Chittaranjan Hens

Chaotic time series are notoriously difficult to forecast: small uncertainties in initial conditions amplify rapidly, while strong nonlinearities and regime-dependent variability constrain predictability. Although modern deep learning often delivers strong short-horizon accuracy, its black-box nature limits scientific insight and practical trust in settings where understanding the underlying dynamics matters. To address this gap, we propose two complementary symbolic forecasters that learn explicit, interpretable algebraic equations from chaotic time series data. Symbolic neural forecaster adapts a neural network-based equation learning architecture to the forecasting setting, enabling end-to-end differentiable discovery of compact and interpretable algebraic relations. The symbolic tree forecaster builds on evolutionary symbolic regression to search directly over equation structures under a principled accuracy–complexity trade-off. We evaluate both approaches in a rolling-window one-step-ahead forecast setting using several accuracy metrics and compare against a broad suite of baselines spanning classical statistical models, tree ensembles, and state-of-the-art deep learning architectures. Numerical experiments cover a benchmark of 132 low-dimensional chaotic attractors and two real-world chaotic time series (weekly dengue incidence in San Juan and the Niño 3.4 sea-surface temperature index). Across datasets, symbolic forecasters achieve competitive one-step-ahead accuracy while providing transparent analytical equations that reveal salient aspects of the underlying dynamics.

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 81 million token transfers across two independent time windows: July 2017 to March 2018 and December 2019 to February 2020. 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 four equal periods (each of 3 months). To characterize and identify specific 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 ≈ 2.3 ), and adherence to TL with scaling coefficients ( β ≈ 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 Δ β = 0.51 ). Moreover, SC-driven activity displays heavier-tailed distributions ( γ < 2 ), indicating bursty and protocol-level activity. The gas fee analysis further supports the difference between EOA and SC, with EOA-SC transactions incurring much higher gas fees, consistent with the greater computational complexity of smart contract execution and reinforcing the structural differences between EOA-driven activity and SC involvement. These findings reveal the characteristic differences between EOA-driven and SC–driven transaction behaviors in blockchain ecosystems. By uncovering 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.

Low-dimensional reductions provide a useful framework for studying high-dimensional dynamics on complex networks, but most existing approaches are restricted to pairwise interactions. Here, we develop a one-dimensional reduction for dynamical systems on networks with purely higher-order interactions. The reduction is formulated through an effective higher-order interaction strength (βΔ), associated with the triangular interactions of the underlying network and the dynamical system's effective state. We present a theoretical framework for the dimension-reduction approach and validate it across three dynamical models with exclusively higher-order interactions. We find that the reduction accuracy is mainly determined by the homogeneity of node states, that is the deviations in state values become very small. Numerical results on synthetic and real networks show that the reduced model captures the effective steady states and transitions of the full system with good accuracy.

Spatiotemporal signal propagation through the human brain during epileptic seizures remains poorly understood. Using intracranial EEG from subjects with medically refractory epilepsy, we introduce an edge-centric framework that tracks how influential functional connections in the time-evolving epileptic brain network form and transition as seizures unfold. Brain regions are grouped into three functional modules – seizure onset area, nearby ipsilateral regions, and other areas – with the most important edges followed over time. A probabilistic entropy approach reveals that path-based centralities exhibit a conserved circular motif of seizure propagation across subjects. In contrast, strength-based centralities separate seizures into two distinct classes: one where cross-module edges serve as dynamic bottlenecks guiding ictal spread, and another where these edges remain stable. These findings demonstrate that an edge-focused perspective may reveal vital information about ictal communication pathways, and may have potential application for improved prediction and classification in epilepsy.

While the multidimensional features of electroencephalographic (EEG) signals have proven to be a valuable source of information, the development of a comprehensive diagnostic tool remains elusive due to variability of responses as observed within the subjects and epochs. We investigate whether ordinal-pattern-based complexity measures of EEG signals can capture stroke-related alterations in motor imagery (MI) tasks. EEG recordings from 36 stroke patients (acute and minor) and 36 healthy controls were analyzed using permutation entropy (PE), a robust symbolic measure of temporal irregularity. Stroke patients perform left- and right-hand MI tasks, while controls are recorded only under eye-open MI and eye-closed resting conditions. Results show that resting-state EEG from healthy participants exhibits low PE values, reflecting structured and regular dynamics, whereas eye-open MI EEG from the same cohort produces high PE values consistent with near-maximally complex, information-rich neural dynamics. Stroke patients demonstrate intermediate PE values during MI tasks, suggesting altered but partially preserved physiological complexity. These findings indicate that entropy-based measures can distinguish between healthy and stroke-related neural dynamics, providing potential biomarkers for tailoring brain–computer interface (BCI) driven rehabilitation strategies.

We investigate the effect of partial order parameter adaptation in the form of general functions on the synchronization behavior of coupled Kuramoto oscillators on top of random hypergraph models. The interactions between the oscillators are considered pairwise and triangular. Using the Ott–Antonsen ansatz, we obtain a set of self-consistent equations of the order parameter that describe the synchronization patterns. A broad diversity of synchronization transitions is observed as a result of the interplay between the partial adaptation approach, generalized adaptation functions, and coupling strengths. The system specifically shows a double-jump transition under a power law form of the adaptation function. A polynomial form of the adaptation function leads to the emergence of an intermediate synchronization state for specific combinations of one negative and one positive coefficient. Moreover, the synchronization transition may become continuous or explosive when the pairwise coupling strength varies. This type of synchronization behavior is further found by using a Gaussian adaptation function.

Understanding and forecasting precipitation events in the Arctic maritime environments, such as Bear Island and Ny-Ålesund, is crucial for assessing climate risk and developing early warning systems in vulnerable marine regions. This study proposes a probabilistic machine learning framework for modeling and predicting the dynamics and severity of precipitation. We begin by analyzing the scale-dependent relationships between precipitation and key atmospheric drivers (e.g., temperature, relative humidity, cloud cover, and air pressure) using wavelet coherence, which captures localized dependencies across time and frequency domains. To assess joint causal influences, we employ synergistic-unique-redundant decomposition, which quantifies the impact of interaction effects among each variable on future precipitation dynamics. These insights inform the development of data-driven forecasting models that incorporate both historical precipitation and causal climate drivers. To account for uncertainty, we employ the conformal prediction method, which enables the generation of calibrated non-parametric prediction intervals. Our results underscore the importance of utilizing a comprehensive framework that combines causal analysis with probabilistic forecasting to enhance the reliability and interpretability of precipitation predictions in Arctic marine environments.