arXiv subjects

Snehal M. Shekatkar

Publications and source records attributed to Snehal M. Shekatkar.

12 recordsLinked to original sources

arXiv2025

Binomial maps: stochastically evolving iterated integer maps for finite populations

Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then. However, this also makes it challenging to use the same models for small populations where finite size effects like demographic noise and extinction cannot be ignored. Moreover, adding noise to the equations does not solve this problem as it can only represent the environmental stochasticity. An approach, sometimes used in ecological literature, but surprisingly uncommon in dynamical systems community, is \emph{Binomial maps}, which allow stochastic evolution of deterministic iterated map models of population. Here we present their formulation in a way so as to make their connection to the agent-based models explicit, and demonstrate it for the Logistic and Ricker maps. We also show that the Binomial maps are not completely equivalent to their deterministic counterparts, and derive sufficient conditions under which the equivalence holds. This approach enables rigorous finite-population analysis within familiar map-based models, bridging the deterministic map models and stochastic agent-based models.

q-bio.PE↗

arXiv2023

Detrimental role of fluctuations in the resource dependency networks

Individual components of many real-world complex networks produce and exchange resources among themselves. However, because the resource production in such networks is almost always stochastic, fluctuations in the production are unavoidable. In this paper, we study the effect of fluctuations on the resource dependencies in complex networks. To this end, we consider a modification of a threshold model of resource dependencies in networks that was recently proposed, where each vertex has a fitness that depends on the total amount of resource it has produced, the amount it has procured from its neighbours, and the fitness threshold. We study how the ``network fitness'', defined as the average fitness of vertices in the network, is affected as the fluctuation size is varied. We show that the fluctuations worsen the network fitness even when average production on vertices is kept fixed. This is true independent of whether more than required amount is produced in the network or not. However, this effect saturates for large fluctuations, and hence very large fluctuations cannot worsen the network fitness beyond a limit. We further show that the networks with a homogeneous degree distribution, such as the Erdos-Renyi network, are less affected by fluctuations and also produce lower wastage than the networks with a heterogeneous degree distribution like the Scale-Free network. Our work shows that fluctuations in the resource production should be avoided in resource dependency networks.

physics.soc-ph↗

arXiv2023

On partial information retrieval: the unconstrained 100 prisoner problem

We consider a generalization of the classical 100 Prisoner problem and its variant, involving empty boxes, whereby winning probabilities for a team depend on the number of attempts, as well as on the number of winners. We call this the unconstrained 100 prisoner problem. After introducing the 3 main classes of strategies, we define a variety of `hybrid' strategies and quantify their winning-efficiency. Whenever analytic results are not available, we make use of Monte Carlo simulations to estimate with high accuracy the winning-probabilities. Based on the results obtained, we conjecture that all strategies, except for the strategy maximizing the winning probability of the classical (constrained) problem, converge to the random strategy under weak conditions on the number of players or empty boxes. We conclude by commenting on the possible applications of our results in understanding processes of information retrieval, such as ``memory'' in living organisms.

math.CO↗

arXiv2022

Effect of money heterogeneity on resource dependency in complex networks

Exchange of resources among individual components of a system is fundamental to systems like a social network of humans and a network of cities and villages. For various reasons, the human society has come up with the notion of money as a proxy for the resources. Here we extend the model of resource dependencies in networks that was recently proposed by one of us, by incorporating the concept of money so that the vertices of a network can sell and buy required resources among themselves. We simulate the model using the configuration model as a substrate for homogeneous as well as heterogeneous degree distributions and using various exchange strategies. We show that a moderate amount of initial heterogeneity in the money on the vertices can significantly improve the survivability of Scale-free networks but not that of homogeneous networks like the Erdos-Renyi network. Our work is a step towards understanding the effect of presence of money on the resource distribution dynamics in complex networks.

cs.SI↗

arXiv2022

Resource dependency and survivability in complex networks

Components in many real-world complex systems depend on each other for the resources required for survival, and may die of a shortage. These patterns of dependencies often take the form of a complex network whose structure potentially affects how the resources produced in the system are efficiently shared among its components, which in turn decides a network's survivability. Here we present a simple threshold model that provides insight into this relationship between the network structure and survivability. We show that, as a combined effect of local sharing and finite lifetime of resources, many components in a complex system may die of lack of resources even when sufficient amount is available in the system. We also obtain a surprising result that although the scale-free networks exhibit a significantly higher survivability compared to their homogeneous counterparts, a vertex in the later survives longer on average. Finally, we demonstrate that the system's survivability can be substantially improved by changing the way vertices distribute resources among the neighbours. Our work is a step towards understanding the relationship between intricate resource dependencies present in many real-world complex systems and their survivability.

physics.soc-ph↗

arXiv2019

Do zealots increase or decrease the polarization in social networks?

Zealots are the vertices in a social network who do not change their opinions under social pressure, and are crucial to the study of opinion dynamics on complex networks. In this paper, we study the effect of zealots on the polarization dynamics of a deterministic majority-rule model using the configuration model as a substrate. To this end, we propose a novel quantifier, called `correlated polarization', for measuring the amount of polarization in the network when vertices can exists in two opposite states. The quantifier takes into account not only the fraction of vertices with each opinion, but also how they are connected to each other. We then show that the presence of zealots does not have a fixed effect on the polarization, and can change it in positive, negative or neutral way depending upon their topological characteristics like degree, their total fraction in the network, density and degree heterogeneity of the network, and the type of initial conditions of the dynamics. Our results particularly highlight the importance of the role played by the initial conditions in drifting the polarization towards lower or higher values as the total number of zealots is increased.

cs.SI↗

arXiv2019

Biases in prime factorizations and Liouville functions for arithmetic progressions

We introduce a refinement of the classical Liouville function to primes in arithmetic progressions. Using this, we discover new biases in the appearances of primes in a given arithmetic progression in the prime factorizations of integers. For example, we observe that the primes of the form $4k+1$ tend to appear an even number of times in the prime factorization of a given integer, more so than for primes of the form $4k+3$. We are led to consider variants of Pólya's conjecture, supported by extensive numerical evidence, and its relation to other conjectures.

math.NT↗

arXiv2018

Importance of initial conditions in the polarization of complex networks

Currently used models of opinion formation use random initial conditions. In reality, most people in a social network, except for a small fraction of the population, are initially either unaware of, or indifferent to, the disputed issue. To explore the consequences of such specific initial conditions, we study the polarization of social networks when conflicting ideas arise on two different seed nodes and then spread according to a majority rule. Using the configuration model and the stochastic block model as examples, we show that this framework leads to substantially different outcomes than those which employ random initial conditions. Moreover, the empirically observed splits in the karate and the dolphins' networks naturally come out of this paradigm. Our work thus suggests that the existing opinion dynamics models should be reevaluated to incorporate the initial condition dependence.

cs.SI↗

arXiv2017

Detecting abnormality in heart dynamics from multifractal analysis of ECG signals

The characterization of heart dynamics with a view to distinguish abnormal from normal behavior is an interesting topic in clinical sciences. Here we present an analysis of the Electro-cardiogram (ECG) signals obtained under controlled conditions from several healthy and unhealthy subjects using the framework of multifractal analysis. Our analysis differs from the conventional nonlinear analysis in that the information contained in the amplitude variations of the signal is being extracted and quantified. The results thus obtained reveal that the attractor underlying the dynamics of the heart has multifractal structure and the resultant multifractal spectra can clearly separate healthy subjects from unhealthy ones. We use supervised machine learning approach to build a model that predicts the group label of a new subject with very high accuracy on the basis of the multifractal parameters. By comparing the range of scaling indices in the multifractal spectra with that of beat replicated data from the same ECG, we show how each ECG can be checked for abnormality for variations within itself.

q-bio.TO↗

arXiv2015

Divisibility patterns of natural numbers on a complex network

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of natural numbers in the context of divisibility. In the present paper, we study the divisibility of natural numbers using the framework of a growing complex network. In particular, using tools from the field of statistical inference, we show that the network is scale-free but has a non-stationary degree distribution. Along with this, we report a new kind of similarity pattern for the local clustering, which we call "stretching similarity", in this network. We also show that the various characteristics like average degree, global clustering coefficient and assortativity coefficient of the network vary smoothly with the size of the network. Using analytical arguments we estimate the asymptotic behavior of global clustering and average degree which is validated using numerical analysis.

cs.SI↗

arXiv2015

Complex networks with scale-free nature and hierarchical modularity

Generative mechanisms which lead to empirically observed structure of networked systems from diverse fields like biology, technology and social sciences form a very important part of study of complex networks. The structure of many networked systems like biological cell, human society and World Wide Web markedly deviate from that of completely random networks indicating the presence of underlying processes. Often the main process involved in their evolution is the addition of links between existing nodes having a common neighbor. In this context we introduce an important property of the nodes, which we call mediating capacity, that is generic to many networks. This capacity decreases rapidly with increase in degree, making hubs weak mediators of the process. We show that this property of nodes provides an explanation for the simultaneous occurrence of the observed scale-free structure and hierarchical modularity in many networked systems. This also explains the high clustering and small-path length seen in real networks as well as non-zero degree-correlations. Our study also provides insight into the local process which ultimately leads to emergence of preferential attachment and hence is also important in understanding robustness and control of real networks as well as processes happening on real networks.

physics.soc-ph↗

arXiv2015

Novel coupling scheme to control dynamics of coupled discrete systems

We present a new coupling scheme to control spatio-temporal patterns and chimeras on 1-d and 2-d lattices and random networks of discrete dynamical systems. The scheme involves coupling with an external lattice or network of damped systems. When the system network and external network are set in a feedback loop, the system network can be controlled to a homogeneous steady state or synchronized periodic state with suppression of the chaotic dynamics of the individual units. The control scheme has the advantage that its design does not require any prior information about the system dynamics or its parameters and works effectively for a range of parameters of the control network. We analyze the stability of the controlled steady state or amplitude death state of lattices using the theory of circulant matrices and Routh-Hurwitz's criterion for discrete systems and this helps to isolate regions of effective control in the relevant parameter planes. The conditions thus obtained are found to agree well with those obtained from direct numerical simulations in the specific context of lattices with logistic map and Henon map as on-site system dynamics. We show how chimera states developed in an experimentally realizable 2-d lattice can be controlled using this scheme. We propose this mechanism can provide a phenomenological model for the control of spatio-temporal patterns in coupled neurons due to non-synaptic coupling with the extra cellular medium. We extend the control scheme to regulate dynamics on random networks and adapt the master stability function method to analyze the stability of the controlled state for various topologies and coupling strengths.

nlin.CD↗