Optimizing Parallel Schemes with Lyapunov Exponents and kNN-LLE Estimation

Inverse parallel schemes remain indispensable tools for computing the roots of nonlinear systems, yet their dynamical behavior can be unexpectedly rich, ranging from strong contraction to oscillatory or chaotic transients depending on the choice of algorithmic parameters and initial states. A unified analytical-data-driven methodology for identifying, measuring, and reducing such instabilities in a family of uni-parametric inverse parallel solvers is presented in this study. On the theoretical side, we derive stability and bifurcation characterizations of the underlying iterative maps, identifying parameter regions associated with periodic or chaotic behavior. On the computational side, we introduce a micro-series pipeline based on kNN-driven estimation of the local largest Lyapunov exponent (LLE), applied to scalar time series derived from solver trajectories. The resulting sliding-window Lyapunov profiles provide fine-grained, real-time diagnostics of contractive or unstable phases and reveal transient behaviors not captured by coarse linearized analysis. Leveraging this correspondence, we introduce a Lyapunov-informed parameter selection strategy that identifies solver settings associated with stable behavior, particularly when the estimated LLE indicates persistent instability. Comprehensive experiments on ensembles of perturbed initial guesses demonstrate close agreement between the theoretical stability diagrams and empirical Lyapunov profiles, and show that the proposed adaptive mechanism significantly improves robustness. The study establishes micro-series Lyapunov analysis as a practical, interpretable tool for constructing self-stabilizing root-finding schemes and opens avenues for extending such diagnostics to higher-dimensional or noise-contaminated problems.

GO-OSC and VASH: Geometry-Aware Representation Learning for Early Degradation Detection in Oscillatory Systems

Early-stage degradation in oscillatory systems often manifests as geometric distortions of the dynamics, such as phase jitter, frequency drift, or loss of coherence, long before changes in signal energy are detectable. In this regime, classical energy-based diagnostics and unconstrained learned representations are structurally insensitive, leading to delayed or unstable detection. We introduce GO-OSC, a geometry-aware representation learning framework for oscillatory time series that enforces a canonical and identifiable latent parameterization, enabling stable comparison and aggregation across short, unlabeled windows. Building on this representation, we define a family of invariant linear geometric probes that target degradation-relevant directions in latent space. We provide theoretical results showing that under early phase-only degradation, energy-based statistics have zero first-order detection power, whereas geometric probes achieve strictly positive sensitivity. Our analysis characterizes when and why linear probing fails under non-identifiable representations and shows how canonicalization restores statistical detectability. Experiments on synthetic benchmarks and real vibration datasets validate the theory, demonstrating earlier detection, improved data efficiency, and robustness to operating condition changes.

UniPACT: A Multimodal Framework for Prognostic Question Answering on Raw ECG and Structured EHR

Accurate clinical prognosis requires synthesizing structured Electronic Health Records (EHRs) with real-time physiological signals like the Electrocardiogram (ECG). Large Language Models (LLMs) offer a powerful reasoning engine for this task but struggle to natively process these heterogeneous, non-textual data types. To address this, we propose UniPACT (Unified Prognostic Question Answering for Clinical Time-series), a unified framework for prognostic question answering that bridges this modality gap. UniPACT's core contribution is a structured prompting mechanism that converts numerical EHR data into semantically rich text. This textualized patient context is then fused with representations learned directly from raw ECG waveforms, enabling an LLM to reason over both modalities holistically. We evaluate UniPACT on the comprehensive MDS-ED benchmark, it achieves a state-of-the-art mean AUROC of 89.37% across a diverse set of prognostic tasks including diagnosis, deterioration, ICU admission, and mortality, outperforming specialized baselines. Further analysis demonstrates that our multimodal, multi-task approach is critical for performance and provides robustness in missing data scenarios.

Kolmogorov Arnold Networks and Multi-Layer Perceptrons: A Paradigm Shift in Neural Modelling

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function approximation, time-series prediction, and multivariate classification. Rooted in Kolmogorov's representation theorem, KANs utilize adaptive spline-based activation functions and grid-based structures, providing a transformative approach compared to traditional neural network frameworks. Utilizing a variety of datasets spanning mathematical function estimation (quadratic and cubic) to practical uses like predicting daily temperatures and categorizing wines, the proposed research thoroughly assesses model performance via accuracy measures like Mean Squared Error (MSE) and computational expense assessed through Floating Point Operations (FLOPs). The results indicate that KANs reliably exceed MLPs in every benchmark, attaining higher predictive accuracy with significantly reduced computational costs. Such an outcome highlights their ability to maintain a balance between computational efficiency and accuracy, rendering them especially beneficial in resource-limited and real-time operational environments. By elucidating the architectural and functional distinctions between KANs and MLPs, the paper provides a systematic framework for selecting the most suitable neural architectures for specific tasks. Furthermore, the proposed study highlights the transformative capabilities of KANs in progressing intelligent systems, influencing their use in situations that require both interpretability and computational efficiency.

XGBoost Forecasting of NEPSE Index Log Returns with Walk Forward Validation

This study develops a robust machine learning framework for one-step-ahead forecasting of daily log-returns in the Nepal Stock Exchange (NEPSE) Index using the XGBoost regressor. A comprehensive feature set is engineered, including lagged log-returns (up to 30 days) and established technical indicators such as short- and medium-term rolling volatility measures and the 14-period Relative Strength Index. Hyperparameter optimization is performed using Optuna with time-series cross-validation on the initial training segment. Out-of-sample performance is rigorously assessed via walk-forward validation under both expanding and fixed-length rolling window schemes across multiple lag configurations, simulating real-world deployment and avoiding lookahead bias. Predictive accuracy is evaluated using root mean squared error, mean absolute error, coefficient of determination (R-squared), and directional accuracy on both log-returns and reconstructed closing prices. Empirical results show that the optimal configuration, an expanding window with 20 lags, outperforms tuned ARIMA and Ridge regression benchmarks, achieving the lowest log-return RMSE (0.013450) and MAE (0.009814) alongside a directional accuracy of 65.15%. While the R-squared remains modest, consistent with the noisy nature of financial returns, primary emphasis is placed on relative error reduction and directional prediction. Feature importance analysis and visual inspection further enhance interpretability. These findings demonstrate the effectiveness of gradient boosting ensembles in modeling nonlinear dynamics in volatile emerging market time series and establish a reproducible benchmark for NEPSE Index forecasting.

NeuroSSM: Multiscale Differential State-Space Modeling for Context-Aware fMRI Analysis

Accurate fMRI analysis requires sensitivity to temporal structure across multiple scales, as BOLD signals encode cognitive processes that emerge from fast transient dynamics to slower, large-scale fluctuations. Existing deep learning (DL) approaches to temporal modeling face challenges in jointly capturing these dynamics over long fMRI time series. Among current DL models, transformers address long-range dependencies by explicitly modeling pairwise interactions through attention, but the associated quadratic computational cost limits effective integration of temporal dependencies across long fMRI sequences. Selective state-space models (SSMs) instead model long-range temporal dependencies implicitly through latent state evolution in a dynamical system, enabling efficient propagation of dependencies over time. However, recent SSM-based approaches for fMRI commonly operate on derived functional connectivity representations and employ single-scale temporal processing. These design choices constrain the ability to jointly represent fast transient dynamics and slower global trends within a single model. We propose NeuroSSM, a selective state-space architecture designed for end-to-end analysis of raw BOLD signals in fMRI time series. NeuroSSM addresses the above limitations through two complementary design components: a multiscale state-space backbone that captures fast and slow dynamics concurrently, and a parallel differencing branch that increases sensitivity to transient state changes. Experiments on clinical and non-clinical datasets demonstrate that NeuroSSM achieves competitive performance and efficiency against state-of-the-art fMRI analysis methods.

DriftGuard: A Hierarchical Framework for Concept Drift Detection and Remediation in Supply Chain Forecasting

Supply chain forecasting models degrade over time as real-world conditions change. Promotions shift, consumer preferences evolve, and supply disruptions alter demand patterns, causing what is known as concept drift. This silent degradation leads to stockouts or excess inventory without triggering any system warnings. Current industry practice relies on manual monitoring and scheduled retraining every 3-6 months, which wastes computational resources during stable periods while missing rapid drift events. Existing academic methods focus narrowly on drift detection without addressing diagnosis or remediation, and they ignore the hierarchical structure inherent in supply chain data. What retailers need is an end-to-end system that detects drift early, explains its root causes, and automatically corrects affected models. We propose DriftGuard, a five-module framework that addresses the complete drift lifecycle. The system combines an ensemble of four complementary detection methods, namely error-based monitoring, statistical tests, autoencoder anomaly detection, and Cumulative Sum (CUSUM) change-point analysis, with hierarchical propagation analysis to identify exactly where drift occurs across product lines. Once detected, Shapley Additive Explanations (SHAP) analysis diagnoses the root causes, and a cost-aware retraining strategy selectively updates only the most affected models. Evaluated on over 30,000 time series from the M5 retail dataset, DriftGuard achieves 97.8% detection recall within 4.2 days and delivers up to 417 return on investment through targeted remediation.

Bridging Temporal and Textual Modalities: A Multimodal Framework for Automated Cloud Failure Root Cause Analysis

Root cause analysis in modern cloud infrastructure demands sophisticated understanding of heterogeneous data sources, particularly time-series performance metrics that involve core failure signatures. While large language models demonstrate remarkable capabilities in textual reasoning, their discrete token-based architecture creates fundamental incompatibilities with continuous numerical sequences exhibiting temporal dependencies. Current methodologies inadequately address this modality mismatch, constraining the potential of language model-driven automation in incident management workflows. This paper presents a multimodal diagnostic framework that harmonizes time-series representations with pretrained language model embedding spaces. Our approach contributes three technical advances: (1) a semantic compression technique that distills temporal segments into single-token abstractions while preserving pattern semantics, (2) an alignment encoder utilizing gated cross-attention to project time-series features into language model latent space, and (3) a retrieval-augmented diagnostic pipeline that synthesizes aligned embeddings with historical incident knowledge for expert-level failure attribution. Comprehensive evaluation across six cloud system benchmarks demonstrates that our framework achieves leading performance, reaching 48.75% diagnostic accuracy with notable improvements on scenarios involving compound failure modes. The results validate embedding-space alignment as an effective strategy for enabling language models to reason over multimodal telemetry data in production incident response contexts.

IceWatch: Forecasting Glacial Lake Outburst Floods (GLOFs) using Multimodal Deep Learning

Glacial Lake Outburst Floods (GLOFs) pose a serious threat in high mountain regions. They are hazardous to communities, infrastructure, and ecosystems further downstream. The classical methods of GLOF detection and prediction have so far mainly relied on hydrological modeling, threshold-based lake monitoring, and manual satellite image analysis. These approaches suffer from several drawbacks: slow updates, reliance on manual labor, and losses in accuracy when clouds interfere and/or lack on-site data. To tackle these challenges, we present IceWatch: a novel deep learning framework for GLOF prediction that incorporates both spatial and temporal perspectives. The vision component, RiskFlow, of IceWatch deals with Sentinel-2 multispectral satellite imagery using a CNN-based classifier and predicts GLOF events based on the spatial patterns of snow, ice, and meltwater. Its tabular counterpart confirms this prediction by considering physical dynamics. TerraFlow models glacier velocity from NASA ITS_LIVE time series while TempFlow forecasts near-surface temperature from MODIS LST records; both are trained on long-term observational archives and integrated via harmonized preprocessing and synchronization to enable multimodal, physics-informed GLOF prediction. Both together provide cross-validation, which will improve the reliability and interpretability of GLOF detection. This system ensures strong predictive performance, rapid data processing for real-time use, and robustness to noise and missing information. IceWatch paves the way for automatic, scalable GLOF warning systems. It also holds potential for integration with diverse sensor inputs and global glacier monitoring activities.

DT-ICU: Towards Explainable Digital Twins for ICU Patient Monitoring via Multi-Modal and Multi-Task Iterative Inference

We introduce DT-ICU, a multimodal digital twin framework for continuous risk estimation in intensive care. DT-ICU integrates variable-length clinical time series with static patient information in a unified multitask architecture, enabling predictions to be updated as new observations accumulate over the ICU stay. We evaluate DT-ICU on the large, publicly available MIMIC-IV dataset, where it consistently outperforms established baseline models under different evaluation settings. Our test-length analysis shows that meaningful discrimination is achieved shortly after admission, while longer observation windows further improve the ranking of high-risk patients in highly imbalanced cohorts. To examine how the model leverages heterogeneous data sources, we perform systematic modality ablations, revealing that the model learnt a reasonable structured reliance on interventions, physiological response observations, and contextual information. These analyses provide interpretable insights into how multimodal signals are combined and how trade-offs between sensitivity and precision emerge. Together, these results demonstrate that DT-ICU delivers accurate, temporally robust, and interpretable predictions, supporting its potential as a practical digital twin framework for continuous patient monitoring in critical care. The source code and trained model weights for DT-ICU are publicly available at https://github.com/GUO-W/DT-ICU-release.