stick at the fingertip. Since time delays and random perturbations (“noise”) are intrinsic properties of this task, we modeled VSB as a delayed pursuit-escape process: the target movements are described by a simple random walk and those movements controlled by the computer mouse by a delayed random walk biased towards the target. As subjects become more skilled, a stereotyped and recurring pursuit-escape pattern develops in which the mouse pursues the target until it overtakes it, causing the target to move in a different direction, followed, after a lag, by the pursing mouse. The delayed pursuit-escape random walk model captured the qualitative nature of this tracking task and provided insights into why this tracking task always fails at some point in time, even for the most expert subjects.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/DETC2011_47312.pdf
23. A. Quan, I. Osorio, T. Ohira and J. Milton. (2011). Vulnerability to paroxysmal oscillations in delayed neural networks: A basis for nocturnal frontal lobe epilepsy? Chaos 21: 047512.
    Abstract – Resonance can occur in bistable dynamical systems due to the interplay between noise and delay ($\tau$) in the absence of a periodic input. We investigate resonance in a two-neuron model with mutual time-delayed inhibitory feedback. For appropriate choices of the parameters and inputs three fixed-point attractors co-exist: two are stable and one is unstable. In the absence of noise, delay-induced transient oscillations (referred to herein as DITOs) arise whenever the initial function is tuned sufficiently close to the unstable fixed-point. In the presence of noisy perturbations, DITOs arise spontaneously. Since the correlation time for the stationary dynamics is $\sim \tau$, we approximated a higher order Markov process by a three-state Markov chain model by rescaling time as $t \rightarrow 2s\tau$, identifying the states based on whether the subintervals were completely confined to one basin of attraction (the two stable attractors) or straddled the separatrix, and then determining the transition probability matrix empirically. The resultant Markov chain model captured the switching behaviors including the statistical properties of the DITOs. Our observations indicate that time-delayed bistable dynamical systems are prone to generate DITOs as switches between the two attractors occur. Asymmetric double-well potentials naturally arise in situations when one attractor is gradually replaced by another. This may explain, for example, why seizures in certain epileptic syndromes tend to occur as sleep stages change.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/chaos_vulner.pdf
24. T. Ohira, A. Kamimura and J. G. Milton. (2011). Pursuit-escape with distance-dependent delay. ENOC2011 7th European Nonlinear Dynamics Conference, July 24-29, Rome, Italy : MS-11.
    Abstract – We introduce a time delay into a simple pursuit-escape model. It is shown that when the delay is state-dependent, the complexity of the dynamics become exquisitely sensitive to the relative positions of the chaser and escapee.
    [Article – Not found]
25. John G. Milton. (2011). The delayed and noisy nervous system: Implications for neural control. Journal of Neural Engineering  8: 065005.
    Abstract – Recent advances in the study of delay differential equations draw attention to the potential benefits of the interplay between random perturbations (“noise”) and delay on neural control. The phenomena include transient stabilizations of unstable steady states by noise, control of fast movements using time-delayed feedback, and the occurrence of long lived delay-induced transients. In particular, this research suggests that the interplay between noise and delay necessitates the use of intermittent, discontinuous control strategies in which corrective movements are made only when controlled variables cross certain thresholds. A potential benefit of such strategies is that they may be optimal for minimizing energy expenditures associated with control. In this review the concepts are made accessible by introducing them through simple illustrative examples that can be readily reproduced using software packages, such as XPPAUT.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/jne_noise_delay.pdf
26. J. Milton, A. Radunskaya, W. Ou and T. Ohira. (2011). A team approach to undergraduate research in biomathematics: Balance control. Math. Model. Nat. Phenom.  6(6): 260-277.
    Abstract – The question, how does an organism maintain balance? provides a unifying theme to introduce undergraduate students to the use of mathematics and modeling techniques in biological research. The availability of inexpensive high speed motion capture cameras makes it possible to collect the precise and reliable data that facilitates the development of relevant mathematical models. An in-house laboratory component ensures that students have the opportunity to directly compare prediction to observation and motivates the development of projects that push the boundaries of the subject. The projects, by their nature, readily lend themselves to the formation of interdisciplinary student research teams. Thus students have the opportunity to learn skills essential for success in today’s workplace including productive teamwork, critical thinking, problem solving, project management, and effective communication.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/mmnp_milton_2011.pdf
27. J. Wu, H. Zivari-Piran, J. D. Hunter and John G. Milton. (2011). Projective clustering using neural networks with adaptive delay and signal transmission loss. Neural Computation  23: 1568-1604.
    Abstract – We develop a new neural network architecture for projective clustering of data sets that incorporates adaptive transmission delays and signal transmission information loss. The resultant selective output signaling mechanism does not require the addition of multiple hidden layers but instead is based on the assumption that the signal transmission velocity between input processing neurons and clustering neurons is proportional to the similarity between the input pattern and the feature vector (the top-down weights) of the clustering neuron. The mathematical model governing the evolution of the signal transmission delay, the short-term memory traces and the long-term memory traces represents a new class of large scale delay differential equations where the evolution of the delay is described by a nonlinear differential equation involving the similarity measure aforementioned. We give a complete description of the computational performance of the network for a wide range of parameter values.
    Article – https://www.mitpressjournals.org/doi/pdf/10.1162/NECO_a_00124
28. Y. Y. Grinberg, J. G. Milton and R. P. Kraig. (2011). Spreading depression sends microglia on Lévy flights. PLoS ONE 6: e19294.
    Abstract – Spreading depression (SD) is thought to cause migraine aura, and perhaps migraine, and includes a transient loss of synaptic activity preceded and followed by increased neuronal excitability. Activated microglia influence neuronal activity and play an important role in homeostatic synaptic scaling via release of cytokines. Furthermore, enhanced neuronal function activates microglia to not only secrete cytokines but also to increase the motility of their branches, with somata remaining stationary. While SD also increases the release of cytokines from microglia, the effects on microglial movement from its synaptic activity fluctuations are unknown. Accordingly, we used time-lapse imaging of rat hippocampal slice cultures to probe for microglial movement associated with SD. We observed that in uninjured brain whole microglial cells moved. The movements were well described by the type of Lévy flight known to be associated with an optimal search pattern. Hours after SD, when synaptic activity rose, microglial cell movement was significantly increased. To test how synaptic activity influenced microglial movement, we enhanced neuronal activity with chemical long-term potentiation or LPS and abolished it with TTX. We found that microglial movement was significantly decreased by enhanced neuronal activity and significantly increased by activity blockade. Finally, application of glutamate and ATP to mimic restoration of synaptic activity in the presence of TTX stopped microglial movement that was otherwise seen with TTX. Thus, synaptic activity retains microglial cells in place and an absence of synaptic activity sends them off to influence wider expanses of brain. Perhaps increased microglial movements after SD are a long-lasting, and thus maladaptive, response in which these cells increase neuronal activity via contact or paracrine signaling, which results in increased susceptibility of larger brain areas to SD. If true, then targeting mechanisms that retard activity-dependent microglial Lévy flights may be a novel means to reduce susceptibility to migraine.
    Article
29. J. G. Milton. (2011). Neurodynamics and ion channels. The intersection of neurosciences, biology, mathematics, engineering and physics I. Osorio, H. P. Zavari, M. G. Frei and S. Arthurs, editors CRC Press, Boca Raton: 111-124.
30. J. Milton, A. Quan and I. Osorio. (2011). Nocturnal frontal lobe epilepsy: Metastability in a dynamic disease? The intersection of neurosciences, biology, mathematics, engineering and physics I. Osorio, H. P. Zavari, M. G. Frei and S. Arthurs, editors CRC Press, Boca Raton : 501-510.
    Abstract – The advantage of graphical approaches to complex dynamical systems, such as the brain, is that they can be used by neuroscientists to develop interpretations and key experiments even if the underlying mechanisms have not yet been fully identified. We illustrate this approach by showing that mathematical models of neural populations are particularly vulnerable for the production of paroxysmal transient events (possibly seizures) at times when changes in state occur as, for example, the transitions from wakefulness to sleep and through the sleep stages while sleeping. These arguments emphasize the importance of careful studies of the timing of seizure occurrences with respect to sleep stage transitions in patients with nocturnal frontal lobe epilepsy.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/NFLE_1.pdf
31. J. Milton, J. Gyorffy, J. L. Cabrera and T. Ohira. (2010). Amplitude control of human postural sway using Achilles tendon vibration. 16th US National Congress of Theoretical & Applied Mechanics :
    Abstract – The effects of low amplitude, periodic bilateral Achilles tendon vibration on center of pressure (COP) fluctuations during quiet standing with eyes closed are shown to be qualitatively similar to those generated by a parametrically excited time–delayed “drift and act” control model for the stabilization of an unstable fixed point.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/USNC_miltonetal_revised.pdf
32. J. Milton. (2010). Discovering golf’s innermost truths: A new approach to teaching the game: A commentary. Annual Review of Golf Coaching 2010: 115-118
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/golf_review_2010.pdf
33. J. G. Milton, A. E. Radunskaya, A. H. Lee, L. G. de Pillis and D. F. Bartlett. (2010). Team research at the biology-mathematics interface: Project management perspectives. CBE-Life Sciences Education 9: 316-322.
    Abstract – The success of interdisciplinary research teams depends largely upon skills related to team performance. We evaluated student and team performance for undergraduate biology and mathematics students who participated in summer research projects conducted in off-campus laboratories. The student teams were composed of a student with a mathematics background and an experimentally oriented biology student. The team mentors, who were blinded to the students prior academic record, typically ranked the students performance very good to excellent over a range of attributes that included creativity and ability to conduct independent research. In contrast, evaluation of team performance indicated that the research teams did not function well in terms of basic project management skills including preparation of a work plan with defined deliverables and deadlines, clear delegation of responsibilities, a proactive plan for problem solving, and an understanding of project scope. Thus typical undergraduate biology and mathematics students do not have the skill sets required to effectively perform within an interdisciplinary research team. Since project management skills can be readily taught and moreover typically reflect good research practices, it should be possible to make simple modifications to undergraduate curricula so that the promise of initiatives, such as MATH-BIO 2010, can be implemented.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/rembi_CBE_2010.pdf
34. J.G. Milton. (2010). Epilepsy as a dynamic disease: A tutorial of the past with an eye to the future. Epilepsy & Behavior   18: 33-44.
    Abstract – How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating and shaping the direction of the efforts of each other.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/epil_behav.pdf
35. John G. Milton. (2010). Quantitative neuroscience: From chalk board to bedside. Math. Model Nat. Phenom. 5: 1-4.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/mmnp_editorial.pdf
36. J. Milton, P. Naik, C. Chan and Sue Ann Campbell. (2010). Indecision in neural decision making models. Mathematical Modeling of Natural Phenomena   5: 125-145.
    Abstract – Computational models for human decision making are typically based on the properties of bistable dynamical systems where each attractor represents a different decision. A limitation of these models is that they do not readily account for the fragilities of human decision making, such as “choking under pressure”, indecisiveness and the role of past experiences on current decision making. Here we examine the dynamics of a model of two interacting neural populations with mutual time–delayed inhibition. When the input to each population is sufficiently high, there is bistability and the dynamics is determined by the relationship of the initial function to the separatrix (the stable manifold of a saddle point) that separates the basins of attraction of two co-existing attractors. The consequences for decision making include long periods of indecisiveness in which trajectories are confined in the neighborhood of the separatrix and wrong decision making, particularly when the effects of past history and irrelevant information (“noise”) are included. Since the effects of delay, past history and noise on bistable dynamical systems are generic, we anticipate that similar phenomena will arise in the setting of other physical, chemical and neural time-delayed systems which exhibit bistability.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/miltonetal_MMNP_revised_final_rev_2.pdf
37. I. Osorio, M.G. Frei, D. Sornette, J. Milton and Y-C Lai. (2010). Epileptic seizures: Quakes of the brain? Physical Rev E  82: 021919.
    Abstract – A dynamical analogy supported by five scale-free statistics the Gutenberg-Richter distribution of event sizes, the distribution of interevent intervals, the Omori and inverse Omori laws, and the conditional waiting time until the next event is shown to exist between two classes of seizures “focal” in humans and generalized in animals and earthquakes. Increments in excitatory interneuronal coupling in animals expose the system’s dependence on this parameter and its dynamical transmutability: moderate increases lead to power-law behavior of seizure energy and interevent times, while marked ones to scale-free power-law coextensive with characteristic scales and events. The coextensivity of power law and characteristic size regimes is predicted by models of coupled heterogeneous threshold oscillators of relaxation and underscores the role of coupling strength in shaping the dynamics of these systems.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/quakes.pdf
38. J.G. Milton. (2009). Introduction to focus issue: Bipedal locomotion – From robots to humans. Chaos 19: 026101.
    Abstract – Running and walking, collectively referred to as bipedal locomotion, represent self-organized behaviors generated by a spatially distributed dynamical system operating under the constraint that a person must be able to move without falling down. The organizing principles involve both forces actively regulated by the nervous system and those generated passively by the biomechanical properties of the musculo-skeletal system and the environment in which the movements occur. With the development of modern motion capture and electro-physiological techniques it has become possible to explore the dynamical interplay between the passive and active controllers of locomotion in a manner that directly compares observation to predictions made by relevant mathematical and computer models. Consequently, many of the techniques initially developed to study nonlinear dynamical systems, including stability analyses, phase resetting and entrainment properties of limit cycles, and fractal and multi-fractal analysis, have come to play major roles in guiding progress. This focus issue discusses bipedal locomotion from the point of view of dynamical systems theory with the goal of stimulating discussion between the dynamical systems, physics, biomechanics and neuroscience communities.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/chaos_focus_2009.pdf
39. J. Milton, J. L. Cabrera, T. Ohira, S. Tajima, Y. Tonosaki, C. W. Eurich, S. A. Campbell. (2009). The time-delayed inverted pendulum: Implications for human balance control. Chaos  19: 026110.
    Abstract – The inverted pendulum is frequently used as a starting point for discussions of how human balance is maintained during standing and locomotion. Here we examine three experimental paradigms of time-delayed balance control: 1) the mechanical inverted time-delayed pendulum, 2) stick balancing at the fingertip, and 3) human postural sway during quiet standing. Measurements of the transfer function (mechanical stick balancing) and the two-point correlation function (Hurst exponent) for the movements of the fingertip (real stick balancing) and the fluctuations in the center of pressure (postural sway) demonstrate that the upright fixed-point is unstable in all three paradigms. These observations imply that the balanced state represents a more complex and bounded time-dependent state than a fixed-point attractor. Although mathematical models indicate that a sufficient condition for instability is that the time delay to make a corrective movement, $\tau_n$, be greater than a critical delay, $\tau_c$, that is proportional to the length of the pendulum, this condition is satisfied only in the case of human stick balancing at the fingertip. Thus it is suggested that a common cause of instability in all three paradigms stems from the difficulty controlling both the angle of the inverted pendulum and the position of the controller simultaneously using time-delayed feedback. Considerations of the problematic nature of control in the presence of delay and random perturbations (“noise”) suggests that neural control for the upright position likely resembles an adaptive–type controller in which the displacement angle is allowed to drift for small displacements with active corrections made only when $\theta$ exceeds a threshold. This mechanism draws attention to an overlooked type of passive control that arises from the interplay between retarded variables and noise.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/chaos_inv_pend.pdf
40.  T. Ohira and J. Milton. (2009). Delayed random walks: Investigating the interplay between noise and delays. Delay Differential Equations: Recent Advances and New Directions (B. Balachandran, T. Kalmar-Nagy and D. E. Gilsinn, eds. Springer-Verlag: New York): 305-335.
    Abstract – A model for a 1-dimensional delayed random walk is developed by generalizing the Ehrenfest model of a discrete random walk evolving on a quadratic, or harmonic, potential to the case of non-zero delay. The Fokker-Planck equation derived from this delayed random walk (DRW) is identical to that obtained starting from the delayed Langevin equation, i.e. a first–order stochastic delay differential equation (SDDE). Thus this DRW and SDDE provide alternate, but complimentary ways for describing the interplay between noise and delay in the vicinity of a fixed point. The DRW representation lends itself to determinations of the joint probability function and, in particular, to the auto-correlation function for both the stationary and transient states. Thus the effects of delay are manifested through experimentally measurable quantities such as the variance, correlation time, and the power spectrum. Our findings are illustrated through applications to the analysis of the fluctuations in the center of pressure that occur during quiet standing.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/DDE_book_chapter_2009.pdf
41. G. B. Ermentrout and J. G. Milton. (2009). The dynamics of toys. DS Web Magazine  January.
    Abstract – The ability of toys to awaken mathematical curiosity stems from their interesting motions, which range from periodic oscillations to even chaos. Since these movements are governed by the toy’s intrinsic physical properties it is relatively easy to generate models in the form of differential equations. However, can these models capture the observed dynamics? The increasing availability of inexpensive, easy-to-use motion capture technologies makes it possible to quantitatively compare model to toy. These approaches identify a number of unresolved mathematical problems whose solutions may ultimately provide insights into why the nervous system is so fascinated with toys and play.
42. I. Osorio, M. G. Frei, D. Sornette, J. Milton. (2009). Pharamco-resistant seizures: self-triggering capacity, scale-free properties and predictability?. European Journal of Neuroscience  30: 1554-1558.
    Abstract – Relevant and timely questions such as regarding the predictability of seizures and their capacity to trigger more seizures remain the subject of debate in epileptology. The present study endeavors to gain insight into these dynamic issues by adopting a non-reductionist approach and via the use of mathematical tools. Probability distribution functions of seizure energies and inter-seizure intervals and the probability of seizure occurrence conditional upon the time elapsed from the previous seizure were estimated from prolonged recordings from subjects with pharmaco-resistant seizures, undergoing surgical resections, on reduced doses of or on so medications. The energy and inter-seizure interval distributions for pharmaco-resistant seizures, under the prevailing study conditions, are governed by power laws (‘scale-free’ behavior). Pharmaco-resistant seizures tend to occur in clusters and the time to the next seizure increases with the duration of the seizure-free interval since the last one. However, characteristic size energy probability density functions were found in a few subjects. These findings suggests that: (i) pharmaco-resistant seizures have an inherent self-triggering capacity; (ii) their time of occurrence and intensity may be predictable in light of the existence of power law distributions and of their self-triggering capacity; and (iii) their lack of typical size and duration (scale-free), features upon which their classification into ictal or interictal is largely based, may be inadequate/insufficient classifiers.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/ejn_6923.pdf
43. J. Milton, J. L. Townsend, M. A. King and T. Ohira. (2009). Balancing with positive feedback: The case for discontinuous control. Philosophical Transactions of the Royal Society, Series A  367: 1181-1193.
    Abstract – Experimental observations indicate that positive feedback plays an important role for maintaining human balance in the upright position. This observation is used to motivate an investigation of a simple switch-like controller for postural sway in which corrective movements are made only when the vertical displacement angle exceeds a certain threshold. This mechanism is shown to be consistent with the experimentally observed variations in the two-point correlation for human postural sway. Analysis of the first passage times for this model suggests that this control mechanism may slow escape by taking advantage of two intrinsic properties of a stochastic unstable first-order delay differential equation: firstly, time delay, and secondly, the possibility that the dynamics can be “temporarily confined” near the origin.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/trans_royal_soc.pdf
44. J.G. Milton, T. Ohira, J.L. Cabrera, R.M. Fraiser, J.B. Gyorffy, F.K. Ruiz, M.A. Strauss, E.C. Balch, P.J. Marin, J.L. Alexander. (2009). Balancing with vibration: A prelude for ‘drift and act’ balance control. PLoS ONE  4: e7427.
    Abstract – Stick balancing at the fingertip is a powerful paradigm for the study of the control of human balance. Here we show that the mean stick balancing time is increased by about two-fold when a subject stands on a vibrating platform that produces vertical vibrations at the fingertip (0.001m, 15-50 Hz). High speed motion capture measurements in three dimensions demonstrate that vibration does not shorten the neural latency for stick balancing or change the distribution of the changes in speed made by the fingertip during stick balancing, but does decrease the amplitude of the fluctuations in the relative positions of the fingertip and the tip of the stick in the horizontal plane, A(x,y). The findings are interpreted in terms of a time-delayed “drift and act” control mechanism in which controlling movements are made only when controlled variables exceed a threshold, i.e. the stick survival time measures the time to cross a threshold. The amplitude of the oscillations produced by this mechanism can be decreased by parametric excitation. It is shown that a plot of the logarithm of the vibration-induced increase in stick balancing skill, a measure of the mean first passage time, versus the standard deviation of the A(x,y) fluctuations, a measure of the distance to the threshold, is linear as expected for the times to cross a threshold in a stochastic dynamical system. These observations suggest that the balanced state represents a complex time-dependent state which is situated in a basin of attraction that is of the same order of size. The fact that vibration amplitude can benefit balance control raises the possibility of minimizing risk of falling through appropriate changes in the design of footwear and roughness of the walking surfaces.
    Article – https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0007427
45. J.G. Milton, S.L. Small and A. Solodkin. (2008). Why did Casey strike out? The neuroscience of hitting. Brain on Cubs: Inside the heads of players and fans (D. Gordon, ed, Dana Press, New York) Dana Press, New York : 43-57.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/baseball.pdf
46.  J.G. Milton, J.L. Cabrera and T. Ohira. (2008). Unstable dynamical systems: Delays, noise and control. EPL   83: 48001.
    Abstract – Escape from an unstable fixed point in a time-delayed dynamical system in the presence of additive noise depends both on the magnitude of the time delay, r, and the initial function. In particular, the longer the delay the smaller the variance and hence the slower the rate of escape. Numerical simulations demonstrate that the distribution of first passage times is bimodal, the longest first passage times are associated with those initial functions that cause the greatest number of delayed zero crossings, i.e. instances where deviations of the controlled variable from the fixed point at times t and t-r have opposite signs. These observations support the utility of control strategies using pulsatile stimuli triggered only when variables exceed certain thresholds.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/epl_2008.pdf
47. John Milton, Steven L. Small and Ana Solodkin. (2008). Imaging motor imagery: Methodological issues related to expertise. Methods  45: 336-341.
    Abstract –  Mental imagery (MI) is the mental rehearsal of movements without overt execution. Brain imaging techniques have made it possible to identify the brain regions that are activated during MI and, for voluntary motor tasks involving hand and finger movements, to make direct comparisons with those areas activate during actual movement. However, the fact that brain activation differs for different types of imagery (visual or kinetic) and depends on the skill level of the individual (e.g. novice or elite athlete) raises a number of important methodological issues for the design of brain imaging protocols to study MI. These include instructing the subject concerning the type of imagery to use, objective measurement of skill level, the design of motor tasks sufficiently difficult to produce a range of skill levels, the effect of different environments on skill level (including the imaging device), and so on. It is suggested that MI is more about the neurobiology of the development of motor skills that have already been learned, but not perfected, than it is about learning motor skills de novo.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/methods_2008.pdf
48. J.D. Hunter, J. Wu and J.G. Milton. (2008). Clustering neural spike trains with transient responses. Proceedings IEEE Decision and Control 47: 2000-2005.
    Abstract – The detection of transient response, i.e. non-stationarities, that arise in a varying and small fraction of the total number of neural spike trains recorded from chronically implanted multielectrode grids becomes increasingly difficult as the number of electrodes grows. This paper presents a novel application of an unsupervised neural network for clustering neural spike trains with transient responses. This network is constructed by incorporating projective clustering into an adaptive resonance type network (ART) architecture resulting in a PART network. Since comparisons are made between inputs and learned patterns using only a subset of the total number of dimensions, PART neural networks are ideally suited to the detection of transients. We show that PART neural networks are an effective tool for clustering neural spike trains that is easily implemented, computationally inexpensive, and well suited for detecting neural responses to dynamic environmental stimuli.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/IEEE_2008.pdf
49. J.G. Milton, S.A. Chkhenkeli and V.L. Towle. (2007). Brain connectivity and the spread of epileptic seizures. Handbook of Brain Connectivity (V. K. Jirsa and A. R. McIntosh, eds. Springer: New York): 477-503.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/Conn.pdf
50. John Milton, Ana Solodkin, Petr Hlustik and Steven L. Small. (2007). The mind of expert motor performance is cool and focused. NeuroImage   35: 804-813.
    Abstract – Extraordinary motor skills required for expert athletic or music performance require longstanding and intensive practice leading to two critical skills, a level of maximal performance that far exceeds that of non-experts and a degree of privileged focus on motor performance that excludes intrusions. This study of motor planning in expert golfers demonstrated their brain activation during their pre-shot routine to be radically different than in novices. The posterior cingulate, the amuygdala-forebrain complex, and the basal ganglia were active only in novices, whereas experts had activation primarily in the superior parietal lobule, the dorsal lateral premotor area, and the occipital area. The fact that these differences are apparent before the golfer swings the club suggests that the disparity between the quality of the performance of novice and expert golfers lies at the level of the organization of neural networks during motor planning. In particular, we suggest that extensive practice over a long period of time leads experts to develop a focused and efficient organization of task-related neural networks, whereas novices have difficulty filtering out irrelevant information.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/golf_neuroimage.pdf
51. Juan Luis Cabrera, Christian Luciani and John Milton. (2006). Neural control on multiple time scales: Insights from human stick balancing. Condensed Matter Physics 9: 373-383.
    Abstract – The time-delayed feedback control mechanisms of the nervous system are continuously subjected to the effects of uncontrolled random perturbations (herein referred to as noise). In this setting the statistical properties of the fluctuations in the controlled variable(s) can provide non-invasive insights into the nature of the underlying control mechanisms. We illustrate this concept through a study of stick balancing at the fingertip using high speed motion capture techniques. Experimental observations together with numberical studies of a stochastic delay differential equation demonstrate that on time scales short compared to the neural time delay (“fast control”), parameetric noise provides a non-predictive mechanism that transiently stabilizes the upright position of the balanced stick. Moreover numerical simulations of a delayed random walker with a repulsive origin indicate that even an unstable fixed points can be transiently stabilized by the interplay between noise and time delay. In contrast, on time scales comparable to the neural time delay (“slow control”), feedback and feedforward control mechanisms become more important. The relative contribution of the fast and slow control mechanisms to stick balancing is dynamic and, for example, depends on the context in which stick balancing is performed and the expertise of the balancer.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/cmp_2006.pdf
52. Tadaaki Hosaka, Toru Ohira, Christian Luciani, Juan Luis Cabrera, and John G Milton. (2006). Balancing with noise and delay. Progress of Theoretical Physics Supplement  161: 314-319.
    Abstract – Motivated by recent studies in human balance control, we study a delayed random walk with an unstable fixed point. It is observed that the random walker moves away from the unstable fixed point more slowly than is observed in the absence of delay. It is shown that, for a given noise level, there exists an optimal delay to achieve the longest first passage time. Our observations support recent demonstrations that noise has a beneficial role for balance control and emphasize that predictive strategies are not necessary to transiently control balance.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/hosakaetal06.pdf
53. John G. Milton. (2005). Noise as therapy: A prelude to computationally-based neurology?. Annals of Neurology  58: 173-174.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/annals_neuro.pdf
54. JL Cabrera and J Milton. (2005). Insights into the control of instability: Human stick balancing. Proceedings of the 2nd COE Workshop on Human Adaptive Mechatronics : 185-190.
    Abstract – Three-dimensional motion analysis shows that fluctuations in the vertical displacement angle of a stick balanced at a human fingertip follows the characteristics of on-off intermittency and that over 98% of the corrective movements happens faster than the physiological time delay. These results are reproduced by a nonlinear equation with time delay and parametric noise. Also the fingertip speed changes can be described by a truncated Lévy distribution. With increased skill, the distribution index remains constant but tails of the distribution become broader so that the truncations decrease as skill level increases. With learning the truncation of the Lévy flight becomes better optimized for balance control. These observations provide the first evidence that changes in a Lévy flight may have functional significance for the nervous system and support strongly the idea of a nonpredictive control for stick balancing.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/COE_HAM_2005.pdf
55. Cabrera JL and Milton JG. (2004). Human stick balancing: Tuning Lévy flights to improve balance control. CHAOS   14(3): 691-698.
    Abstract – State-dependent, or parametric, noise is an essential component of the neural control mechanism for stick balancing at the fingertip. High-speed motion analysis in three dimensions demonstrates that the controlling movements made by the fingertip during stick balancing can be described by a Lévy flight. The Lévy index, is approximately 0.9; a value close to optimal for a random search. With increased skill, the index does not change. However, the tails of the L�vy distribution become broader. These observations suggest a L�vy flight that is truncated by the properties of the nervous and musculoskeletal system; the truncation decreasing as skill level increases. Measurements of the cross-correlation between the position of the tip of the stick and the fingertip demonstrate that the role of closed-loop feedback changes with increased skill. Moreover, estimation of the neural latencies for stick balancing show that for a given stick length, the latency increases with skill level. It is suggested that the neural control for stick balancing involves a mechanism in which brief intervals of consciously generated, corrective movements alternate with longer intervals of prediction-free control. With learning the truncation of the Lévy flight becomes better optimized for balance control and hence the time between successive conscious corrections increases. These observations provide the first evidence that changes in a Lévy flight may have functional significance for the nervous system. This work has implications for the control of balancing problems ranging from falling in the elderly to the design of two-legged robots and earthquake proof buildings
    [Article – URL not found]
56. Cabrera JL, Bormann R, Eurich C, Ohira T and Milton J. (2004). State-dependent noise and human balance control. Fluctuations Noise Letters 4: L107-L118.
    Abstract – The fluctuations observed in the task of stick balancing at the fingertip exhibit many of the properties predicted to occur in parametric stochastic dynamical systems, namely intermittency, truncated Lévy flights and truncated Lévy distributions. The development of virtual balancing tasks that involve the interplay between a human and computer and that exhibit the same dynamical properties as seen for stick balancing opens the door for experimental investigations into the nature of the neural motor control mechanisms that underlie these phenomena.
    Article
57. Milton J., Small S. and Solodkin A. (2004). On the road to automatic: Dynamic aspects of skill acquisition. J. Clinical Neurophysiology   21(3): 134-143.
    Abstract – One of the important steps on the road to becoming expert in a motor skill occurs when the individual can perform the movements in a seemingly effortless and automatic fashion. The authors review two lines of investigations, namely, fMRI and mathematically guided studies of the dynamics of skill acquisition, that suggest that this road to automatic involves two steps: (1) an increasing reliance on the self-regulatory aspects of the motor task, and (2) a minimization of the role of mechanisms based on intentionally directed corrective movements. The interplay between these two mechanisms implies that, at a given skill level, performance decreases whenever intention intervenes. The observation that psychological factors may be as important as mechanical repetition for the development of expertise has important implications for the design of neurorehabilitative strategies.
    [Article – URL not found]
58. Bormann R, Cabrera JL, Milton JG and Eurich CW. (2004). Visuomotor tracking on a computer screen: An experimental paradigm to study the dynamics of motor control. Neurocomputing 58-60C: 517-523.
    Abstract – In this work we propose a new experimental paradigm in the context of human motor control. Human subjects track a target with a mouse-pointer on a computer screen while the underlying dynamics is similar to a stick-balancing problem. This approach gives wide control over system parameters. We show that there are two scaling regions in the power spectrum of the distance r between mouse and target and find a power law in the laminar phases distribution of r. We propose a model for this dynamics and compare the model results to the experimental findings.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/bormann.pdf
59. Cabrera JL and Milton JG. (2004). Stick balancing: On-off intermittency and survival times. Nonlinear Science 11(3): 305-317.
    Abstract – The fluctuations in the vertical displacement angle of a stick balanced at the fingertip exhibit on-off intermittency. However, even a skilled balancer cannot indefinitely maintain a stick balanced at their fingertip. The survival function for stick balancing, P(t_esc > t), is shown to have the form of a Weibul function, exp(- kt)^c, where k is a constant and c > 1. The measured survival function can be reproduced by a stochastic delayed discrete map possessing only unstable solutions. These observations emphasize the importance of state-dependent, or parametric, noise in this balancing task.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/nonlin_sci.pdf
60. Milton JG, Foss J, Hunter JD and Cabrera JL. (2004). Controlling neurological disease at the edge of instability. Quantitative Neurosciences: Models, Algorithms, Diagnostics, and Therapeutic Applications (P. M. Pardalos, J. C. Sackellares, P. R. Carney and L. D. Iasemidis, eds. Kluwer Academic: Boston) Kluwer Academic Publishers: Boston : 117-143.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/Chap_Milton.pdf
61.  Foss J and Milton J. (2003). Multistability in delayed recurrent neural loops. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds, Springer-Verlag, New York) Springer-Verlag: New York: 283-295.
62. Cabrera JL and Milton JG. (2003). Delays, scaling and the acquisition of motor skill. In Bezrukov, S, ed. Unsolved Problems of Noise and Fluctuations: UpoN 2002. Biology and High Technology Third International Conference on Unsolved Problems of Noise and Fluctuations in Physics AIP Proceedings 665, American Institute of Physics, Melville, NY : 250-256.
    Abstract – Motion analysis in three dimensions reveals a number of surprising features of the neural control of stick balancing at the fingertip, namely, 1) on-off intermittency in the controlled variable, and 2) controlling motor forces that exhibit self-similarity. The growing evidence in support of scaling and critical behaviors in neural motor control necessitates a re-thinking of how the nervous system works.
    [Article – URL not found]
63. Milton JG and Jung P. (2003). Epilepsy as a dynamic disease (Springer-Verlag, New York, pp. 1-417.) 
64. Milton J and Jung P. (2003). Brain defibrillators: Synopsis, problems and future directions. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds. Springer-Verlag: New York) Springer-Verlag: New York: 341-352.
65. Chkhenkeli SA and Milton J . (2003). Dynamic epileptic systems versus static epileptic foci. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds., Springer-Verlag: New York) Springer-Verlag: New York: 24-36.
66.  Milton JG. (2003). Insights into seizure propagation from axonal conduction times. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds., Springer-Verlag: New York) Springer-Verlag: New York: 15-23.
67. Milton JG. (2003). Medically intractable epilepsy. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds., Springer-Verlag, New York) Springer-Verlag: New York : 1-14.
68. J. Foss and J. Milton. (2003). Multistability in delayed recurrent inhibitory loops. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds. Springer-Verlag: New York)  : 283-295.
69. Ebersole JS and Milton J. (2003). The electro-encephalogram (EEG): A measure of neural synchrony. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds. Springer-Verlag, New York)  : 51-68.
70. Hunter JD and Milton J. (2003). Using inhibitory interneurons to control neural synchrony. Epilepsy as a Dynamic Disease (J. Milton and P. Jung, eds., Springer-Verlag, New York) Springer-Verlag: New York: 115-130.
71. Mundel T, Milton JG, Dimitrov A, Wilson HW, Pelizarri C, Uftring S, Torres I, Erickson RK, Spire J-P and Towle VL . (2003). Transient inability to distinguish between faces: Electrophysiological studies. J. Clinical Neurophysiology   20: 102-110.
    Abstract – It is not known with certainty at which level of face processing by the cortex the distinction between a familiar and an unfamiliar face is made. Subdural electrodes were implanted under the fusiform gyrus of the right temporal lobe in a patient who developed an unusual inability to distinguish differences between faces as part of the epileptic aura (“all faces looked the same”). A cortical region located posterior to the epileptic focus was identified that exhibited a maximum evoked response to the presentation of facial images (N165), but not to objects, scenes, or character strings. Evoked potentials elicited by a variety of visual images indicated that any perturbation away from novel whole-face stimuli produced submaximal responses from this region of the right temporal lobe. Electrical stimulation of this region resulted in an impairment of face discrimination. It was found that presentation of familiar faces (grandmother, treating physician) produced a different response from that observed for novel faces. These observations demonstrate that within 165 msec of face presentation, and before the conscious precept of face familiarity has formed, this cortical region has already begun to distinguish between a familiar and an unfamiliar face.
    [Article – URL not found]
72. Hunter JD and Milton J. (2003). Amplitude and frequency dependence of spike timing: Implications for dynamic regulation. J. Neurophysiology 90: 387-394.
    Abstract – The spike-time reliability of motoneurons in the Aplysia buccal motor ganglion was studied as a function of the frequency content and the relative amplitude of the fluctuations in the neuronal input, calculated as the coefficient of variation (CV). Measurements of spike-time reliability to sinusoidal and aperiodic inputs, as well as simulations of a noisy leaky integrate-and-fire neuron stimulated by spike trains drawn from a periodically modulated process, demonstrate that there are three qualitatively different CV-dependent mechanisms that determine reliability: noise-dominated (CV < 0.05 for Aplysia motoneurons) where spike timing is unreliable regardless of frequency content; resonance-dominated (CV 0.05–0.25) where reliability is reduced by removal of input frequencies equal to motoneuron firing rate; and amplitude-dominated (CV >0.35) where reliability depends on input frequencies greater than motoneuron firing rate. In the resonance-dominated regime, changes in the activity of the presynaptic inhibitory interneuron B4/5 alter motoneuron spike-time reliability. The increases or decreases in reliability occur coincident with small changes in motoneuron spiking rate due to changes in interneuron activity. Injection of a hyperpolarizing current into the motoneuron reproduces the interneuron-induced changes in reliability. The rate-dependent changes in reliability can be understood from the phase-locking properties of regularly spiking motoneurons to periodic inputs. Our observations demonstrate that the ability of a neuron to support a spike-time code can be actively controlled by varying the properties of the neuron and its input.
    Article – https://journals.physiology.org/doi/full/10.1152/jn.00074.2003?hits=10&volume=90&HITS=10&sortspec=relevance&searchid=1099335965440_1948&firstpage=387&maxtoshow=&FIRSTINDEX=0&stored_search=&RESULTFORMAT=
73. Moss F and Milton J. (2003). Balancing the unbalanced. Nature  (News and Reviews) 425: 911-912.
    [Article – URL not found]
74. Milton J. (2003). Pupil light reflex: Delays, oscillations and noise. Nonlinear Dynamics in Physiology and Medicine (A. Beuter, L. Glass, M. C. Mackey and M. S. Titcombe, eds, Springer-Verlag: New York) Springer-Verlag: New York : 269-299.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/pupil_mcgill.pdf
75. Cabrera JL and Milton JG. (2002). On-off intermittency in a human balancing task. Phys. Rev. Lett.   89: 157802-1-4.
    Abstract – Motion analysis in three dimensions demonstrate that the fluctuations in the vertical displacement angle of a stick balanced at the fingertip obey a scaling law characteristic of on-off intermittency and that >98% of the corrective movements occur fast compared to the measured time delay. These experimental observations are reproduced by a model for an inverted pendulum with time-delayed feedback in which parametric noise forces a control parameter across a particular stability boundary. Our observations suggest that parametric noise is an essential, but up until now underemphasized, component of the neural control of balance.
    [Article – URL not found]
76. JL Cabrera and J Milton. (2002). Self-similarity in a human balancing task. Proceedings of the Second Joint EMBS/BMES Conference : 3-4.
    Abstract – High speed motion analysis techniques in 3-D are used to demonstrate that the magnitude of the corrective forces made by a finger of a trained individual during stick balancing are self-similar and in particular are described by a truncated Lévy flight (TLF). The presence of scaling in a balancing task requires that current theories of motor control be re-evaluated.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/cabrera_self_sim.pdf
77.  Hunter JD and Milton JG. (2001). Synaptic heterogeneity and stimulus-induced modulation of depression in central synapses. J. Neuroscience  21: 5781-5793.
    Abstract – Short-term plasticity is a pervasive feature of synapses. Synapses exhibit many forms of plasticity operating over a range of time scales. We develop an optimization method that allows rapid characterization of synapses with multiple time scales of facilitation and depression. Investigation of paired neurons that are postsynaptic to the same identified interneuron in the buccal ganglion of Aplysia reveals that the responses of the two neurons differ in the magnitude of synaptic depression. Also, for single neurons, prolonged stimulation of the presynaptic neuron causes stimulus-induced increases in the early phase of synaptic depression. These observations can be described by a model that incorporates two availability factors, e.g., depletable vesicle pools or desensitizing receptor populations, with different time courses of recovery, and a single facilitation component. This model accurately predicts the responses to novel stimuli. The source of synaptic heterogeneity is identified with variations in the relative sizes of the two availability factors, and the stimulus-induced decrement in the early synaptic response is explained by a slowing of the recovery rate of one of the availability factors. The synaptic heterogeneity and stimulus-induced modifications in synaptic depression observed here emphasize that synaptic efficacy depends on both the individual properties of synapses and their past history.
    Article
78. Foss J and Milton J. (2000). Multistability in recurrent neural loops arising from delay. J. Neurophysiol  84: 975-985.
    Abstract – Multistability in Recurrent Neural Loops Arising From Delay. J. Neurophysiol. 84: 975-985, 2000. The dynamics of a recurrent inhibitory neural loop composed of a periodically spiking Aplysia motoneuron reciprocally connected to a computer are investigated as a function of the time delay, for propagation around the loop. It is shown that for certain choices of , multiple qualitatively different neural spike trains co-exist. A mathematical model is constructed for the dynamics of this pulsed-coupled recurrent loop in which all parameters are readily measured experimentally: the phase resetting curve of the neuron for a given simulated postsynaptic current and. For choices of the parameters for which multiple spiking patterns co-exist in the experimental paradigm, the model exhibits multistability. Numerical simulations suggest that qualitatively similar results will occur if the motoneuron is replaced by several other types of neurons and that once becomes sufficiently long, multistability will be the dominant form of dynamical behavior. These observations suggest that great care must be taken in determining the etiology of qualitative changes in neural spiking patterns, particularly when propagation times around polysynaptic loops are long.
    Article
79. Milton JG and Mackey JG. (2000). Neural ensemble coding and statistical periodicity: Speculations on the operation of the mind’s eye. J. Physiol.  94: 489-503.
    Abstract – Statistical periodicity is a statistical property of densities which arises in the description of retarded dynamical systems. This property is particularly attractive as a possible mechanism for the ensemble coding of information in the nervous system because it operates rapidly and has high storage capacity. For a population of neurons which exhibits statistical periodicity, information would not be encoded by the periodicity, but rather by the spatio-temporal distributions of neural activity. Statistical periodicity is discussed in relation to the temporal binding hypothesis and to the occurrence of multistability in neural systems.
    [Article – URL not found]
80. Milton JG. (2000). Epilepsy and the multistable nervous system. Self-organized Biological Dynamics and Nonlinear Control by External Stimuli (J Walleczek, ed, Cambridge University Press: Cambridge, MA) Cambridge University Press: Cambridge MA: 374-386.
    Article – https://faculty.jsd.claremont.edu/jmilton/reprints/milton_multi_2000.pdf