Dimitri Volchenkov

Mathematical Analysis of Urban Spatial Networks

Complex Networks of Urban Environments.- Wayfinding and Affine Representations of Urban Environments.- Exploring Community Structure by Diffusion Processes.- Spectral Analysis of Directed Graphs and Interacting Networks.- Urban Area Networks and Beyond.

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 us to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.

Exploration-exploitation trade-off features a saltatory search behaviour

Searching experiments conducted in different virtual environments over a gender-balanced group of people revealed a gender irrelevant scale-free spread of searching activity on large spatio-temporal scales. We have suggested and solved analytically a simple statistical model of the coherent-noise type describing the exploration–exploitation trade-off in humans (‘should I stay’ or ‘should I go’). The model exhibits a variety of saltatory behaviours, ranging from Lévy flights occurring under uncertainty to Brownian walks performed by a treasure hunter confident of the eventual success.

Spatio-temporal analysis of kinematic signals in classical ballet

Abstract Motions of markers arranged on a dancers body can be approximated by the sum of a minimal set of linear trajectories with given accuracy. The composition of approximating linear trajectories features the movement traits and discloses the level of movement expertise in the dancers. We suggest the computationally simple methods for the analysis of trajectories and body shape changes attested directly from the motion capture data. We have tested our approach for 6 figures from the classical ballet repertoire performed by 24 dancers varying in expertise. The methods allow to estimate the level of movement expertise, to draw the detailed structure of movements, and to classify movements into a given repertoire automatically.

Fair and Biased Random Walks on Undirected Graphs and Related Entropies

The entropy rates of Markov chains (random walks) defined on connected undirected graphs are well studied in many surveys. We study the entropy rates related to the first-passage time probability distributions of fair random walks, their relative (Kullback–Leibler) entropies, and the entropy related to two biased random walks – with the random absorption of walkers and the shortest paths random walks. We show that uncertainty of first-passage times quantified by the entropy rates characterizes the connectedness of the graph. The relative entropy derived for the biased random walks estimates the level of uncertainty between connectivity and connectedness – the local and global properties of nodes in the graph.

Networking Phylogeny for Indo-European and Austronesian Languages

Harnessing cognitive abilities of many individuals, a language evolves upon their mutual interactions establishing a persistent social environment to which language is closely attuned. Human history is encoded in the rich sets of linguistic data by means of symmetry patterns that are not always feasibly represented by trees. Here we use the methods developed in the study of complex networks to decipher accurately symmetry records on the language phylogeny of the Indo-European and the Austronesian language families, considering, in both cases, the samples of fifty different languages. In particular, we support the Anatolian theory of IndoEuropean origin and the ‘express train’ model of Austronesian expansion from South-East Asia, with an essential role for the Batanes islands located between the Philippines and Taiwan.

Success, Hierarchy, and Inequality Under Uncertainty

Domains with a lot of uncertainty have the highest likelihood of skilled people failing. Those that succeed the most under uncertainty are often simply those that tried harder and whose early luck compounded. By fostering hierarchical organization in a group, uncertainty ultimately leads to inequality. Wealth inequality in a population arises from risky decisions being taken under uncertainty by the vital few: The more adventurous traders are, the greater their fortune, and the fewer lucky ones there are. Scarcity also promotes inequality by necessitating competition and fueling conspicuous consumption. Existing econometric data suggest that rising income inequality is a global phenomenon, occurring whenever the national economy is out of step with the world average. Rampant inequality may transform the uncertainty of national economic development into uncertainty of international relations.

Hidden Geometry of Urban Landscapes for Smart City Planners

Urbanization has been the dominant demographic trend in the entire world, during the last half century. Rural to urban migration, international migration, and the reclassification or expansion of existing city boundaries have been among the major reasons for increasing urban population. The essentially fast growth of cities in the last decades urgently calls for a profound insight into the common principles stirring the structure of urban developments all over the world. In the present chapter, we discuss the graph representations of urban spatial structures and suggested a computationally simple technique that can be used in order to spot the relatively isolated locations and neighborhoods, to detect urban sprawl, and to illuminate the hidden community structures in complex urban textures. The approach may be implemented for the detailed expertise of any urban pattern and the associated transport networks that may include many transportation modes.

Impersonal Methods of Decision Making Under Uncertainty: Social Conformity, Market Economy, and Authoritarianism

Under conditions of uncertainty, people try to evade personal decision making by using impersonal methods of thought. We have introduced and analyzed a simple probability model for social conformity and a simple deterministic dynamical model of markets. We have discussed the idea that, when societal institutions dissolve but people’s social identity remains intact, they tend to think that the end justifies the means, and would deliberately reject democracy in favor of authoritarianism as a way of getting an opportunity for social revenge.

We Speak Up for Time, and Time Speaks Up for Us

Time is a fundamental dimension of social interaction. We present a first study, integrating the analysis of temporal patterns of interaction, interaction preferences, and the local vs. global structure of communication in two organizations over a period of 3 weeks. Our results suggest that simple principles reflecting interaction propensities, time budget, and institutional constraints underlie the distribution of interaction events. As a result, the duration of interactions (as well as the interval between interactions) reveal deep aspects of social systems. Not only does the interaction duration reveal a multiplicity of regimes affecting interaction parameters, but it also offers differentiated windows over different social network structures corresponding to such regimes. We show that institutions never die, as once interrupted communication can be resumed anytime.