arXiv subjects

D. Volchenkov

Publications and source records attributed to D. Volchenkov.

At least 19 recordsLinked to original sources

arXiv2015

Path integral distance for data interpretation

The process of data interpretation is always based on the implicit introduction of equivalence relations on the set of walks over the database. Every equivalence relation on the set of walks specifies a Markov chain describing the transitions of a discrete time random walk. In order to geometrize and interpret the data, we propose the new distance between data units defined as a "Feynman path integral", in which all possible paths between any two nodes in a graph model of the data are taken into account, although some paths are more preferable than others. Such a path integral distance approach to the analysis of databases has proven its efficiency and success, especially on multivariate strongly correlated data where other methods fail to detect structural components (urban planning, historical language phylogenies, music, street fashion traits analysis, etc. ). We believe that it would become an invaluable tool for the intelligent complexity reduction and big data interpretation.

physics.soc-ph↗

arXiv2011

Heavy-tailed Distributions In Stochastic Dynamical Models

Heavy-tailed distributions are found throughout many naturally occurring phenomena. We have reviewed the models of stochastic dynamics that lead to heavy-tailed distributions (and power law distributions, in particular) including the multiplicative noise models, the models subjected to the Degree-Mass-Action principle (the generalized preferential attachment principle), the intermittent behavior occurring in complex physical systems near a bifurcation point, queuing systems, and the models of Self-organized criticality. Heavy-tailed distributions appear in them as the emergent phenomena sensitive for coupling rules essential for the entire dynamics.

math-ph↗

arXiv2011

Malagasy Dialects and the Peopling of Madagascar

The origin of Malagasy DNA is half African and half Indonesian, nevertheless the Malagasy language, spoken by the entire population, belongs to the Austronesian family. The language most closely related to Malagasy is Maanyan (Greater Barito East group of the Austronesian family), but related languages are also in Sulawesi, Malaysia and Sumatra. For this reason, and because Maanyan is spoken by a population which lives along the Barito river in Kalimantan and which does not possess the necessary skill for long maritime navigation, the ethnic composition of the Indonesian colonizers is still unclear. There is a general consensus that Indonesian sailors reached Madagascar by a maritime trek, but the time, the path and the landing area of the first colonization are all disputed. In this research we try to answer these problems together with other ones, such as the historical configuration of Malagasy dialects, by types of analysis related to lexicostatistics and glottochronology which draw upon the automated method recently proposed by the authors \cite{Serva:2008, Holman:2008, Petroni:2008, Bakker:2009}. The data were collected by the first author at the beginning of 2010 with the invaluable help of Joselin\`a Soafara N\'er\'e and consist of Swadesh lists of 200 items for 23 dialects covering all areas of the Island.

cs.CL↗

arXiv2010

Markov Chain Analysis of Musical Dice Games

We have studied entropy, redundancy, complexity, and first passage times to notes for 804 pieces of 29 composers. The successful understanding of tonal music calls for an experienced listener, as entropy dominates over redundancy in musical messages. First passage times to notes resolve tonality and feature a composer. We also discuss the possible distances in space of musical dice games and introduced the geodesic distance based on the Riemann structure associated to the probability vectors (rows of the transition matrices).

physics.data-an↗

arXiv2010

Random Walks Estimate Land Value

Expected urban population doubling calls for a compelling theory of the city. Random walks and diffusions defined on spatial city graphs spot hidden areas of geographical isolation in the urban landscape going downhill. First--passage time to a place correlates with assessed value of land in that. The method accounting the average number of random turns at junctions on the way to reach any particular place in the city from various starting points could be used to identify isolated neighborhoods in big cities with a complex web of roads, walkways and public transport systems.

physics.soc-ph↗

arXiv2008

Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces

Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron, and a finite 2-dimensional lattice.

math-ph↗

arXiv2008

Intelligibility and First Passage Times In Complex Urban Networks

Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node scales apparently linearly in all urban patterns we have studied In space syntax theory, a positive relation between the local property of a node (qualified by connectivity or by the recurrence time) and the global property of the node (estimated in our approach by the first passage time to it) is known as intelligibility. Our approach based on random walks allows to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.

physics.soc-ph↗

arXiv2008

Exploring Urban Environments By Random Walks

A complex web of roads, walkways and public transport systems can hide areas of geographical isolation very difficult to analyze. Random walks are used to spot the structural details of urban fabric.

physics.soc-ph↗

arXiv2007

Scale-free Segregation in Transport Networks

Every route of a transport network approaching equilibrium can be represented by a vector of Euclidean space which length quantifies its segregation from the rest of the graph. We have empirically observed that the distribution of lengths over the edge connectivity in many transport networks exhibits scaling invariance phenomenon. We give an example of the canal network of Veneice to demonstrate our result. The method is applicable to any transport network.

physics.soc-ph↗

arXiv2007

Transport Networks Revisited: Why Dual Graphs?

Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the graph spanning the spatial network of a city naturally interpreted as random walks. Random walks assign absolute scores to all nodes of a graph and embed space syntax into Euclidean space.

physics.soc-ph↗

arXiv2007

Magnetohydrodynamics In The Context Of Nelson's Stochastic Mechanics

A simple generalization of the MHD model accounting for the fluctuations of the configurations due to kinetic effects in plasmas in short times small scales is considered. The velocity of conductive fluid and the magnetic field are considerd as the stochastic fields (or random trial trajectories) for which the classical MHD equations play the role of the mean field equations in the spirit of stochastic mechanics of E. Nelson.

physics.plasm-ph↗

arXiv2007

Markov Chain Methods For Analyzing Complex Transport Networks

We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph representations of transport networks allowing for the effective network design, network performance evaluation, embedding, partitioning, and network fault tolerance analysis. Random walks embed graphs into Euclidean space in which distances and angles acquire a clear statistical interpretation. Being defined on the dual graph representations of transport networks random walks describe the equilibrium configurations of not random commodity flows on primary graphs. This theory unifies many network concepts into one framework and can also be elegantly extended to describe networks represented by directed graphs and multiple interacting networks.

physics.soc-ph↗

arXiv2007

Ghetto of Venice: Access to the Target Node and the Random Target Access Time

Random walks defined on undirected graphs assign the absolute scores to all nodes based on the quality of path they provide for random walkers. In city space syntax, the notion of segregation acquires a statistical interpretation with respect to random walks. We analyze the spatial network of Venetian canals and detect its most segregated part which can be identified with canals adjacent to the Ghetto of Venice.

physics.soc-ph↗

arXiv2007

Sestieri of Venice

We have investigated space syntax of Venice by means of random walks. Random walks being defined on an undirected graph establish the Euclidean space in which distances and angles between nodes acquire the clear statistical interpretation. The properties of nodes with respect to random walks allow partitioning the city canal network into disjoint divisions which may be identified with the traditional divisions of the city (sestieri).

physics.soc-ph↗

arXiv2007

City Space Syntax as a Complex Network

The encoding of cities into non-planar dual graphs reveals their complex structure. We investigate the statistics of the typical space syntax measures for the five different compact urban patterns. Universal statistical behavior of space syntax measures uncovers the universality of the city creation mechanism.

physics.soc-ph↗

arXiv2007

Discovering Important Nodes Through Graph Entropy Encoded in Urban Space Syntax

Potentially influential spaces in the spatial networks of cities can be detected by means of the entropy participation ratios. Local (connectivity) and global (centrality) entropies are considered. While the connectivity entropy has a tendency to increase with the city size, the centrality entropy is decreasing that reflects the global connectedness of cities. In urban networks, the local and global properties of nodes are positively correlated that indicates the intelligibility of cities. Correlations between entropy participation ratios can be used in purpose of intelligibility measurements and city networks comparisons.

physics.soc-ph↗

arXiv2007

Comparative Study of Cities as Complex Networks

Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial networks. We investigate the statistics of far-away neighbors and propose the new method for automatic structural classification of cities.

physics.soc-ph↗

arXiv2007

Scaling and Universality in City Space Syntax: between Zipf and Matthew

We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents for other spaces directly linked to it in a city follows a power law statistic. Universal statistical behavior of space syntax measures uncovers the universality of the city creation mechanism. We suggest that the observed universality may help to establish the international definition of a city as a specific land use pattern.

physics.soc-ph↗