We present a data-efficient, multiscale framework for predicting the density profiles of confined fluids at the nanoscale. While accurate density estimates require prohibitively long timescales that are inaccessible by ab initio molecular dynamics (AIMD) simulations, machine-learned molecular dynamics (MLMD) offers a scalable alternative, enabling the generation of force predictions at ab initio accuracy with reduced computational cost. However, despite their efficiency, MLMD simulations remain constrained by femtosecond timesteps, which limit their practicality for computing long-time averages needed for accurate density estimation. To address this, we propose a conditional denoising diffusion probabilistic model (DDPM) based quasi-continuum approach that predicts the long-time behavior of force profiles along the confinement direction, conditioned on noisy forces extracted from a limited AIMD dataset. The predicted smooth forces are then linked to continuum theory via the Nernst-Planck equation to reveal the underlying density behavior. We test the framework on water confined between two graphene nanoscale slits and demonstrate that density profiles for channel widths outside of the training domain can be recovered with ab initio accuracy. Compared to AIMD and MLMD simulations, our method achieves orders-of-magnitude speed-up in runtime and requires significantly less training data than prior works.

In decision making, the cognitive fuzzy set (CFS) is a useful tool in expressing experts' complex assessments of alternatives. The distance of CFS, which plays an important role in decision analyses, is necessary when the CFS is applied in solving practical issues. However, as far as we know, the studies on the distance of CFS are few, and the current Minkowski distance of CFS ignores the hesitancy degree of CFS, which might cause errors. To fill the gap of the studies on the distance of CFS, because of the practicality of the Hausdorff distance, this paper proposes the improved cognitive fuzzy Minkowski (CF-IM) distance and the cognitive fuzzy Hausdorff (CF-H) distance to enrich the studies on the distance of CFS. It is found that the anti-perturbation ability of the CF-H distance is stronger than that of the CF-IM distance, but the information utilization of the CF-IM distance is higher than that of the CF-H distance. To balance the anti-perturbation ability and information utilization of the CF-IM distance and CF-H distance, the cognitive fuzzy combined (CF-C) distance is proposed by establishing the linear combination of the CF-IM distance and CF-H distance. Based on the CF-C distance, a combined-distanced-based score function of CFS is proposed to compare CFSs. The proposed score function is employed in lung cancer pain evaluation issues. The sensitivity and comparison analyses demonstrate the reliability and advantages of the proposed methods.

Transformers have exhibited exceptional capabilities in sequence modeling tasks, leveraging self-attention and in-context learning. Critical to this success are induction heads, attention circuits that enable copying tokens based on their previous occurrences. In this work, we introduce a novel framework that showcases transformers' ability to dynamically handle causal structures. Existing works rely on Markov Chains to study the formation of induction heads, revealing how transformers capture causal dependencies and learn transition probabilities in-context. However, they rely on a fixed causal structure that fails to capture the complexity of natural languages, where the relationship between tokens dynamically changes with context. To this end, our framework varies the causal structure through interleaved Markov chains with different lags while keeping the transition probabilities fixed. This setting unveils the formation of Selective Induction Heads, a new circuit that endows transformers with the ability to select the correct causal structure in-context. We empirically demonstrate that transformers learn this mechanism to predict the next token by identifying the correct lag and copying the corresponding token from the past. We provide a detailed construction of a 3-layer transformer to implement the selective induction head, and a theoretical analysis proving that this mechanism asymptotically converges to the maximum likelihood solution. Our findings advance the understanding of how transformers select causal structures, providing new insights into their functioning and interpretability.

Sparse regression problems, where the goal is to identify a small set of relevant predictors, often require modeling not only main effects but also meaningful interactions through other variables. While the pliable lasso has emerged as a powerful frequentist tool for modeling such interactions under strong heredity constraints, it lacks a natural framework for uncertainty quantification and incorporation of prior knowledge. In this paper, we propose a Bayesian pliable lasso that extends this approach by placing sparsity-inducing priors, such as the horseshoe, on both main and interaction effects. The hierarchical prior structure enforces heredity constraints while adaptively shrinking irrelevant coefficients and allowing important effects to persist. We extend this framework to Generalized Linear Models (GLMs) and develop a tailored approach to handle missing responses. To facilitate posterior inference, we develop an efficient Gibbs sampling algorithm based on a reparameterization of the horseshoe prior. Our Bayesian framework yields sparse, interpretable interaction structures, and principled measures of uncertainty. Through simulations and real-data studies, we demonstrate its advantages over existing methods in recovering complex interaction patterns under both complete and incomplete data. Our method is implemented in the package \texttt{hspliable} available on Github.

The Organization for Economic Cooperation and Development (OECD) Working Party on Nuclear Criticality Safety (WPNCS) proposed a benchmark exercise to assess the performance of current nuclear data adjustment techniques applied to nonlinear applications and experiments with low correlation to applications. This work introduces Bayesian Inverse Uncertainty Quantification (IUQ) as a method for nuclear data adjustments in this benchmark, and compares IUQ to the more traditional methods of Generalized Linear Least Squares (GLLS) and Monte Carlo Bayes (MOCABA). Posterior predictions from IUQ showed agreement with GLLS and MOCABA for linear applications. When comparing GLLS, MOCABA, and IUQ posterior predictions to computed model responses using adjusted parameters, we observe that GLLS predictions fail to replicate computed response distributions for nonlinear applications, while MOCABA shows near agreement, and IUQ uses computed model responses directly. We also discuss observations on why experiments with low correlation to applications can be informative to nuclear data adjustments and identify some properties useful in selecting experiments for inclusion in nuclear data adjustment. Performance in this benchmark indicates potential for Bayesian IUQ in nuclear data adjustments.

Causal relationships play a fundamental role in understanding the world around us. The ability to identify and understand cause-effect relationships is critical to making informed decisions, predicting outcomes, and developing effective strategies. However, deciphering causal relationships from observational data is a difficult task, as correlations alone may not provide definitive evidence of causality. In recent years, the field of machine learning (ML) has emerged as a powerful tool, offering new opportunities for uncovering hidden causal mechanisms and better understanding complex systems. In this work, we address the issue of detecting the intrinsic causal links of a large class of complex systems in the framework of the response theory in physics. We develop some theoretical ideas put forward by [1], and technically we use state-of-the-art ML techniques to build up models from data. We consider both linear stochastic and non-linear systems. Finally, we compute the asymptotic efficiency of the linear response based causal predictor in a case of large scale Markov process network of linear interactions.

Figure 1: We introduce OmniMap, a general online mapping framework integrating optics, geometry, and semantics. OmniMap incrementally maintains an open-vocabulary instance-level voxel representation and a 3DGS (3D Gaussian Splatting) representation, from which color and geometric meshes are derived. OmniMap supports multi-modal rendering (RGB / depth / normal / instance), and achieves state-of-the-art performance in rendering fidelity, mesh quality, and semantic understanding. This holistic framework enables versatile support for a wide range of downstream applications. Abstract--Robotic systems demand accurate and comprehensive 3D environment perception, requiring simultaneous capture of photo-realistic appearance (optical), precise layout shape (geometric), and open-vocabulary scene understanding (semantic). Existing methods typically achieve only partial fulfillment of these requirements while exhibiting optical blurring, geometric irregularities, and semantic ambiguities. T o address these challenges, we propose OmniMap. Overall, OmniMap represents the first online mapping framework that simultaneously captures optical, geometric, and semantic scene attributes while maintaining real-time performance and model compactness. This work is supported by the National Natural Science Foundation of China under Grant 92370203, 62473050, 62233002, Beijing Natural Science Foundation Undergraduate Research Program QY24180. Mengyin Fu is with the School of Automation, Beijing Institute of Technology, Beijing 100081, China, and the School of Automation, Nanjing University of Science and Technology, Nanjing 210018, China (e-mail: fumy@bit.edu.cn). The project page of OmniMap is available at https://omni-map.github.io/. At the implementation level, OmniMap identifies key challenges across different modalities and introduces several innovations: adaptive camera modeling for motion blur and exposure compensation, hybrid incremental representation with normal constraints, and probabilistic fusion for robust instance-level understanding. Extensive experiments show OmniMap's superior performance in rendering fidelity, geometric accuracy, and zero-shot semantic segmentation compared to state-of-the-art methods across diverse scenes. The framework's versatility is further evidenced through a variety of downstream applications, including multi-domain scene Q&A, interactive editing, perception-guided manipulation, and map-assisted navigation. The quality of a robot's 3D environmental representation, measured by its accuracy and dimensionality, fundamentally impacts the robot's task operational performance and execution capabilities.

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and port-Hamiltonian systems might share the same initial total energy of a closed system, it is challenging for a single Hamiltonian network model to capture the distinctive and varying motion dynamics and physics of a phase space, from sampled observational phase space trajectories. To address this complicated Hamiltonian manifold learning challenge, we extend sparse symplectic, random Fourier Gaussian processes learning with predictive successive numerical estimations of the Hamiltonian landscape, using a generalized form of state and conjugate momentum Hamiltonian dynamics, appropriate to different classes of conservative, dissipative and port-Hamiltonian physical systems. In addition to the kernelized evidence lower bound (ELBO) loss for data fidelity, we incorporate stability and conservation constraints as additional hyper-parameter balanced loss terms to regularize the model's multi-gradients, enforcing physics correctness for improved prediction accuracy with bounded uncertainty.

Abstract--Controllable Singing V oice Synthesis (SVS) aims to generate expressive singing voices reflecting user intent. While recent SVS systems achieve high audio quality, most rely on probabilistic modeling, limiting precise control over attributes such as dynamics. We address this by focusing on dynamic control--temporal loudness variation essential for musical expressiveness--and explicitly condition the SVS model on energy sequences extracted from ground-truth spectrograms, reducing annotation costs and improving controllability. We also propose a phoneme-level energy sequence for user-friendly control. T o the best of our knowledge, this is the first attempt enabling user-driven dynamics control in SVS. Experiments show our method achieves over 50% reduction in mean absolute error of energy sequences for phoneme-level inputs compared to baseline and energy-predictor models, without compromising synthesis quality.

Multi-criteria decision-making methods provide decision-makers with appropriate tools to make better decisions in uncertain, complex, and conflicting situations. Fuzzy set theory primarily deals with the uncertainty inherent in human thoughts and perceptions and attempts to quantify this uncertainty. Fuzzy logic and fuzzy set theory are utilized with multi-criteria decision-making methods because they effectively handle uncertainty and fuzziness in decision-makers' judgments, allowing for verbal judgments of the problem. This study utilizes the Fermatean fuzzy environment, a generalization of fuzzy sets. An optimization model based on the deviation maximization method is proposed to determine partially known feature weights. This method is combined with interval-valued Fermatean fuzzy sets. The proposed method was applied to the problem of selecting renewable energy sources. The reason for choosing renewable energy sources is that meeting energy needs from renewable sources, balancing carbon emissions, and mitigating the effects of global climate change are among the most critical issues of the recent period. Even though selecting renewable energy sources is a technical issue, the managerial and political implications of this issue are also important, and are discussed in this study.