Random walks on simplicial complexes

The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the consideration of associated simplicial complexes is interesting to understand its shape. Whereas the Laplacian of a graph has a simple probabilistic interpretation as the generator of a continuous time Markov chain on the graph, things are not so direct when considering simplicial complexes. We define here new Markov chains on simplicial complexes. For a given order~$k$, the state space is the set of $k$-cycles that are chains of $k$-simplexes with null boundary. This new framework is a natural generalization of the canonical Markov chains on graphs. We show that the generator of our Markov chain is the upper Laplacian defined in the context of algebraic topology for discrete structure. We establish several key properties of this new process: in particular, when the number of vertices is finite, the Markov chain is positive recurrent. This result is not trivial, since the cycles can loop over themselves an unbounded number of times. We study the diffusive limits when the simplicial complexes under scrutiny are a sequence of ever refining triangulations of the flat torus. Using the analogy between singular and Hodge homologies, we express this limit as valued in the set of currents. The proof of tightness and the identification of the limiting martingale problem make use of the flat norm and carefully controls of the error terms in the convergence of the generator. Uniqueness of the solution to the martingale problem is left open. An application to hole detection is carried.

Automatic Quantification of Serial PET/CT Images for Pediatric Hodgkin Lymphoma Patients Using a Longitudinally-Aware Segmentation Network

$\textbf{Purpose}$: Automatic quantification of longitudinal changes in PET scans for lymphoma patients has proven challenging, as residual disease in interim-therapy scans is often subtle and difficult to detect. Our goal was to develop a longitudinally-aware segmentation network (LAS-Net) that can quantify serial PET/CT images for pediatric Hodgkin lymphoma patients. $\textbf{Materials and Methods}$: This retrospective study included baseline (PET1) and interim (PET2) PET/CT images from 297 patients enrolled in two Children's Oncology Group clinical trials (AHOD1331 and AHOD0831). LAS-Net incorporates longitudinal cross-attention, allowing relevant features from PET1 to inform the analysis of PET2. Model performance was evaluated using Dice coefficients for PET1 and detection F1 scores for PET2. Additionally, we extracted and compared quantitative PET metrics, including metabolic tumor volume (MTV) and total lesion glycolysis (TLG) in PET1, as well as qPET and $\Delta$SUVmax in PET2, against physician measurements. We quantified their agreement using Spearman's $\rho$ correlations and employed bootstrap resampling for statistical analysis. $\textbf{Results}$: LAS-Net detected residual lymphoma in PET2 with an F1 score of 0.606 (precision/recall: 0.615/0.600), outperforming all comparator methods (P<0.01). For baseline segmentation, LAS-Net achieved a mean Dice score of 0.772. In PET quantification, LAS-Net's measurements of qPET, $\Delta$SUVmax, MTV and TLG were strongly correlated with physician measurements, with Spearman's $\rho$ of 0.78, 0.80, 0.93 and 0.96, respectively. The performance remained high, with a slight decrease, in an external testing cohort. $\textbf{Conclusion}$: LAS-Net achieved high performance in quantifying PET metrics across serial scans, highlighting the value of longitudinal awareness in evaluating multi-time-point imaging datasets.

Exploring Physiological Responses in Virtual Reality-based Interventions for Autism Spectrum Disorder: A Data-Driven Investigation

Virtual Reality (VR) has emerged as a promising tool for enhancing social skills and emotional well-being in individuals with Autism Spectrum Disorder (ASD). Through a technical exploration, this study employs a multiplayer serious gaming environment within VR, engaging 34 individuals diagnosed with ASD and employing high-precision biosensors for a comprehensive view of the participants' arousal and responses during the VR sessions. Participants were subjected to a series of 3 virtual scenarios designed in collaboration with stakeholders and clinical experts to promote socio-cognitive skills and emotional regulation in a controlled and structured virtual environment. We combined the framework with wearable non-invasive sensors for bio-signal acquisition, focusing on the collection of heart rate variability, and respiratory patterns to monitor participants behaviors. Further, behavioral assessments were conducted using observation and semi-structured interviews, with the data analyzed in conjunction with physiological measures to identify correlations and explore digital-intervention efficacy. Preliminary analysis revealed significant correlations between physiological responses and behavioral outcomes, indicating the potential of physiological feedback to enhance VR-based interventions for ASD. The study demonstrated the feasibility of using real-time data to adapt virtual scenarios, suggesting a promising avenue to support personalized therapy. The integration of quantitative physiological feedback into digital platforms represents a forward step in the personalized intervention for ASD. By leveraging real-time data to adjust therapeutic content, this approach promises to enhance the efficacy and engagement of digital-based therapies.

Efficient Online Unlearning via Hessian-Free Recollection of Individual Data Statistics

Machine unlearning strives to uphold the data owners' right to be forgotten by enabling models to selectively forget specific data. Recent methods suggest that one approach of data forgetting is by precomputing and storing statistics carrying second-order information to improve computational and memory efficiency. However, they rely on restrictive assumptions and the computation/storage suffer from the curse of model parameter dimensionality, making it challenging to apply to most deep neural networks. In this work, we propose a Hessian-free online unlearning method. We propose to maintain a statistical vector for each data point, computed through affine stochastic recursion approximation of the difference between retrained and learned models. Our proposed algorithm achieves near-instantaneous online unlearning as it only requires a vector addition operation. Based on the strategy that recollecting statistics for forgetting data, the proposed method significantly reduces the unlearning runtime. Experimental studies demonstrate that the proposed scheme surpasses existing results by orders of magnitude in terms of time and memory costs, while also enhancing accuracy.

Protein intrinsic disorder prediction using Attention U-Net and ProtTrans protein language model

The prediction of intrinsic disorder regions has significant implications for understanding protein function, structure, and dynamics. It can help to discover novel functions or protein-protein interactions essential to designing new drugs, therapies, or enzymes. Recently, a new generation of predictors based on protein language models is emerging. These algorithms reach state-of-the-art accuracy without calculating time-consuming multiple sequence alignments (MSAs). The article pre-sents a new protein intrinsic disorder predictor DisorderUnetLM based on the Attention U-Net convolutional neural network using features from the protein language model ProtTrans. DisorderUnetLM shows top results in the direct comparison with flDPnn and IDP-CRF predictors using MSAs and with the SETH predictor using features from the same ProtTrans model. Moreover, among 41 predictors from the latest Critical Assessment of Protein Intrinsic Disorder Prediction (CAID-2) benchmark, it ranks 9th for the Disorder-PDB subset (with ROC-AUC of 0.924) and 1st for the Disorder-NOX subset (with ROC-AUC of 0.844) which confirms its potential to perform well in the upcoming CAID-3 challenge for which Disor-derUnetLM was submitted.

Low-rank Adaptation for Spatio-Temporal Forecasting

Spatio-temporal forecasting is crucial in real-world dynamic systems, predicting future changes using historical data from diverse locations. Existing methods often prioritize the development of intricate neural networks to capture the complex dependencies of the data, yet their accuracy fails to show sustained improvement. Besides, these methods also overlook node heterogeneity, hindering customized prediction modules from handling diverse regional nodes effectively. In this paper, our goal is not to propose a new model but to present a novel low-rank adaptation framework as an off-the-shelf plugin for existing spatial-temporal prediction models, termed ST-LoRA, which alleviates the aforementioned problems through node-level adjustments. Specifically, we first tailor a node adaptive low-rank layer comprising multiple trainable low-rank matrices. Additionally, we devise a multi-layer residual fusion stacking module, injecting the low-rank adapters into predictor modules of various models. Across six real-world traffic datasets and six different types of spatio-temporal prediction models, our approach minimally increases the parameters and training time of the original models by less than 4%, still achieving consistent and sustained performance enhancement.

WaveCatBoost for Probabilistic Forecasting of Regional Air Quality Data

Accurate and reliable air quality forecasting is essential for protecting public health, sustainable development, pollution control, and enhanced urban planning. This letter presents a novel WaveCatBoost architecture designed to forecast the real-time concentrations of air pollutants by combining the maximal overlapping discrete wavelet transform (MODWT) with the CatBoost model. This hybrid approach efficiently transforms time series into high-frequency and low-frequency components, thereby extracting signal from noise and improving prediction accuracy and robustness. Evaluation of two distinct regional datasets, from the Central Air Pollution Control Board (CPCB) sensor network and a low-cost air quality sensor system (LAQS), underscores the superior performance of our proposed methodology in real-time forecasting compared to the state-of-the-art statistical and deep learning architectures. Moreover, we employ a conformal prediction strategy to provide probabilistic bands with our forecasts.

Autonomous Evaluation and Refinement of Digital Agents

We show that domain-general automatic evaluators can significantly improve the performance of agents for web navigation and device control. We experiment with multiple evaluation models that trade off between inference cost, modularity of design, and accuracy. We validate the performance of these models in several popular benchmarks for digital agents, finding between 74.4 and 92.9% agreement with oracle evaluation metrics. Finally, we use these evaluators to improve the performance of existing agents via fine-tuning and inference-time guidance. Without any additional supervision, we improve state-of-the-art performance by 29% on the popular benchmark WebArena, and achieve a 75% relative improvement in a challenging domain transfer scenario.

Samba: Semantic Segmentation of Remotely Sensed Images with State Space Model

High-resolution remotely sensed images pose a challenge for commonly used semantic segmentation methods such as Convolutional Neural Network (CNN) and Vision Transformer (ViT). CNN-based methods struggle with handling such high-resolution images due to their limited receptive field, while ViT faces challenges in handling long sequences. Inspired by Mamba, which adopts a State Space Model (SSM) to efficiently capture global semantic information, we propose a semantic segmentation framework for high-resolution remotely sensed images, named Samba. Samba utilizes an encoder-decoder architecture, with Samba blocks serving as the encoder for efficient multi-level semantic information extraction, and UperNet functioning as the decoder. We evaluate Samba on the LoveDA, ISPRS Vaihingen, and ISPRS Potsdam datasets, comparing its performance against top-performing CNN and ViT methods. The results reveal that Samba achieved unparalleled performance on commonly used remote sensing datasets for semantic segmentation. Our proposed Samba demonstrates for the first time the effectiveness of SSM in semantic segmentation of remotely sensed images, setting a new benchmark in performance for Mamba-based techniques in this specific application. The source code and baseline implementations are available at https://github.com/zhuqinfeng1999/Samba.

TC4D: Trajectory-Conditioned Text-to-4D Generation

Recent techniques for text-to-4D generation synthesize dynamic 3D scenes using supervision from pre-trained text-to-video models. However, existing representations for motion, such as deformation models or time-dependent neural representations, are limited in the amount of motion they can generate-they cannot synthesize motion extending far beyond the bounding box used for volume rendering. The lack of a more flexible motion model contributes to the gap in realism between 4D generation methods and recent, near-photorealistic video generation models. Here, we propose TC4D: trajectory-conditioned text-to-4D generation, which factors motion into global and local components. We represent the global motion of a scene's bounding box using rigid transformation along a trajectory parameterized by a spline. We learn local deformations that conform to the global trajectory using supervision from a text-to-video model. Our approach enables the synthesis of scenes animated along arbitrary trajectories, compositional scene generation, and significant improvements to the realism and amount of generated motion, which we evaluate qualitatively and through a user study. Video results can be viewed on our website: https://sherwinbahmani.github.io/tc4d.