Uncovering the topology of configuration space networks

The configuration space network (CSN) of a dynamical system is an effective approach to represent the ensemble of configurations sampled during a simulation and their dynamic connectivity. To elucidate the connection between the CSN topology and the underlying free-energy landscape governing the system dynamics and thermodynamics, an analytical soluti on is provided to explain the heavy tail of the degree distribution, neighbor co nnectivity and clustering coefficient. This derivation allows to understand the universal CSN network topology observed in systems ranging from a simple quadratic well to the native state of the beta3s peptide and a 2D lattice heteropolymer. Moreover CSN are shown to fall in the general class of complex networks describe d by the fitness model.Comment: 6 figure

Preliminary Measurements of Be-10/Be-7 Ratio in Rainwater for Atmospheric Transport Analysis

The meteoric cosmogenic beryllium has been used as an essential geophysical tracer in the analysis of atmospheric flows and erosion soils since 1960. The first measurements Be-7 and Be-10 concentrations in rainwater from Mexico, have been carried out by using gamma decay spectroscopy and AMS techniques, respectively for each isotope. With this it was possible to report a preliminar value for the Be-10/Be-7 isotopic ratio in such environmental samples. The present work described preliminary results related to rainwater collected at mountain and metropolitan areas. Results are compared with predictions and previous measurements for both radioisotopes, observing a very sensible behavior particularly for the case of Be-7 activities

Bovine oviductal and embryonic insulin-like growth factor binding proteins: possible regulators of embryotrophic insulin-like growth factor circuits.

Bovine oviductal monolayer and vesicle primary cultures express insulin-like growth factor (IGF)-I and -II mRNAs and polypeptides. Early bovine embryos also express IGF-I, IGF-II, IGF-I receptor, IGF-II receptor, and insulin receptor mRNAs. This study reports the expression of IGF binding protein (IGFBP) mRNAs and polypeptides in bovine oviduct primary cultures and IGFBP mRNAs in preattachment embryos. Release of immunoreactive IGF-I and IGF-II by oviduct cultures and bovine blastocysts was also determined. IGFBP-2, -3, -4, and -5 transcripts were observed in oviduct primary cultures throughout an 8-day interval. IGFBP-1 and -6 mRNAs were consistently not detected in the oviduct. Messenger RNAs encoding IGFBPs -2, -3, and -4 were detected throughout bovine preattachment development, while transcripts encoding IGFBP-5 were detected only in blastocysts. IGFBP-1 and -6 transcripts were not detected in early embryos. Ligand blot analysis with 125I-labeled IGF-II revealed the presence of four prominent polypeptide bands of approximate molecular masses 24, 31, and 36 kDa, and a broad band extending from 46 to 53 kDa, in conditioned media samples prepared from oviduct primary cultures. Western immunoblot analysis confirmed the identity of the 24-kDa, 31-kDa, and 36-kDa species as IGFBP-4, -5, and -2, respectively. Levels of the release of IGF-II from oviductal vesicle cultures were significantly greater than levels observed for monolayer cultures (p \u3c 0.005). No significant difference in the levels of IGF-I release between monolayer and vesicle cultures was observed. Pools of 10 blastocysts released on average 36.2 +/- 3.9 pg of IGF-II per embryo, while the release of embryonic IGF-I was below the levels of detection for our assay. The results suggest that maternally derived IGF may be regulated by IGFBPs to support bovine preattachment development

Scale-free random branching tree in supercritical phase

We study the size and the lifetime distributions of scale-free random branching tree in which $k$ branches are generated from a node at each time step with probability $q_k\sim k^{-\gamma}$. In particular, we focus on finite-size trees in a supercritical phase, where the mean branching number $C=\sum_k k q_k$ is larger than 1. The tree-size distribution $p(s)$ exhibits a crossover behavior when $2 < \gamma < 3$; A characteristic tree size $s_c$ exists such that for $s \ll s_c$, $p(s)\sim s^{-\gamma/(\gamma-1)}$ and for $s \gg s_c$, $p(s)\sim s^{-3/2}\exp(-s/s_c)$, where $s_c$ scales as $\sim (C-1)^{-(\gamma-1)/(\gamma-2)}$. For $\gamma > 3$, it follows the conventional mean-field solution, $p(s)\sim s^{-3/2}\exp(-s/s_c)$ with $s_c\sim (C-1)^{-2}$. The lifetime distribution is also derived. It behaves as $\ell(t)\sim t^{-(\gamma-1)/(\gamma-2)}$ for $2 < \gamma < 3$, and $\sim t^{-2}$ for $\gamma > 3$ when branching step $t \ll t_c \sim (C-1)^{-1}$, and $\ell(t)\sim \exp(-t/t_c)$ for all $\gamma > 2$ when $t \gg t_c$. The analytic solutions are corroborated by numerical results.Comment: 6 pages, 6 figure

d_c=4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d_c=4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we find that avalanches are compact for all dimensions d<=4, and are fractal for d>4. Under those conditions, scaling arguments predict a d_c=4, where hyperscaling relations hold for d<=4. Other properties of avalanches, studied for 1<=d<=6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.Comment: 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers available at http://userwww.service.emory.edu/~sboettc

Universal 1/f Noise from Dissipative SOC Models

We introduce a model able to reproduce the main features of 1/f noise: hyper-universality (the power-law exponents are independent on the dimension of the system; we show here results in d=1,2) and apparent lack of a low-frequency cutoff in the power spectrum. Essential ingredients of this model are an activation-deactivation process and dissipation.Comment: 3 Latex pages, 2 eps Figure

Quantitative description and modeling of real networks

In this letter we present data analysis and modeling of two particular cases of study in the field of growing networks. We analyze WWW data set and authorship collaboration networks in order to check the presence of correlation in the data. The results are reproduced with a pretty good agreement through a suitable modification of the standard AB model of network growth. In particular, intrinsic relevance of sites plays a role in determining the future degree of the vertex.Comment: 4 pages, 3 figure

Fractal Dimension and Localization of DNA Knots

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the gyration radius of the adsorbed DNA knot scales with the 3D Flory exponent $\nu\approx 0.58$ within error. In (ii), we find $\nu\approx 0.66$, a value between the 3D and 2D ($\nu=3/4$) exponents, indicating an incomplete 2D relaxation or a different polymer universality class. Compelling evidence is also presented for the localization of the knot crossings in 2D.Comment: 4 pages, 3 figure

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

Discretized Diffusion Processes

We study the properties of the ``Rigid Laplacian'' operator, that is we consider solutions of the Laplacian equation in the presence of fixed truncation errors. The dynamics of convergence to the correct analytical solution displays the presence of a metastable set of numerical solutions, whose presence can be related to granularity. We provide some scaling analysis in order to determine the value of the exponents characterizing the process. We believe that this prototype model is also suitable to provide an explanation of the widespread presence of power-law in social and economic system where information and decision diffuse, with errors and delay from agent to agent.Comment: 4 pages 5 figure, to be published in PR