47 citations · 82 across the 13 of their papers we have counts for
15 papers
Attractors and basins generated by repeated sums of prime factors of natural numbers
Snehal Shekatkar, Ivano Lodato
Integer maps are discrete dynamical systems defined on the natural numbers. In this paper, we investigate the dynamics of the shifted Alladi-Erd{\H o}s map, a one-parameter family…
Binomial maps: stochastically evolving iterated integer maps for finite populations
Snehal M. Shekatkar
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 size…
Detrimental role of fluctuations in the resource dependency networks
Saumitra Kulkarni, Snehal M. Shekatkar
Individual components of many real-world complex networks produce and exchange resources among themselves. However, because the resource production in such networks is almost alway…
Effect of money heterogeneity on resource dependency in complex networks
Harshit Agrawal, Ashwin Lahorkar, Snehal M. Shekatkar
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, t…
On partial information retrieval: the unconstrained 100 prisoner problem
Ivano Lodato, Snehal M. Shekatkar, Tian An Wong
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…
Resource dependency and survivability in complex networks
Madhusudan Ingale, Snehal M. Shekatkar
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…
Do zealots increase or decrease the polarization in social networks?
Snehal M. Shekatkar
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 p…
Importance of initial conditions in the polarization of complex networks
Snehal M. Shekatkar, Sukratu Barve
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…
Shifts of the prime divisor function of Alladi and Erdős
Snehal Shekatkar, Tian An Wong
We introduce a variation on the prime divisor function of Alladi and Erdős, a close relative of the sum of proper divisors function . After proving some basic properti…
Detecting abnormality in heart dynamics from multifractal analysis of ECG signals
Snehal M. Shekatkar, Yamini Kotriwar, K. P. Harikrishnan +1
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 Ele…
Biases in prime factorizations and Liouville functions for arithmetic progressions
Peter Humphries, Snehal M. Shekatkar, Tian An Wong
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 arith…
Divisibility patterns of natural numbers on a complex network
Snehal M. Shekatkar, Chandrasheel Bhagwat, G. Ambika
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 di…
Complex networks with scale-free nature and hierarchical modularity
Snehal M. Shekatkar, G. Ambika
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…
Novel coupling scheme to control dynamics of coupled discrete systems
Snehal M. Shekatkar, G. Ambika
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 cou…
The sum of the r'th roots of first n natural numbers and new formula for factorial
Snehal Shekatkar
Using the simple properties of Riemman integrable functions, Ramanujan's formula for sum of the square roots of first n natural numbers has been generalized to include r'th roots w…