arXiv subjects

Daniel ben-Avraham

Publications and source records attributed to Daniel ben-Avraham.

At least 19 recordsLinked to original sources

arXiv2021

Spanning Trees of Recursive Scale-Free Graphs

We present a link-by-link rule-based method for constructing all members of the ensemble of spanning trees for any recursively generated, finitely articulated graph, such as the DGM net. The recursions allow for many large-scale properties of the ensemble of spanning trees to be analytically solved exactly. We show how a judicious application of the prescribed growth rules selects for certain subsets of the spanning trees with particular desired properties (small-world or extended diameter, degree distribution, etc.), and thus provides solutions to several optimization problems. The analysis of spanning trees enhances the usefulness of recursive graphs as sophisticated models for everyday life complex networks.

physics.soc-ph↗

arXiv2021

Stochastic and mixed flower graphs

Stochasticity is introduced to a well studied class of recursively grown graphs: $(u,v)$-flower nets, which have power-law degree distributions as well as small-world properties (when $u=1$). The stochastic variant interpolates between different (deterministic) flower graphs and might better model real-world networks. The random multiplicative growth process involved, however, leads to a spread ensemble of networks with finite variance for the number of links, nodes, and loops. Nevertheless, the degree exponent and loopiness exponent attain unique values in the thermodynamic limit of infinitely large graphs. We also study a class of mixed flower networks, closely related to the stochastic flowers, but which are grown recursively in a deterministic way. The deterministic growth of mixed flower-nets eliminates ensemble spreads, and their recursive growth allows for exact analysis of their (uniquely defined) mixed properties.

physics.soc-ph↗

arXiv2018

Slow Normal Modes of Proteins are Accurately Reproduced across Different Platforms

The Protein Data Bank (PDB) contains the atomic structures of over 105 biomolecules with better than 2.8A resolution. The listing of the identities and coordinates of the atoms comprising each macromolecule permits an analysis of the slow-time vibrational response of these large systems to minor perturbations. 3D video animations of individual modes of oscillation demonstrate how regions interdigitate to create cohesive collective motions, providing a comprehensive framework for and familiarity with the overall 3D architecture. Furthermore, the isolation and representation of the softest, slowest deformation coordinates provide opportunities for the development of me- chanical models of enzyme function. The eigenvector decomposition, therefore, must be accurate, reliable as well as rapid to be generally reported upon. We obtain the eigenmodes of a 1.2A 34kDa PDB entry using either exclusively heavy atoms or partly or fully reduced atomic sets; Cartesian or internal coordinates; interatomic force fields derived either from a full Cartesian potential, a reduced atomic potential or a Gaussian distance-dependent potential; and independently devel- oped software. These varied technologies are similar in that each maintains proper stereochemistry either by use of dihedral degrees of freedom which freezes bond lengths and bond angles, or by use of a full atomic potential that includes realistic bond length and angle restraints. We find that the shapes of the slowest eigenvectors are nearly identical, not merely similar.

q-bio.BM↗

arXiv2018

Ordering statistics of 4 random walkers on the line

We study the ordering statistics of 4 random walkers on the line, obtaining a much improved estimate for the long-time decay exponent of the probability that a particle leads to time $t$; $P_{\rm lead}(t)\sim t^{-0.91287850}$, and that a particle lags to time $t$ (never assumes the lead); $P_{\rm lag}(t)\sim t^{-0.30763604}$. Exponents of several other ordering statistics for $N=4$ walkers are obtained to 8 digits accuracy as well. The subtle correlations between $n$ walkers that lag {\em jointly}, out of a field of $N$, are discussed: For $N=3$ there are no correlations and $P_{\rm lead}(t)\sim P_{\rm lag}(t)^2$. In contrast, our results rule out the possibility that $P_{\rm lead}(t)\sim P_{\rm lag}(t)^3$ for $N=4$, though the correlations in this borderline case are tiny.

cond-mat.stat-mech↗

arXiv2017

PDB-NMA of a Protein Homodimer Reproduces Distinct Experimental Motility Asymmetry

We have extended our analytically derived PDB-NMA formulation, ATMAN [1], to include protein dimers using mixed internal and Cartesian coordinates. A test case on a 1.3Å resolution model of a small homodimer, ActVA-ORF6, consisting of two 112-residue subunits identically folded in a compact 50Å sphere, reproduces the distinct experimental Debye-Waller motility asymmetry for the two chains, demonstrating that structure sensitively selects vibrational signatures. The vibrational analysis of this PDB entry, together with biochemical and crystallographic data, demonstrates the cooperative nature of the dimeric interaction of the two subunits and suggests a mechanical model for subunit interconversion during the catalytic cycle.

q-bio.BM↗

arXiv2017

Modeling spatial social complex networks for dynamical processes

The study of social networks --- where people are located, geographically, and how they might be connected to one another --- is a current hot topic of interest, because of its immediate relevance to important applications, from devising efficient immunization techniques for the arrest of epidemics, to the design of better transportation and city planning paradigms, to the understanding of how rumors and opinions spread and take shape over time. We develop a spatial social complex network (SSCN) model that captures not only essential connectivity features of real-life social networks, including a heavy-tailed degree distribution and high clustering, but also the spatial location of individuals, reproducing Zipf's law for the distribution of city populations as well as other observed hallmarks. We then simulate Milgram's Small-World experiment on our SSCN model, obtaining good qualitative agreement with the known results and shedding light on the role played by various network attributes and the strategies used by the players in the game. This demonstrates the potential of the SSCN model for the simulation and study of the many social processes mentioned above, where both connectivity and geography play a role in the dynamics.

physics.soc-ph↗

arXiv2016

Universality of Vibrational Spectra of Globular Proteins

It is shown that the density of modes of the vibrational spectrum of globular proteins is universal, i.e., regardless of the protein in question it closely follows one universal curve. The present study, including 135 proteins analyzed with a full atomic empirical potential (CHARMM22) and using the full complement of all atoms Cartesian degrees of freedom, goes far beyond previous claims of universality, confirming that universality holds even in the high-frequency range (300- 4000 1/cm), where peaks and turns in the density of states are faithfully reproduced from one protein to the next. We also characterize fluctuations of the spectral density from the average, paving the way to a meaningful discussion of rare, unusual spectra and the structural reasons for the deviations in such "outlier" proteins. Since the method used for the derivation of the vibrational modes (potential energy formulation, set of degrees of freedom employed, etc.) has a dramatic effect on the spectral density, another significant implication of our findings is that the universality can provide an exquisite tool for assessing and improving the quality of various models used for NMA computations. Finally, we show that the input configuration too affects the density of modes, thus emphasizing the importance of simplified potential energy formulations that are minimized at the outset.

physics.bio-ph↗

arXiv2015

Analytical results for the distribution of shortest path lengths in random networks

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdos-Rényi networks, based on recursion equations for the shells around a reference node and for the paths originating from it. The results are in agreement with numerical simulations for a broad range of network sizes and connectivities. The average and standard deviation of the distribution are also obtained. In the case that the mean degree scales as $N^α$ with the network size, the distribution becomes extremely narrow in the asymptotic limit, namely almost all pairs of nodes are equidistant, at distance $d=\lfloor 1/α\rfloor$ from each other. The distribution of shortest path lengths between nodes of degree $m$ and the rest of the network is calculated. Its average is shown to be a monotonically decreasing function of $m$, providing an interesting relation between a local property and a global property of the network. The methodology presented here can be applied to more general classes of networks.

cond-mat.dis-nn↗

arXiv2015

Sampling with Costs

We consider the problem of choosing the best of $n$ samples, out of a large random pool, when the sampling of each member is associated with a certain cost. The quality (worth) of the best sample clearly increases with $n$, but so do the sampling costs, and one important question is how many to sample for optimal gain (worth minus costs). If, in addition, the assessment of worth for each sample is associated with some "measurement error," the perceived best out of $n$ might not be the actual best, complicating the issue. Situations like this are typical in mate selection, job hiring, and food foraging, to name just a few. We tackle the problem by standard order statistics, yielding suggestions for optimal strategies, as well as some unexpected insights.

math.ST↗

arXiv2015

Growing Networks with Super-Joiners

We study the Krapivsky-Redner (KR) network growth model but where new nodes can connect to any number of existing nodes, $m$, picked from a power-law distribution $p(m)\sim m^{-α}$. Each of the $m$ new connections is still carried out as in the KR model with probability redirection $r$ (corresponding to degree exponent $γ_{\rm KR}=1+1/r$, in the original KR model). The possibility to connect to any number of nodes resembles a more realistic type of growth in several settings, such as social networks, routers networks, and networks of citations. Here we focus on the in-, out-, and total-degree distributions and on the potential tension between the degree exponent $α$, characterizing new connections (outgoing links), and the degree exponent $γ_{\rm KR}(r)$ dictated by the redirection mechanism.

physics.soc-ph↗

arXiv2015

Atomic Torsional Modal Analysis for high-resolution proteins

We introduce a formulation for normal mode analyses of globular proteins that significantly improves on an earlier, 1-parameter formulation (M. Tirion, PRL 77, 1905 (1996)) that characterized the slow modes associated with protein data bank structures. Here we develop that empirical potential function which is minimized at the outset to include two features essential to reproduce the eigenspectra and associated density of states over all frequencies, not merely the slow ones. First, introduction of preferred dihedral-angle configurations via use of torsional stiffness constants eliminates anomalous dispersion characteristics due to insufficiently bound surface sidechains. Second, we take into account the atomic identities and the distance of separation of all pairwise interactions. With these modifications we obtain stable, reliable eigenmodes over a wide range of frequencies.

physics.bio-ph↗

arXiv2014

A model of human population motion

We introduce a basic model for human mobility that accounts for the different dynamics arising from individuals embarking on short trips (and returning to their home locations) and individuals relocating to a new home. The differences between the two modes of motion comes to light on contrasting two recent studies, one tracking the geographical location of dollar bills \cite{brockmann}, the other that of mobile cell phones \cite{gonzalez}. Trips introduce two characteristic time scales; the time between trips, $θ$, and the duration of each trip, $τ$, and relocations introduces a third time scale, $T$, for the time between relocations. In practice, $T\sim{\rm years}$, $θ\sim{\rm months}$, and $τ\sim{\rm days}$, so the three time scales are widely separated. Traditionally, studies incorporating human motion assume only a single mode, using a generic rate to account for all types of motion.

physics.soc-ph↗

arXiv2014

Spatially distributed social complex networks

We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrat's law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.

physics.soc-ph↗

arXiv2013

Random walk with priorities in communication-like networks

We study a model for a random walk of two classes of particles (A and B). Where both species are present in the same site, the motion of A's takes precedence over that of B's. The model was originally proposed and analyzed in Maragakis et al., Phys. Rev. E 77, 020103 (2008); here we provide additional results. We solve analytically the diffusion coefficients of the two species in lattices for a number of protocols. In networks, we find that the probability of a B particle to be free decreases exponentially with the node degree. In scale-free networks, this leads to localization of the B's at the hubs and arrest of their motion. To remedy this, we investigate several strategies to avoid trapping of the B's: moving an A instead of the hindered B; allowing a trapped B to hop with a small probability; biased walk towards non-hub nodes; and limiting the capacity of nodes. We obtain analytic results for lattices and networks, and discuss the advantages and shortcomings of the possible strategies.

cond-mat.dis-nn↗

arXiv2012

Retention capacity of random surfaces

We introduce a "water retention" model for liquids captured on a random surface with open boundaries, and investigate it for both continuous and discrete surface heights 0, 1, ... n-1, on a square lattice with a square boundary. The model is found to have several intriguing features, including a non-monotonic dependence of the retention on the number of levels in the discrete case: for many n, the retention is counterintuitively greater than that of an n+1-level system. The behavior is explained using percolation theory, by mapping it to a 2-level system with variable probability. Results in 1-dimension are also found.

cond-mat.dis-nn↗

arXiv2011

Exact solution of the Nonconsensus Opinion Model on the line

The nonconcensus opinion model (NCO) introduced recently by Shao et al., [Phys. Rev. Lett.103, 018701 (2009)] is solved exactly on the line. Although, as expected, the model exhibits no phase transition in one dimension, its study is interesting because of the connection with invasion percolation with trapping. The system evolves exponentially fast to the steady-state, rapidly developing long-range correlations: The average cluster size in the steady state scales as the square of the initial cluster size, of the (uncorrelated) initial state. We also discuss briefly the NCO model on Bethe lattices, arguing that its phase transition diagram is different than that of regular percolation.

cond-mat.stat-mech↗

arXiv2011

Entropy production in nonequilibrium steady states: A different approach and an exactly solvable canonical model

We discuss entropy production in nonequilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to study directly entropy production in systems with microscopic irreversibility, for the first time. The two sampling methods are equivalent, otherwise, and the fluctuation theorem holds also for the novel paths. We focus on a fully irreversible three-state loop, as a canonical model of microscopic irreversibility, finding its entropy distribution, rate of entropy pr oduction, and large deviation function in closed analytical form, and showing that the widely observed kink in the large deviation function arises solely f rom microscopic irreversibility.

cond-mat.stat-mech↗

arXiv2011

Realm of Validity of the Crooks Relation

We consider the distribution $P(ϕ)$ of the Hatano-Sasa entropy, $ϕ$, in reversible and irreversible processes, finding that the Crooks relation for the ratio of the pdf's of the forward and backward processes, $P_F(ϕ)/P_R(-ϕ)=e^ϕ$, is satisfied not only for reversible, but also for irreversible processes, in general, in the adiabatic limit of "slow processes." Focusing on systems with a finite set of discrete states (and no absorbing states), we observe that two-state systems always fulfill detailed balance, and obey Crooks relation. We also identify a wide class of systems, with more than two states, that can be "coarse-grained" into two-state systems and obey Crooks relation despite their irreversibility and violation of detailed balance. We verify these results in selected cases numerically.

cond-mat.stat-mech↗