Understanding how the brain's complex nonlinear dynamics give rise to adaptive cognition and behavior is a central challenge in neuroscience. These dynamics exhibit scale-free and multifractal properties, influencing the reconfiguration of neural networks. However, conventional neuroimaging models are constrained by linear and stationary assumptions, limiting their ability to capture these processes. Transformer-based architectures, known for capturing long-range dependencies, align well with the brain's hierarchical and temporal organization. We introduce Multi-Band Brain Net (MBBN), a transformer-based framework that models frequency-specific spatiotemporal brain dynamics from fMRI by integrating scale-free network principles with frequency-resolved multi-band self-attention. Trained on three large-scale neuroimaging cohorts (UK Biobank, ABCD, ABIDE) totaling 45,951 individuals, MBBN reveals previously undetectable frequency-dependent network interactions, shedding light on connectivity disruptions in psychiatric conditions (ADHD, ASD, depression). This validation shows robust generalizability and highlights core neural principles conserved across populations. MBBN achieves up to 30.59% higher predictive accuracy than state-of-the-art methods, demonstrating the advantage of frequency-informed spatiotemporal modeling in capturing latent neural computations. MBBN's interpretability uncovers novel frequency-specific biomarkers for neurodevelopmental disorders, providing insights into the hierarchical organization of brain function. By offering an interpretable framework for spatiotemporal learning, MBBN provides insights into how neural computations underpin cognitive function and psychiatric vulnerability, with implications for brain decoding, cognitive neuroscience, and precision psychiatry.

This paper presents a novel Integer Programming (IP) approach for discovering the Markov Equivalent Class (MEC) of Bayesian Networks (BNs) through observational data. The MEC-IP algorithm utilizes a unique clique-focusing strategy and Extended Maximal Spanning Graphs (EMSG) to streamline the search for MEC, thus overcoming the computational limitations inherent in other existing algorithms. Our numerical results show that not only a remarkable reduction in computational time is achieved by our algorithm but also an improvement in causal discovery accuracy is seen across diverse datasets. These findings underscore this new algorithm's potential as a powerful tool for researchers and practitioners in causal discovery and BNSL, offering a significant leap forward toward the efficient and accurate analysis of complex data structures.

We present a memetic algorithm (\maa) approach for finding a Hamiltonian cycle in a Hamiltonian graph. The \ma is based on a proven approach to the Asymmetric Travelling Salesman Problem (\atspp) that, in this contribution, is boosted by the introduction of more powerful local searches. Our approach also introduces a novel technique that sparsifies the input graph under consideration for Hamiltonicity and dynamically augments it during the search. Such a combined heuristic approach helps to prove Hamiltonicity by finding a Hamiltonian cycle in less time. In addition, we also employ a recently introduced polynomial-time reduction from the \hamcyc to the Symmetric \tsp, which is based on computing the transitive closure of the graph. Although our approach is a metaheuristic, i.e., it does not give a theoretical guarantee for finding a Hamiltonian cycle, we have observed that the method is successful in practice in verifying the Hamiltonicity of a larger number of instances from the \textit{Flinder University Hamiltonian Cycle Problem Challenge Set} (\fhcpsc), even for the graphs that have large treewidth. The experiments on the \fhcpscc instances and a computational comparison with five recent state-of-the-art baseline approaches show that the proposed method outperforms those for the majority of the instances in the \fhcpsc.

Discovering a correlation from one variable to another variable is of fundamental scientific and practical interest. While existing correlation measures are suitable for discovering average correlation, they fail to discover hidden or potential correlations. To bridge this gap, (i) we postulate a set of natural axioms that we expect a measure of potential correlation to satisfy; (ii) we show that the rate of information bottleneck, i.e., the hypercontractivity coefficient, satisfies all the proposed axioms; (iii) we provide a novel estimator to estimate the hypercontractivity coefficient from samples; and (iv) we provide numerical experiments demonstrating that this proposed estimator discovers potential correlations among various indicators of WHO datasets, is robust in discovering gene interactions from gene expression time series data, and is statistically more powerful than the estimators for other correlation measures in binary hypothesis testing of canonical examples of potential correlations.