Scaling of mean first-passage time as efficiency measure of nodes sending information on scale-free Koch networks

A lot of previous work showed that the sectional mean first-passage time (SMFPT), i.e., the average of mean first-passage time (MFPT) for random walks to a given hub node (node with maximum degree) averaged over all starting points in scale-free small-world networks exhibits a sublinear or linear dependence on network order $N$ (number of nodes), which indicates that hub nodes are very efficient in receiving information if one looks upon the random walker as an information messenger. Thus far, the efficiency of a hub node sending information on scale-free small-world networks has not been addressed yet. In this paper, we study random walks on the class of Koch networks with scale-free behavior and small-world effect. We derive some basic properties for random walks on the Koch network family, based on which we calculate analytically the partial mean first-passage time (PMFPT) defined as the average of MFPTs from a hub node to all other nodes, excluding the hub itself. The obtained closed-form expression displays that in large networks the PMFPT grows with network order as $N \ln N$, which is larger than the linear scaling of SMFPT to the hub from other nodes. On the other hand, we also address the case with the information sender distributed uniformly among the Koch networks, and derive analytically the entire mean first-passage time (EMFPT), namely, the average of MFPTs between all couples of nodes, the leading scaling of which is identical to that of PMFPT. From the obtained results, we present that although hub nodes are more efficient for receiving information than other nodes, they display a qualitatively similar speed for sending information as non-hub nodes. Moreover, we show that the location of information sender has little effect on the transmission efficiency. The present findings are helpful for better understanding random walks performed on scale-free small-world networks.Comment: Definitive version published in European Physical Journal

First-passage times in complex scale-invariant media

How long does it take a random walker to reach a given target point? This quantity, known as a first passage time (FPT), has led to a growing number of theoretical investigations over the last decade1. The importance of FPTs originates from the crucial role played by first encounter properties in various real situations, including transport in disordered media, neuron firing dynamics, spreading of diseases or target search processes. Most methods to determine the FPT properties in confining domains have been limited to effective 1D geometries, or for space dimensions larger than one only to homogeneous media1. Here we propose a general theory which allows one to accurately evaluate the mean FPT (MFPT) in complex media. Remarkably, this analytical approach provides a universal scaling dependence of the MFPT on both the volume of the confining domain and the source-target distance. This analysis is applicable to a broad range of stochastic processes characterized by length scale invariant properties. Our theoretical predictions are confirmed by numerical simulations for several emblematic models of disordered media, fractals, anomalous diffusion and scale free networks.Comment: Submitted version. Supplementary Informations available on Nature websit

Role of fractal dimension in random walks on scale-free networks

Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks. The first is deterministic, often called $(x,y)$-flowers; the other is random, which is a combination of $(1,3)$-flower and $(2,4)$-flower and thus called hybrid networks. The two network families display rich behavior as observed in various real systems, as well as some unique topological properties not shared by other networks. We derive analytically the average trapping time for random walks on both the $(x,y)$-flowers and the hybrid networks with an immobile trap positioned at an initial node, i.e., a hub node with the highest degree in the networks. Based on these analytical formulae, we show how the average trapping time scales with the network size. Comparing the obtained results, we further uncover that fractal dimension plays a decisive role in the behavior of average trapping time on fractal scale-free networks, i.e., the average trapping time decreases with an increasing fractal dimension.Comment: Definitive version published in European Physical Journal

Mean first-passage time for random walks on undirected networks

In this paper, by using two different techniques we derive an explicit formula for the mean first-passage time (MFPT) between any pair of nodes on a general undirected network, which is expressed in terms of eigenvalues and eigenvectors of an associated matrix similar to the transition matrix. We then apply the formula to derive a lower bound for the MFPT to arrive at a given node with the starting point chosen from the stationary distribution over the set of nodes. We show that for a correlated scale-free network of size $N$ with a degree distribution $P(d)\sim d^{-\gamma}$, the scaling of the lower bound is $N^{1-1/\gamma}$. Also, we provide a simple derivation for an eigentime identity. Our work leads to a comprehensive understanding of recent results about random walks on complex networks, especially on scale-free networks.Comment: 7 pages, no figures; definitive version published in European Physical Journal

Organic residues in archaeology - the highs and lows of recent research

YesThe analysis of organic residues from archaeological materials has become increasingly important to our understanding of ancient diet, trade and technology. Residues from diverse contexts have been retrieved and analysed from the remains of food, medicine and cosmetics to hafting material on stone arrowheads, pitch and tar from shipwrecks, and ancient manure from soils. Research has brought many advances in our understanding of archaeological, organic residues over the past two decades. Some have enabled very specific and detailed interpretations of materials preserved in the archaeological record. However there are still areas where we know very little, like the mechanisms at work during the formation and preservation of residues, and areas where each advance produces more questions rather than answers, as in the identification of degraded fats. This chapter will discuss some of the significant achievements in the field over the past decade and the ongoing challenges for research in this area.Full text was made available in the Repository on 15th Oct 2015, at the end of the publisher's embargo period

Ernest Lindl. — Das Priester-und Beamtentum der altbabylonischen Kontrakte. Mit einer Zusammenstellung sämtliclier Kontrakte der I. Dynastie von Babylon in Begestenform. F. Schoningh, Paderborn, 1913

Condamin Albert. Ernest Lindl. — Das Priester-und Beamtentum der altbabylonischen Kontrakte. Mit einer Zusammenstellung sämtliclier Kontrakte der I. Dynastie von Babylon in Begestenform. F. Schoningh, Paderborn, 1913. In: Mélanges de la Faculté orientale, tome 6, 1913. pp. 3-4

Giustino Boson. — Assiriologia : Elementi di Grammatica, Sillabario, Crestoma-zia e Dizionarietto. (Manuali Haepli), Milan, Ulrico Hœpli, 1918

Condamin Albert. Giustino Boson. — Assiriologia : Elementi di Grammatica, Sillabario, Crestoma-zia e Dizionarietto. (Manuali Haepli), Milan, Ulrico Hœpli, 1918. In: Mélanges de la Faculté orientale, tome 7, 1914. pp. 407-408

Anastasius Schollmeyer. — Sumerisch-babylonisclie Hymnen und Gebete an Samas ; dans Studien zur Geschichte und Kultur des Altertums. F. Schoningh, Paderborn, 1912

Condamin Albert. Anastasius Schollmeyer. — Sumerisch-babylonisclie Hymnen und Gebete an Samas ; dans Studien zur Geschichte und Kultur des Altertums. F. Schoningh, Paderborn, 1912. In: Mélanges de la Faculté orientale, tome 6, 1913. pp. 2-3