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Shlomo Havlin

Publications and source records attributed to Shlomo Havlin.

At least 217 records · Page 12Linked to original sources
arXiv2009

Statistical analysis of the overnight and daytime return

We investigate the two components of the total daily return (close-to-close), the overnight return (close-to-open) and the daytime return (open-to-close), as well as the corresponding volatilities of the 2215 NYSE stocks from 1988 to 2007. The tail distribution of the volatility, the long-term memory in the sequence, and the cross-correlation between different returns are analyzed. Our results suggest that: (i) The two component returns and volatilities have similar features as that of the total return and volatility. The tail distribution follows a power law for all volatilities, and long-term correlations exist in the volatility sequences but not in the return sequences. (ii) The daytime return contributes more to the total return. Both the tail distribution and the long-term memory of the daytime volatility are more similar to that of the total volatility, compared to the overnight records. In addition, the cross-correlation between the daytime return and the total return is also stronger. (iii) The two component returns tend to be anti-correlated. Moreover, we find that the cross-correlations between the three different returns (total, overnight, and daytime) are quite stable over the entire 20-year period.

q-fin.ST↗
arXiv2009

Dynamic networks and directed percolation

We introduce a model for dynamic networks, where the links or the strengths of the links change over time. We solve the model by mapping dynamic networks to the problem of directed percolation, where the direction corresponds to the evolution of the network in time. We show that the dynamic network undergoes a percolation phase transition at a critical concentration $p_c$, which decreases with the rate $r$ at which the network links are changed. The behavior near criticality is universal and independent of $r$. We find fundamental network laws are changed. (i) For Erdős-Rényi networks we find that the size of the giant component at criticality scales with the network size $N$ for all values of $r$, rather than as $N^{2/3}$. (ii) In the presence of a broad distribution of disorder, the optimal path length between two nodes in a dynamic network scales as $N^{1/2}$, compared to $N^{1/3}$ in a static network.

cond-mat.dis-nn↗
arXiv2008

Transport in networks with multiple sources and sinks

We investigate the electrical current and flow (number of parallel paths) between two sets of n sources and n sinks in complex networks. We derive analytical formulas for the average current and flow as a function of n. We show that for small n, increasing n improves the total transport in the network, while for large n bottlenecks begin to form. For the case of flow, this leads to an optimal n* above which the transport is less efficient. For current, the typical decrease in the length of the connecting paths for large n compensates for the effect of the bottlenecks. We also derive an expression for the average flow as a function of n under the common limitation that transport takes place between specific pairs of sources and sinks.

cs.DM↗
arXiv2008

Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $ρ(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $ρ(t) \propto \exp(-Act)$, for longer times $ρ(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $ρ(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find $ρ(t)\propto\exp\left[-At/N^\frac{γ-2}{γ-1}\av{k}\right]$ for all $γ>2$, where $γ$ is the exponent of the degree distribution $P(k)\propto k^{-γ}$.

cond-mat.dis-nn↗
arXiv2008

Structure of Business Firm Networks and Scale-Free Models

We study the structure of business firm networks and scale-free models with degree distribution $P(q) \propto (q+c)^{-λ}$ using the method of $k$-shell decomposition.We find that the Life Sciences industry network consist of three components: a ``nucleus,'' which is a small well connected subgraph, ``tendrils,'' which are small subgraphs consisting of small degree nodes connected exclusively to the nucleus, and a ``bulk body'' which consists of the majority of nodes. At the same time we do not observe the above structure in the Information and Communication Technology sector of industry. We also conduct a systematic study of these three components in random scale-free networks. Our results suggest that the sizes of the nucleus and the tendrils decrease as $λ$ increases and disappear for $λ\geq 3$. We compare the $k$-shell structure of random scale-free model networks with two real world business firm networks in the Life Sciences and in the Information and Communication Technology sectors. Our results suggest that the observed behavior of the $k$-shell structure in the two industries is consistent with a recently proposed growth model that assumes the coexistence of both preferential and random agreements in the evolution of industrial networks.

physics.soc-ph↗
arXiv2008

Multifactor Analysis of Multiscaling in Volatility Return Intervals

We study the volatility time series of 1137 most traded stocks in the US stock markets for the two-year period 2001-02 and analyze their return intervals $τ$, which are time intervals between volatilities above a given threshold $q$. We explore the probability density function of $τ$, $P_q(τ)$, assuming a stretched exponential function, $P_q(τ) \sim e^{-τ^γ}$. We find that the exponent $γ$ depends on the threshold in the range between $q=1$ and 6 standard deviations of the volatility. This finding supports the multiscaling nature of the return interval distribution. To better understand the multiscaling origin, we study how $γ$ depends on four essential factors, capitalization, risk, number of trades and return. We show that $γ$ depends on the capitalization, risk and return but almost does not depend on the number of trades. This suggests that $γ$ relates to the portfolio selection but not on the market activity. To further characterize the multiscaling of individual stocks, we fit the moments of $τ$, $μ_m \equiv <(τ/<τ>)^m>^{1/m}$, in the range of $10 < <τ> \le 100$ by a power-law, $μ_m \sim <τ>^δ$. The exponent $δ$ is found also to depend on the capitalization, risk and return but not on the number of trades, and its tendency is opposite to that of $γ$. Moreover, we show that $δ$ decreases with $γ$ approximately by a linear relation. The return intervals demonstrate the temporal structure of volatilities and our findings suggest that their multiscaling features may be helpful for portfolio optimization.

q-fin.ST↗
arXiv2008

The structural role of weak and strong links in a financial market network

We investigate the properties of correlation based networks originating from economic complex systems, such as the network of stocks traded at the New York Stock Exchange (NYSE). The weaker links (low correlation) of the system are found to contribute to the overall connectivity of the network significantly more than the strong links (high correlation). We find that nodes connected through strong links form well defined communities. These communities are clustered together in more complex ways compared to the widely used classification according to the economic activity. We find that some companies, such as General Electric (GE), Coca Cola (KO), and others, can be involved in different communities. The communities are found to be quite stable over time. Similar results were obtained by investigating markets completely different in size and properties, such as the Athens Stock Exchange (ASE). The present method may be also useful for other networks generated through correlations.

q-fin.ST↗
arXiv2008

Comparison of detrending methods for fluctuation analysis

We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). In particular, we present a detailed comparison between the regular DFA and two recently suggested methods: the Centered Moving Average (CMA) Method and a Modified Detrended Fluctuation Analysis (MDFA). We find that CMA is performing equivalently as DFA in long data with weak trends and slightly superior to DFA in short data with weak trends. When comparing standard DFA to MDFA we observe that DFA performs slightly better in almost all examples we studied. We also discuss how several types of trends affect the different types of DFA. For weak trends in the data, the new methods are comparable with DFA in these respects. However, if the functional form of the trend in data is not a-priori known, DFA remains the method of choice. Only a comparison of DFA results, using different detrending polynomials, yields full recognition of the trends. A comparison with independent methods is recommended for proving long-range correlations.

q-fin.ST↗
arXiv2008

Structural properties of spatially embedded networks

We study the effects of spatial constraints on the structural properties of networks embedded in one or two dimensional space. When nodes are embedded in space, they have a well defined Euclidean distance $r$ between any pair. We assume that nodes at distance $r$ have a link with probability $p(r) \sim r^{- δ}$. We study the mean topological distance $l$ and the clustering coefficient $C$ of these networks and find that they both exhibit phase transitions for some critical value of the control parameter $δ$ depending on the dimensionality $d$ of the embedding space. We have identified three regimes. When $δ 2d$ the networks are ``large'' worlds $l \sim N^{1/d}$ with high clustering. Our results indicate that spatial constrains have a significant impact on the network properties, a fact that should be taken into account when modeling complex networks.

physics.soc-ph↗
arXiv2008

Fractal Boundaries of Complex Networks

We introduce the concept of boundaries of a complex network as the set of nodes at distance larger than the mean distance from a given node in the network. We study the statistical properties of the boundaries nodes of complex networks. We find that for both Erdös-Rényi and scale-free model networks, as well as for several real networks, the boundaries have fractal properties. In particular, the number of boundaries nodes {\it B} follows a power-law probability density function which scales as $B^{-2}$. The clusters formed by the boundary nodes are fractals with a fractal dimension $d_{f} \approx 2$. We present analytical and numerical evidence supporting these results for a broad class of networks. Our findings imply potential applications for epidemic spreading.

math-ph↗
arXiv2008

Climate Networks around the Globe are Significantly Effected by El Nino

The temperatures in different zones in the world do not show significant changes due to El-Nino except when measured in a restricted area in the Pacific Ocean. We find, in contrast, that the dynamics of a climate network based on the same temperature records in various geographical zones in the world is significantly influenced by El-Nino. During El-Nino many links of the network are broken, and the number of surviving links comprises a specific and sensitive measure for El-Nino events. While during non El-Nino periods these links which represent correlations between temperatures in different sites are more stable, fast fluctuations of the correlations observed during El-Nino periods cause the links to break.

physics.ao-ph↗
arXiv2007

Priority diffusion model in lattices and complex networks

We introduce a model for diffusion of two classes of particles ($A$ and $B$) with priority: where both species are present in the same site the motion of $A$'s takes precedence over that of $B$'s. This describes realistic situations in wireless and communication networks. In regular lattices the diffusion of the two species is normal but the $B$ particles are significantly slower, due to the presence of the $A$ particles. From the fraction of sites where the $B$ particles can move freely, which we compute analytically, we derive the diffusion coefficients of the two species. In heterogeneous networks the fraction of sites where $B$ is free decreases exponentially with the degree of the sites. This, coupled with accumulation of particles in high-degree nodes leads to trapping of the low priority particles in scale-free networks.

cond-mat.stat-mech↗
arXiv2007

Volatility return intervals analysis of the Japanese market

We investigate scaling and memory effects in return intervals between price volatilities above a certain threshold $q$ for the Japanese stock market using daily and intraday data sets. We find that the distribution of return intervals can be approximated by a scaling function that depends only on the ratio between the return interval $τ$ and its mean $<τ>$. We also find memory effects such that a large (or small) return interval follows a large (or small) interval by investigating the conditional distribution and mean return interval. The results are similar to previous studies of other markets and indicate that similar statistical features appear in different financial markets. We also compare our results between the period before and after the big crash at the end of 1989. We find that scaling and memory effects of the return intervals show similar features although the statistical properties of the returns are different.

q-fin.ST↗
arXiv2007

Indication of multiscaling in the volatility return intervals of stock markets

The distribution of the return intervals $τ$ between volatilities above a threshold $q$ for financial records has been approximated by a scaling behavior. To explore how accurate is the scaling and therefore understand the underlined non-linear mechanism, we investigate intraday datasets of 500 stocks which consist of the Standard & Poor's 500 index. We show that the cumulative distribution of return intervals has systematic deviations from scaling. We support this finding by studying the m-th moment $μ_m \equiv <(τ/<τ>)^m>^{1/m}$, which show a certain trend with the mean interval $<τ>$. We generate surrogate records using the Schreiber method, and find that their cumulative distributions almost collapse to a single curve and moments are almost constant for most range of $<τ>$. Those substantial differences suggest that non-linear correlations in the original volatility sequence account for the deviations from a single scaling law. We also find that the original and surrogate records exhibit slight tendencies for short and long $<τ>$, due to the discreteness and finite size effects of the records respectively. To avoid as possible those effects for testing the multiscaling behavior, we investigate the moments in the range $10<<τ>\leq100$, and find the exponent $α$ from the power law fitting $μ_m\sim<τ>^α$ has a narrow distribution around $α\neq0$ which depend on m for the 500 stocks. The distribution of $α$ for the surrogate records are very narrow and centered around $α=0$. This suggests that the return interval distribution exhibit multiscaling behavior due to the non-linear correlations in the original volatility.

q-fin.ST↗
arXiv2007

Numerical evaluation of the upper critical dimension of percolation in scale-free networks

We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erdős-Rényi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-λ}$, where $k$ is the degree of a node and $λ$ is the broadness of the degree distribution. Our results report the theoretical prediction, $d_c = 2(λ- 1)/(λ- 3)$ for scale-free networks with $3 < λ< 4$ and $d_c = 6$ for Erdős-Rényi networks and scale-free networks with $λ> 4$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain $d_c = 6$ for all $λ> 2$. Our method also yields a better numerical evaluation of the critical percolation threshold, $p_c$, for scale-free networks. Our results suggest that the finite size effects increases when $λ$ approaches 3 from above.

cond-mat.dis-nn↗
arXiv2007

Transport and Percolation Theory in Weighted Networks

We study the distribution $P(σ)$ of the equivalent conductance $σ$ for Erdős-Rényi (ER) and scale-free (SF) weighted resistor networks with $N$ nodes. Each link has conductance $g\equiv e^{-ax}$, where $x$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ represents the strength of the disorder. We provide an iterative fast algorithm to obtain $P(σ)$ and compare it with the traditional algorithm of solving Kirchhoff equations. We find, both analytically and numerically, that $P(σ)$ for ER networks exhibits two regimes. (i) A low conductance regime for $σ< e^{-ap_c}$ where $p_c=1/\av{k}$ is the critical percolation threshold of the network and $\av{k}$ is average degree of the network. In this regime $P(σ)$ is independent of $N$ and follows the power law $P(σ) \sim σ^{-α}$, where $α=1-\av{k}/a$. (ii) A high conductance regime for $σ>e^{-ap_c}$ in which we find that $P(σ)$ has strong $N$ dependence and scales as $P(σ) \sim f(σ,ap_c/N^{1/3})$. For SF networks with degree distribution $P(k)\sim k^{-λ}$, $k_{min} \le k \le k_{max}$, we find numerically also two regimes, similar to those found for ER networks.

cond-mat.stat-mech↗
arXiv2007

Improving immunization strategies

We introduce an immunization method where the percentage of required vaccinations for immunity are close to the optimal value of a targeted immunization scheme of highest degree nodes. Our strategy retains the advantage of being purely local, without the need of knowledge on the global network structure or identification of the highest degree nodes. The method consists of selecting a random node and asking for a neighbor that has more links than himself or more than a given threshold and immunizing him. We compare this method to other efficient strategies on three real social networks and on a scale-free network model, and find it to be significantly more effective.

physics.soc-ph↗
arXiv2007

Limited path percolation in complex networks

We study the stability of network communication after removal of $q=1-p$ links under the assumption that communication is effective only if the shortest path between nodes $i$ and $j$ after removal is shorter than $a\ell_{ij} (a\geq1)$ where $\ell_{ij}$ is the shortest path before removal. For a large class of networks, we find a new percolation transition at $\tilde{p}_c=(κ_o-1)^{(1-a)/a}$, where $κ_o\equiv < k^2>/< k>$ and $k$ is the node degree. Below $\tilde{p}_c$, only a fraction $N^δ$ of the network nodes can communicate, where $δ\equiv a(1-|\log p|/\log{(κ_o-1)}) < 1$, while above $\tilde{p}_c$, order $N$ nodes can communicate within the limited path length $a\ell_{ij}$. Our analytical results are supported by simulations on Erdős-Rényi and scale-free network models. We expect our results to influence the design of networks, routing algorithms, and immunization strategies, where short paths are most relevant.

cond-mat.stat-mech↗