Collaborative analysis of decentralized confidential datasets is important, but direct sharing of original datasets is often restricted by privacy and institutional constraints. Data collaboration (DC) analysis transforms each dataset into privacy-preserving intermediate representations via party-specific obfuscation functions and integrates them into common collaboration representations using an anchor dataset. However, many existing DC analysis methods rely on linear transformations for data obfuscation and integration, which may increase reconstruction risk. Although nonlinear dimensionality reduction can mitigate this risk, conventional linear integration methods cannot accurately align intermediate representations produced by nonlinear transformations. Moreover, existing integration methods mainly minimize discrepancies among parties and do not explicitly incorporate geometric or target-variable information useful for downstream analysis. To overcome these limitations, we first formulate linear kernel integration (LKI) as a linear integration method and then kernelize it to obtain nonlinear kernel integration (NKI). NKI admits a globally optimal solution via kernel ridge regression and an eigenvalue problem. We also introduce graph regularization and a centering constraint so that the target representation can capture geometric and target-variable information useful for downstream analysis. Experiments on image classification tasks demonstrate that NKI improves classification accuracy over existing linear integration methods under nonlinear dimensionality reduction, with further gains from target-variable-aware graph regularization and centering. The results also show that dimensionality reduction choices substantially affect both classification accuracy and reconstruction risk.

The integration of multi-omics single-cell data remains challenging due to high-dimensionality and complex inter-modality relationships. To address this, we introduce MoRE-GNN (Multi-omics Relational Edge Graph Neural Network), a heterogeneous graph autoencoder that combines graph convolution and attention mechanisms to dynamically construct relational graphs directly from data. Evaluations on six publicly available datasets demonstrate that MoRE-GNN captures biologically meaningful relationships and outperforms existing methods, particularly in settings with strong inter-modality correlations. Furthermore, the learned representations allow for accurate downstream cross-modal predictions. While performance may vary with dataset complexity, MoRE-GNN offers an adaptive, scalable and interpretable framework for advancing multi-omics integration.

We have read and appreciate all comments, due to page limit we will only address a subset of questions/concerns. We do not expect this will significantly change our performance. R1: Can you evaluate the coarseness of the approximation? By sampling 1000 random singular values with an L2 norm < 50 we get the following results. R4: Approximation = loss not necessarily convex: This is true.

The advent of single-cell multi-omics technologies has enabled the simultaneous profiling of diverse omics layers within individual cells. Integrating such multimodal data provides unprecedented insights into cellular identity, regulatory processes, and disease mechanisms. However, it remains challenging, as current methods often rely on selecting highly variable genes or peaks during preprocessing, which may inadvertently discard crucial biological information. Here, we present scMamba, a foundation model designed to integrate single-cell multi-omics data without the need for prior feature selection while preserving genomic positional information. scMamba introduces a patch-based cell tokenization strategy that treats genomics regions as words (tokens) and cells as sentences. Building upon the concept of state space duality, scMamba distills rich biological insights from high-dimensional, sparse single-cell multi-omics data. Additionally, our novel contrastive learning approach, enhanced with cosine similarity regularization, enables superior alignment across omics layers compared to traditional methods. Systematic benchmarking across multiple datasets demonstrates that scMamba significantly outperforms state-of-the-art methods in preserving biological variation, aligning omics layers, and enhancing key downstream tasks such as clustering, cell type annotation, and trajectory inference. Our findings position scMamba as a powerful tool for large-scale single-cell multi-omics integration, capable of handling large-scale atlases and advancing biological discovery.

Public transportation is a major source of greenhouse gas emissions, highlighting the need to improve bus fuel efficiency. Clustering algorithms assist in analyzing fuel efficiency by grouping data into clusters, but irrelevant features may complicate the analysis and choosing the optimal number of clusters remains a challenging task. Therefore, this paper employs the Gaussian mixture models to cluster the solo fuel-efficiency dataset. Moreover, an integration method that combines the Silhouette index, Calinski-Harabasz index, and Davies-Bouldin index is developed to select the optimal cluster numbers. A dataset with 4006 bus trips in North Jutland, Denmark is utilized as the case study. Trips are first split into three groups, then one group is divided further, resulting in four categories: extreme, normal, low, and extremely low fuel efficiency. A preliminary study using visualization analysis is conducted to investigate how driving behaviors and route conditions affect fuel efficiency. The results indicate that both individual driving habits and route characteristics have a significant influence on fuel efficiency.

Recent advances in Large Language Models (LLMs) are fostering their integration into several reasoning-related fields, including Automated Planning (AP). However, their integration into Hierarchical Planning (HP), a subfield of AP that leverages hierarchical knowledge to enhance planning performance, remains largely unexplored. In this preliminary work, we propose a roadmap to address this gap and harness the potential of LLMs for HP. To this end, we present a taxonomy of integration methods, exploring how LLMs can be utilized within the HP life cycle. Additionally, we provide a benchmark with a standardized dataset for evaluating the performance of future LLM-based HP approaches, and present initial results for a state-of-the-art HP planner and LLM planner. As expected, the latter exhibits limited performance (3\% correct plans, and none with a correct hierarchical decomposition) but serves as a valuable baseline for future approaches.

Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of neural ODEs. In our earlier work, we addressed this challenge by utilizing single-step implicit methods for solving stiff neural ODEs. While effective, these implicit methods are computationally costly and can be complex to implement. This paper expands on our earlier work by exploring explicit exponential integration methods as a more efficient alternative. We evaluate the potential of these explicit methods to handle stiff dynamics in neural ODEs, aiming to enhance their applicability to a broader range of scientific and engineering problems. We found the integrating factor Euler (IF Euler) method to excel in stability and efficiency. While implicit schemes failed to train the stiff Van der Pol oscillator, the IF Euler method succeeded, even with large step sizes. However, IF Euler's first-order accuracy limits its use, leaving the development of higher-order methods for stiff neural ODEs an open research problem.

We propose a novel zero-order control barrier function (ZOCBF) for sampled-data systems to ensure system safety. Our formulation generalizes conventional control barrier functions and straightforwardly handles safety constraints with high-relative degrees or those that explicitly depend on both system states and inputs. The proposed ZOCBF condition does not require any differentiation operation. Instead, it involves computing the difference of the ZOCBF values at two consecutive sampling instants. We propose three numerical approaches to enforce the ZOCBF condition, tailored to different problem settings and available computational resources. We demonstrate the effectiveness of our approach through a collision avoidance example and a rollover prevention example on uneven terrains.

Symbolic integration is a fundamental problem in mathematics: we consider how machine learning may be used to optimise this task in a Computer Algebra System (CAS). We train transformers that predict whether a particular integration method will be successful, and compare against the existing human-made heuristics (called guards) that perform this task in a leading CAS. We find the transformer can outperform these guards, gaining up to 30% accuracy and 70% precision. We further show that the inference time of the transformer is inconsequential which shows that it is well-suited to include as a guard in a CAS. Furthermore, we use Layer Integrated Gradients to interpret the decisions that the transformer is making. If guided by a subject-matter expert, the technique can explain some of the predictions based on the input tokens, which can lead to further optimisations.

Abstract--Partially Observable Markov Decision Processes (POMDPs) provide a structured framework for decision-making under uncertainty, but their application requires efficient belief updates. Sequential Importance Resampling Particle Filters (SIRPF), also known as Bootstrap Particle Filters, are commonly used as belief updaters in large approximate POMDP solvers, but they face challenges such as particle deprivation and high computational costs as the system's state dimension grows. To address these issues, this study introduces Rao-Blackwellized POMDP (RB-POMDP) approximate solvers and outlines generic methods to apply Rao-Blackwellization in both belief updates and online planning. POMCPOW (left) and RB-POMCPOW (right) Tree Structure Comparison. Moreover, as Partially Observable Markov Decision Processes (POMDPs) the system's effective dimension grows, a substantial increase are a powerful mathematical framework for modeling in the number of particles may be required to maintain decision-making under uncertainty where an agent operates performance, resulting in high computational costs (e.g. Rao-Blackwellized Particle Filtering (RBPF) offer a promising POMDPs have been widely applied to various domains such solution to address some of these limitations of the SIRPF.