Equivalence between spectral properties of graphs with and without loops

In this paper we introduce a spectra preserving relation between graphs with loops and graphs without loops. This relation is achieved in two steps. First, by generalizing spectra results got on (m, k)-stars to a wider class of graphs, the (m, k, s)-stars with or without loops. Second, by defining a covering space of graphs with loops that allows to remove the presence of loops by increasing the graph dimension. The equivalence of the two class of graphs allows to study graph with loops as simple graph without loosing information

A stochastic model of randomly accelerated walkers for human mobility

The recent availability of large databases allows to study macroscopic properties of many complex systems. However, inferring a model from a fit of empirical data without any knowledge of the dynamics might lead to erroneous interpretations [6]. We illustrate this in the case of human mobility [1-3] and foraging human patterns [4] where empirical long-tailed distributions of jump sizes have been associated to scale-free super-diffusive random walks called L\'evy flights [5]. Here, we introduce a new class of accelerated random walks where the velocity changes due to acceleration kicks at random times, which combined with a peaked distribution of travel times [7], displays a jump length distribution that could easily be misinterpreted as a truncated power law, but that is not governed by large fluctuations. This stochastic model allows us to explain empirical observations about the movements of 780,000 private vehicles in Italy, and more generally, to get a deeper quantitative understanding of human mobility.Comment: 10 pages, 6 figures + Supplementary informatio

On the multiplicity of Laplacian eigenvalues and Fiedler partitions

In this paper we study two classes of graphs, the (m,k)-stars and l-dependent graphs, investigating the relation between spectrum characteristics and graph structure: conditions on the topology and edge weights are given in order to get values and multiplicities of Laplacian matrix eigenvalues. We prove that a vertex set reduction on graphs with (m,k)-star subgraphs is feasible, keeping the same eigenvalues with reduced multiplicity. Moreover, some useful eigenvectors properties are derived up to a product with a suitable matrix. Finally, we relate these results with Fiedler spectral partitioning of the graph. The physical relevance of the results is shortly discussed

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

Statistical Laws in Urban Mobility from microscopic GPS data in the area of Florence

The application of Statistical Physics to social systems is mainly related to the search for macroscopic laws, that can be derived from experimental data averaged in time or space,assuming the system in a steady state. One of the major goals would be to find a connection between the statistical laws to the microscopic properties: for example to understand the nature of the microscopic interactions or to point out the existence of interaction networks. The probability theory suggests the existence of few classes of stationary distributions in the thermodynamics limit, so that the question is if a statistical physics approach could be able to enroll the complex nature of the social systems. We have analyzed a large GPS data base for single vehicle mobility in the Florence urban area, obtaining statistical laws for path lengths, for activity downtimes and for activity degrees. We show also that simple generic assumptions on the microscopic behavior could explain the existence of stationary macroscopic laws, with an universal function describing the distribution. Our conclusion is that understanding the system complexity requires dynamical data-base for the microscopic evolution, that allow to solve both small space and time scales in order to study the transients.Comment: 17 pages, 14 figures .jpg, use imsart.cl

Stochastic approach to diffusion inside the chaotic layer of a resonance

We model chaotic diffusion, in a symplectic 4D map by using the result of a theorem that was developed for stochastically perturbed integrable Hamiltonian systems. We explicitly consider a map defined by a free rotator (FR) coupled to a standard map (SM). We focus in the diffusion process in the action, $I$, of the FR, obtaining a semi--numerical method to compute the diffusion coefficient. We study two cases corresponding to a thick and a thin chaotic layer in the SM phase space and we discuss a related conjecture stated in the past. In the first case the numerically computed probability density function for the action $I$ is well interpolated by the solution of a Fokker-Planck (F-P) equation, whereas it presents a non--constant time delay respect to the concomitant F-P solution in the second case suggesting the presence of an anomalous diffusion time scale. The explicit calculation of a diffusion coefficient for a 4D symplectic map can be useful to understand the slow diffusion observed in Celestial Mechanics and Accelerator Physics.Comment: This is the author's version of a work that was submitted to Physical Review E (http://pre.aps.org

Understanding the variability of daily travel-time expenditures using GPS trajectory data

12+6 Pages, 6+2 Figures, 1+1 TablesTransportation planning is strongly influenced by the assumption that every individual has for his daily mobility a constant daily budget of ~1 hour. However, recent experimental results are proving this assumption as wrong. Here, we study the differences in daily travel-time expenditures among 24 Italian cities, extracted from a large set of GPS data on vehicles mobility. To understand these variations at the level of individual behaviour, we introduce a trip duration model that allows for a description of the distribution of travel-time expenditures in a given city using two parameters. The first parameter reflects the accessibility of desired destinations, whereas the second one can be associated to a travel-time budget and represents physiological limits due to stress and fatigue. Within the same city, we observe variations in the distributions according to home position, number of mobility days and a driver's average number of daily trips. These results can be interpreted by a stochastic time-consumption model, where the generalised cost of travel times is given by a logarithmic-like function, in agreement with the Weber-Fechner law. Our experimental results show a significant variability in the travel-time budgets in different cities and for different categories of drivers within the same city. This explicitly clashes with the idea of the existence of a constant travel-time budget and opens new perspectives for the modeling and governance of urban mobility

Venice As Pedestrian City And Tourist Magnet Mass Events And Ordinary Life

In Venice the famous network of pedestrian foot-ways deserves attention and research since has to face very often mass events. Even the ordinary mobility has peculiar needs. The efficiency of main road and rail transportation infrastructures and of the principal hub of modal interchange, relays on the service quality of the pedestrian infrastructure in the old city. This is matter for an original investigation.En Venecia, la famosa red de vías peatonales merece atención y análisis ya que se enfrenta muy frecuentemente a eventos masificados. Incluso la movilidad ordinaria cuenta con necesidades particulares. La eficiencia de la carretera principal, las infraestructuras ferroviarias, y el hub principal de intercambio modal, depende de la calidad del servicio de la infraestructura peatonal de la antigua ciudad. Este es el tema de una original investigación.  

Application of Wavelet Packet Transform to detect genetic polymorphisms by the analysis of inter-Alu PCR patterns

<p>Abstract</p> <p>Background</p> <p>The analysis of Inter-Alu PCR patterns obtained from human genomic DNA samples is a promising technique for a simultaneous analysis of many genomic loci flanked by Alu repetitive sequences in order to detect the presence of genetic polymorphisms. Inter-Alu PCR products may be separated and analyzed by capillary electrophoresis using an automatic sequencer that generates a complex pattern of peaks. We propose an algorithmic method based on the Haar-Walsh Wavelet Packet Transformation (WPT) for an efficient detection of fingerprint-type patterns generated by PCR-based methodologies. We have tested our algorithmic approach on inter-Alu patterns obtained from the genomic DNA of three couples of monozygotic twins, expecting that the inter-Alu patterns of each twins couple will show differences due to unavoidable experimental variability. On the contrary the differences among samples of different twins are supposed to originate from genetic variability. Our goal is to automatically detect regions in the inter-Alu pattern likely associated to the presence of genetic polymorphisms.</p> <p>Results</p> <p>We show that the WPT algorithm provides a reliable tool to identify sample to sample differences in complex peak patterns, reducing the possible errors and limits associated to a subjective evaluation. The redundant decomposition of the WPT algorithm allows for a procedure of best basis selection which maximizes the pattern differences at the lowest possible scale. Our analysis points out few classifying signal regions that could indicate the presence of possible genetic polymorphisms.</p> <p>Conclusions</p> <p>The WPT algorithm based on the Haar-Walsh wavelet is an efficient tool for a non-supervised pattern classification of inter-ALU signals provided by a genetic analyzer, even if it was not possible to estimate the power and false positive rate due to the lacking of a suitable data base. The identification of non-reproducible peaks is usually accomplished comparing different experimental replicates of each sample. Moreover, we remark that, albeit we developed and optimized an algorithm able to analyze patterns obtained through inter-Alu PCR, the method is theoretically applicable to whatever fingerprint-type pattern obtained analyzing anonymous DNA fragments through capillary electrophoresis, and it could be usefully applied on a wide range of fingerprint-type methodologies.</p

Venice as pedestrian city and tourist magnet: mass events and ordinary life

In Venice the famous network of pedestrian foot-ways deserves attention and research since has to face very often mass events. Even the ordinary mobility has peculiar needs. The efficiency of main road and rail transportation infrastructures and of the principal hub of modal interchange, relays on the service quality of the pedestrian infrastructure in the old city. This is matter for an original investigation.Peer Reviewe