Lévy flights in human behavior and cognition

In this research we have analyzed functional magnetic resonance imaging (fMRI) signals of different networks in the brain under resting state condition. To such end, the dynamics of signal variation, have been conceived as a stochastic motion, namely it has been modelled through a generalized Langevin stochastic differential equation, which combines a deter-ministic drift component with a stochastic component where the Gaussian noise source has been replaced with α-stable noise. The parameters of the deterministic and stochastic parts of the model have been fitted from fluctuating data. Results show that the deterministic part is characterized by a simple, linear decreasing trend, and, most important, the α-stable noise, at varying characteristic index α, is the source of a spectrum of activity modes across the networks, from those originated by classic Gaussian noise (α = 2), to longer tailed behaviors generated by the more general Lévy noise (1 α < 2). Lévy motion is a specific instance of scale-free behavior, it is a source of anomalous diffusion and it has been related to many aspects of human cognition, such as information foraging through memory retrieval or visual exploration. Finally, some conclusions have been drawn on the functional significance of the dynamics corresponding to different α values.

Nature, 2006

Decision making in an uncertain environment poses a conflict between the opposing demands of gathering and exploiting information. In a classic illustration of this 'exploration-exploitation' dilemma 1 , a gambler choosing between multiple slot machines balances the desire to select what seems, on the basis of accumulated experience, the richest option, against the desire to choose a less familiar option that might turn out more advantageous (and thereby provide information for improving future decisions). Far from representing idle curiosity, such exploration is often critical for organisms to discover how best to harvest resources such as food and water. In appetitive choice, substantial experimental evidence, underpinned by computational reinforcement learning 2 (RL) theory, indicates that a dopaminergic 3,4 , striatal 5-9 and medial prefrontal network mediates learning to exploit. In contrast, although exploration has been well studied from both theoretical 1 and ethological 10 perspectives, its neural substrates are much less clear. Here we show, in a gambling task, that human subjects' choices can be characterized by a computationally well-regarded strategy for addressing the explore/exploit dilemma. Furthermore, using this characterization to classify decisions as exploratory or exploitative, we employ functional magnetic resonance imaging to show that the frontopolar cortex and intraparietal sulcus are preferentially active during exploratory decisions. In contrast, regions of striatum and ventromedial prefrontal cortex exhibit activity characteristic of an involvement in value-based exploitative decision making. The results suggest a model of action selection under uncertainty that involves switching between exploratory and exploitative behavioural modes, and provide a computationally precise characterization of the contribution of key decision-related brain systems to each of these functions.

A lively debate exists on the inherent stochasticity involved in many animal search displacements and its possible adaptive value. When animals have no prior information about the location of targets, such as patches of food resource or potential mates, different random search strategies may provide different degrees of success. It has been suggested that a particular class of random walks, known as Lévy walks, offers optimal stochastic search strategies when faced with environmental uncertainty. The properties of Lévy walks, which include superdiffusion and fractality, have been shown to be particularly useful in non-destructive searching cases; cases in which a site or a resource is not eliminated after it has been located, and therefore can be revisited. In this project we conducted a human behavioral searching experiment on a group blind folded human volunteers whom were asked to search for targets in a soccer field. By recording the walking path of each volunteer, our goal was to categorize the properties of human random searches. Our results show that the general search strategy of blind folded humans resembles pure Brownian motion. However, when categorizing the volunteers according to their degree of success, we found that the searching strategy of the most successful group clearly deviated from a Brownian type of motion towards a Lévy-like type motion. We discuss the relevance of these results in animal search context, and the potential of Lévy walks in terms of adaptive behavior.

Hippocampus, 2007

Finding your way in large-scale space requires knowing where you currently are and how to get to your goal destination. While much is understood about the neural basis of one's current position during navigation, surprisingly little is known about how the human brain guides navigation to goals. Computational accounts argue that specific brain regions support navigational guidance by coding the proximity and direction to the goal, but empirical evidence for such mechanisms is lacking. Here, we scanned subjects with functional MRI (fMRI) as they navigated to goal destinations in a highly accurate virtual simulation of a real city. Brain activity was then analysed in combination with metric measures of proximity and direction to goal destinations which were derived from each individual subject's coordinates at every second of navigation. We found that activity in the medial prefrontal cortex was positively correlated, and activity in a right subicular/ entorhinal region was negatively correlated with goal proximity. By contrast, activity in bilateral posterior parietal cortex was correlated with egocentric direction to goals. Our results provide empirical evidence for a navigational guidance system in the human brain, and define more precisely the contribution of these three brain regions to human navigation. In addition, these findings may also have wider implications for how the brain monitors and integrates different types of information in the service of goal-directed behaviour in general.

Journal of Neuroscience, 2007

Young healthy participants spontaneously use different strategies in a virtual radial maze, an adaptation of a task typically used with rodents. Functional magnetic resonance imaging confirmed previously that people who used spatial memory strategies showed increased activity in the hippocampus, whereas response strategies were associated with activity in the caudate nucleus. Here, voxel based morphometry was used to identify brain regions covarying with the navigational strategies used by individuals. Results showed that spatial learners had significantly more gray matter in the hippocampus and less gray matter in the caudate nucleus compared with response learners. Furthermore, the gray matter in the hippocampus was negatively correlated to the gray matter in the caudate nucleus, suggesting a competitive interaction between these two brain areas. In a second analysis, the gray matter of regions known to be anatomically connected to the hippocampus, such as the amygdala, parahippocampal, perirhinal, entorhinal and orbitofrontal cortices were shown to covary with gray matter in the hippocampus. Because low gray matter in the hippocampus is a risk factor for Alzheimer's disease, these results have important implications for intervention programs that aim at functional recovery in these brain areas. In addition, these data suggest that spatial strategies may provide protective effects against degeneration of the hippocampus that occurs with normal aging.

A considerable amount of research has claimed that animals’ foraging behaviors display movement lengths with power-law distributed tails, characteristic of Le ́vy flights and Le ́vy walks. Though these claims have recently come into question, the proposal that many animals forage using Le ́vy processes nonetheless remains. A Le ́vy process does not consider when or where resources are encountered, and samples movement lengths independently of past experience. However, Le ́vy processes too have come into question based on the observation that in patchy resource environments resource-sensitive foraging strategies, like area-restricted search, perform better than Le ́vy flights yet can still generate heavy-tailed distributions of movement lengths. To investigate these questions further, we tracked humans as they searched for hidden resources in an open-field virtual environment, with either patchy or dispersed resource distributions. Supporting previous research, for both conditions logarithmic binning methods were consistent with Le ́vy flights and rank-frequency methods– comparing alternative distributions using maximum likelihood methods–showed the strongest support for bounded power-law distributions (truncated Le ́vy flights). However, goodness-of-fit tests found that even bounded power-law distributions only accurately characterized movement behavior for 4 (out of 32) participants. Moreover, paths in the patchy environment (but not the dispersed environment) showed a transition to intensive search following resource encounters, characteristic of area-restricted search. Transferring paths between environments revealed that paths generated in the patchy environment were adapted to that environment. Our results suggest that though power-law distributions do not accurately reflect human search, Le ́vy processes may still describe movement in dispersed environments, but not in patchy environments–where search was area-restricted. Furthermore, our results indicate that search strategies cannot be inferred without knowing how organisms respond to resources–as both patched and dispersed conditions led to similar Le ́vy-like movement distributions.

Humans consistently make suboptimal decisions involving random events, yet the underlying neural mechanisms remain elusive. Using functional MRI and a matching pennies game that captured subjects' increasing tendency to predict the break of a streak as it continued [i.e., the "gambler's fallacy" (GF)], we found that a strong blood oxygen level-dependent response in the left lateral prefrontal cortex (LPFC) to the current outcome preceded the use of the GF strategy 10 s later. Furthermore, anodal transcranial direct current stimulation over the left LPFC, which enhances neuronal firing rates and cerebral excitability, increased the use of the GF strategy, and made the decisions more "sticky." These results reveal a causal role of the LPFC in implementing suboptimal decision strategy guided by false world models, especially when such strategy requires great resources for cognitive control.

Cerebral Cortex, 2015

Best choice problems have a long mathematical history, but their neural underpinnings remain unknown. Best choice tasks are optimal stopping problem that require subjects to view a list of options one at a time and decide whether to take or decline each option. The goal is to find a high ranking option in the list, under the restriction that declined options cannot be chosen in the future. Conceptually, the decision to take or decline an option is related to threshold crossing in drift diffusion models, when this process is thought of as a value comparison. We studied this task in healthy volunteers using fMRI, and used a Markov decision process to quantify the value of continuing to search versus committing to the current option. Decisions to take versus decline an option engaged parietal and dorsolateral prefrontal cortices, as well ventral striatum, anterior insula, and anterior cingulate. Therefore, brain regions previously implicated in evidence integration and reward representation encode threshold crossings that trigger decisions to commit to a choice.

Frontiers in Human Neuroscience

NeuroImage, 2006

How does the human brain allow us to interact with and navigate through a constantly changing world? Whilst controlled experiments using functional brain imaging can give insightful snapshots of neuronal responses to relatively simplified stimuli, they cannot hope to mirror the challenges faced by the brain in the real world. However, trying to study the brain mechanisms supporting daily living represents a huge challenge. By combining functional neuroimaging, an accurate interactive virtual simulation of a bustling central London (UK), and a novel means of &#39;reading&#39; participants&#39; thoughts whilst they moved around the city, we ascertained the online neural correlates underpinning navigation in this real-world context. A complex choreography of neural dynamics was revealed comprising focal and distributed, transient and sustained brain activity. Our results provide new insights into the specific roles of individual brain areas, in particular the hippocampus, retrosplenial...