Entropic measures of individual mobility patterns

Understanding human mobility from a microscopic point of view may represent a fundamental breakthrough for the development of a statistical physics for cognitive systems and it can shed light on the applicability of macroscopic statistical laws for social systems. Even if the complexity of individual behaviors prevents a true microscopic approach, the introduction of mesoscopic models allows the study of the dynamical properties for the non-stationary states of the considered system. We propose to compute various entropy measures of the individual mobility patterns obtained from GPS data that record the movements of private vehicles in the Florence district, in order to point out new features of human mobility related to the use of time and space and to define the dynamical properties of a stochastic model that could generate similar patterns. Moreover, we can relate the predictability properties of human mobility to the distribution of time passed between two successive trips. Our analysis suggests the existence of a hierarchical structure in the mobility patterns which divides the performed activities into three different categories, according to the time cost, with different information contents. We show that a Markov process defined by using the individual mobility network is not able to reproduce this hierarchy, which seems the consequence of different strategies in the activity choice. Our results could contribute to the development of governance policies for a sustainable mobility in modern cities

Horizontal Visibility graphs generated by type-I intermittency

The type-I intermittency route to (or out of) chaos is investigated within the Horizontal Visibility graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct, according to the Horizontal Visibility algorithm, their associated graphs. We show how the alternation of laminar episodes and chaotic bursts has a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values of several network parameters. In particular, we predict that the characteristic power law scaling of the mean length of laminar trend sizes is fully inherited in the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of the block entropy over the degree distribution. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization group framework, where the fixed points of its graph-theoretical RG flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibit extremal entropic properties.Comment: 8 figure

Incidence of nonextensive thermodynamics in temporal scaling at Feigenbaum points

Recently, in Phys. Rev. Lett. 95, 140601 (2005), P. Grassberger addresses the interesting issue of the applicability of q-statistics to the renowned Feigenbaum attractor. He concludes there is no genuine connection between the dynamics at the critical attractor and the generalized statistics and argues against its usefulness and correctness. Yet, several points are not in line with our current knowledge, nor are his interpretations. We refer here only to the dynamics on the attractor to point out that a correct reading of recent developments invalidates his basic claim.Comment: To be published in Physica

Music adapting to the brain: From diffusion chains to neurophysiology

During the last decade, the use of experimental approaches on cultural evolution research has provided novel insights, and supported theoretical predictions, on the principles driving the evolution of human cultural systems. Laboratory simulations of language evolution showed how general-domain constraints on learning, in addition to pressures for language to be expressive, may be responsible for the emergence of linguistic structure. Languages change when culturally transmitted, adapting to fit, among all, the cognitive abilities of their users. As a result, they become regular and compressed, easier to acquire and reproduce. Although a similar theory has been recently extended to the musical domain, the empirical investigation in this field is still scarce. In addition, no study to our knowledge directly addressed the role of cognitive constraints in cultural transmission with neurophysiological investigation. In my thesis I addressed both these issues with a combination of behavioral and neurophysiological methods, in three experimental studies. In study 1 (Chapter 2), I examined the evolution of structural regularities in artificial melodic systems while they were being transmitted across individuals via coordination and alignment. To this purpose I used a new laboratory model of music transmission: the multi-generational signaling games (MGSGs), a variant of the signaling games. This model combines classical aspects of lab-based semiotic models of communication, coordination and interaction (horizontal transmission), with the vertical transmission across generations of the iterated learning model (vertical transmission). Here, two-person signaling games are organized in diffusion chains of several individuals (generations). In each game, the two players (a sender and a receiver) must agree on a common code - here a miniature system where melodic riffs refer to emotions. The receiver in one game becomes the sender in the next game, possibly retransmitting the code previously learned to another generation of participants, and so on to complete the diffusion chain. I observed the gradual evolution of several structures features of musical phrases over generations: proximity, continuity, symmetry, and melodic compression. Crucially, these features are found in most of musical cultures of the world. I argue that we tapped into universal processing mechanisms of structured sequence processing, possibly at work in the evolution of real music. In study 2 (Chapter 3), I explored the link between cultural adaptation and neural information processing. To this purpose, I combined behavioral and EEG study on 2 successive days. I show that the latency of the mismatch negativity (MMN) recorded in a pre-attentive auditory sequence processing task on day 1, predicts how well participants learn and transmit an artificial tone system with affective semantics in two signaling games on day 2. Notably, MMN latencies also predict which structural changes are introduced by participants into the artificial tone system. In study 3 (Chapter 4), I replicated and extended behavioral and neurophysiological findings on the temporal domain of music, with two independent experiments. In the first experiment, I used MGSGs as a laboratory model of cultural evolution of rhythmic equitone patterns referring to distinct emotions. As a result of transmission, rhythms developed a universal property of music structure, namely temporal regularity (or isochronicity). In the second experiment, I anchored this result with neural predictors. I showed that neural information processing capabilities of individuals, as measured with the MMN on day 1, can predict learning, transmission, and regularization of rhythmic patterns in signaling games on day 2. In agreement with study 2, I observe that MMN brain timing may reflect the efficiency of sensory systems to process auditory patterns. Functional differences in those systems, across individuals, may produce a different sensitivity to pressures for regularities in the cultural system. Finally, I argue that neural variability can be an important source of variability of cultural traits in a population. My work is the first to systematically describe the emergence of structural properties of melodic and rhythmic systems in the laboratory, using an explicit game-theoretic model of cultural transmission in which agents freely interact and exchange information. Critically, it provides the first demonstration that social learning, transmission, and cultural adaptation are constrained and driven by individual differences in the functional organization of sensory systems

Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.Comment: Published in PLoS ONE (Sep 2011

Biological sequences as pictures – a generic two dimensional solution for iterated maps

<p>Abstract</p> <p>Background</p> <p>Representing symbolic sequences graphically using iterated maps has enjoyed an enduring popularity since it was first proposed in Jeffrey 1990 as chaos game representation (CGR). The usefulness of this representation goes beyond the convenience of a scale independent representation. It provides a variable memory length representation of transition. This includes the representation of succession with non-integer order, which comes with the promise of generalizing Markovian formalisms. The original proposal targeted genomic sequences only but since then several generalizations have been proposed, many specifically designed to handle protein data.</p> <p>Results</p> <p>The challenge of a general solution is that of deriving a bijective transformation of symbolic sequences into bi-dimensional planes. More specifically, it requires the regular fractal nesting of polygons. A first attempt at a general solution was proposed by Fiser 1994 by using non-overlapping circles that contain the polygons. This was used as a starting point to identify a more efficient solution where the encapsulating circles can overlap without the same happening for the sequence maps which are circumscribed to fractal polygon domains.</p> <p>Conclusion</p> <p>We identified the optimal inscribed packing solution for iterated maps of any Biological sequence, indeed of any symbolic sequence. The new solution maintains the prized bijective mapping property and includes the Sierpinski triangle and the CGR square as particular solutions of the more encompassing formulation.</p

Self-organized criticality in deterministic systems with disorder

Using the Bak-Sneppen model of biological evolution as our paradigm, we investigate in which cases noise can be substituted with a deterministic signal without destroying Self-Organized Criticality (SOC). If the deterministic signal is chaotic the universality class is preserved; some non-universal features, such as the threshold, depend on the time correlation of the signal. We also show that, if the signal introduced is periodic, SOC is preserved but in a different universality class, as long as the spectrum of frequencies is broad enough.Comment: RevTex, 8 pages, 8 figure

Efficient ConvNets for Analog Arrays

Analog arrays are a promising upcoming hardware technology with the potential to drastically speed up deep learning. Their main advantage is that they compute matrix-vector products in constant time, irrespective of the size of the matrix. However, early convolution layers in ConvNets map very unfavorably onto analog arrays, because kernel matrices are typically small and the constant time operation needs to be sequentially iterated a large number of times, reducing the speed up advantage for ConvNets. Here, we propose to replicate the kernel matrix of a convolution layer on distinct analog arrays, and randomly divide parts of the compute among them, so that multiple kernel matrices are trained in parallel. With this modification, analog arrays execute ConvNets with an acceleration factor that is proportional to the number of kernel matrices used per layer (here tested 16-128). Despite having more free parameters, we show analytically and in numerical experiments that this convolution architecture is self-regularizing and implicitly learns similar filters across arrays. We also report superior performance on a number of datasets and increased robustness to adversarial attacks. Our investigation suggests to revise the notion that mixed analog-digital hardware is not suitable for ConvNets