arXiv subjects

Md. Nurujjaman

Publications and source records attributed to Md. Nurujjaman.

At least 19 recordsLinked to original sources

arXiv2026

Scaling laws of Stablecoin Transactions: Evidence from USDT and USDC on the Ethereum blockchain

Stablecoins have rapidly emerged as an important class of digital assets and a component of the digital financial ecosystem. Despite their growing importance, the statistical properties of stablecoin transaction activity remain largely unexplored. To the best of our knowledge, this is the first study to investigate scaling behavior in stablecoin transaction data, focusing on USDT and USDC. We analyze approximately 370 million USDT and USDC transactions recorded on the Ethereum blockchain across six periods spanning June 2024 to February 2026. Based on interactions between Externally Owned Accounts (EOAs) and Smart Contracts (SCs), we classify transactions into four categories: EOA-EOA, EOA-SC, SC-EOA, and SC-SC. Using maximum-likelihood estimation of power-law exponents, we find that transaction value distributions exhibit heavy-tailed scaling for both stablecoins across all periods and interaction categories. We identify two distinct scaling regimes: EOA-involved categories cluster around 1.45-1.60, whereas SC-SC transactions exhibit higher exponents of approximately 1.72-1.73. Sensitivity analysis confirms that this separation is robust across periods, stablecoins, and fitting sample sizes. Counterfactual analysis shows that changes in category weights alone cannot explain the observed variation in the overall exponent. Across different sample sizes, the counterfactual path accounts for only about 10%-35% of the total temporal range observed in the actual data. Overall, our results indicate two broadly differentiated scaling regimes in the tail of stablecoin transaction values. Power-law tail behavior is observed throughout stablecoin transaction activity, but the exponent depends on whether transactions are driven by EOAs or SCs. These findings provide a basis for further research on scaling behavior and transaction heterogeneity in blockchain-based financial systems.

q-fin.ST↗

arXiv2026

Structural Dynamics of G5 Stock Markets During Exogenous Shocks: A Random Matrix Theory-Based Complexity Gap Approach

We identify a robust structural signature of stock markets during exogenous shock events by analyzing collective return dynamics across G5 countries. Using Random Matrix Theory, we introduce the complexity gap, defined as the difference between the normalized largest eigenvalue and the average pairwise correlation, to quantify changes in market structure. This measure reveals a consistent three-phase pattern across multiple shocks, including the 2025 U.S. tariff event, the COVID-19 crisis, and country-specific shocks in Japan and China during 2024. Before a shock, markets show a positive complexity gap, reflecting a rich structure with multiple interacting factors. During shocks, the gap collapses to near zero, signaling strong synchronization under a single dominant mode. Post-shock recovery follows a nonmonotonic path: an initial widening (a false recovery), a temporary recollapse, and final sustained restoration. This pattern holds at both market and sector levels and across global and local shocks. Ordinal entropy analysis confirms the same sequence of collapse and false recovery in directional diversity. We further demonstrate that lower complexity gap values predict higher future portfolio volatility, especially after shocks, establishing its value as a state-dependent risk indicator. For investors, initial gap widening may mislead, while sustained widening signals genuine structural stabilization. These findings reveal a robust structural signature governing financial market dynamics during crisis and recovery periods.

q-fin.ST↗

arXiv2026

Interpretable Classification of Time Series Using Euler Characteristic Surfaces

Persistent homology (PH) -- the conventional method in topological data analysis -- is computationally expensive, requires further vectorization of its signatures before machine learning (ML) can be applied, and captures information along only the spatial axis. For time series data, we propose Euler Characteristic Surfaces (ECS) as an alternative topological signature based on the Euler characteristic ($χ$) -- a fundamental topological invariant. The ECS provides a computationally efficient, spatiotemporal, and inherently discretized feature representation that can serve as direct input to ML models. We prove a stability theorem guaranteeing that the ECS remains stable under small perturbations of the input time series. We first demonstrate that ECS effectively captures the nontrivial topological differences between the limit cycle and the strange attractor in the Rössler system. We then develop an ECS-based classification framework and apply it to five benchmark biomedical datasets (four ECG, one EEG) from the UCR/UEA archive. On $\textit{ECG5000}$, our single-feature ECS classifier achieves $98\%$ accuracy with $O(n+R\cdot T)$ complexity, compared to $62\%$ reported by a recent PH-based method. An AdaBoost extension raises accuracy to $98.6\%$, matching the best deep learning results while retaining full interpretability. Strong results are also obtained on $\textit{TwoLeadECG}$ ($94.1\%$) and $\textit{Epilepsy2}$ ($92.6\%$).

cs.LG↗

arXiv2026

Regime Discovery and Intra-Regime Return Dynamics in Global Equity Markets

Financial markets alternate between tranquil periods and episodes of stress, and return dynamics can change substantially across these regimes. We study regime-dependent dynamics in developed and developing equity indices using a data-driven Hilbert--Huang-based regime identification and profiling pipeline, followed by variable-length Markov modeling of categorized returns. Market regimes are identified using an Empirical Mode Decomposition-based Hilbert--Huang Transform, where instantaneous energy from the Hilbert spectrum separates Normal, High, and Extreme regimes. We then profile each regime using Holo--Hilbert Spectral Analysis, which jointly resolves carrier frequencies, amplitude-modulation frequencies, and amplitude-modulation energy (AME). AME, interpreted as volatility intensity, declines monotonically from Extreme to High to Normal regimes. This decline is markedly sharper in developed markets, while developing markets retain higher baseline volatility intensity even in Normal regimes. Building on these regime-specific volatility signatures, we discretize daily returns into five quintile states $\mathtt{R}_1$ to $\mathtt{R}_5$ and estimate Variable-Length Markov Chains via context trees within each regime. Unconditional state probabilities show tail states dominate in Extreme regimes and recede as regimes stabilize, alongside persistent downside asymmetry. Entropy peaks in High regimes, indicating maximum unpredictability during moderate-volatility periods. Conditional transition dynamics, evaluated over contexts of length up to three days from the context-tree estimates, indicate that developed markets normalize more effectively as stress subsides, whereas developing markets retain residual tail dependence and downside persistence even in Normal regimes, consistent with a coexistence of continuation and burst-like shifts.

q-fin.ST↗

arXiv2026

Intraday Limit Order Price Change Transition Dynamics Across Market Capitalizations Through Markov Analysis

Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency NASDAQ100 tick data. Employing a discrete-time Markov chain framework, we categorize consecutive price changes into nine states and estimate transition probability matrices (TPMs) for six intraday intervals across High ($\mathtt{HMC}$), Medium ($\mathtt{MMC}$), and Low ($\mathtt{LMC}$) market cap stocks. Element-wise TPM comparison reveals systematic patterns: price inertia peaks during opening and closing hours, stabilizing midday. A capitalization gradient is observed: $\mathtt{HMC}$ stocks exhibit the strongest inertia, while $\mathtt{LMC}$ stocks show lower stability and wider spreads. Markov metrics, including spectral gap, entropy rate, and mean recurrence times, quantify these dynamics. Clustering analysis identifies three distinct temporal phases on the bid side -- Opening, Midday, and Closing, and four phases on the ask side by distinguishing Opening, Midday, Pre-Close, and Close. This indicates that sellers initiate end-of-day positioning earlier than buyers. Stationary distributions show limit order dynamics are dominated by neutral and mild price changes. Jensen-Shannon divergence confirms the closing hour as the most distinct phase, with capitalization modulating temporal contrasts and bid-ask asymmetry. These findings support capitalization-aware and time-adaptive execution algorithms.

q-fin.ST↗

arXiv2025

Early-Warning Signals of Political Risk in Stablecoin Markets: Human and Algorithmic Behavior Around the 2024 U.S. Election

We study how the 2024 U.S. presidential election, viewed as a major political risk event, affected cryptocurrency markets by distinguishing human-driven peer-to-peer stablecoin transactions from automated algorithmic activity. Using structural break analysis, we find that human-driven Ethereum Request for Comment 20 (ERC-20) transactions shifted on November 3, two days before the election, while exchange trading volumes reacted only on Election Day. Automated smart-contract activity adjusted much later, with structural breaks appearing in January 2025. We validate these shifts using surrogate-based robustness tests. Complementary energy-spectrum analysis of Bitcoin and Ethereum identifies pronounced post-election turbulence, and a structural vector autoregression confirms a regime shift in stablecoin dynamics. Overall, human-driven stablecoin flows act as early-warning indicators of political stress, preceding both exchange behavior and algorithmic responses.

q-fin.ST↗

arXiv2025

Universal Patterns in the Blockchain: Analysis of EOAs and Smart Contracts in ERC20 Token Networks

Scaling laws offer a powerful lens to understand complex transactional behaviors in decentralized systems. This study reveals distinctive statistical signatures in the transactional dynamics of ERC20 tokens on the Ethereum blockchain by examining over 44 million token transfers between July 2017 and March 2018 (9-month period). Transactions are categorized into four types: EOA--EOA, EOA--SC, SC-EOA, and SC-SC based on whether the interacting addresses are Externally Owned Accounts (EOAs) or Smart Contracts (SCs), and analyzed across three equal periods (each of 3 months). To identify universal statistical patterns, we investigate the presence of two canonical scaling laws: power law distributions and temporal Taylor's law (TL). EOA-driven transactions exhibit consistent statistical behavior, including a near-linear relationship between trade volume and unique partners with stable power law exponents ($γ\approx 2.3$), and adherence to TL with scaling coefficients ($β\approx 2.3$). In contrast, interactions involving SCs, especially SC-SC, exhibit sublinear scaling, unstable power-law exponents, and significantly fluctuating Taylor coefficients (variation in $β$ to be $Δβ= 0.51$). Moreover, SC-driven activity displays heavier-tailed distributions ($γ< 2$), indicating bursty and algorithm-driven activity. These findings reveal the characteristic differences between human-controlled and automated transaction behaviors in blockchain ecosystems. By uncovering universal scaling behaviors through the integration of complex systems theory and blockchain data analytics, this work provides a principled framework for understanding the underlying mechanisms of decentralized financial systems.

q-fin.ST↗

arXiv2025

Causality Analysis of COVID-19 Induced Crashes in Stock and Commodity Markets: A Topological Perspective

The paper presents a comprehensive causality analysis of the US stock and commodity markets during the COVID-19 crash. The dynamics of different sectors are also compared. We use Topological Data Analysis (TDA) on multidimensional time-series to identify crashes in stock and commodity markets. The Wasserstein Distance WD shows distinct spikes signaling the crash for both stock and commodity markets. We then compare the persistence diagrams of stock and commodity markets using the WD metric. A significant spike in the $WD$ between stock and commodity markets is observed during the crisis, suggesting significant topological differences between the markets. Similar spikes are observed between the sectors of the US market as well. Spikes obtained may be due to either a difference in the magnitude of crashes in the two markets (or sectors), or from the temporal lag between the two markets suggesting information flow. We study the Granger-causality between stock and commodity markets and also between different sectors. The results show a bidirectional Granger-causality between commodity and stock during the crash period, demonstrating the greater interdependence of financial markets during the crash. However, the overall analysis shows that the causal direction is from stock to commodity. A pairwise Granger-causal analysis between US sectors is also conducted. There is a significant increase in the interdependence between the sectors during the crash period. TDA combined with Granger-causality effectively analyzes the interdependence and sensitivity of different markets and sectors.

q-fin.ST↗

arXiv2025

Intraday order transition dynamics in high, medium, and low market cap stocks: A Markov chain approach

An empirical stochastic analysis of high-frequency, tick-by-tick order data of NASDAQ100 listed stocks is conducted using a first-order discrete-time Markov chain model to explore intraday order transition dynamics. This analysis focuses on three market cap categories: High, Medium, and Low. Time-homogeneous transition probability matrices are estimated and compared across time-zones and market cap categories, and we found that limit orders exhibit higher degree of inertia (DoI), i.e., the probability of placing consecutive limit order is higher, during the opening hour. However, in the subsequent hour, the DoI of limit order decreases, while that of market order increases. Limit order adjustments via additions and deletions of limit orders increases significantly after the opening hour. All the order transitions then stabilize during mid-hours. As the closing hour approaches, consecutive order executions surge, with decreased placement of buy and sell limit orders following sell and buy executions, respectively. In terms of the differences in order transitions between stocks of different market cap, DoI of orders is stronger in high and medium market cap stocks. On the other hand, lower market cap stocks show a higher probability of limit order modifications and greater likelihood of submitting sell/buy limit orders after buy/sell executions. Further, order transitions are clustered across all stocks, except during opening and closing hours. The findings of this study may be useful in understanding intraday order placement dynamics across stocks of varying market cap, thus aiding market participants in making informed order placements at different times of trading hour.

q-fin.ST↗

arXiv2024

Identifying Extreme Events in the Stock Market: A Topological Data Analysis

This paper employs Topological Data Analysis (TDA) to detect extreme events (EEs) in the stock market at a continental level. Previous approaches, which analyzed stock indices separately, could not detect EEs for multiple time series in one go. TDA provides a robust framework for such analysis and identifies the EEs during the crashes for different indices. The TDA analysis shows that $L^1$, $L^2$ norms and Wasserstein distance ($W_D$) of the world leading indices rise abruptly during the crashes, surpassing a threshold of $μ+4*σ$ where $μ$ and $σ$ are the mean and the standard deviation of norm or $W_D$, respectively. Our study identified the stock index crashes of the 2008 financial crisis and the COVID-19 pandemic across continents as EEs. Given that different sectors in an index behave differently, a sector-wise analysis was conducted during the COVID-19 pandemic for the Indian stock market. The sector-wise results show that after the occurrence of EE, we have observed strong crashes surpassing $μ+2*σ$ for an extended period for the banking sector. While for the pharmaceutical sector, no significant spikes were noted. Hence, TDA also proves successful in identifying the duration of shocks after the occurrence of EEs. This also indicates that the Banking sector continued to face stress and remained volatile even after the crash. This study gives us the applicability of TDA as a powerful analytical tool to study EEs in various fields.

q-fin.ST↗

arXiv2024

High-Frequency Stock Market Order Transitions during the US-China Trade War 2018: A Discrete-Time Markov Chain Analysis

Statistical analysis of high-frequency stock market order transaction data is conducted to understand order transition dynamics. We employ a first-order time-homogeneous discrete-time Markov chain model to the sequence of orders of stocks belonging to six different sectors during the USA-China trade war of 2018. The Markov property of the order sequence is validated by the Chi-square test. We estimate the transition probability matrix of the sequence using maximum likelihood estimation. From the heat-map of these matrices, we found the presence of active participation by different types of traders during high volatility days. On such days, these traders place limit orders primarily with the intention of deleting the majority of them to influence the market. These findings are supported by high stationary distribution and low mean recurrence values of add and delete orders. Further, we found similar spectral gap and entropy rate values, which indicates that similar trading strategies are employed on both high and low volatility days during the trade war. Among all the sectors considered in this study, we observe that there is a recurring pattern of full execution orders in Finance & Banking sector. This shows that the banking stocks are resilient during the trade war. Hence, this study may be useful in understanding stock market order dynamics and devise trading strategies accordingly on high and low volatility days during extreme macroeconomic events.

q-fin.ST↗

arXiv2021

A sentiment-based modeling and analysis of stock price during the COVID-19: U- and Swoosh-shaped recovery

Recently, a stock price model is proposed by A. Mahata et al. [Physica A, 574, 126008 (2021)] to understand the effect of COVID-19 on stock market. It describes V- and L-shaped recovery of the stocks and indices, but fails to simulate the U- and Swoosh-shaped recovery that arises due to sharp crisis and prolong drop followed by quick recovery (U-shaped) or slow recovery for longer period (Swoosh-shaped recovery). We propose a modified model by introducing a new variable $θ$ that quantifies the sentiment of the investors. $θ=+1,~0,~-1$ for positive, neutral and negative sentiment, respectively. The model explains the movement of sectoral indices with positive $ϕ$ showing U- and Swoosh-shaped recovery. The simulation using synthetic fund-flow ($Ψ_{st}$) with different shock lengths ($T_S$), $ϕ$, negative sentiment period ($T_N$) and portion of fund-flow ($λ$) during recovery period show U- and Swoosh-shaped recovery. The results show that the recovery of the indices with positive $ϕ$ becomes very weak with the extended $T_S$ and $T_N$. The stocks with higher $ϕ$ and $λ$ recover quickly. The simulation of the Nifty Bank, Nifty Financial and Nifty Realty show U-shaped recovery and Nifty IT shows Swoosh-shaped recovery. The simulation result is consistent with the real stock price movement. The time-scale ($τ$) of the shock and recovery of these indices during the COVID-19 are consistent with the time duration of the change of negative sentiment from the onset of the COVID-19. This study may help the investors to plan their investment during different crises.

q-fin.ST↗

arXiv2011

Effect of discrete time observations on synchronization in Chua model and applications to data assimilation

Recent studies show indication of the effectiveness of synchronization as a data assimilation tool for small or meso-scale forecast when less number of variables are observed frequently. Our main aim here is to understand the effects of changing observational frequency and observational noise on synchronization and prediction in a low dimensional chaotic system, namely the Chua circuit model. We perform {\it identical twin experiments} in order to study synchronization using discrete-in-time observations generated from independent model run and coupled unidirectionally to the model through $x$, $y$ and $z$ separately. We observe synchrony in a finite range of coupling constant when coupling the x and y variables of the Chua model but not when coupling the z variable. This range of coupling constant decreases with increasing levels of noise in the observations. The Chua system does not show synchrony when the time gap between observations is greater than about one-seventh of the Lyapunov time. Finally, we also note that prediction errors are much larger when noisy observations are used than when using observations without noise.

nlin.CD↗

arXiv2010

Effect of a sub and supra-threshold periodic forcing an excitable glow discharge plasma near its bifurcation point

In this paper non-linear dynamics of a periodically forced excitable glow discharge plasma has been studied. The experiments were performed in glow discharge plasma where excitability was achieved for suitable discharge voltage and gas pressure. The plasma was first perturbed by a sub-threshold sawtooth periodic signal, and we obtained small sub-threshold oscillations. These oscillations showed resonance when the frequency of the perturbation was around the characteristic frequency the plasma, and hence may be useful to estimate characteristic of an excitable system. On the other hand, when the perturbation was supra-threshold, system showed frequency entrainments. We obtained harmonic frequency entrainments for perturbation frequency greater than the characteristic frequency of the system and for lesser than the characteristic frequency, system showed only excitable behaviour.

nlin.CD↗

arXiv2009

Modeling noise induced resonance in an excitable system: An alternative approach

Recently, it is observed [Md. Nurujjaman et al, Phy. Rev. E \textbf{80}, 015201 (R) (2009)] that in an excitable system, one can maintain noise induced coherency in the coherence resonance by blocking the destructive effect of the noise on the system at higher noise level. This phenomenon of constant coherence resonance (CCR) cannot be explained by the existing way of simulation of the model equations of an excitable system with added noise. In this paper, we have proposed a general model which explains the noise induced resonance phenomenon CCR as well as coherence resonance (CR) and stochastic resonance (SR). The simulation has been carried out considering the basic mechanism of noise induced resonance phenomena: noise only perturbs the system control parameter to excite coherent oscillations, taking proper precautions so that the destructive effect of noise does not affect the system. In this approach, the CR has been obtained from the interference between the system output and noise, and the SR has been obtained by adding noise and a subthreshold signal. This also explains the observation of the frequency shift of coherent oscillations in the CCR with noise level.

nlin.CD↗

arXiv2009

Continuous wavelet transform based time-scale and multi-fractal analysis of the nonlinear oscillations in a hollow cathode glow discharge plasma

Continuous wavelet transform (CWT) based time-scale and multi-fractal analyses have been carried out on the anode glow related nonlinear floating potential fluctuations in a hollow cathode glow discharge plasma. CWT has been used to obtain the contour and ridge plots. Scale shift (or inversely frequency shift) which is a typical nonlinear behaviour, has been detected from the undulating contours. From the ridge plots, we have identified the presence of nonlinearity and degree of chaoticity. Using the wavelet transform modulus maxima technique we have obtained the multi-fractal spectrum for the fluctuations at different discharge voltages and the spectrum was observed to become a monofractal for periodic signals. These multi-fractal spectra were also used to estimate different quantities like the correlation and fractal dimension, degree of multi-fractality and complexity parameters. These estimations have been found to be consistent with the nonlinear time series analysis.

physics.plasm-ph↗

arXiv2009

Nonlinear dynamics experiments in plasmas

The study of nonlinear dynamics or chaos theory has emerged in the last three decades or so as an important interdisciplinary area of research encompassing a wide range of fields like: fluids, plasmas, biomedical sciences, finance, turbulence, astronomy, material sciences, etc. In plasma chaos was first experimentally observed by Boswell. Different other nonlinear dynamics related phenomena like, the intermittency route to a chaos, Homoclinic chaos, Period adding route to chaos and period subtracting, mode locking, period pulling, etc., had been observed by several researchers. In this thesis, we have presented (a) anode glow related observation of chaos to order transition and homoclinic bifurcation; (b) coherence resonance and stochastic resonance; and self organized criticality behavior in glow discharge plasma.

physics.plasm-ph↗

arXiv2009

Comparative study of nonlinear properties of EEG signals of a normal person and an epileptic patient

Background: Investigation of the functioning of the brain in living systems has been a major effort amongst scientists and medical practitioners. Amongst the various disorder of the brain, epilepsy has drawn the most attention because this disorder can affect the quality of life of a person. In this paper we have reinvestigated the EEGs for normal and epileptic patients using surrogate analysis, probability distribution function and Hurst exponent. Results: Using random shuffled surrogate analysis, we have obtained some of the nonlinear features that was obtained by Andrzejak \textit{et al.} [Phys Rev E 2001, 64:061907], for the epileptic patients during seizure. Probability distribution function shows that the activity of an epileptic brain is nongaussian in nature. Hurst exponent has been shown to be useful to characterize a normal and an epileptic brain and it shows that the epileptic brain is long term anticorrelated whereas, the normal brain is more or less stochastic. Among all the techniques, used here, Hurst exponent is found very useful for characterization different cases. Conclusions: In this article, differences in characteristics for normal subjects with eyes open and closed, epileptic subjects during seizure and seizure free intervals have been shown mainly using Hurst exponent. The H shows that the brain activity of a normal man is uncorrelated in nature whereas, epileptic brain activity shows long range anticorrelation.

physics.med-ph↗