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Perspective ARTICLE

Front. Hum. Neurosci., 24 April 2015 | https://doi.org/10.3389/fnhum.2015.00222

How can we study reasoning in the brain?

  • GISC and Laboratory of Biological Networks, Center for Biomedical Technology, Universidad Politécnica de Madrid, Madrid, Spain

The brain did not develop a dedicated device for reasoning. This fact bears dramatic consequences. While for perceptuo-motor functions neural activity is shaped by the input's statistical properties, and processing is carried out at high speed in hardwired spatially segregated modules, in reasoning, neural activity is driven by internal dynamics and processing times, stages, and functional brain geometry are largely unconstrained a priori. Here, it is shown that the complex properties of spontaneous activity, which can be ignored in a short-lived event-related world, become prominent at the long time scales of certain forms of reasoning. It is argued that the neural correlates of reasoning should in fact be defined in terms of non-trivial generic properties of spontaneous brain activity, and that this implies resorting to concepts, analytical tools, and ways of designing experiments that are as yet non-standard in cognitive neuroscience. The implications in terms of models of brain activity, shape of the neural correlates, methods of data analysis, observability of the phenomenon, and experimental designs are discussed.

Introduction

Consider an individual trying to solve a problem and reasoning for 10 min before attaining a solution. Take the middle 5 min. Clearly, though containing no behaviorally salient event, these 5 min represent a genuine, indeed rather general, instance of reasoning. What do we know about the brain regime far from its conclusion? Can we use this regime to predict a solution, and a solution to retrodict this regime?

Here, I concentrate on a form of reasoning, of which the above scenario constitutes an example, which can broadly be defined as “thinking in which there is a conscious intent to reach a conclusion and in which methods are used that are logically justified” (Moshman, 1995), with no a priori assumption on the type of reasoning process that may take place during it. It is argued that finding the generic properties of this form of reasoning entails addressing the following fundamental issues: What are reasoning's temporal and spatial scales? When is a given observation time sufficient? How should we integrate the information contained in various reasoning episodes?

A Mini Literature Review

The neural correlates of reasoning have traditionally been expressed in terms of brain spatial coordinates. Early neuropsychological work viewed reasoning as emerging from global brain processing (Gloning and Hoff, 1969), consistent with evidence indicating that it is negatively affected by diffuse brain damage (Lezak, 1995). Neuroimaging studies have framed the neural correlates of reasoning in terms of local functionally specialized brain activity, either by taking a normative approach to reasoning (Goel et al., 1997, 1998; Osherson et al., 1998; Parsons and Osherson, 2001; Noveck et al., 2004; Prado et al., 2011), or by fractionating it into sub-component processes (Houdé et al., 2001; Acuna et al., 2002; Kroger et al., 2002; Reverberi et al., 2012). The results often lack specificity to reasoning (Papo et al., 2007). Most importantly, these investigations provide a static characterization of reasoning.

The neuroimaging literature mostly focused on short-term and normative forms of reasoning (Prado et al., 2011; Bonnefond et al., 2013, 2014). This minimizes variability in reasoning episode length and allows segmenting reasoning episodes into separable chunks, but does that at the price of limitations in the phenomenology and ecologic value of its stimuli. Some neuroimaging (Luo et al., 2004; Subramaniam et al., 2008) and electrophysiological (Jung-Beeman et al., 2004; Mai et al., 2004; Kounios et al., 2006, 2008; Lang et al., 2006; Bowden and Jung-Beeman, 2007; Qiu et al., 2008; Sandkühler and Bhattacharya, 2008; Sheth et al., 2008) studies examined more ecological forms of reasoning, viz. insight problems (Knoblich et al., 1999). However, even electrophysiological studies, despite optimal temporal resolution, adopted an event-related perspective, concentrating on activity occurring a few seconds before insight emergence, which only documents the outcome of the reasoning process, not the process itself.

Event-related neural activity associated with the solution of riddles with insight was found to be related to properties of preceding resting activity (Kounios et al., 2006, 2008). These studies had the remarkable merit of using spontaneous brain activity to characterize reasoning, but in essence provided a comparative statics description. Although some behavioral studies treated reasoning as a dynamical process (Stephen et al., 2009), a comparable neurophysiological characterization is still incomplete.

The Problem(s) with Reasoning

The generalized form of reasoning considered in this study comes in episodes offering scant behaviorally salient events with no characteristic temporal length. Each episode is a non-reproducible instance, as a reasoning task can be carried out in multiple ways. Brain activity associated with reasoning is not event-related, and many neurophysiological processes interact in a wide range of spatial and temporal scales.

These phenomena can all be traced back to a basic fact: the brain did not develop a dedicated device for reasoning. Hardwired partially segregated modules ensure that perceptuo-motor functions are carried out at great speed, with stereotyped duration and time-varying profile, and identifiable stages, largely determined by input statistical properties. Reasoning, on the contrary, is associated with an internally-driven dynamics: processing times and stages, and functional brain geometry are largely unconstrained.

Considering these extraordinary challenges, can we still find general reasoning properties, over and above specific task demands and individual differences? What sort of process is reasoning in its general form? Is it a series of simpler reasoning cycles? Can we segment it into stages? What are the best neural variables and tools to make these properties observable?

Characterizing the Reasoning Process

Robust characterizations of reasoning should incorporate properties consistently appearing across different subjects and in different periods of time, and select analytical tools accordingly. For instance, perceptual response sensitivity to incoming signals, stability against noise, and minimal dependence on initial conditions favor tools capturing transient dynamics, which naturally reproduce these properties under appropriate conditions, over tools handling asymptotic activity, which fail to do so (Rabinovich et al., 2008).

Reasoning's relative instability and inefficiency suggest that optimal circuitry may need constant reconstruction and protection from interference, summoning protracted support of energetically costly long-range communications. Reasoning may be a sort of resonant regime, where functional efficiency would be achieved with specific, though unstable, spatio-temporal patterns. This suggests that reasoning should be studied with tools which can describe spatially-extended dynamic transients and can quantify information transfer and the corresponding energetic cost.

Reasoning Dynamics

Each cognitive process can be translated in dynamical terms and corresponding aspects of neural activity.

Perceptual processes are relaxational, quasi-stereotyped short duration processes. The brain can prima facie be modeled as an excitable medium: perturbations above a threshold induce a dynamical cycle before the system reverts to its initial silent state.

Learning too is a relaxational process. Following a gradient dynamics, the brain incorporates the environment's statistical relationships by representing them in terms of its functional connectivity (Sporns et al., 2000). Cycles can be of much longer duration and non-trivial shape than perceptual ones. No single instant summarizes the entire process, and the dynamics consists of fluctuations much shorter than the whole process.

Reasoning may not be purely relaxational. As in the case of learning, no instant summarizes the whole dynamics but, contrary to learning, there is no clear gradient. Neural activity is an out-of-equilibrium endogenously modulated spontaneous brain activity. Its phenomenology is considerably more complex than the equilibrium event-related short time-scale one of perception or the gradient-driven regression to equilibrium dynamics of learning.

To study reasoning, one should therefore first consider properties of spontaneous activity that are generic (i.e., that hold for almost all conditions) at long time scales and then see how these properties are modulated during reasoning (Papo, 2014a).

The Starting Point: Spontaneous Brain Activity

When observed long enough, brain fluctuations appear to be characterized by structured patterns (Kenet et al., 2003). The temporal sequence with which these patterns are re-edited across the cortical space also appears to have non-random structure (Beggs and Plenz, 2003, 2004; Cossart et al., 2003; Ikegaya et al., 2004; Dragoi and Tonegawa, 2011; Betzel et al., 2012). The structure with which these fluctuations appear can be described in the same way one would describe an object, characterizing its component parts, the relationships between them, and the way one can inspect it. For instance, if we think of brain fluctuations as the steps of a random walker, one can describe the phase space, i.e., the space of all states attainable by the system's dynamics, but also of traveled distances, times to reach a given target and memory of previous steps.

In the equilibrium world of perceptual scientists, brain steps are Gaussian distributed, and memory of past steps is lost so rapidly that no structure is apparent when considering the time course of activity. Spontaneous activity has no evident temporal structure and can be treated as a null state to which the brain reverts in the absence of stimulation.

At the long time scales of reasoning, the random walker takes steps from a non-Gaussian distribution. Like a fractal object, it displays similar properties at all scales (Novikov et al., 1997; Linkenkaer-Hansen et al., 2001; Gong et al., 2002; Freeman et al., 2003; Stam and de Bruin, 2004; Expert et al., 2010; van de Ville et al., 2010; Fraiman and Chialvo, 2012). While self-similarity may not be exact (Suckling et al., 2009; Zilber et al., 2012), these scaling patterns indicate that activity at different temporal scales is characterized by non-trivial relationships between them (Bacry et al., 2001; Friedrich et al., 2011; Papo, 2013b). Not all regions of the phase space are equally visited, with some taking an extremely long time to be reached (Bianco et al., 2007). Transitions from one region to the other depend on past history of the dynamics (Gilboa et al., 2005). Memory of past steps decays so slowly that the time it takes two time-points to totally decorrelate may diverge, so that a characteristic time ceases to exist (Grigolini et al., 1999; Fairhall et al., 2001; Gilboa et al., 2005; Lundstrom et al., 2008). Temporal correlations are not stationary, but time-dependent (Bianco et al., 2007). If, rather than an ordinary watch, one measured time with a watch ticking at every step taken by the walker, the passage of time would appear to be highly irregular and clustered, alternating between relatively quiet phases and more turbulent ones (Gong et al., 2007; Allegrini et al., 2010).

The temporal structure can be used to define landmarks within time-windows where no behaviorally salient event occurs. This can be done by identifying segments that can be considered stationary (Kaplan et al., 2005). The distribution of these segments' durations and their correlations and specific sequences may help clarify whether reasoning far away from both problem presentation and solution is merely a repetition of simple cycles seen in more controlled forms of reasoning, or is of a qualitatively different nature, and if so, may help determine the time scales at which simpler cycles are reedited.

To fully describe the phase space, one needs to consider that the brain as a whole consists of a great number of local random walkers. Local walkers interact to form transient patterns of connectivity. These patterns can be endowed with topological properties at all spatial scales by resorting to complex networks theory (Bullmore and Sporns, 2009). Eventually, one deals with an abstract structure consisting of spatial patterns endowed with topological properties, the temporal evolution of which displays the complex properties described above.

Overall, the space in which the random walker turns out to live, and which reflects the brain's dynamical repertoire, can be represented as a complex spatio-temporal structure (Zaslavsky, 2002). This structure can be described in terms of symmetries and universal properties, which are robust with respect to the nature of microscopic details, by resorting to a variety of methods, e.g., algebraic and differential topology, renormalization group methods etc. (Lesne, 2008; Petri et al., 2014). Using these methods it is possible (1) to partition the phase space, (2) to identify dynamical pathways leading to specific regions of this space, and (3) to relate descriptions of the same brain at different scales and of different brains exhibiting the same large-scale behavior (Lesne, 2008).

From Spontaneous Activity to Reasoning

Cognitive processes can be thought of as selections and orchestrations of cortical states already present in spontaneous activity (Kenet et al., 2003; Fiser et al., 2004; Luczak et al., 2009). Each process reveals a specific part of the phase space, and can be associated with its own topological properties and symmetries, and characteristic kinematics, memory, aging properties, degree of ergodicity, and internal clock (Papo, 2014a). For example, different conditions under which subjects carried out a reasoning task were shown to modulate the scaling regime of fluctuations of the corresponding brain activity (Buiatti et al., 2007), suggesting that reasoning may modulate not brain activity's amplitude but its functional form (Papo, 2014a), e.g., by forcing the system's stationary distribution to equal a target one. These modulations may correspond to cross-overs between universality classes, resulting from transitions between different dynamical regimes (Burov and Barkai, 2008).

The statistics of fluctuations can be used to study insight and to evaluate whether insight occurrence can be predicted. The sudden onset of insight may be thought of as an extreme event comparable to earthquakes, financial crashes, or epileptic seizures (Contoyiannis and Eftaxias, 2008; Osorio et al., 2010), e.g., as a rupture phenomenon, and the route to it as a long charging process, with nested hierarchical “earthquakes.” The probability distribution of fluctuations gives an estimate of the likelihood of the occurrence of such events: for a Gaussian distribution, extreme events are exponentially rare. However, for non-Gaussian distributions, such events do occur with non-zero probability. It is tempting to conjecture that, in analogy with results of studies of these phenomena, insight onset may be predicted by monitoring changes in anomalous diffusion parameters (Contoyiannis and Eftaxias, 2008), Gaussianity (Manshour et al., 2009), or fractal spectrum complexity (de Arcangelis and Herrmann, 1989; Kapiris et al., 2004).

Assessing Reasoning: from Dynamics to Thermodynamics and Information

Considering the functions reasoning fulfills and the constraints the brain faces while performing it can shed light on ways in which brain fluctuations can help quantify how the brain carries out reasoning.

Reasoning, as other cognitive processes, e.g., memory recall (Rhodes and Turvey, 2007; Baronchelli and Radicchi, 2013), can be represented as a search process similar to that of animals foraging in an unknown environment (Viswanathan et al., 2011). This search process can be characterized in terms of random walks (Shlesinger et al., 1993; Codling et al., 2008; Lomholt et al., 2008; Bénichou et al., 2011). Importantly, the statistics of random steps and their correlations indicate the extent to which a given trajectory optimizes search, given the characteristics of the explored space and the resources available to the individual (Bénichou et al., 2011). Such a characterisation would allow assessing in a context-specific way the quality of both the reasoning and the “reasoned.” That behavioral aspects of human cognition (Rhodes and Turvey, 2007; Baronchelli and Radicchi, 2013) and brain activity both show non-Gaussian, heavy-tailed distributions might indicate search optimality (Lomholt et al., 2008; Humphries et al., 2012). However, because these properties are generic in spontaneous activity, reasoning's quality can only be described in terms of its modulations, and finding the neural property and spatial scale showing such scaling modulations are the crucial steps.

Because it lacks a hardwired structure, reasoning faces both a stability and an energetic problem. Fluctuation dynamics can help address the first issue, but may not be sufficient per se to address the second. While a graph theoretical representation of functional brain activity may provide indications as to the ways the brain tackles both problems (Bullmore and Sporns, 2012; Papo et al., 2014), a direct characterization can be achieved by considering the brain as a very complex engine and by characterizing its thermodynamics. Crucially, thermodynamics can be deduced from dynamics (Sekimoto, 1998). Such a characterisation could be used to quantify variations in thermodynamic variables such as free energy, entropy, or temperature (Papo, 2013a) during a reasoning task, but also possible transitions in some other property of neural activity, for particular values of these variables. For instance, a suitably modified equilibrium temperature accounting for the non-equilibrium nature of brain activity (Cugliandolo, 2011) can quantify deviations of each spatio-temporal scale from equilibrium, entropy production, etc. (Papo, 2014b).

Finally, one may want to quantify reasoning in terms of the information created, erased, and transferred during its execution. Simple fluctuations can be thought of as letters of an alphabet, fluctuation complexes as words, and the reasoning process represented as a network traffic regulation problem. Characterizing traffic regulation and phenomena such as overload or jamming may involve using information-theoretical tools and complex network theory and understanding the interplay between the underlying network's topology, the dynamics of information packets and the shape of fluctuation distributions (DeDeo and Krakauer, 2012; Delvenne et al., 2013; Lambiotte et al., 2013). Although only causal information (Shalizi and Moore, 2003) may directly serve reasoning purposes, the total information encoded in the network may describe the noise-control mechanisms indirectly optimizing it. Interestingly, non-equilibrium systems such as the brain, information, and thermodynamics can be thought of as the opposite side of the same coin (Parrondo et al., 2015). Ultimately, the information content of reasoning-related neural activity could be extracted from its dynamics, via thermodynamics.

From Theory to Experiment

Observing Reasoning

Reasoning is a difficult phenomenon to observe: tasks can be executed in more than one-way, each possibly corresponding to a neural phase space with convoluted geometry and the processes involved in reasoning may evolve over time-scales exceeding those typical of laboratory testing.

Proper observation of a given process requires that the observation time be much larger than any scale in the system. A process is observable if it has a finite ratio between the characteristic time of the independent variable and the length of the available time series (Reiner, 1964). Factors including long-term memory, aging and weak ergodicity breaking may result in a diverging ratio (Rebenshtok and Barkai, 2007).

The observation time should also be much larger than the time needed to visit the neural phase space. The time needed to explore this space may far exceed the typical reasoning episode duration. Cognitive neuroscientists observe phenomena through experiments where subjects typically carry out given tasks a large number of times, assumed to be independent realizations of the same observable, and to adequately sample the phase space of task-related brain activity. However, in the presence of complex fluctuations, trials may not self-average, i.e., dispersion would not vanish even for an infinite number of trials (Aharony and Harris, 1996). Thus, trials may explore different aspects of the space of available strategies and may therefore improve phase space exploration rather than the signal-to-noise ratio (Ghosh et al., 2007).

Experimental Implications

Reasoning's characteristics, particularly its lack of characteristic temporal duration, have implications at various levels. First, episodes cannot be compared in an event-related fashion. Second, defining reliable neural correlates of reasoning requires defining its characteristic temporal scales. Third, measures of brain activity should be invariant with respect to overall duration. Scaling exponents, data collapse and universality of fluctuations statistics (Bramwell et al., 1998; Bhattacharya, 2009; Friedman et al., 2012), or explicit evolution equations for the particle's momenta and for the cross-scale fluctuation probabilities (Friedrich et al., 2011) can be retrieved from data and applied to unevenly lengthen trials. Thermodynamic quantities such as free energy or temperature can also be estimated for stochastic trajectories over finite time durations (Ruelle, 1978; Beck and Schlögl, 1997; Canessa, 2000; Olemskoi and Kokhan, 2006; Papo, 2014b). In all cases, the reconstruction of the underlying dynamics improves with the recording device's resolution.

Reasoning presents a dilemma between ensuring complete phase space exploration, which may require extremely long trials, and signal stationarity, which is guaranteed only for time scales much shorter than the reasoning episodes' duration. At fast time scales, the window in which relevant quantities are calculated should not introduce spurious time scales, filtering out genuine ones. Altogether, reasoning's inherently unstable nature suggests that describing it may boil down to characterizing non-stationarities and their aetiologies.

Reasoning tasks may be so difficult that only few participants manage to produce solutions within a reasonable time. This represents a shortcoming when trials are considered as independent and identically distributed, as the signal-to-noise ratio improves with the square root of the number of trials. Smoothing response times is a frequent strategy to obviate this problem, but limits or distorts the reasoning process. Furthermore, however many, short trials may insufficiently explore the phase space. Designs with few long trials may express richer spatio-temporal brain dynamics than many short ones of equivalent overall length.

Finally, while observed scaling properties may help us understand whether insight is predictable, i.e., whether it is an outlier or it is generated by the same distribution producing anonymous events, predicting insight onset in real data appears to be a challenging task, as reasoning episodes are various orders of magnitude shorter than earthquake, financial, or epilepsy time series (Sornette, 2002).

Conclusions

Reasoning elicits an exceptionally rich repertoire of otherwise unexpressed neural properties. Its neural correlates are therefore as helpful to neuroscientists, who are compelled to consider hitherto neglected brain properties, as they are to psychologists who strive to understand its underlying processes.

Defining general and robust mechanistic properties of healthy and dysfunctional reasoning will require as yet non-standard brain metrics, experimental designs, and analytical tools, and may ultimately help us understand and fine-tune the action of brain enhancers.

Conflict of Interest Statement

The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

The author acknowledges the support of MINECO (FIS201238949-C03-01).

References

Acuna, B. D., Eliassen, J. C., Donoghue, J. P., and Sanes, J. N. (2002). Frontal and parietal lobe activation during transitive inference in humans. Cereb. Cortex 12, 1312–1321. doi: 10.1093/cercor/12.12.1312

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Aharony, A., and Harris, A. B. (1996). Absence of self-averaging and universal fluctuations in random systems near critical points. Phys. Rev. Lett. 77, 3700–3703. doi: 10.1103/PhysRevLett.77.3700

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Allegrini, P., Menicucci, D., Paradisi, P., and Gemignani, A. (2010). Fractal complexity in spontaneous EEG metastable-state transitions: new vistas on integrated neural dynamics. Front. Physiol. 1:128. doi: 10.3389/fphys.2010.00128

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bacry, E., Delour, J., and Muzy, J. F. (2001). Multifractal random walk. Phys. Rev. E 64:026103. doi: 10.1103/PhysRevE.64.026103

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Baronchelli, A., and Radicchi, F. (2013). Lévy flights in human behaviour and cognition. Chaos Solitons Fract. 56, 101–105. doi: 10.1016/j.chaos.2013.07.013

CrossRef Full Text | Google Scholar

Beck, C., and Schlögl, F. (1997). Thermodynamics of Chaotic Systems: An Introduction. Cambridge: Cambridge University press.

Google Scholar

Beggs, J. M., and Plenz, D. (2003). Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11177.

PubMed Abstract | Full Text | Google Scholar

Beggs, J. M., and Plenz, D. (2004). Neuronal avalanches are diverse and precise activity patterns that are stable for many hours in cortical slice cultures. J. Neurosci. 24, 5216–5229. doi: 10.1523/JNEUROSCI.0540-04.2004

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bénichou, O., Loverdo, C., Moreau, M., and Voituriez, R. (2011). Intermittent search strategies. Rev. Mod. Phys. 83:81. doi: 10.1103/RevModPhys.83.81

CrossRef Full Text | Google Scholar

Betzel, R. F., Erickson, M. A., Abell, M., O'Donnell, B. F., Hetrick, W. P., and Sporns, O. (2012). Synchronization dynamics and evidence for a repertoire of network states in resting EEG. Front. Comput. Neurosci. 6:74. doi: 10.3389/fncom.2012.00074

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bhattacharya, J. (2009). Increase of universality in human brain during mental imagery from visual perception. PLoS ONE 4:e4121. doi: 10.1371/journal.pone.0004121

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bianco, S., Ignaccolo, M., Rider, M. S., Ross, M. J., Winsor, P., and Grigolini, P. (2007). Brain, music, and non-poisson renewal processes. Phys. Rev. E 75:061911. doi: 10.1103/PhysRevE.75.061911

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bonnefond, M., Kaliuzhna, M., Van der Henst, J. B., and De Neys, W. (2014). Disabling conditional inferences: an EEG study. Neuropsychologia 56, 255–262. doi: 10.1016/j.neuropsychologia.2014.01.022

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bonnefond, M., Noveck, I., Baillet, S., Cheylus, A., Delpuech, C., Bertrand, O., et al. (2013). What MEG can reveal about reasoning: the case of if… then sentences. Hum. Brain Mapp. 34, 684–697. doi: 10.1002/hbm.21465

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bowden, E. M., and Jung-Beeman, M. (2007). Methods for investigating the neural components of insight. Methods 42, 87–99. doi: 10.1016/j.ymeth.2006.11.007

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bramwell, S. T., Holdsworth, P. C. W., and Pinton, J.-F. (1998). Universality of rare fluctuations in turbulence and critical phenomena. Nature 396, 552–554. doi: 10.1038/25083

CrossRef Full Text | Google Scholar

Buiatti, M., Papo, D., Baudonnière, P. M., and van Vreeswijk, C. (2007). Feedback modulates the temporal scale-free dynamics of brain electrical activity in a hypothesis testing task. Neuroscience 146, 1400–1412. doi: 10.1016/j.neuroscience.2007.02.048

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bullmore, E. T., and Sporns, O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198. doi: 10.1038/nrn2575

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Bullmore, E. T., and Sporns, O. (2012). The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349. doi: 10.1038/nrn3214

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Burov, S., and Barkai, E. (2008). Critical exponent of the fractional Langevin equation. Phys. Rev. Lett. 100:070601. doi: 10.1103/PhysRevLett.100.070601

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Canessa, E. (2000). Multifractality in time series. J. Phys. A Math. Gen. 33, 3637–3651. doi: 10.1088/0305-4470/33/19/302

CrossRef Full Text | Google Scholar

Codling, E. A., Plank, M. J., and Benhamou, S. (2008). Random walk models in biology. J. R. Soc. Interface 5, 813–834. doi: 10.1098/rsif.2008.0014

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Contoyiannis, Y. F., and Eftaxias, K. A. (2008). Tsallis and Levy statistics in the preparation of an earthquake. Nonlinear Process. Geophys. 15, 379–388. doi: 10.5194/npg-15-379-2008

CrossRef Full Text | Google Scholar

Cossart, R., Aronov, D., and Yuste, R. (2003). Attractor dynamics of network UP states in the neocortex. Nature 423, 283–288. doi: 10.1038/nature01614

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Cugliandolo, L. F. (2011). The effective temperature. J. Phys. A Math. Theor. 44, 483001. doi: 10.1088/1751-8113/44/48/483001

CrossRef Full Text | Google Scholar

de Arcangelis, L., and Herrmann, H. J. (1989). Scaling and multiscaling laws in random fuse networks. Phys. Rev. B 39:2678. doi: 10.1103/PhysRevB.39.2678

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

DeDeo, S., and Krakauer, D. C. (2012). Dynamics and processing in finite self-similar networks. J. R. Soc. Interface 9, 2131–2144. doi: 10.1098/rsif.2011.0840

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Delvenne, J.-C., Lambiotte, R., and Rocha, L. E. C. (2013). Bottlenecks, burstiness, and fat tails regulate mixing times of non-poissonian random walks. arXiv:1309.4155.

Google Scholar

Dragoi, G., and Tonegawa, S. (2011). Preplay of future place cell sequences by hippocampal cellular assemblies. Nature 469, 397–401. doi: 10.1038/nature09633

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Expert, P., Lambiotte, R., Chialvo, D. R., Christensen, K., Jensen, H. J., Sharp, D. J., et al. (2010). Self-similar correlation function in brain resting-state functional magnetic resonance imaging. J. R. Soc. Interface 8, 472–479. doi: 10.1098/rsif.2010.0416

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Fairhall, A. L., Lewen, G. D., Bialek, W., and de Ruyter van Steveninck, R. (2001). “Multiple timescales of adaptation in a neural code,” in Advances in Neural Information Processing Systems 13, eds T. K. Leen, T. G. Dietterich, and V.Tresp (Cambridge, MA: MIT Press), 124–130.

Fiser, J., Chiu, C., and Weliky, M. (2004). Small modulation of ongoing cortical dynamics by sensory input during natural vision. Nature 431, 573–578. doi: 10.1038/nature02907

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Fraiman, D., and Chialvo, D. R. (2012). What kind of noise is brain noise: anomalous scaling behavior of the resting brain activity fluctuations. Front. Physiol. 3:307. doi: 10.3389/fphys.2012.00307

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Freeman, W. J., Holmes, M. D., Burke, B. C., and Vanhatalo, S. (2003). Spatial spectra of scalp EEG and EMG from awake humans. Clin. Neurophysiol. 114, 1053–1068. doi: 10.1016/S1388-2457(03)00045-2

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Friedman, N., Ito, S., Brinkman, B. A., Shimono, M., Deville, R. E., Dahmen, K. A., et al. (2012). Universal critical dynamics in high resolution neuronal avalanche data. Phys. Rev. Lett. 108:208102. doi: 10.1103/PhysRevLett.108.208102

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Friedrich, R., Peinke, J., Sahimi, M., and Reza Rahimi Tabar, M. (2011). Approaching complexity by stochastic methods: from biological systems to turbulence. Phys. Rep. 506, 87–162. doi: 10.1016/j.physrep.2011.05.003

CrossRef Full Text | Google Scholar

Ghosh, A., Rho, Y., McIntosh, A. R., Kötter, R., and Jirsa, V. K. (2007). Noise during rest enables the exploration of the brain's dynamic repertoire. PLoS Comput. Biol. 4:e1000196. doi: 10.1371/journal.pcbi.1000196

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Gilboa, G., Chen, R., and Brenner, N. (2005). History-dependent multiple-timescale dynamics in a single-neuron model. J. Neurosci. 25, 6479–6489. doi: 10.1523/JNEUROSCI.0763-05.2005

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Gloning, K., and Hoff, H. (1969). “Cerebral localization of disorders of higher nervous activity,” in Handbook of Clinical Neurology, Vol. 3, Disorders of Higher Nervous Activity, eds P. J. Vincken and G. N. Bruyn (New York, NY: Wiley).

Goel, V., Gold, B., Kapur, S., and Houle, S. (1997). The seats of reason? An imaging study of deductive and inductive reasoning. Neuroreport 8, 1305–1310.

PubMed Abstract | Full Text | Google Scholar

Goel, V., Gold, B., Kapur, S., and Houle, S. (1998). Neuroanatomical correlates of human reasoning. J. Cogn. Neurosci. 10, 293–302. doi: 10.1162/089892998562744

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Gong, P., Nikolaev, A. R., and van Leeuwen, C. (2002). Scale-invariant fluctuations of the dynamical synchronization in human brain electrical activity. Neurosci. Lett. 336, 33–36. doi: 10.1016/S0304-3940(02)01247-8

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Gong, P., Nikolaev, A. R., and van Leeuwen, C. (2007). Intermittent dynamics underlying the intrinsic fluctuations of the collective synchronization patterns in electrocortical activity. Phys. Rev. E 76:011904. doi: 10.1103/PhysRevE.76.011904

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Grigolini, P., Rocco, A., and West, B. J. (1999). Fractional calculus as a macroscopic manifestation of randomness. Phys. Rev. E 59, 2603–2613. doi: 10.1103/PhysRevE.59.2603

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Houdé, O., Zago, L., Crivello, F., Moutier, S., Pineau, A., Mazoyer, B., et al. (2001). Access to deductive logic depends on a right ventromedial prefrontal area devoted to emotion and feeling: evidence from a training paradigm. Neuroimage 14, 1486–1492. doi: 10.1006/nimg.2001.0930

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Humphries, N. E., Weimerskirch, H., Queiroz, N., Southall, E. J., and Sims, D. W. (2012). Foraging success of biological Lévy flights recorded in situ. Proc. Natl. Acad. Sci. U.S.A. 109, 7169–7174. doi: 10.1073/pnas.1121201109

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Ikegaya, Y., Aaron, G., Cossart, R., Aronov, D., Lampl, I., Ferster, D., et al. (2004). Synfire chains and cortical songs: temporal modules of cortical activity. Science 304, 559–564. doi: 10.1126/science.1093173

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Jung-Beeman, M., Bowden, E. M., Haberman, J., Frymiare, J. L., Arambel-Liu, S., Greenblatt, R., et al. (2004). Neural activity when people solve verbal problems with insight. PLoS Biol. 2:e97. doi: 10.1371/journal.pbio.0020097

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Kapiris, P. G., Eftaxias, K. A., and Chelidze, T. L. (2004). Electromagnetic signature of prefracture criticality in heterogeneous media. Phys. Rev. Lett. 92:065702. doi: 10.1103/PhysRevLett.92.065702

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Kaplan, A. Y., Fingelkurts, A. A., Fingelkurts, A. A., Borisov, B. S., and Darkhovsky, B. S. (2005). Nonstationary nature of the brain activity as revealed by EEG/MEG: methodological, practical and conceptual challenges. Signal Process. 85, 2190–2212. doi: 10.1016/j.sigpro.2005.07.010

CrossRef Full Text | Google Scholar

Kenet, T., Bibitchkov, D., Tsodyks, M., Grinvald, A., and Arieli, A. (2003). Spontaneously emerging cortical representations of visual attributes. Nature 425, 954–956. doi: 10.1038/nature02078

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Knoblich, G., Ohlsson, S., Haider, H., and Rhenius, D. (1999). Constraint relaxation and chunk decomposition in insight problem solving. J. Exp. Psychol. Learn. Mem. Cogn. 25, 1534–1556. doi: 10.1037/0278-7393.25.6.1534

CrossRef Full Text | Google Scholar

Kounios, J., Fleck, J. I., Green, D. L., Payne, L., Stevenson, J. L., Bowden, E. M., et al. (2008). The origins of insight in resting-state brain activity. Neuropsychologia 46, 281–291. doi: 10.1016/j.neuropsychologia.2007.07.013

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Kounios, J., Frymiare, J. L., Bowden, E. M., Fleck, J. I., Subramaniam, K., Parrish, T. B., et al. (2006). The prepared mind: neural activity prior to problem presentation predicts subsequent solution by sudden insight. Psychol. Sci. 17, 882–890. doi: 10.1111/j.1467-9280.2006.01798.x

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Kroger, J. K., Sabb, F. W., Fales, C. L., Bookheimer, S. Y., Cohen, M. S., and Holyoak, K. J. (2002). Recruitment of anterior dorsolateral prefrontal cortex in human reasoning: a parametric study of relational complexity. Cereb. Cortex 12, 477–485. doi: 10.1093/cercor/12.5.477

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Lambiotte, R., Tabourier, L., and Delvenne, J.-C. (2013). Burstiness and spreading on temporal networks. Eur. Phys. J. B 86, 320. doi: 10.1140/epjb/e2013-40456-9

CrossRef Full Text | Google Scholar

Lang, S., Kanngieser, N., Jaśkowski, P., Haider, H., Rose, M., and Verleger, R. (2006). Precursors of insight in event-related brain potentials. J. Cogn. Neurosci. 18, 2052–2066. doi: 10.1162/jocn.2006.18.12.2152

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Lesne, A. (2008). “Regularization, renormalization, and renormalization groups: relationships and epistemological aspects,” in Vision of Oneness, eds I. Licata and A. Sakaji (Roma, QL: Aracne), 121–154.

Google Scholar

Lezak, M. D. (1995). Neuropsychological Assessment, 3rd Edn. Oxford: Oxford University Press.

Google Scholar

Linkenkaer-Hansen, K., Nikouline, V. V., Palva, J. M., and Ilmoniemi, R. (2001). Long-range temporal correlations and scaling behavior in human oscillations. J. Neurosci. 15, 1370–1377.

Google Scholar

Lomholt, M., Tal, K., Metzler, R., and Joseph, K. (2008). Lévy strategies in intermittent search processes are advantageous. Proc. Natl. Acad. Sci. U.S.A. 105, 11055–11059. doi: 10.1073/pnas.0803117105

CrossRef Full Text | Google Scholar

Luczak, A., Barthó, P., and Harris, K. D. (2009). Spontaneous events outline the realm of possible sensory responses in neocortical populations. Neuron 62, 413–425. doi: 10.1016/j.neuron.2009.03.014

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Lundstrom, B. N., Higgs, M. H., Spain, W. J., and Fairhall, A. L. (2008). Fractional differentiation by neocortical pyramidal neurons. Nat. Neurosci. 11, 1335–13342. doi: 10.1038/nn.2212

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Luo, J., Niki, K., and Phillips, S. (2004). Neural correlates of the ‘Aha! reaction’. Neuroreport 15, 2013–2017. doi: 10.1097/00001756-200409150-00004

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Mai, X.-Q., Luo, J., Wu, J.-H., and Luo, Y.-J. (2004). “Aha!” Effects in a guessing riddle task: an event-related potential study. Hum. Brain Mapp. 22, 261–270. doi: 10.1002/hbm.20030

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Manshour, P., Saberi, S., Sahimi, M., Peinke, J., Pacheco, A. F., and Rahimi Tabar, M. R. (2009). Turbulencelike behavior of seismic time series. Phys. Rev. Lett. 102:014101. doi: 10.1103/PhysRevLett.102.014101

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Moshman, D. (1995). Reasoning as self-constrained thinking. Hum. Dev. 38, 53–64. doi: 10.1159/000278299

CrossRef Full Text | Google Scholar

Noveck, I. A., Goel, V., and Smith, K. W. (2004). The neural basis of conditional reasoning with arbitrary content. Cortex 40, 613–622. doi: 10.1016/S0010-9452(08)70157-6

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Novikov, E., Novikov, A., Shannahoff-Khalsa, D., Schwartz, B., and Wright, J. (1997). Scale-similar activity in the brain. Phys. Rev. E 56, R2387–R2389. doi: 10.1103/PhysRevE.56.R2387

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Olemskoi, A., and Kokhan, S. (2006). Effective temperature of self-similar time series: analytical and numerical developments. Phys. A 360, 37–58. doi: 10.1016/j.physa.2005.06.048

CrossRef Full Text | Google Scholar

Osherson, D., Perani, D., Cappa, S., Schnur, T., Grassi, F., and Fazio, F. (1998). Distinct brain foci in deductive versus probabilistic reasoning. Neuropsychologia 36, 369–376. doi: 10.1016/S0028-3932(97)00099-7

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Osorio, I., Frei, M. G., Sornette, D., Milton, J., and Lai, Y. C. (2010). Epileptic seizures: quakes of the brain? Phys. Rev. E 82:021919. doi: 10.1103/PhysRevE.82.021919

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Papo, D. (2013a). Brain temperature: what it means and what it can do for (cognitive) neuroscientists. arXiv:1310.2906v1.

Google Scholar

Papo, D. (2013b). Time scales in cognitive neuroscience. Front. Physiol. 4:86. doi: 10.3389/fphys.2013.00086

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Papo, D. (2014a). Functional significance of complex fluctuations in brain activity: from resting state to cognitive neuroscience. Front. Syst. Neurosci. 8:112. doi: 10.3389/fnsys.2014.00112

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Papo, D. (2014b). Measuring brain temperature without a thermometer. Front. Physiol. 5, 124. doi: 10.3389/fphys.2014.00124

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Papo, D., Douiri, A., Bouchet, F., Bourzeix, J.-C., Caverni, J.-P., and Baudonnière, P.-M. (2007). Time-frequency intracranial source localization of feedback-related EEG activity in hypothesis testing. Cereb. Cortex 17, 1314–1322. doi: 10.1093/cercor/bhl042

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Papo, D., Zanin, M., Pineda, J. A., Boccaletti, S., and Buldú, J. M. (2014). Brain networks: great expectations, hard times, and the big leap forward. Philos. Trans. R. Soc. B Biol. Sci. 369, 20130525. doi: 10.1098/rstb.2013.0525

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Parrondo, M. R., Horowitz, J. M., and Sagawa, T. (2015). Thermodynamics of information. Nat. Phys. 11, 131–139. doi: 10.1038/nphys3230

CrossRef Full Text | Google Scholar

Parsons, L. M., and Osherson, D. (2001). New evidence for distinct right and left brain systems for deductive versus probabilistic reasoning. Cereb. Cortex 11, 954–965. doi: 10.1093/cercor/11.10.954

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Petri, G., Expert, P., Turkheimer, F., Carhart-Harris, R., Nutt, D., Hellyer, J., et al. (2014). Homological scaffolds of brain functional networks. J. R. Soc. Interface 11:20140873. doi: 10.1098/rsif.2014.0873

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Prado, J., Chadha, A., and Booth, J. R. (2011). The brain network for deductive reasoning: a quantitative meta-analysis of 28 neuroimaging studies. J. Cogn. Neurosci. 23, 3483–3497. doi: 10.1162/jocn_a_00063

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Qiu, J., Li, H., Yang, D., Luo, Y., Li, Y., Wu, Z., et al. (2008). The neural basis of insight problem solving: an event-related potential study. Brain Cogn. 68, 100–106. doi: 10.1016/j.bandc.2008.03.004

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Rabinovich, M., Huerta, R., and Laurent, G. (2008). Transient dynamics for neural processing. Science 321, 48–50. doi: 10.1126/science.1155564

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Rebenshtok, A., and Barkai, E. (2007). Distribution of time-averaged observables for weak ergodicity breaking. Phys. Rev. Lett. 99:210601. doi: 10.1103/PhysRevLett.99.210601

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Reiner, M. (1964). The Deborah number. Phys. Today 17, 62. doi: 10.1063/1.3051374

CrossRef Full Text | Google Scholar

Reverberi, C., Bonatti, L. L., Frackowiak, R. S., Paulesu, E., Cherubini, P., and Macaluso, E. (2012). Large scale brain activations predict reasoning profiles. Neuroimage 59, 1752–1764. doi: 10.1016/j.neuroimage.2011.08.027

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Rhodes, T., and Turvey, M. T. (2007). Human memory retrieval as Lévy foraging. Phys. A 385, 255–260. doi: 10.1016/j.physa.2007.07.001

CrossRef Full Text | Google Scholar

Ruelle, D. (1978). Thermodynamic Formalism. Reading, MA: Addison Wesley Publ. Co.

Google Scholar

Sandkühler, S., and Bhattacharya, J. (2008). Deconstructing insight: EEG correlates of insightful problem solving. PLoS ONE 3:e1459. doi: 10.1371/journal.pone.0001459

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Sekimoto, K. (1998). Langevin equation and thermodynamics. Prog. Theor. Phys. Suppl. 130, 17–27. doi: 10.1143/PTPS.130.17

CrossRef Full Text | Google Scholar

Shalizi, C. R., and Moore, C. (2003). What is a macrostate? Subjective observations and objective dynamics. arXiv:cond-mat/0303625v1.

Google Scholar

Sheth, B. R., Sandkühler, S., and Bhattacharya, J. (2008). Posterior beta and anterior gamma oscillations predict cognitive insight. J. Cogn. Neurosci. 21, 1269–1279. doi: 10.1162/jocn.2009.21069

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Shlesinger, M., Zaslavsky, G., and Klafter, J. (1993). Strange kinetics. Nature 363, 31–37. doi: 10.1038/363031a0

CrossRef Full Text | Google Scholar

Sornette, D. (2002). Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes, and human birth. Proc. Natl. Acad. Sci. U.S.A. 99, 2522–2529. doi: 10.1073/pnas.022581999

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Sporns, O., Tononi, G., and Edelman, G. M. (2000). Connectivity and complexity: the relationship between neuroanatomy and brain dynamics. Neural Netw. 13, 909–922. doi: 10.1016/S0893-6080(00)00053-8

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Stam, C. J., and de Bruin, E. A. (2004). Scale-free dynamics of global functional connectivity in the human brain. Hum. Brain Mapp. 22, 97–109. doi: 10.1002/hbm.20016

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Stephen, D. G., Boncoddo, R. A., Magnuson, J. S., and Dixon, J. A. (2009). The dynamics of insight: mathematical discovery as a phase transition. Mem. Cogn. 37, 1132–1149. doi: 10.3758/MC.37.8.1132

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Subramaniam, K., Kounios, J., Parrish, T. B., and Jung-Beeman, M. (2008). A brain mechanism for facilitation of insight by positive affect. J. Cogn. Neurosci. 21, 415–432. doi: 10.1162/jocn.2009.21057

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Suckling, J., Wink, A. M., Bernard, F. A., Barnes, A., and Bullmore, E. (2009). Endogenous multifractal brain dynamics are modulated by age, cholinergic blockade and cognitive performance. J. Neurosci. Methods 174, 292–300. doi: 10.1016/j.jneumeth.2008.06.037

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

van de Ville, D., Britz, J., and Michel, C. M. (2010). EEG microstate sequences in healthy humans at rest reveal scale-free dynamics. Proc. Natl. Acad. Sci. U.S.A. 107, 18179–18184. doi: 10.1073/pnas.1007841107

PubMed Abstract | Full Text | CrossRef Full Text | Google Scholar

Viswanathan, G. M., da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. (2011). The Physics of Foraging: an Introduction to Random Searches and Biological Encounters. Cambridge: Cambridge University Press. doi: 10.1017/CBO9780511902680

CrossRef Full Text | Google Scholar

Zaslavsky, G. M. (2002). Chaos, fractional kinetics, and anomalous transport. Phys. Rep. 371, 461–580. doi: 10.1016/S0370-1573(02)00331-9

CrossRef Full Text | Google Scholar

Zilber, N., Ciuciu, P., Abry, P., and van Wassenhove, V. (2012). Modulation of scale-free properties of brain activity in MEG. IEEE I. S. Biomed. Imaging (Barcelona) 1531–1534. doi: 10.1109/ISBI.2012.6235864

CrossRef Full Text | Google Scholar

Keywords: cognitive neuroscience, reasoning, scaling, non-stationarity, non-ergodicity, characteristic scales, observation time, resting brain activity

Citation: Papo D (2015) How can we study reasoning in the brain? Front. Hum. Neurosci. 9:222. doi: 10.3389/fnhum.2015.00222

Received: 18 November 2014; Accepted: 08 April 2015;
Published: 24 April 2015.

Edited by:

Ira Andrew Noveck, Centre Nationale de la Recherche Scientifique, France

Reviewed by:

Jascha Ruesseler, University of Bamberg, Germany
Jérôme Prado, Centre National de la Recherche Scientifique, France

Copyright © 2015 Papo. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: David Papo, GISC and Laboratory of Biological Networks, Center for Biomedical Technology, Universidad Politécnica de Madrid, Calle Ramiro de Maeztu, 7, 28040 Madrid, Spain papodav@gmail.com