Biomedical subjects

H Eugene Stanley

Publications and source records attributed to H Eugene Stanley.

At least 19 recordsLinked to original sources

PubMed2005

Relating airway diameter distributions to regular branching asymmetry in the lung.

We study the distribution Pi(n)(D) of airway diameters D as a function of generation N in asymmetric airway trees of mammalian lungs. We find that the airway bifurcations are self-similar in four species studied. Specifically, the ratios of diameters of the major and minor daughters to their parent are constants independent of N until a cutoff diameter is reached. We derive closed form expressions for Pi(N)(D) and examine the flow resistance of the tree based on an asymmetric flow division model. Our findings suggest that the observed diameter heterogeneity is consistent with an underlying regular branching asymmetry.

Animals↗

PubMed2005

Phase diagram of amorphous solid water: low-density, high-density, and very-high-density amorphous ices.

We calculate the phase diagram of amorphous solid water by performing molecular dynamics simulations using the extended simple point charge (SPC/E) model. Our simulations follow different paths in the phase diagram: isothermal compression/decompression, isochoric cooling/heating, and isobaric cooling/heating. We are able to identify low-density amorphous (LDA), high-density amorphous (HDA), and very-high density amorphous (VHDA) ices. The density rho of these glasses at different pressure P and temperature T agree well with experimental values. We also study the radial distribution functions of glassy water. In agreement with experiments, we find that LDA, HDA, and VHDA are characterized by a tetrahedral hydrogen-bonded network and that, as compared to LDA, HDA has an extra interstitial molecule between the first and second shell. VHDA appears to have two such extra molecules. We obtain VHDA, as in experiment, by isobaric heating of HDA. We also find that "other forms" of glassy water can be obtained upon isobaric heating of LDA, as well as amorphous ices formed during the transformation of LDA to HDA. We argue that these other forms of amorphous ices, as well as VHDA, are not altogether new glasses but rather are the result of aging induced by heating. Samples of HDA and VHDA with different densities are recovered at normal P, showing that there is a continuum of glasses. Furthermore, the two ranges of densities of recovered HDA and recovered VHDA overlap at ambient P. Our simulations reproduce the experimental findings of HDA --> LDA and VHDA --> LDA transformations. We do not observe a VHDA --> HDA transformation, and our final phase diagram of glassy water together with equilibrium liquid data suggests that for the SPC/E model the VHDA --> HDA transformation cannot be observed with the present heating rates accessible in simulations. Finally, we discuss the consequences of our findings for the understanding of the transformation between the different amorphous ices and the two hypothesized phases of liquid water.

Journal Article↗

PubMed2005

Structural order for one-scale and two-scale potentials.

We perform molecular dynamics simulations to investigate the relationship between structural order and waterlike dynamic and thermodynamic anomalies in spherically symmetric potentials having either one or two characteristic length scales. Structural order is characterized by translational and orientational order parameters. We find that (i) dynamic and thermodynamic anomalies exist for both one-scale and two-scale ramp potentials, and (ii) waterlike structural order anomalies exist only for the two-scale ramp potential. Our findings suggest that the waterlike relationship between structural order and anomalies is related to the presence of two different length scales in the potential.

Journal Article↗

PubMed2005

Fractionally integrated process with power-law correlations in variables and magnitudes.

Motivated by the fact that many empirical time series--including changes of heartbeat intervals, physical activity levels, intertrade times in finance, and river flux values--exhibit power-law anticorrelations in the variables and power-law correlations in their magnitudes, we propose a simple stochastic process that can account for both types of correlations. The process depends on only two parameters, where one controls the correlations in the variables and the other controls the correlations in their magnitudes. We apply the process to time series of heartbeat interval changes and air temperature changes and find that the statistical properties of the modeled time series are in agreement with those observed in the data.

Algorithms↗

PubMed2005

Scaling of optimal-path-lengths distribution in complex networks.

We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight tau(i) = exp (a r(i)), where r(i) is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form that is controlled by the expression (1/p(c)) (l(infinity)/a), where l(infinity) is the optimal path length in strong disorder (a --> infinity) and p(c) is the percolation threshold. This relation is supported by numerical simulations for Erdos-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network.

Journal Article↗

PubMed2005

Static and dynamic anomalies in a repulsive spherical ramp liquid: theory and simulation.

We compare theoretical and simulation results for static and dynamic properties for a model of particles interacting via a spherically symmetric repulsive ramp potential. The model displays anomalies similar to those found in liquid water, namely, expansion upon cooling and an increase of diffusivity upon compression. In particular, we calculate the state points P (rho,T) from the simulation and successfully compare it with the state points P (rho,T) obtained using the Rogers-Young (RY) closure for the Ornstein-Zernike (OZ) equation. Both the theoretical and the numerical calculations confirm the presence of a line of isobaric density maxima, and lines of compressibility minima and maxima. Indirect evidence of a liquid-liquid critical point is found. Dynamic properties also show anomalies. Along constant temperature paths, as the density increases, the dynamics alternate between slowing down and speeding up, and we associate this behavior with the progressive structuring and destructuring of the liquid. Finally we confirm that mode coupling theory successfully predicts the nonmonotonic behavior of dynamics and the presence of multiple glass phases, providing strong evidence that structure (the only input of mode coupling theory) controls dynamics.

Journal Article↗

PubMed2005

Structural relaxation in the glass transition region of water.

We perform molecular dynamics (MD) simulations using the extended simple-point-charge (SPC/E) model for water to study the structural relaxation through the glass transition region. We follow the same standard protocol used in differential scanning calorimetry experiments. Specifically, we cool liquid configurations at different cooling rates to produce a glass, and then we heat the glass back to the liquid state. We also study aging effects in the glass before heating. We find that MD simulations can reproduce the phenomenology observed in experiments. We review the Tool-Narayanaswamy-Moynihan (TNM) phenomenological approach, introduced to describe the behavior of the specific heat upon heating glass to the liquid phase. The TNM approach requires, as an ansatz, an expression for the temperature dependence of the relaxation time. We compare the simulation results with the prediction of the TNM approach supplemented with two well-known expressions for the relaxation time: the Narayanaswamy-Moynihan (NM) and the Adam-Gibbs-Scherer (AGS) expressions. We find that, in the case of slow cooling rates, our simulations are well represented by the TNM approach, but only if the AGS expression is adopted. We also find that the TNM approach fails in the case of fast cooling rates for both NM and AGS expressions. Several attempts to provide more freedom to the fitting procedure by allowing the fitting parameters to depend on temperature, cooling, and/or heating rates do not improve the agreement between the simulation data and the TNM predictions.

Journal Article↗

PubMed2005

Clusters of mobile molecules in supercooled water.

We study the spatially heterogeneous dynamics in water via molecular dynamics simulations using the extended simple point charge potential. We identify clusters formed by mobile molecules and study their properties. We find that these clusters grow in size and become more compact as temperature decreases. We analyze the probability density function of cluster size, and we study the cluster correlation length. We find that clusters appear to be characterized by a fractal dimension consistent with that of lattice animals. We relate the cluster size and correlation length to the configurational entropy, S(conf). We find that these quantities depend weakly on 1/ S(conf). In particular, the linearity found between the cluster mass n(*) and 1/ S(conf) suggests that n(*) may be interpreted as the mass of the cooperatively rearranging regions that form the basis of the Adam-Gibbs approach to the dynamics of supercooled liquids. We study the motion of molecules within a cluster, and find that each molecule preferentially follows a neighboring molecule in the same cluster. Based on this finding we hypothesize that stringlike cooperative motion may be a general mechanism for molecular rearrangement of complex, as well as simple liquids. By mapping each equilibrium configuration onto its corresponding local potential energy minimum or inherent structure (IS), we are able to compare the mobile molecule clusters in the equilibrium system with the molecules forming the clusters identified in the transitions between IS. We find that (i) mobile molecule clusters obtained by comparing different system configurations and (ii) clusters obtained by comparing the corresponding IS are completely different for short time scales, but are the same on the longer time scales of diffusive motion.

Journal Article↗

PubMed2005

Structural order in glassy water.

We investigate structural order in glassy water by performing classical molecular dynamics simulations using the extended simple point charge (SPC/E) model of water. We perform isochoric cooling simulations across the glass transition temperature at different cooling rates and densities. We quantify structural order by orientational and translational order metrics. Upon cooling the liquid into the glassy state, both the orientational order parameter Q and translational order parameter tau increase. At T=0 K, the glasses fall on a line in the Q-tau plane or order map. The position of this line depends only on density and coincides with the location in the order map of the inherent structures (IS) sampled upon cooling. We evaluate the energy of the IS, eIS(T), and find that both order parameters for the IS are proportional to eIS. We also study the structural order during the transformation of low-density amorphous ice (LDA) to high-density amorphous ice (HDA) upon isothermal compression and are able to identify distinct regions in the order map corresponding to these glasses. Comparison of the order parameters for LDA and HDA with those obtained upon isochoric cooling indicates major structural differences between glasses obtained by cooling and glasses obtained by compression. These structural differences are only weakly reflected in the pair correlation function. We also characterize the evolution of structural order upon isobaric annealing, leading at high pressure to very-high density amorphous ice (VHDA).

Journal Article↗

PubMed2005

Scaling and memory in volatility return intervals in financial markets.

For both stock and currency markets, we study the return intervals tau between the daily volatilities of the price changes that are above a certain threshold q. We find that the distribution function Pq(tau) scales with the mean return interval tau as Pq(tau)=tau(-1)f(tau/tau). The scaling function fx is similar in form for all seven stocks and for all seven currency databases analyzed, and fx is consistent with a power-law form, fx approximately x(-gamma) with gamma approximately 2. We also quantify how the conditional distribution Pq(tau/tau0) depends on the previous return interval tau0 and find that small (or large) return intervals are more likely to be followed by small (or large) return intervals. This "clustering" of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long-term correlations known to be present in the volatility.

Journal Article↗

PubMed2005

Anomalous transport in scale-free networks.

To study transport properties of scale-free and Erdos-Rényi networks, we analyze the conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)-k(-lambda) in which all links have unit resistance. We predict a broad range of values of G, with a power-law tail distribution phi(SF)(G)-G(-g(G)), where g(G)=2lambda-1, and confirm our predictions by simulations. The power-law tail in phi(SF)(G) leads to large values of G, signaling better transport in scale-free networks compared to Erdos-Rényi networks where the tail of the conductivity distribution decays exponentially. Based on a simple physical "transport backbone" picture we show that the conductances of scale-free and Erdos-Rényi networks are well approximated by ck(A)k(B)/(k(A)+k(B)) for any pair of nodes A and B with degrees k(A) and k(B), where c emerges as the main parameter characterizing network transport.

Computer Systems↗

PubMed2005

Liquid-liquid phase transition for an attractive isotropic potential with wide repulsive range.

We investigate how the phase diagram of a repulsive soft-core attractive potential, with a liquid-liquid phase transition in addition to the standard gas-liquid phase transition, changes by varying the parameters of the potential. We extend our previous work on short soft-core ranges to the case of large soft-core ranges, by using an integral equation approach in the hypernetted-chain approximation. We show, using a modified van der Waals equation we recently introduced, that if there is a balance between the attractive and repulsive part of the potential this potential has two fluid-fluid critical points well separated in temperature and in density. This implies that for the repulsive (attractive) energy U(R)(U(A)) and the repulsive (attractive) range w(R)(w(A)) the relation U(R)/U(A) proportional to w(R)/w(A) holds for short soft-core ranges, while U(R)/U(A) proportional to 3w(R)/w(A) holds for large soft-core ranges.

Journal Article↗

PubMed2005

Quantifying signals with power-law correlations: a comparative study of detrended fluctuation analysis and detrended moving average techniques.

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy nonstationary signals. We systematically study the performance of different variants of the DMA method when applied to artificially generated long-range power-law correlated signals with an a priori known scaling exponent alpha(0) and compare them with the DFA method. We find that the scaling results obtained from different variants of the DMA method strongly depend on the type of the moving average filter. Further, we investigate the optimal scaling regime where the DFA and DMA methods accurately quantify the scaling exponent alpha(0) , and how this regime depends on the correlations in the signal. Finally, we develop a three-dimensional representation to determine how the stability of the scaling curves obtained from the DFA and DMA methods depends on the scale of analysis, the order of detrending, and the order of the moving average we use, as well as on the type of correlations in the signal.

Journal Article↗

PubMed2005

Quantifying fluctuations in market liquidity: analysis of the bid-ask spread.

Quantifying the statistical features of the bid-ask spread offers the possibility of understanding some aspects of market liquidity. Using quote data for the 116 most frequently traded stocks on the New York Stock Exchange over the two-year period 1994-1995, we analyze the fluctuations of the average bid-ask spread S over a time interval deltat. We find that S is characterized by a distribution that decays as a power law P[S>x] approximately x(-zeta(S) ), with an exponent zeta(S) approximately = 3 for all 116 stocks analyzed. Our analysis of the autocorrelation function of S shows long-range power-law correlations, (S(t)S(t + tau)) approximately tau(-mu(s)), similar to those previously found for the volatility. We next examine the relationship between the bid-ask spread and the volume Q, and find that S approximately ln Q; we find that a similar logarithmic relationship holds between the transaction-level bid-ask spread and the trade size. We then study the relationship between S and other indicators of market liquidity such as the frequency of trades N and the frequency of quote updates U, and find S approximately ln N and S approximately ln U. Lastly, we show that the bid-ask spread and the volatility are also related logarithmically.

Journal Article↗

PubMed2005

Folding events in the 21-30 region of amyloid beta-protein (Abeta) studied in silico.

Oligomeric assemblies of the amyloid beta-protein (Abeta) have been implicated in the pathogenesis of Alzheimer's disease as a primary source of neurotoxicity. Recent in vitro studies have suggested that a 10-residue segment, Ala-21-Ala-30, forms a turn-like structure that nucleates the folding of the full-length Abeta. To gain a mechanistic insight, we simulated Abeta(21-30) folding by using a discrete molecular dynamics algorithm and a united-atom model incorporating implicit solvent and a variable electrostatic interaction strength (EIS). We found that Abeta(21-30) folds into a loop-like conformation driven by an effective hydrophobic attraction between Val-24 and the butyl portion of the Lys-28 side chain. At medium EIS [1.5 kcal/mol (1 cal = 4.18 J)], unfolded conformations almost disappear, in agreement with experimental observations. Under optimal conditions for folding, Glu-22 and Asp-23 form transient electrostatic interactions (EI) with Lys-28 that stabilize the loop conformations. Glu-22-Lys-28 is the most favored interaction. High EIS, as it occurs in the interior of proteins and aggregates, destabilizes the packing of Val-24 and Lys-28. Analysis of the unpacked structures reveals strong EI with predominance of the Asp-23-Lys-28 interaction, in agreement with studies of molecular modeling of full-length Abeta fibrils. The binary nature of the EI involving Lys-28 provides a mechanistic explanation for the linkage of amino acid substitutions at Glu-22 with Alzheimer's disease and cerebral amyloid angiopathy. Substitutions may alter the frequency of Glu-22 or Asp-23 involvement in contact formation and affect the stability of the folding nucleus formed in the Abeta(21-30) region.

Algorithms↗

PubMed2005

Current flow in random resistor networks: the role of percolation in weak and strong disorder.

We study the current flow paths between two edges in a random resistor network on a L X L square lattice. Each resistor has resistance e(ax) , where x is a uniformly distributed random variable and a controls the broadness of the distribution. We find that: (a) The scaled variable u identical with u congruent to L/a(nu) , where nu is the percolation connectedness exponent, fully determines the distribution of the current path length l for all values of u . For u >> 1, the behavior corresponds to the weak disorder limit and l scales as l approximately L, while for u << 1 , the behavior corresponds to the strong disorder limit with l approximately L(d(opt) ), where d(opt) =1.22+/-0.01 is the optimal path exponent. (b) In the weak disorder regime, there is a length scale xi approximately a(nu), below which strong disorder and critical percolation characterize the current path.

Journal Article↗

PubMed2005

Relation between the high density phase and the very-high density phase of amorphous solid water.

It has been suggested that high-density amorphous (HDA) ice is a structurally arrested form of high-density liquid (HDL) water, while low-density amorphous ice is a structurally arrested form of low-density liquid (LDL) water. Recent experiments and simulations have been interpreted to support the possibility of a second distinct high-density structural state, named very high-density amorphous (VHDA) ice, questioning the LDL-HDL hypothesis. We test this interpretation using extensive computer simulations and find that VHDA is a more stable form of HDA and that, in fact, VHDA should be considered as the amorphous ice of the quenched HDL.

Journal Article↗

PubMed2005

Power-law correlated processes with asymmetric distributions.

Motivated by the fact that many physical systems display (i) power-law correlations together with (ii) an asymmetry in the probability distribution, we propose a stochastic process that can model both properties. The process depends on only two parameters, where one controls the scaling exponent of the power-law correlations, and the other controls the degree of asymmetry in the distributions leaving the correlations unaffected. We apply the process to air humidity data and find that the statistical properties of the process are in a good agreement with those observed in the data.

Algorithms↗