Electroencephalography (EEG)-based Brain-Computer Interfaces (BCIs) have emerged as a transformative technology with applications spanning robotics, virtual reality, medicine, and rehabilitation. However, existing BCI frameworks face several limitations, including a lack of stage-wise flexibility essential for experimental research, steep learning curves for researchers without programming expertise, elevated costs due to reliance on proprietary software, and a lack of all-inclusive features leading to the use of multiple external tools affecting research outcomes. To address these challenges, we present PyNoetic, a modular BCI framework designed to cater to the diverse needs of BCI research. PyNoetic is one of the very few frameworks in Python that encompasses the entire BCI design pipeline, from stimulus presentation and data acquisition to channel selection, filtering, feature extraction, artifact removal, and finally simulation and visualization. Notably, PyNoetic introduces an intuitive and end-to-end GUI coupled with a unique pick-and-place configurable flowchart for no-code BCI design, making it accessible to researchers with minimal programming experience. For advanced users, it facilitates the seamless integration of custom functionalities and novel algorithms with minimal coding, ensuring adaptability at each design stage. PyNoetic also includes a rich array of analytical tools such as machine learning models, brain-connectivity indices, systematic testing functionalities via simulation, and evaluation methods of novel paradigms. PyNoetic's strengths lie in its versatility for both offline and real-time BCI development, which streamlines the design process, allowing researchers to focus on more intricate aspects of BCI development and thus accelerate their research endeavors.

Trade-based manipulation (TBM) undermines the fairness and stability of financial markets drastically. Spoofing, one of the most covert and deceptive TBM strategies, exhibits complex anomaly patterns across multilevel prices, while often being simplified as a single-level manipulation. These patterns are usually concealed within the rich, hierarchical information of the Limit Order Book (LOB), which is challenging to leverage due to high dimensionality and noise. To address this, we propose a representation learning framework combining a cascaded LOB representation architecture with supervised contrastive learning. Extensive experiments demonstrate that our framework consistently improves detection performance across diverse models, with Transformer-based architectures achieving state-of-the-art results. In addition, we conduct systematic analyses and ablation studies to investigate multilevel manipulation and the contributions of key components for detection, offering broader insights into representation learning and anomaly detection for complex time series data.

We analyze the convergence behavior of stochastic gradient descent with momentum (SGDM) under dynamic learning-rate and batch-size schedules by introducing a novel and simpler Lyapunov function. We extend the existing theoretical framework to cover three practical scheduling strategies commonly used in deep learning: a constant batch size with a decaying learning rate, an increasing batch size with a decaying learning rate, and an increasing batch size with an increasing learning rate. Our results reveal a clear hierarchy in convergence: a constant batch size does not guarantee convergence of the expected gradient norm, whereas an increasing batch size does, and simultaneously increasing both the batch size and learning rate achieves a provably faster decay. Empirical results validate our theory, showing that dynamically scheduled SGDM significantly outperforms its fixed-hyperparameter counterpart in convergence speed. We also evaluated a warm-up schedule in experiments, which empirically outperformed all other strategies in convergence behavior.

Zero-order optimization techniques are becoming increasingly popular in robotics due to their ability to handle non-differentiable functions and escape local minima. These advantages make them particularly useful for trajectory optimization and policy optimization. In this work, we propose a mathematical tutorial on random search. It offers a simple and unifying perspective for understanding a wide range of algorithms commonly used in robotics. Leveraging this viewpoint, we classify many trajectory optimization methods under a common framework and derive novel competitive RL algorithms.

Current evaluation frameworks for foundation models rely heavily on static, manually curated benchmarks, limiting their ability to capture the full breadth of model capabilities. This paper introduces Active learning for Capability Evaluation (ACE), a novel framework for scalable, automated, and fine-grained evaluation of foundation models. ACE leverages the knowledge embedded in powerful frontier models to decompose a domain into semantically meaningful capabilities and generates diverse evaluation tasks, significantly reducing human effort. In Mathematics, ACE generated 433 capabilities and 11,800 tasks, covering 94% of Wikipedia-defined skills in the domain while introducing novel, coherent ones. To maximize efficiency, ACE fits a capability model in latent semantic space, allowing reliable approximation of a subject model's performance by evaluating only a subset of capabilities via active learning. It reaches within 0.01 RMSE of exhaustive evaluation by evaluating less than half of capabilities. Compared to static datasets, ACE provides more balanced coverage and uncovers fine-grained differences that aggregate metrics fail to capture. Our results demonstrate that ACE provides a more complete and informative picture of model capabilities, which is essential for safe and well-informed deployment of foundation models.

Dynamical systems in the life sciences are often composed of complex mixtures of overlapping behavioral regimes. Cellular subpopulations may shift from cycling to equilibrium dynamics or branch towards different developmental fates. The transitions between these regimes can appear noisy and irregular, posing a serious challenge to traditional, flow-based modeling techniques which assume locally smooth dynamics. To address this challenge, we propose MODE (Mixture Of Dynamical Experts), a graphical modeling framework whose neural gating mechanism decomposes complex dynamics into sparse, interpretable components, enabling both the unsupervised discovery of behavioral regimes and accurate long-term forecasting across regime transitions. Crucially, because agents in our framework can jump to different governing laws, MODE is especially tailored to the aforementioned noisy transitions. We evaluate our method on a battery of synthetic and real datasets from computational biology. First, we systematically benchmark MODE on an unsupervised classification task using synthetic dynamical snapshot data, including in noisy, few-sample settings. Next, we show how MODE succeeds on challenging forecasting tasks which simulate key cycling and branching processes in cell biology. Finally, we deploy our method on human, single-cell RNA sequencing data and show that it can not only distinguish proliferation from differentiation dynamics but also predict when cells will commit to their ultimate fate, a key outstanding challenge in computational biology.

Kidneys are the filter of the human body. About 10% of the global population is thought to be affected by Chronic Kidney Disease (CKD), which causes kidney function to decline. To protect in danger patients from additional kidney damage, effective risk evaluation of CKD and appropriate CKD monitoring are crucial. Due to quick and precise detection capabilities, Machine Learning models can help practitioners accomplish this goal efficiently; therefore, an enormous number of diagnosis systems and processes in the healthcare sector nowadays are relying on machine learning due to its disease prediction capability. In this study, we designed and suggested disease predictive computer-aided designs for the diagnosis of CKD. The dataset for CKD is attained from the repository of machine learning of UCL, with a few missing values; those are filled in using "mean-mode" and "Random sampling method" strategies. After successfully achieving the missing data, eight ML techniques (Random Forest, SVM, Naive Bayes, Logistic Regression, KNN, XGBoost, Decision Tree, and AdaBoost) were used to establish models, and the performance evaluation comparisons among the result accuracies are measured by the techniques to find the machine learning models with the highest accuracy. Among them, Random Forest as well as Logistic Regression showed an outstanding 99% accuracy, followed by the Ada Boost, XGBoost, Naive Bayes, Decision Tree, and SVM, whereas the KNN classifier model stands last with an accuracy of 73%.

Small and Medium-sized Enterprises (SMEs) are known to play a vital role in economic growth, employment, and innovation. However, they tend to face significant challenges in accessing credit due to limited financial histories, collateral constraints, and exposure to macroeconomic shocks. These challenges make an accurate credit risk assessment by lenders crucial, particularly since SMEs frequently operate within interconnected firm networks through which default risk can propagate. This paper presents and tests a novel approach for modelling the risk of SME credit, using a unique large data set of SME loans provided by a prominent financial institution. Specifically, our approach employs Graph Neural Networks to predict SME default using multilayer network data derived from common ownership and financial transactions between firms. We show that combining this information with traditional structured data not only improves application scoring performance, but also explicitly models contagion risk between companies. Further analysis shows how the directionality and intensity of these connections influence financial risk contagion, offering a deeper understanding of the underlying processes. Our findings highlight the predictive power of network data, as well as the role of supply chain networks in exposing SMEs to correlated default risk.

While these alternatives improve efficiency, their fundamental differences in information processing remain poorly understood. In this work, we leverage the recently proposed dynamical systems framework to represent softmax, norm and linear attention as dynamical systems, enabling a structured comparison with SSMs by analyzing their respective eigenvalue spectra. Since eigenvalues capture essential aspects of dynamical system behavior, we conduct an extensive empirical analysis across diverse sequence models and benchmarks. We first show that eigenvalues influence essential aspects of memory and long-range dependency modeling, revealing spectral signatures that align with task requirements. Building on these insights, we then investigate how architectural modifications in sequence models impact both eigenvalue spectra and task performance. This correspondence further strengthens the position of eigenvalue analysis as a principled metric for interpreting, understanding, and ultimately improving the capabilities of sequence models. Deep sequence models have emerged as the backbone of modern artificial intelligence applications, demonstrating remarkable capabilities through their ability to learn complex patterns in large-scale datasets (Bommasani et al., 2021). The transformer (V aswani et al., 2017), with softmax attention as its backbone, has been the dominant paradigm driving these advances. However, its quadratic complexity with respect to sequence length represents a critical bottleneck, limiting the practical deployment of these models for long-context applications (Tay et al., 2021).

We study the problem of constructing Steiner Minimal Trees (SMTs) in hyperbolic space. Exact SMT computation is NP-hard, and existing hyperbolic heuristics such as HyperSteiner are deterministic and often get trapped in locally suboptimal configurations. We introduce Randomized HyperSteiner (RHS), a stochastic Delaunay triangulation heuristic that incorporates randomness into the expansion process and refines candidate trees via Riemannian gradient descent optimization. Experiments on synthetic data sets and a real-world single-cell transcrip-tomic data show that RHS outperforms Minimum Spanning Tree (MST), Neighbour Joining, and vanilla HyperSteiner (HS). In near-boundary configurations, RHS can achieve a 32% reduction in total length over HS, demonstrating its effectiveness and robustness in diverse data regimes.