A range of applications, from predicting the spread of human and electronic viruses to city planning and resource management in mobile communications, depend on our ability to foresee the whereabouts and mobility of individuals, raising a fundamental question: To what degree is human behavior predictable? Here we explore the limits of predictability in human dynamics by studying the mobility patterns of anonymized mobile phone users. By measuring the entropy of each individual's trajectory, we find a 93% potential predictability in user mobility across the whole user base. Despite the significant differences in the travel patterns, we find a remarkable lack of variability in predictability, which is largely independent of the distance users cover on a regular basis.

Limits of Predictability in Human Mobility

Stochastic resonance is said to be observed when increases in levels of unpredictable fluctuations— e.g., random noise—cause an increase in a metric of the quality of signal transmission or detection performance, rather than a decrease. This counterintuitive effect relies on system nonlinearities and on some parameter ranges being ''suboptimal''. Stochastic resonance has been observed, quantified, and described in a plethora of physical and biological systems, including neurons. Being a topic of widespread multidisciplinary interest, the definition of stochastic resonance has evolved significant- ly over the last decade or so, leading to a number of debates, misunderstandings, and controversies. Perhaps the most important debate is whether the brain has evolved to utilize random noise in vivo, as part of the ''neural code''. Surprisingly, this debate has been for the most part ignored by neuroscientists, despite much indirect evidence of a positive role for noise in the brain. We explore some of the reasons for this and argue why it would be more surprising if the brain did not exploit randomness provided by noise—via stochastic resonance or otherwise—than if it did. We also challenge neurosci- entists and biologists, both computational and experi- mental, to embrace a very broad definition of stochastic resonance in terms of signal-processing ''noise benefits'', and to devise experiments aimed at verifying that random variability can play a functional role in the brain, nervous system, or other areas of biology.

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What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology

Increased intraindividual variability (IIV), reflecting within-person fluctuations in behavioral performance, is commonly observed in aging as well as in select disorders including traumatic brain injury, schizophrenia, attention-deficit hyperactivity disorder (ADHD), and dementia. Much recent progress has been made toward understanding the functional significance of IIV in cognitive performance (MacDonald, Nyberg, & Backman, 2006) and biological information processing (Stein, Gossen, & Jones 2005), with parallel efforts devoted to investigating the links between older adults' deficient neuromodulation and their more variable neuronal and cognitive functions (Backman, Nyberg, Lindenberger, Li, & Farde, 2006). Despite these advances in the study of IIV, there has been little empirical examination of underlying neural correlates and virtually no synthesis of extant findings. The present review summarizes the accumulating empirical evidence linking age-related increases in IIV in cognitive performance to neural correlates at anatomical, functional, neuromodulatory, and genetic levels. Computational theories of neural dynamics (e.g., Li, Lindenberger, & Sikstrom, 2001) are also introduced to illustrate how age-related neuromodulatory deficiencies may contribute to increased neuronal noise and render information processing in aging neurocognitive systems to be less robust. The potential benefits of stochastic resonance and external noise are also discussed with respect to processing subthreshold stimuli (e.g., Li, von Oertzen, & Lindenberger, 2006). We conclude by highlighting important challenges and outstanding research issues that remain to be answered in the study of IIV.

Neural underpinnings of within-person variability in cognitive functioning.

In a recent study, De Haart et al. (Arch Phys Med Rehabil 85:886-895, 2004) investigated the recovery of balance in stroke patients using traditional analyses of center-of-pressure (COP) trajectories to assess the effects of health status, rehabilitation, and task conditions like standing with eyes open or closed and standing while performing a cognitive dual task. To unravel the underlying control processes, we reanalyzed these data in terms of stochastic dynamics using more advanced analyses. Dimensionality, local stability, regularity, and scaling behavior of COP trajectories were determined and compared with shuffled and phase-randomized surrogate data. The presence of long-range correlations discarded the possibility that the COP trajectories were purely random. Compared to the healthy controls, the COP trajectories of the stroke patients were characterized by increased dimensionality and instability, but greater regularity in the frontal plane. These findings were taken to imply that the stroke patients actively (i.e., cognitively) coped with the stroke-induced impairment of posture, as reflected in the increased regularity and decreased local stability, by recruiting additional control processes (i.e., more degrees of freedom) and/or by tightening the present control structure while releasing non-essential degrees of freedom from postural control. In the course of rehabilitation, dimensionality stayed fairly constant, whereas local stability increased and regularity decreased. The progressively less regular COP trajectories were interpreted to indicate a reduction of cognitive involvement in postural control as recovery from stroke progressed. Consistent with this interpretation, the dual task condition resulted in less regular COP trajectories of greater dimensionality, reflecting a task-related decrease of active, cognitive contributions to postural control. In comparison with conventional posturography, our results show a clear surplus value of dynamical measures in studying postural control.

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Dynamical structure of center-of-pressure trajectories in patients recovering from stroke

The control and perception of body orientation and motion are subserved by multiple sensory and motor mechanisms ranging from relatively simple, peripheral mechanisms to complex ones involving the highest levels of cognitive function and sensory-motor integration. Vestibular contributions to body orientation and to spatial localization of auditory and visual stimuli have long been recognized. These contributions are reviewed here along with new insights relating to sensory-motor calibration of the body gained from space flight, parabolic flight, and artificial gravity environments. Recently recognized contributions of proprioceptive and somatosensory signals to the appreciation of body orientation and configuration are described. New techniques for stabilizing posture by means of haptic touch and for studying and modeling postural mechanisms are reviewed. Path integration, place cells, and head direction cells are described along with implications for using immersive virtual environments for training geographic spatial knowledge of real environments.

Vestibular, proprioceptive, and haptic contributions to spatial orientation.

We review our work on using input noise (mechanical and electrical, respectively) to enhance somatosensation in humans and improve the performance of the human balance control system. We also discuss bioengineering applications and future directions for stochastic resonance (SR) based techniques and devices. Age- and disease-related sensory loss may be reversible by exploiting SR-type effects.

Noise-enhanced human sensorimotor function

Research teams at Afferent Corp. and at Boston University have been collaborating to develop and test a new class of neurotherapy devices that have the promise of directly improving mechanical sensory function to help prevent falls in the elderly and foot injuries and amputations in people with diabetes. These devices are based on the discovery that certain forms of electrical or mechanical stimulation applied to mechanoreceptors increase their ability to detect sensory information. Results show that the best type of stimulation signal is not a finely tuned frequency but rather white noise. When presented with this stimulus over an extended period, the sensory neurons were unable to adapt to it. These findings reinforce the growing body of research that establishes the connection between sensory activity and the ability of the nervous system to repair itself following injury.

J.B. Niemi

Papers

Noise-enhanced human sensorimotor function

Balancing act [noise based sensory enhancement technology]