Clustering and information in correlation based financial networks

Networks of companies can be constructed by using return correlations. A crucial issue in this approach is to select the relevant correlations from the correlation matrix. In order to study this problem, we start from an empty graph with no edges where the vertices correspond to stocks. Then, one by one, we insert edges between the vertices according to the rank of their correlation strength, resulting in a network called asset graph. We study its properties, such as topologically different growth types, number and size of clusters and clustering coefficient. These properties, calculated from empirical data, are compared against those of a random graph. The growth of the graph can be classified according to the topological role of the newly inserted edge. We find that the type of growth which is responsible for creating cycles in the graph sets in much earlier for the empirical asset graph than for the random graph, and thus reflects the high degree of networking present in the market. We also find the number of clusters in the random graph to be one order of magnitude higher than for the asset graph. At a critical threshold, the random graph undergoes a radical change in topology related to percolation transition and forms a single giant cluster, a phenomenon which is not observed for the asset graph. Differences in mean clustering coefficient lead us to conclude that most information is contained roughly within 10% of the edges.Comment: 11 pages including 14 figures. Uses REVTeX4. To be published in a special volume of EPJ on network

Limited resolution and multiresolution methods in complex network community detection

Detecting community structure in real-world networks is a challenging problem. Recently, it has been shown that the resolution of methods based on optimizing a modularity measure or a corresponding energy is limited; communities with sizes below some threshold remain unresolved. One possibility to go around this problem is to vary the threshold by using a tuning parameter, and investigate the community structure at variable resolutions. Here, we analyze the resolution limit and multiresolution behavior for two different methods: a q-state Potts method proposed by Reichard and Bornholdt, and a recent multiresolution method by Arenas, Fernandez, and Gomez. These methods are studied analytically, and applied to three test networks using simulated annealing.Comment: 6 pages, 2 figures.Minor changes from previous version, shortened a couple of page

Dynamics of polymer ejection from capsid

Polymer ejection from a capsid through a nanoscale pore is an important biological process with relevance to modern biotechnology. Here, we study generic capsid ejection using Langevin dynamics. We show that even when the ejection takes place within the drift-dominated region there is a very high probability for the ejection process not to be completed. Introducing a small aligning force at the pore entrance enhances ejection dramatically. Such a pore asymmetry is a candidate for a mechanism by which a viral ejection is completed. By detailed high-resolution simulations we show that such capsid ejection is an out-of-equilibrium process that shares many common features with the much studied driven polymer translocation through a pore in a wall or a membrane. We find that the escape times scale with polymer length, $\tau \sim N^\alpha$. We show that for the pore without the asymmetry the previous predictions corroborated by Monte Carlo simulations do not hold. For the pore with the asymmetry the scaling exponent varies with the initial monomer density (monomers per capsid volume) $\rho$ inside the capsid. For very low densities $\rho \le 0.002$ the polymer is only weakly confined by the capsid, and we measure $\alpha = 1.33$, which is close to $\alpha = 1.4$ obtained for polymer translocation. At intermediate densities the scaling exponents $\alpha = 1.25$ and $1.21$ for $\rho = 0.01$ and $0.02$, respectively. These scalings are in accord with a crude derivation for the lower limit $\alpha = 1.2$. For the asymmetrical pore precise scaling breaks down, when the density exceeds the value for complete confinement by the capsid, $\rho \gtrapprox 0.25$. The high-resolution data show that the capsid ejection for both pores, analogously to polymer translocation, can be characterized as a multiplicative stochastic process that is dominated by small-scale transitions.Comment: 10 pages, 6 figure

Critical evaluation of the computational methods used in the forced polymer translocation

In forced polymer translocation, the average translocation time, $\tau$, scales with respect to pore force, $f$, and polymer length, $N$, as $\tau \sim f^{-1} N^{\beta}$. We demonstrate that an artifact in Metropolis Monte Carlo method resulting in breakage of the force scaling with large $f$ may be responsible for some of the controversies between different computationally obtained results and also between computational and experimental results. Using Langevin dynamics simulations we show that the scaling exponent $\beta \le 1 + \nu$ is not universal, but depends on $f$. Moreover, we show that forced translocation can be described by a relatively simple force balance argument and $\beta$ to arise solely from the initial polymer configuration

The “broken escalator” phenomenon: Vestibular dizziness interferes with locomotor adaptation

BACKGROUND: Although vestibular lesions degrade postural control we do not know the relative contributions of the magnitude of the vestibular loss and subjective vestibular symptoms to locomotor adaptation. OBJECTIVE: To study how dizzy symptoms interfere with adaptive locomotor learning. METHODS: We examined patients with contrasting peripheral vestibular deficits, vestibular neuritis in the chronic stable phase (n = 20) and strongly symptomatic unilateral Meniere’s disease (n = 15), compared to age-matched healthy controls (n = 15). We measured locomotor adaptive learning using the “broken escalator” aftereffect, simulated on a motorised moving sled. RESULTS: Patients with Meniere’s disease had an enhanced “broken escalator” postural aftereffect. More generally, the size of the locomotor aftereffect was related to how symptomatic patients were across both groups. Contrastingly, the degree of peripheral vestibular loss was not correlated with symptom load or locomotor aftereffect size. During the MOVING trials, both patient groups had larger levels of instability (trunk sway) and reduced adaptation than normal controls. CONCLUSION: Dizziness symptoms influence locomotor adaptation and its subsequent expression through motor aftereffects. Given that the unsteadiness experienced during the “broken escalator” paradigm is internally driven, the enhanced aftereffect found represents a new type of self-generated postural challenge for vestibular/unsteady patients