arXiv subjects

Hirdesh K. Pharasi

Publications and source records attributed to Hirdesh K. Pharasi.

16 recordsLinked to original sources

arXiv2026

Chaotic Dynamics and Bifurcation Analysis of the Hindmarsh-Rose Neuron Model with Blue-Sky Catastrophe under Magnetic Field Influence

We investigate the impact of magnetic-field-induced feedback on the dynamics of a Hindmarsh-Rose neuron model exhibiting a blue-sky catastrophe. By introducing a magnetic flux variable that couples nonlinearly to the membrane potential, we demonstrate that electromagnetic effects profoundly reshape neuronal firing patterns and bifurcation structure. Interspike-interval bifurcation analysis reveals a nonmonotonic dependence on the magnetic coupling strength, with weak coupling preserving regular spiking and bursting, intermediate coupling promoting chaotic bursting, and strong coupling yielding structured irregular dynamics. These transitions are quantitatively characterized using the largest Lyapunov exponent computed via the Wolf algorithm and supported by Poincaré sections and time-series analysis. Our results establish electromagnetic feedback as a robust and tunable mechanism for controlling instability and chaos in slow-fast neuronal systems.

physics.comp-ph↗

arXiv2024

Coarse graining correlation matrices according to macrostructures: Financial markets as a paradigm

We analyze correlation structures in financial markets by coarse graining the Pearson correlation matrices according to market sectors to obtain Guhr matrices using Guhr's correlation method according to Ref. [P. Rinn {\it et. al.}, Europhysics Letters 110, 68003 (2015)]. We compare the results for the evolution of market states and the corresponding transition matrices with those obtained using Pearson correlation matrices. The behavior of market states is found to be similar for both the coarse grained and Pearson matrices. However, the number of relevant variables is reduced by orders of magnitude.

q-fin.ST↗

arXiv2023

Investigation of Indian stock markets using topological data analysis and geometry-inspired network measures

Geometry-inspired measures (such as discrete Ricci curvatures) and topological data analysis (TDA) based methods (such as persistent homology) have become attractive tools for characterizing the higher-order structure of networks representing the financial systems. In this study, our goal is to perform a comparative analysis of both these approaches, especially by assessing the fragility and systemic risk in the Indian stock markets, which is known for its high volatility and risk. To achieve this goal, we analyze the time series of daily log-returns of stocks comprising the National Stock Exchange (NSE) and the Bombay Stock Exchange (BSE). Specifically, our aim is to monitor the changes in standard network measures, edge-centric discrete Ricci curvatures, and persistent homology based topological measures computed from cross-correlation matrices of stocks. In this study, the edge-centric discrete Ricci curvatures have been employed for the first time in the analysis of the Indian stock markets. The Indian stock markets are known to be less diverse in comparison to the US market, and hence provides us an interesting example. Our results point that, among the persistent homology based topological measures, persistent entropy is simple and more robust than $L^1$-norm and $L^2$-norm of persistence landscape. In a broader comparison between network analysis and TDA, we highlight that the network analysis is sensitive to the way of constructing the networks (threshold or minimum spanning tree), as well as the threshold values used to construct the correlation-based threshold networks. On the other hand, the persistent homology is a more robust approach and is able to capture the higher-order interactions and eliminate noisy data in financial systems, since it does not take into account a single value of threshold but rather a range of values.

physics.soc-ph↗

arXiv2023

Dynamics of market states and risk assessment

Previous research explored various conditions of financial markets based on the similarity of correlation structures and classified as market states. We introduce modifications to previous selection criteria for these market states, mainly due to increased attention to the transition matrix between the states. Clustering and thus market states are fixed by the optimization of two parameters -- number of clusters and noise suppression, but in similar conditions, we give preference to the clustering which avoids large jumps in the transition matrix. We found statistically significant results applying this model to the SP 500 and Nikkei 225 markets for the pre-COVID-19 pandemic era (2006-2019). Retaining the epoch length of 20 trading days but reducing the shift of the epoch to a single trading day we are led to the concept of a trajectory of the market in the space of correlation matrices. We may visualize these states after dimensional scaling to two or three dimensions. This approach, using dynamics, improves the options of risk assessment, opens the door to dynamical treatments of markets (e.g. hedging), and shows noise suppression in a new light.

q-fin.ST↗

arXiv2021

Dynamics of the market states in the space of correlation matrices with applications to financial markets

The concept of states of financial markets based on correlations has gained increasing attention during the last 10 years. We propose to retrace some important steps up to 2018, and then give a more detailed view of recent developments that attempt to make the use of this more practical. Finally, we try to give a glimpse to the future proposing the analysis of trajectories in correlation matrix space directly or in terms of symbolic dynamics as well as attempts to analyze the clusters that make up the states in a random matrix context.

q-fin.ST↗

arXiv2021

Network geometry and market instability

The complexity of financial markets arise from the strategic interactions among agents trading stocks, which manifest in the form of vibrant correlation patterns among stock prices. Over the past few decades, complex financial markets have often been represented as networks whose interacting pairs of nodes are stocks, connected by edges that signify the correlation strengths. However, we often have interactions that occur in groups of three or more nodes, and these cannot be described simply by pairwise interactions but we also need to take the relations between these interactions into account. Only recently, researchers have started devoting attention to the higher-order architecture of complex financial systems, that can significantly enhance our ability to estimate systemic risk as well as measure the robustness of financial systems in terms of market efficiency. Geometry-inspired network measures, such as the Ollivier-Ricci curvature and Forman-Ricci curvature, can be used to capture the network fragility and continuously monitor financial dynamics. Here, we explore the utility of such discrete Ricci curvatures in characterizing the structure of financial systems, and further, evaluate them as generic indicators of the market instability. For this purpose, we examine the daily returns from a set of stocks comprising the USA S&P-500 and the Japanese Nikkei-225 over a 32-year period, and monitor the changes in the edge-centric network curvatures. We find that the different geometric measures capture well the system-level features of the market and hence we can distinguish between the normal or `business-as-usual' periods and all the major market crashes. This can be very useful in strategic designing of financial systems and regulating the markets in order to tackle financial instabilities.

q-fin.ST↗

arXiv2020

Market states: A new understanding

We present the clustering analysis of the financial markets of S&P 500 (USA) and Nikkei 225 (JPN) markets over a period of 2006-2019 as an example of a complex system. We investigate the statistical properties of correlation matrices constructed from the sliding epochs. The correlation matrices can be classified into different clusters, named as market states based on the similarity of correlation structures. We cluster the S&P 500 market into four and Nikkei 225 into six market states by optimizing the value of intracluster distances. The market shows transitions between these market states and the statistical properties of the transitions to critical market states can indicate likely precursors to the catastrophic events. We also analyze the same clustering technique on surrogate data constructed from average correlations of market states and the fluctuations arise due to the white noise of short time series. We use the correlated Wishart orthogonal ensemble for the construction of surrogate data whose average correlation equals the average of the real data.

q-fin.CP↗

arXiv2020

Phase separation and scaling in correlation structures of financial markets

Financial markets, being spectacular examples of complex systems, display rich correlation structures among price returns of different assets. The correlation structures change drastically, akin to phase transitions in physical phenomena, as do the influential stocks (leaders) and sectors (communities), during market events like crashes. It is crucial to detect their signatures for timely intervention or prevention. Here we use eigenvalue decomposition and eigen-entropy, computed from eigen-centralities of different stocks in the cross-correlation matrix, to extract information about the disorder in the market. We construct a `phase space', where different market events (bubbles, crashes, etc.) undergo phase separation and display order-disorder transitions. An entropy functional exhibits scaling behavior. We propose a generic indicator that facilitates the continuous monitoring of the internal structure of the market -- important for managing risk and stress-testing the financial system. Our methodology would help in understanding and foreseeing tipping points or fluctuation patterns in complex systems.

q-fin.ST↗

arXiv2020

A perspective on correlation-based financial networks and entropy measures

In this brief review, we critically examine the recent work done on correlation-based networks in financial systems. The structure of empirical correlation matrices constructed from the financial market data changes as the individual stock prices fluctuate with time, showing interesting evolutionary patterns, especially during critical events such as market crashes, bubbles, etc. We show that the study of correlation-based networks and their evolution with time is useful for extracting important information of the underlying market dynamics. We, also, present our perspective on the use of recently developed entropy measures such as structural entropy and eigen-entropy for continuous monitoring of correlation-based networks.

q-fin.CP↗

arXiv2018

Complex market dynamics in the light of random matrix theory

We present a brief overview of random matrix theory (RMT) with the objectives of highlighting the computational results and applications in financial markets as complex systems. An oft-encountered problem in computational finance is the choice of an appropriate epoch over which the empirical cross-correlation return matrix is computed. A long epoch would smoothen the fluctuations in the return time series and suffers from non-stationarity, whereas a short epoch results in noisy fluctuations in the return time series and the correlation matrices turn out to be highly singular. An effective method to tackle this issue is the use of the power mapping, where a non-linear distortion is applied to a short epoch correlation matrix. The value of distortion parameter controls the noise-suppression. The distortion also removes the degeneracy of zero eigenvalues. Depending on the correlation structures, interesting properties of the eigenvalue spectra are found. We simulate different correlated Wishart matrices to compare the results with empirical return matrices computed using the S&P 500 (USA) market data for the period 1985-2016. We also briefly review two recent applications of RMT in financial stock markets: (i) Identification of "market states" and long-term precursor to a critical state; (ii) Characterization of catastrophic instabilities (market crashes).

q-fin.ST↗

arXiv2018

Identifying long-term precursors of financial market crashes using correlation patterns

The study of the critical dynamics in complex systems is always interesting yet challenging. Here, we choose financial market as an example of a complex system, and do a comparative analyses of two stock markets - the S&P 500 (USA) and Nikkei 225 (JPN). Our analyses are based on the evolution of crosscorrelation structure patterns of short time-epochs for a 32-year period (1985-2016). We identify "market states" as clusters of similar correlation structures, which occur more frequently than by pure chance (randomness). The dynamical transitions between the correlation structures reflect the evolution of the market states. Power mapping method from the random matrix theory is used to suppress the noise on correlation patterns, and an adaptation of the intra-cluster distance method is used to obtain the "optimum" number of market states. We find that the USA is characterized by four market states and JPN by five. We further analyze the co-occurrence of paired market states; the probability of remaining in the same state is much higher than the transition to a different state. The transitions to other states mainly occur among the immediately adjacent states, with a few rare intermittent transitions to the remote states. The state adjacent to the critical state (market crash) may serve as an indicator or a "precursor" for the critical state and this novel method of identifying the long-term precursors may be very helpful for constructing the early warning system in financial markets, as well as in other complex systems.

q-fin.ST↗

arXiv2018

Characterization of catastrophic instabilities: Market crashes as paradigm

Catastrophic events, though rare, do occur and when they occur, they have devastating effects. It is, therefore, of utmost importance to understand the complexity of the underlying dynamics and signatures of catastrophic events, such as market crashes. For deeper understanding, we choose the US and Japanese markets from 1985 onward, and study the evolution of the cross-correlation structures of stock return matrices and their eigenspectra over different short time-intervals or "epochs". A slight non-linear distortion is applied to the correlation matrix computed for any epoch, leading to the emerging spectrum of eigenvalues. The statistical properties of the emerging spectrum display: (i) the shape of the emerging spectrum reflects the market instability, (ii) the smallest eigenvalue may be able to statistically distinguish the nature of a market turbulence or crisis -- internal instability or external shock, and (iii) the time-lagged smallest eigenvalue has a statistically significant correlation with the mean market cross-correlation. The smallest eigenvalue seems to indicate that the financial market has become more turbulent in a similar way as the mean does. Yet we show features of the smallest eigenvalue of the emerging spectrum that distinguish different types of market instabilities related to internal or external causes. Based on the paradigmatic character of financial time series for other complex systems, the capacity of the emerging spectrum to understand the nature of instability may be a new feature, which can be broadly applied.

q-fin.GN↗

arXiv2016

Spectra and probability distributions of thermal flux in turbulent Rayleigh-Bénard convection

The spectra of turbulent heat flux $\mathrm{H}(k)$ in Rayleigh-Bénard convection with and without uniform rotation are presented. The spectrum $\mathrm{H}(k)$ scales with wave number $k$ as $\sim k^{-2}$. The scaling exponent is almost independent of the Taylor number $\mathrm{Ta}$ and Prandtl number $\mathrm{Pr}$ for higher values of the reduced Rayleigh number $r$ ($ > 10^3$). The exponent, however, depends on $\mathrm{Ta}$ and $\mathrm{Pr}$ for smaller values of $r$ ($<10^3$). The probability distribution functions of the local heat fluxes are non-Gaussian and have exponential tails.

physics.flu-dyn↗

arXiv2014

Frequency spectra of turbulent thermal convection with uniform rotation

The frequency spectra of the entropy and kinetic energy along with the power spectrum of the thermal flux are computed from direct numerical simulations for turbulent Rayleigh-Bénard convection with uniform rotation about a vertical axis in low-Prandtl-number fluids ($\mathrm{Pr} < 0.6$). Simulations are done for convective Rossby numbers $\mathrm{Ro} \ge 0.2$. The temporal fluctuations of these global quantities show two scaling regimes: (i) $ω^{-2}$ at higher frequencies for all values of $\mathrm{Ro}$ and (ii) $ω^{-γ_1}$ at intermediate frequencies with $γ_1 \approx 4$ for $\mathrm{Ro} > 1$, while $4 < γ_1 < 6.6$ for $0.2 \le \mathrm{Ro} < 1$.

physics.flu-dyn↗

arXiv2014

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

We present the results of direct numerical simulations of flow patterns in a low-Prandtl-number ($Pr = 0.1$) fluid above the onset of oscillatory convection in a Rayleigh-Bénard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box ($L_x \times L_y \times 1$) and a wide range of Taylor numbers ($750 \le Ta \le 5000$) for the purpose. The horizontal aspect ratio $η= L_y/L_x$ of the box was varied from $0.5$ to $10$. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes ($0.5 \le η< 1$ and $1 < η< 2$). The flow patterns observed in boxes with $η= 1$ and $η= 2$ were different from those with $η< 1$ and $1 < η< 2$. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell ($η= 1$) for $Ta < 2700$, but observed a set of parallel rolls in the form of standing waves for $Ta \geq 2700$. The three-dimensional convection was quasiperiodic or chaotic for $750 \le Ta < 2700$, and then bifurcated into a two-dimensional periodic flow for $Ta \ge 2700$. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle $ϕ= \fracπ{2} - \arctan{(η^{-1})}$ with the straight rolls.

physics.flu-dyn↗

arXiv2014

Entropy and energy spectra in low-Prandtl-number convection with rotation

We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number ($Pr < 1$) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of Taylor number ($ 0 \leq Ta \leq 10^8$) and reduced Rayleigh number $r = Ra/Ra_{\circ} (Ta, Pr)$ ($1.0 \times 10^2 \le r \le 5.0 \times 10^3$). The Rossby number $Ro$ varies in the range $1.34 \le Ro \le 73$. The entropy spectrum $E_θ(k)$ shows bi-splitting into two branches for lower values of wave number $k$. The entropy in the lower branch scales with $k$ as $k^{-1.4\pm 0.1}$ for $r > 10^3$ for the rotation rates considered here. The entropy in the upper branch also shows scaling behavior with $k$, but the scaling exponent decreases with increasing $Ta$ for all $r$. The energy spectrum $E_v(k)$ is also found to scale with the wave number $k$ as $k^{-1.4\pm 0.1}$ for $r > 10^3$. The scaling exponent for the energy spectrum and the lower branch of the entropy spectrum vary between $-1.7$ to $-2.4$ for lower values of $r$ ($< 10^3$). We also provide some simple arguments based on the variation of the Kolmogorov picture to support the results of simulations.

physics.flu-dyn↗