arXiv subjects

Sergei Maslov

Publications and source records attributed to Sergei Maslov.

At least 55 records · Page 3Linked to original sources

arXiv2006

Propagation of fluctuations in interaction networks governed by the law of mass action

Using an example of physical interactions between proteins, we study how perturbations propagate in interconnected networks whose equilibrium state is governed by the law of mass action. We introduce a comprehensive matrix formalism which predicts the response of this equilibrium to small changes in total concentrations of individual molecules, and explain it using a heuristic analogy to a current flow in a network of resistors. Our main conclusion is that on average changes in free concentrations exponentially decay with the distance from the source of perturbation. We then study how this decay is influenced by such factors as the topology of a network, binding strength, and correlations between concentrations of neighboring nodes. An exact analytic expression for the decay constant is obtained for the case of uniform interactions on the Bethe lattice. Our general findings are illustrated using a real biological network of protein-protein interactions in baker's yeast with experimentally determined protein concentrations.

q-bio.MN↗

arXiv2006

Exploring an opinion network for taste prediction: an empirical study

We develop a simple statistical method to find affinity relations in a large opinion network which is represented by a very sparse matrix. These relations allow us to predict missing matrix elements. We test our method on the Eachmovie data of thousands of movies and viewers. We found that significant prediction precision can be achieved and it is rather stable. There is an intrinsic limit to further improve the prediction precision by collecting more data, implying perfect prediction can never obtain via statistical means.

physics.soc-ph↗

arXiv2005

Optimal ranking in networks with community structure

The World-Wide Web (WWW) is characterized by a strong community structure in which groups of webpages (e.g. those devoted to a common topic or belonging to the same organization) are densely interconnected by hyperlinks. We study how such network architecture affects the average Google rank of individual communities. Using a mean-field approximation, we quantify how the average Google rank of community webpages depends on the degree to which it is isolated from the rest of the world in both incoming and outgoing directions, and $α$ -- the only intrinsic parameter of Google's PageRank algorithm. Based on this expression we introduce a concept of a web-community being decoupled or conversely coupled to the rest of the network. We proceed with empirical study of several internal web-communities within two US universities. The predictions of our mean-field treatment were qualitatively verified in those real-life networks. Furthermore, the value $α=0.15$ used by Google seems to be optimized for the degree of isolation of communities as they exist in the actual WWW.

physics.soc-ph↗

arXiv2005

Binding properties and evolution of homodimers in protein-protein interaction networks

We demonstrate that Protein-Protein Interaction (PPI) networks in several eucaryotic organisms contain significantly more self-interacting proteins than expected if such homodimers randomly appeared in the course of the evolution. We also show that on average homodimers have twice as many interaction partners than non-self-interacting proteins. More specifically the likelihood of a protein to physically interact with itself was found to be proportional to the total number of its binding partners. These properties of dimers are are in agreement with a phenomenological model in which individual proteins differ from each other by the degree of their ``stickiness'' or general propensity towards interaction with other proteins including oneself. A duplication of self-interacting proteins creates a pair of paralogous proteins interacting with each other. We show that such pairs occur more frequently than could be explained by pure chance alone. Similar to homodimers, proteins involved in heterodimers with their paralogs on average have twice as many interacting partners than the rest of the network. The likelihood of a pair of paralogous proteins to interact with each other was also shown to decrease with their sequence similarity. This all points to the conclusion that most of interactions between paralogs are inherited from ancestral homodimeric proteins, rather than established de novo after the duplication. We finally discuss possible implications of our empirical observations from functional and evolutionary standpoints.

q-bio.GN↗

arXiv2004

Effects of Community Structure on Search and Ranking in Information Network

The World-Wide Web (WWW) is characterized by a strong community structure in which communities of webpages (e.g. those sharing a common keyword) are densely interconnected by hyperlinks. We study how such network architecture affects the average Google ranking of individual webpages in the comunity. It is shown that the Google rank of community webpages could either increase or decrease with the density of inter-community links depending on the exact balance between average in- and out-degrees in the community. The magnitude of this effect is described by a simple analytical formula and subsequently verified by numerical simulations of random scale-free networks with a desired level of the community structure. A new algorithm allowing for generation of such networks is proposed and studied. The number of inter-community links in such networks is controlled by a temperature-like parameter with the strongest community structure realized in "low-temperature" networks.

cond-mat.other↗

arXiv2004

Hierarchy Measures in Complex Networks

Using each node's degree as a proxy for its importance, the topological hierarchy of a complex network is introduced and quantified. We propose a simple dynamical process used to construct networks which are either maximally or minimally hierarchical. Comparison with these extremal cases as well as with random scale-free networks allows us to better understand hierarchical versus modular features in several real-life complex networks. For random scale-free topologies the extent of topological hierarchy is shown to smoothly decline with $γ$ -- the exponent of a degree distribution -- reaching its highest possible value for $γ\leq 2$ and quickly approaching zero for $γ>3$.

cond-mat.soft↗

arXiv2003

Diffusion on Complex Networks : A way to probe their large scale topological structures

A diffusion process on complex networks is introduced in order to uncover their large scale topological structures. This is achieved by focusing on the slowest decaying diffusive modes of the network. The proposed procedure is applied to real-world networks like a friendship network of known modular structure, and an Internet routing network. For the friendship network, its known structure is well reproduced. In case of the Internet, where the structure is far less well-known, one indeed finds a modular structure, and modules can roughly be associated with individual countries. Quantitatively the modular structure of the Internet manifests itself in an approximately 10 times larger participation ratio of its slowest decaying modes as compared to the null model -- a random scale-free network. The extreme edges of the Internet are found to correspond to Russian and US military sites.

cond-mat.stat-mech↗

arXiv2003

The conundrum of stock versus bond prices

In a general way, stock and bond prices do not display any significant correlation. Yet, if we concentrate our attention on specific episodes marked by a crash followed by a rebound, then we observe that stock prices have a strong connection with interest rates on the one hand, and with bond yield spreads on the other hand. That second relationship is particularly stable in the course of time having been observed for over 140 years. Throughout the paper we use a quasi-experimental approach. By observing how markets respond to well-defined exogenous shocks (such as the shock of September 11, 2001) we are able to determine how investors organize their ``flight to safety'': which safe haven they select, how long their collective panic lasts, and so on. As rebounds come to an end the correlation of stock and bond prices fades away, a clear sign that the collective behavior of investors loses some of its coherence; this observation can be used as an objective criterion for assessing the end of a market rebound. Based on the behavior of investors, we introduce a distinction between ``genuine stock market rallies'', as opposed to spurious rallies such as those brought about by the buyback programs implemented by large companies. The paper ends with a discussion of testable predictions.

cond-mat↗

arXiv2003

Does the price multiplier effect also hold for stocks?

The price multiplier effect provides precious insight into the behavior of investors during episodes of speculative trading. It tells us that the higher the price of an asset is (within a set of similar assets) the more its price is likely to increase during the upgoing phase of a speculative price peak. In short, instead of being risk averse, as is often assumed, investors rather seem to be ``risk prone''. While this effect is known to hold for several sorts of assets, it has not yet been possible to test it for stocks because the price of one share has no intrinsic significance which means that one cannot say that a stock $ A $ is more expensive than a stock $ B $ on the basis of its price. In this paper we show that the price-dividend ratio gives a good basis for assessing the price of stocks in an intrinsic way. When this alternative measure is used instead, it turns out that the price multiplier effect also holds for stocks, at least if one concentrates on samples of companies which are sufficiently homogeneous.

cond-mat↗

arXiv2003

Upstream Plasticity and Downstream Robustness in Evolution of Molecular Networks

Evolving biomolecular networks have to combine the stability against perturbations with flexibility allowing their constituents to assume new roles in the cell. Gene duplication followed by functional divergence of associated proteins is a major force shaping molecular networks in living organisms. Recent availability of system-wide data for yeast S. Cerevisiae allow us to access the effects of gene duplication on robustness and plasticity of molecular networks. We demonstrate that the upstream transcriptional regulation of duplicated genes diverges fast, losing on average 4% of their common transcription factors for every 1% divergence of their amino acid sequences. In contrast, the set of physical interaction partners of their protein products changes much slower. The relative stability of downstream functions of duplicated genes, is further corroborated by their ability to substitute for each other in gene knockout experiments. We believe that the combination of the upstream plasticity and the downstream robustness is a general feature determining the evolvability of molecular networks.

q-bio.MN↗

arXiv2002

Modularity and Extreme Edges of the Internet

We study the spectral properties of a diffusion process taking place on the Internet network focusing on the slowest decaying modes. These modes allow us to identify an underlying modular structure of the Internet roughly corresponding to individual countries. For instance in the slowest decaying mode the diffusion current flows from Russia towards US military sites. These two regions thus constitute the extreme edges of the Internet. Quantitatively the modular structure of the Internet manifests itself in approximately 10 times larger participation ratio of its slow decaying modes compared to the null model - a random scale-free network. We propose to use the fraction of nodes participating in slow decaying modes as a general measure of the modularity of a network. For the 100 slowest decaying modes of the Internet we measured this fraction to be around 30%. Finally we suggest, that the degree of isolation of an individual module can be assessed by comparing its participation in different diffusion modes. Using the proportionality of response as a criterion we find that the independent module approximation works well for the Internet.

cond-mat.stat-mech↗

arXiv2002

Pattern Detection in Complex Networks: Correlation Profile of the Internet

A general scheme for detecting and analyzing topological patterns in large complex networks is presented. In this scheme the network in question is compared with its properly randomized version that preserves some of its low-level topological properties. Statistically significant deviation of any measurable property of a network from this null model likely reflect its design principles and/or evolutionary history. We illustrate this basic scheme on the example of the correlation profile of the Internet quantifying correlations between connectivities of its neighboring nodes. This profile distinguishes the Internet from previously studied molecular networks with a similar scale-free connectivity distribution. We finally demonstrate that clustering in a network is very sensitive to both the connectivity distribution and its correlation profile and compare the clustering in the Internet to the appropriate null model.

cond-mat.stat-mech↗

arXiv2002

Specificity and stability in topology of protein networks

Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory network. To address topological properties of these two networks we quantify correlations between connectivities of interacting nodes and compare them to a null model of a network, in which al links were randomly rewired. We find that for both interaction and regulatory networks, links between highly connected proteins are systematically suppressed, while those between a highly-connected and low-connected pairs of proteins are favored. This effect decreases the likelihood of cross talk between different functional modules of the cell, and increases the overall robustness of a network by localizing effects of deleterious perturbations.

cond-mat.soft↗

arXiv2002

Extracting Hidden Information from Knowledge Networks

We develop a method allowing us to reconstruct individual tastes of customers from a sparsely connected network of their opinions on products, services, or each other. Two distinct phase transitions occur as the density of edges in this network is increased: above the first - macroscopic prediction of tastes becomes possible, while above the second - all unknown opinions can be uniquely reconstructed. We illustrate our ideas using a simple Gaussian model, which we study using both field-theoretical methods and numerical simulations. We point out a potential relevance of our approach to the field of bioinformatics.

cond-mat.stat-mech↗

arXiv2001

Measures of globalization based on cross-correlations of world financial indices

The cross-correlation matrix of daily returns of stock market indices in a diverse set of 37 countries worldwide was analyzed. Comparison of the spectrum of this matrix with predictions of random matrix theory provides an empirical evidence of strong interactions between individual economies, as manifested by three largest eigenvalues and the corresponding set of stable, non-random eigenvectors. The observed correlation structure is robust with respect to changes in the time horizon of returns ranging from 1 to 10 trading days, and to replacing individual returns with just their signs. This last observation confirms that it is mostly correlations in signs and not absolute values of fluctuations, which are responsible for the observed effect. Correlations between different trading days seem to persist for up to 3 days before decaying to the level of the background noise.

cond-mat.stat-mech↗

arXiv2001

Price fluctuations from the order book perspective - empirical facts and a simple model

Statistical properties of an order book and the effect they have on price dynamics were studied using the high-frequency NASDAQ Level II data. It was observed that the size distribution of marketable orders (transaction sizes) has power law tails with an exponent 1+mu_{market}=2.4 \pm 0.1. The distribution of limit order sizes was found to be consistent with a power law with an exponent close to 2. A somewhat better fit to this distribution was obtained by using a log-normal distribution with an effective power law exponent equal to 2 in the middle of the observed range. The depth of the order book measured as a price impact of a hypothetical large market order was observed to be a non-linear function of its size. A large imbalance in the number of limit orders placed at bid and ask sides of the book was shown to lead to a short term deterministic price change, which is in accord with the law of supply and demand.

cond-mat.stat-mech↗

arXiv2000

Exact solution of stochastic directed sandpile model

We introduce and analytically solve a directed sandpile model with stochastic toppling rules. The model clearly belongs to a different universality class from its counterpart with deterministic toppling rules, previously solved by Dhar and Ramaswamy. The critical exponents are D_||=7/4, τ=10/7 in two dimensions and D_||=3/2, τ=4/3 in one dimension. The upper critical dimension of the model is three, at which the exponents apart from logarithmic corrections reach their mean-field values D_||=2, τ=3/2.

cond-mat.stat-mech↗

arXiv1999

Simple model of a limit order-driven market

We introduce and study a simple model of a limit order-driven market. Traders in this model can either trade at the market price or place a limit order, i.e. an instruction to buy (sell) a certain amount of the stock if its price falls below (raises above) a predefined level. The choice between these two options is purely random (there are no strategies involved), and the execution price of a limit order is determined simply by offsetting the most recent market price by a random amount. Numerical simulations of this model revealed that despite such minimalistic rules the price pattern generated by the model has such realistic features as ``fat'' tails of the price fluctuations distribution, characterized by a crossover between two power law exponents, long range correlations of the volatility, and a non-trivial Hurst exponent of the price signal.

cond-mat.stat-mech↗