arXiv subjects

Srikanth K. Iyer

Publications and source records attributed to Srikanth K. Iyer.

15 recordsLinked to original sources

arXiv2026

Recovering Structural Organization in Noisy Correlation Networks Using Financial Systems as a Testbed

Empirical correlation matrices estimated from financial return time series are contaminated by statistical noise arising from finite sample size, obscuring genuine interactions among assets. We apply spectral decomposition to separate the empirical correlation matrix into a structured component associated with eigenvalues exceeding the Marchenko-Pastur bounds and a random component representing statistical noise. Using daily returns from the NIFTY 200, NIFTY 500, and S&P 500 over 2010-2022, we show that the structured component, constructed from only 10-16 eigenmodes, reproduces the main statistical properties of the full correlation matrix while removing most noise-dominated eigenmodes. Financial networks derived from the structured component exhibit significantly stronger and more stable core-periphery organization than networks constructed from the full or random matrices. Degree-preserving randomization, Kolmogorov-Smirnov, and Wasserstein distance tests confirm a clear statistical separation between structured and random components. We further show that structured networks display pronounced scale-free degree distributions in the Indian markets. As a practical application, portfolios constructed from peripheral assets of the denoised networks consistently outperform portfolios based on unfiltered correlations and standard benchmarks on a risk-adjusted basis, with robustness verified through Monte Carlo subsampling. These results demonstrate that spectral denoising effectively recovers meaningful network structure from noisy financial correlations.

q-fin.ST↗

arXiv2023

Data-driven discovery of stochastic dynamical equations of collective motion

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, many real flocks are small sized (10 to 100 individuals), called the mesoscopic scales, where stochasticity arising from the finite flock sizes is important. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models. Here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple self-propelled particle (SPP) model of collective motion. In our SPP model, a focal individual can interact with k randomly chosen neighbours within an interaction radius. We consider k = 1 (called stochastic pairwise interactions), k = 2 (stochastic ternary interactions), and k equalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). The data-driven mesoscopic equations reveal that the stochastic pairwise interaction model produces a novel form of collective motion driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, yield collective motion driven primarily by the deterministic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasizes the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

q-bio.QM↗

arXiv2020

Poisson Approximation and Connectivity in a Scale-free Random Connection Model

We study an inhomogeneous random connection model in the connectivity regime. The vertex set of the graph is a homogeneous Poisson point process $\mathcal{P}_s$ of intensity $s>0$ on the unit cube $S=\left(-\frac{1}{2},\frac{1}{2}\right]^{d},$ $d \geq 2$ . Each vertex is endowed with an independent random weight distributed as $W$, where $P(W>w)=w^{-β}1_{[1,\infty)}(w)$, $β>0$. Given the vertex set and the weights an edge exists between $x,y\in \mathcal{P}_s$ with probability $\left(1 - \exp\left( - \frac{ηW_xW_y}{\left(d(x,y)/r\right)^α} \right)\right),$ independent of everything else, where $η, α> 0$, $d(\cdot, \cdot)$ is the toroidal metric on $S$ and $r > 0$ is a scaling parameter. We derive conditions on $α, β$ such that under the scaling $r_s(ξ)^d= \frac{1}{c_0 s} \left( \log s +(k-1) \log\log s +ξ+\log\left(\frac{αβ}{k!d} \right)\right),$ $ξ\in \mathbb{R}$, the number of vertices of degree $k$ converges in total variation distance to a Poisson random variable with mean $e^{-ξ}$ as $s \to \infty$, where $c_0$ is an explicitly specified constant that depends on $α, β, d$ and $η$ but not on $k$. In particular, for $k=0$ we obtain the regime in which the number of isolated nodes stabilizes, a precursor to establishing a threshold for connectivity. We also derive a sufficient condition for the graph to be connected with high probability for large $s$. The Poisson approximation result is derived using the Stein's method.

math.PR↗

arXiv2020

Phase transitions and percolation at criticality in enhanced random connection models

We study phase transition and percolation at criticality for three random graph models on the plane, viz., the homogeneous and inhomogeneous enhanced random connection models (RCM) and the Poisson stick model. These models are built on a homogeneous Poisson point process $\mathcal{P}_λ$ in $\mathbb{R}^2$ of intensity $λ$. In the homogenous RCM, the vertices at $x,y$ are connected with probability $g(|x-y|)$, independent of everything else, where $g:[0,\infty) \to [0,1]$ and $| \cdot |$ is the Euclidean norm. In the inhomogenous version of the model, points of $\mathcal{P}_λ$ are endowed with weights that are non-negative independent random variables with distribution $P(W>w)= w^{-β}1_{[1,\infty)}(w)$, $β>0$. Vertices located at $x,y$ with weights $W_x,W_y$ are connected with probability $1 - \exp\left( - \frac{ηW_xW_y}{|x-y|^α} \right)$, $η, α> 0$, independent of all else. The graphs are enhanced by considering the edges of the graph as straight line segments starting and ending at points of $\mathcal{P}_λ$. A path in the graph is a continuous curve that is a subset of the union of all these line segments. The Poisson stick model consists of line segments of independent random lengths and orientation with the mid point of each segment located at a distinct point of $\mathcal{P}_λ$. Intersecting lines form a path in the graph. A graph is said to percolate if there is an infinite connected component or path. We derive conditions for the existence of a phase transition and show that there is no percolation at criticality.

math.PR↗

arXiv2019

Fission-fusion dynamics and group-size dependent composition in heterogeneous populations

Many animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behaviour, however, typically assume that groups and populations consist of identical individuals. In this paper, using the mathematical framework of the coagulation-fragmentation process, we develop and analyse a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups, forming two daughter groups whose compositions are drawn uniformly from all possible partitions. We analytically derive a master equation for group size and compositions and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type/species. Despite the propensity of heterogeneous groups to split at higher rates, we find that groups are more likely to be heterogeneous but only above the critical group size. Monte-Carlo simulation of the model show excellent agreement with these analytical model results. Thus, our model makes a testable prediction that composition of flocks are group-size dependent and do not merely reflect the population level heterogeneity. We discuss the implications of our results to empirical studies on flocking systems.

nlin.AO↗

arXiv2018

Thresholds for vanishing of `Isolated' faces in random Čech and Vietoris-Rips complexes

We study combinatorial connectivity for two models of random geometric complexes. These two models - Čech and Vietoris-Rips complexes - are built on a homogeneous Poisson point process of intensity $n$ on a $d$-dimensional torus using balls of radius $r_n$. In the former, the $k$-simplices/faces are formed by subsets of $(k+1)$ Poisson points such that the balls of radius $r_n$ centred at these points have a mutual interesection and in the latter, we require only a pairwise intersection of the balls. Given a (simplicial) complex (i.e., a collection of $k$-simplices for all $k \geq 1$), we can connect $k$-simplices via $(k+1)$-simplices (`up-connectivity') or via $(k-1)$-simplices (`down-connectivity). Our interest is to understand these two combinatorial notions of connectivity for the random Čech and Vietoris-Rips complexes asymptically as $n \to \infty$. In particular, we analyse in detail the threshold radius for vanishing of isolated $k$-faces for up and down connectivity of both types of random geometric complexes. Though it is expected that the threshold radius $r_n = Θ((\frac{\log n}{n})^{1/d})$ in coarse scale, our results give tighter bounds on the constants in the logarithmic scale as well as shed light on the possible second-order correction factors. Further, they also reveal interesting differences between the phase transition in the Čech and Vietoris-Rips cases. The analysis is interesting due to the non-monotonicity of the number of isolated $k$-faces (as a function of the radius) and leads one to consider `monotonic' vanishing of isolated $k$-faces. The latter coincides with the vanishing threshold mentioned above at a coarse scale (i.e., $\log n$ scale) but differs in the $\log \log n$ scale for the Čech complex with $k = 1$ in the up-connected case.

math.PR↗

arXiv2015

Achieving Non-Zero Information Velocity in Wireless Networks

In wireless networks, where each node transmits independently of other nodes in the network (the ALOHA protocol), the expected delay experienced by a packet until it is successfully received at any other node is known to be infinite for signal-to-interference-plus-noise-ratio (SINR) model with node locations distributed according to a Poisson point process. Consequently, the information velocity, defined as the limit of the ratio of the distance to the destination and the time taken for a packet to successfully reach the destination over multiple hops, is zero, as the distance tends to infinity. A nearest neighbor distance based power control policy is proposed to show that the expected delay required for a packet to be successfully received at the nearest neighbor can be made finite. Moreover, the information velocity is also shown to be non-zero with the proposed power control policy. The condition under which these results hold does not depend on the intensity of the underlying Poisson point process.

cs.IT↗

arXiv2015

Connecting the Random Connection Model

Consider the random graph $G({\mathcal P}_{n},r)$ whose vertex set ${\mathcal P}_{n}$ is a Poisson point process of intensity $n$ on $(- \frac{1}{2}, \frac{1}{2}]^d$, $d \geq 2$. Any two vertices $X_i,X_j \in {\mathcal P}_{n}$ are connected by an edge with probability $g\left( \frac{d(X_i,X_j)}{r} \right)$, independently of all other edges, and independent of the other points of ${\mathcal P}_{n}$. $d$ is the toroidal metric, $r > 0$ and $g:[0,\infty) \to [0,1]$ is non-increasing and $α= \int_{\mathbb{R}^d} g(|x|) dx < \infty$. Under suitable conditions on $g$, almost surely, the critical parameter $d_n$ for which $G({\mathcal P}_{n}, \cdot)$ does not have any isolated nodes satisfies $\lim_{n \to \infty} \frac{αn d_n^d}{\log n} = 1$. Let $β= \inf\{x > 0: x g\left( \fracα{x θ} \right) > 1 \}$, and $θ$ be the volume of the unit ball in $\mathbb{R}^d$. Then for all $γ> β$, $G\left({\mathcal P}_{n}, \left( \frac{γ\log n}{αn} \right)^{\frac{1}{d}}\right)$ is connected with probability approaching one as $n \to \infty$. The bound can be seen to be tight for the usual random geometric graph obtained by setting $g = 1_{[0,1]}$. We also prove some useful results on the asymptotic behaviour of the length of the edges and the degree distribution in the {\it connectivity regime}.

math.PR↗

arXiv2014

Autoregressive Cascades on Random Networks

This paper considers a model for cascades on random networks in which the cascade propagation at any node depends on the load at the failed neighbor, the degree of the neighbor as well as the load at that node. Each node in the network bears an initial load that is below the capacity of the node. The trigger for the cascade emanates at a single node or a small fraction of the nodes from some external shock. Upon failure, the load at the failed node gets divided randomly and added to the existing load at those neighboring nodes that have not yet failed. Subsequently, a neighboring node fails if its accumulated load exceeds its capacity. The failed node then plays no further part in the process. The cascade process stops as soon as the accumulated load at all nodes that have not yet failed is below their respective capacities. The model is shown to operate in two regimes, one in which the cascade terminates with only a finite number of node failures. In the other regime there is a positive probability that the cascade continues indefinitely. Bounds are obtained on the critical parameter where the phase transition occurs.

physics.soc-ph↗

arXiv2012

Nonuniform random geometric graphs with location-dependent radii

We propose a distribution-free approach to the study of random geometric graphs. The distribution of vertices follows a Poisson point process with intensity function $nf(\cdot)$, where $n\in \mathbb{N}$, and $f$ is a probability density function on $\mathbb{R}^d$. A vertex located at $x$ connects via directed edges to other vertices that are within a cut-off distance $r_n(x)$. We prove strong law results for (i) the critical cut-off function so that almost surely, the graph does not contain any node with out-degree zero for sufficiently large $n$ and (ii) the maximum and minimum vertex degrees. We also provide a characterization of the cut-off function for which the number of nodes with out-degree zero converges in distribution to a Poisson random variable. We illustrate this result for a class of densities with compact support that have at most polynomial rates of decay to zero. Finally, we state a sufficient condition for an enhanced version of the above graph to be almost surely connected eventually.

math.PR↗

arXiv2010

Percolation and Connectivity in AB Random Geometric Graphs

Given two independent Poisson point processes $Φ^{(1)},Φ^{(2)}$ in $R^d$, the continuum AB percolation model is the graph with points of $Φ^{(1)}$ as vertices and with edges between any pair of points for which the intersection of balls of radius $2r$ centred at these points contains at least one point of $Φ^{(2)}$. This is a generalization of the $AB$ percolation model on discrete lattices. We show the existence of percolation for all $d > 1$ and derive bounds for a critical intensity. We also provide a characterization for this critical intensity when $d = 2$. To study the connectivity problem, we consider independent Poisson point processes of intensities $n$ and $cn$ in the unit cube. The $AB$ random geometric graph is defined as above but with balls of radius $r$. We derive a weak law result for the largest nearest neighbour distance and almost sure asymptotic bounds for the connectivity threshold.

math.PR↗

arXiv2009

Criticality of the Exponential Rate of Decay for the Largest Nearest Neighbor Link in Random Geometric Graph

Let n points be placed independently in d-dimensional space according to the densities $f(x) = A_d e^{-λ\|x\|^α}, λ> 0, x \in \Re^d, d \geq 2.$ Let $d_n$ be the longest edge length for the nearest neighbor graph on these points. We show that $(\log(n))^{1-1/α}d_n -b_n$ converges weakly to the Gumbel distribution where $b_n \sim \log \log n.$ We also show that the strong law result, % \lim_{n \to \infty} \frac{(λ^{-1}\log(n))^{1-1/α}d_n}{\sqrt{\log \log n}} \to \frac{d}{αλ}, a.s. % Thus, the exponential rate of decay i.e. $α= 1$ is critical, in the sense that for $α> 1, d_n \to 0,$ where as $α< 1, d_n \to \infty$ a.s. as $n \to \infty.$

math.PR↗

arXiv2008

Limit laws for k-coverage of paths by a Markov-Poisson-Boolean model

Let P := {X_i,i >= 1} be a stationary Poisson point process in R^d, {C_i,i >= 1} be a sequence of i.i.d. random sets in R^d, and {Y_i^t; t \geq 0, i >= 1} be i.i.d. {0,1}-valued continuous time stationary Markov chains. We define the Markov-Poisson-Boolean model C_t := {Y_i^t(X_i + C_i), i >= 1}. C_t represents the coverage process at time t. We first obtain limit laws for k-coverage of an area at an arbitrary instant. We then obtain the limit laws for the k-coverage seen by a particle as it moves along a one-dimensional path.

math.PR↗

arXiv2006

On the topological Properties of the One Dimensional Exponential Random Geometric Graph

In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties associated with this random graph. We show that the asymptotic properties of a graph with a truncated exponential distribution can be obtained using the exponential random geometric graph.

math.PR↗

arXiv2006

A Strong Law for the Largest Nearest-Neighbor Link on Normally Distributed Points

Let $n$ points be placed independently in $d-$dimensional space according to the standard $d-$dimensional normal distribution. Let $d_n$ be the longest edge length for the nearest neighbor graph on these points. We show that \[\lim_{n \rar \infty} \frac{\sqrt{\log n} d_n}{\log \log n} = \frac{d}{\sqrt{2}}, \qquad d \geq 2, {a.s.} \]

math.PR↗