We consider the problem of finding the shortest possible period for an exactly periodic solution to some given autonomous ordinary differential equation. We show that, given a pair of Lyapunov-like observable functions defined over the state space of the corresponding dynamical system and satisfying a certain pointwise inequality, we can obtain a global lower bound for such periods. We give a method valid for the case of bounding the period of only those solutions which are invariant under a symmetry transformation, as well as bounds for general periodic orbits. If the governing equations are polynomial in the state variables, we can use semidefinite programming to find such auxiliary functions computationally, and thus compute lower bounds which can be rigorously validated using rational arithmetic. We apply our method to the Lorenz and Henon-Heiles systems. For both systems we are able to give validated bounds which are sharp to several decimal places.

MRI synthesis promises to mitigate the challenge of missing MRI modality in clinical practice. Diffusion model has emerged as an effective technique for image synthesis by modelling complex and variable data distributions. However, most diffusion-based MRI synthesis models are using a single modality. As they operate in the original image domain, they are memory-intensive and less feasible for multi-modal synthesis. Moreover, they often fail to preserve the anatomical structure in MRI. Further, balancing the multiple conditions from multi-modal MRI inputs is crucial for multi-modal synthesis. Here, we propose the first diffusion-based multi-modality MRI synthesis model, namely Conditioned Latent Diffusion Model (CoLa-Diff). To reduce memory consumption, we design CoLa-Diff to operate in the latent space. We propose a novel network architecture, e.g., similar cooperative filtering, to solve the possible compression and noise in latent space. To better maintain the anatomical structure, brain region masks are introduced as the priors of density distributions to guide diffusion process. We further present auto-weight adaptation to employ multi-modal information effectively. Our experiments demonstrate that CoLa-Diff outperforms other state-of-the-art MRI synthesis methods, promising to serve as an effective tool for multi-modal MRI synthesis.

Two approaches are presented for computing upper bounds on Lyapunov exponents and their sums, and on Lyapunov dimension, among all trajectories of a dynamical system governed by ordinary differential equations. The first approach expresses a sum of Lyapunov exponents as a time average in an augmented dynamical system and then applies methods for bounding time averages. This generalizes the work of Oeri & Goluskin (Nonlinearity 36:5378-5400, 2023), who bounded the single leading Lyapunov exponent. The second approach considers a different augmented dynamical system, where bounds on sums of Lyapunov exponents are implied by stability of certain sets, and such stability is verified using Lyapunov function methods. Both of our approaches also can be adapted to directly compute bounds on Lyapunov dimension, which in turn implies bounds on the fractal dimension of a global attractor. For systems of ordinary differential equations with polynomial right-hand sides, all of our bounding formulations lead to polynomial optimization problems with sum-of-squares constraints. These sum-of-squares problems can be solved computationally for any particular system to yield numerical bounds, provided the number of variables and degree of polynomials is not prohibitive. Most of our upper bounds are proven to be sharp under relatively weak assumptions. In the case of the polynomial optimization problems, sharpness means that upper bounds converge to the exact values as polynomial degrees are raised. Computational examples demonstrate upper bounds that are sharp to several digits, including for a six-dimensional dynamical system where sums of Lyapunov exponents are maximized on periodic orbits.

The Segment Anything Model (SAM) has revolutionized natural image segmentation, nevertheless, its performance on underwater images is still restricted. This work presents AquaSAM, the first attempt to extend the success of SAM on underwater images with the purpose of creating a versatile method for the segmentation of various underwater targets. To achieve this, we begin by classifying and extracting various labels automatically in SUIM dataset. Subsequently, we develop a straightforward fine-tuning method to adapt SAM to general foreground underwater image segmentation. Through extensive experiments involving eight segmentation tasks like human divers, we demonstrate that AquaSAM outperforms the default SAM model especially at hard tasks like coral reefs. AquaSAM achieves an average Dice Similarity Coefficient (DSC) of 7.13 (%) improvement and an average of 8.27 (%) on mIoU improvement in underwater segmentation tasks.

Atomic-level simulations are widely used to study biomolecules and their dynamics. A common goal in such studies is to compare simulations of a molecular system under several conditions -- for example, with various mutations or bound ligands -- in order to identify differences between the molecular conformations adopted under these conditions. However, the large amount of data produced by simulations of ever larger and more complex systems often renders it difficult to identify the structural features that are relevant for a particular biochemical phenomenon. We present a flexible software package named PENSA that enables a comprehensive and thorough investigation into biomolecular conformational ensembles. It provides featurizations and feature transformations that allow for a complete representation of biomolecules like proteins and nucleic acids, including water and ion binding sites, thus avoiding bias that would come with manual feature selection. PENSA implements methods to systematically compare the distributions of molecular features across ensembles to find the significant differences between them and identify regions of interest. It also includes a novel approach to quantify the state-specific information between two regions of a biomolecule, which allows, e.g., tracing information flow to identify allosteric pathways. PENSA also comes with convenient tools for loading data and visualizing results, making them quick to process and easy to interpret. PENSA is an open-source Python library maintained at this https URL along with an example workflow and a tutorial. We demonstrate its usefulness in real-world examples by showing how it helps to determine molecular mechanisms efficiently.

Multi-contrast magnetic resonance imaging (MRI) is the most common management tool used to characterize neurological disorders based on brain tissue contrasts. However, acquiring high-resolution MRI scans is time-consuming and infeasible under specific conditions. Hence, multi-contrast super-resolution methods have been developed to improve the quality of low-resolution contrasts by leveraging complementary information from multi-contrast MRI. Current deep learning-based super-resolution methods have limitations in estimating restoration uncertainty and avoiding mode collapse. Although the diffusion model has emerged as a promising approach for image enhancement, capturing complex interactions between multiple conditions introduced by multi-contrast MRI super-resolution remains a challenge for clinical applications. In this paper, we propose a disentangled conditional diffusion model, DisC-Diff, for multi-contrast brain MRI super-resolution. It utilizes the sampling-based generation and simple objective function of diffusion models to estimate uncertainty in restorations effectively and ensure a stable optimization process. Moreover, DisC-Diff leverages a disentangled multi-stream network to fully exploit complementary information from multi-contrast MRI, improving model interpretation under multiple conditions of multi-contrast inputs. We validated the effectiveness of DisC-Diff on two datasets: the IXI dataset, which contains 578 normal brains, and a clinical dataset with 316 pathological brains. Our experimental results demonstrate that DisC-Diff outperforms other state-of-the-art methods both quantitatively and visually.

Objective: Cone-beam computed tomography (CBCT) provides a low-dose imaging alternative to conventional CT, but suffers from noise, scatter, and artifacts that degrade image quality. Synthetic CT (sCT) aims to translate CBCT to high-quality CT-like images for improved anatomical accuracy and dosimetric precision. Although deep learning approaches have shown promise, they often face limitations in generalizability and detail preservation. Conditional diffusion models (CDMs), with their iterative refinement process, offers a novel solution. This review systematically examines the use of CDMs for CBCT-to-sCT synthesis. Methods: A systematic search was conducted in Web of Science, Scopus, and Google Scholar for studies published between 2013 and 2024. Inclusion criteria targeted works employing conditional diffusion models specifically for sCT generation. Eleven relevant studies were identified and analyzed to address three questions: (1) What conditional diffusion methods are used? (2) How do they compare to conventional deep learning in accuracy? (3) What are their clinical implications? Results: CDMs incorporating anatomical priors and spatial-frequency features demonstrated improved structural preservation and noise robustness. Energy-guided and hybrid latent models enabled enhanced dosimetric accuracy and personalized image synthesis. Across studies, CDMs consistently outperformed traditional deep learning models in noise suppression and artefact reduction, especially in challenging cases like lung imaging and dual-energy CT. Conclusion: Conditional diffusion models show strong potential for generalized, accurate sCT generation from CBCT. However, clinical adoption remains limited. Future work should focus on scalability, real-time inference, and integration with multi-modal imaging to enhance clinical relevance.

An accurate computational model for image quality assessment (IQA) benefits many vision applications, such as image filtering, image processing, and image generation. Although the study of face images is an important subfield in computer vision research, the lack of face IQA data and models limits the precision of current IQA metrics on face image processing tasks such as face superresolution, face enhancement, and face editing. To narrow this gap, in this paper, we first introduce the largest annotated IQA database developed to date, which contains 20,000 human faces -- an order of magnitude larger than all existing rated datasets of faces -- of diverse individuals in highly varied circumstances. Based on the database, we further propose a novel deep learning model to accurately predict face image quality, which, for the first time, explores the use of generative priors for IQA. By taking advantage of rich statistics encoded in well pretrained off-the-shelf generative models, we obtain generative prior information and use it as latent references to facilitate blind IQA. The experimental results demonstrate both the value of the proposed dataset for face IQA and the superior performance of the proposed model.

Novel view synthesis in 360$^\circ$ scenes from extremely sparse input views is essential for applications like virtual reality and augmented reality. This paper presents a novel framework for novel view synthesis in extremely sparse-view cases. As typical structure-from-motion methods are unable to estimate camera poses in extremely sparse-view cases, we apply DUSt3R to estimate camera poses and generate a dense point cloud. Using the poses of estimated cameras, we densely sample additional views from the upper hemisphere space of the scenes, from which we render synthetic images together with the point cloud. Training 3D Gaussian Splatting model on a combination of reference images from sparse views and densely sampled synthetic images allows a larger scene coverage in 3D space, addressing the overfitting challenge due to the limited input in sparse-view cases. Retraining a diffusion-based image enhancement model on our created dataset, we further improve the quality of the point-cloud-rendered images by removing artifacts. We compare our framework with benchmark methods in cases of only four input views, demonstrating significant improvement in novel view synthesis under extremely sparse-view conditions for 360$^\circ$ scenes.

Spatial transcriptomics (ST) reveals spatial heterogeneity of gene expression, yet its resolution is limited by current platforms. Recent methods enhance resolution via H&E-stained histology, but three major challenges persist: (1) isolating expression-relevant features from visually complex H&E images; (2) achieving spatially precise multimodal alignment in diffusion-based frameworks; and (3) modeling gene-specific variation across expression channels. We propose HaDM-ST (Histology-assisted Differential Modeling for ST Generation), a high-resolution ST generation framework conditioned on H&E images and low-resolution ST. HaDM-ST includes: (i) a semantic distillation network to extract predictive cues from H&E; (ii) a spatial alignment module enforcing pixel-wise correspondence with low-resolution ST; and (iii) a channel-aware adversarial learner for fine-grained gene-level modeling. Experiments on 200 genes across diverse tissues and species show HaDM-ST consistently outperforms prior methods, enhancing spatial fidelity and gene-level coherence in high-resolution ST predictions.

In this paper, we propose a model-agnostic cost-effective approach to developing bilingual base large language models (LLMs) to support English and any target language. The method includes vocabulary expansion, initialization of new embeddings, model training and evaluation. We performed our experiments with three languages, each using a non-Latin script - Ukrainian, Arabic, and Georgian. Our approach demonstrates improved language performance while reducing computational costs. It mitigates the disproportionate penalization of underrepresented languages, promoting fairness and minimizing adverse phenomena such as code-switching and broken grammar. Additionally, we introduce new metrics to evaluate language quality, revealing that vocabulary size significantly impacts the quality of generated text.

Noninvasive medical neuroimaging has yielded many discoveries about the brain connectivity. Several substantial techniques mapping morphological, structural and functional brain connectivities were developed to create a comprehensive road map of neuronal activities in the human brain -namely brain graph. Relying on its non-Euclidean data type, graph neural network (GNN) provides a clever way of learning the deep graph structure and it is rapidly becoming the state-of-the-art leading to enhanced performance in various network neuroscience tasks. Here we review current GNN-based methods, highlighting the ways that they have been used in several applications related to brain graphs such as missing brain graph synthesis and disease classification. We conclude by charting a path toward a better application of GNN models in network neuroscience field for neurological disorder diagnosis and population graph integration. The list of papers cited in our work is available at this https URL.

Large Language Models (LLMs) have attained human-level accuracy on medical question-answer (QA) benchmarks. However, their limitations in navigating open-ended clinical scenarios have recently been shown, raising concerns about the robustness and generalizability of LLM reasoning across diverse, real-world medical tasks. To probe potential LLM failure modes in clinical problem-solving, we present the medical abstraction and reasoning corpus (M-ARC). M-ARC assesses clinical reasoning through scenarios designed to exploit the Einstellung effect -- the fixation of thought arising from prior experience, targeting LLM inductive biases toward inflexible pattern matching from their training data rather than engaging in flexible reasoning. We find that LLMs, including current state-of-the-art o1 and Gemini models, perform poorly compared to physicians on M-ARC, often demonstrating lack of commonsense medical reasoning and a propensity to hallucinate. In addition, uncertainty estimation analyses indicate that LLMs exhibit overconfidence in their answers, despite their limited accuracy. The failure modes revealed by M-ARC in LLM medical reasoning underscore the need to exercise caution when deploying these models in clinical settings.

Wearable health devices have a strong demand in real-time biomedical signal processing. However traditional methods often require data transmission to centralized processing unit with substantial computational resources after collecting it from edge devices. Neuromorphic computing is an emerging field that seeks to design specialized hardware for computing systems inspired by the structure, function, and dynamics of the human brain, offering significant advantages in latency and power consumption. This paper explores a novel neuromorphic implementation approach for gesture recognition by extracting spatiotemporal spiking information from surface electromyography (sEMG) data in an event-driven manner. At the same time, the network was designed by implementing a simple-structured and hardware-friendly Physical Reservoir Computing (PRC) framework called Rotating Neuron Reservoir (RNR) within the domain of Spiking neural network (SNN). The spiking RNR (sRNR) is promising to pipeline an innovative solution to compact embedded wearable systems, enabling low-latency, real-time processing directly at the sensor level. The proposed system was validated by an open-access large-scale sEMG database and achieved an average classification accuracy of 74.6\% and 80.3\% using a classical machine learning classifier and a delta learning rule algorithm respectively. While the delta learning rule could be fully spiking and implementable on neuromorphic chips, the proposed gesture recognition system demonstrates the potential for near-sensor low-latency processing.

Histopathology remains the gold standard for cancer diagnosis and prognosis. With the advent of transcriptome profiling, multi-modal learning combining transcriptomics with histology offers more comprehensive information. However, existing multi-modal approaches are challenged by intrinsic multi-modal heterogeneity, insufficient multi-scale integration, and reliance on paired data, restricting clinical applicability. To address these challenges, we propose a disentangled multi-modal framework with four contributions: 1) To mitigate multi-modal heterogeneity, we decompose WSIs and transcriptomes into tumor and microenvironment subspaces using a disentangled multi-modal fusion module, and introduce a confidence-guided gradient coordination strategy to balance subspace optimization. 2) To enhance multi-scale integration, we propose an inter-magnification gene-expression consistency strategy that aligns transcriptomic signals across WSI magnifications. 3) To reduce dependency on paired data, we propose a subspace knowledge distillation strategy enabling transcriptome-agnostic inference through a WSI-only student model. 4) To improve inference efficiency, we propose an informative token aggregation module that suppresses WSI redundancy while preserving subspace semantics. Extensive experiments on cancer diagnosis, prognosis, and survival prediction demonstrate our superiority over state-of-the-art methods across multiple settings. Code is available at this https URL.

Some of the major limitations identified in the areas of argument mining, argument generation, and natural language argument analysis are related to the complexity of annotating argumentatively rich data, the limited size of these corpora, and the constraints that represent the different languages and domains in which these data is annotated. To address these limitations, in this paper we present the following contributions: (i) an effective methodology for the automatic generation of natural language arguments in different topics and languages, (ii) the largest publicly available corpus of natural language argumentation schemes, and (iii) a set of solid baselines and fine-tuned models for the automatic identification of argumentation schemes.

The recent advancement of spatial transcriptomics (ST) allows to characterize spatial gene expression within tissue for discovery research. However, current ST platforms suffer from low resolution, hindering in-depth understanding of spatial gene expression. Super-resolution approaches promise to enhance ST maps by integrating histology images with gene expressions of profiled tissue spots. However, current super-resolution methods are limited by restoration uncertainty and mode collapse. Although diffusion models have shown promise in capturing complex interactions between multi-modal conditions, it remains a challenge to integrate histology images and gene expression for super-resolved ST maps. This paper proposes a cross-modal conditional diffusion model for super-resolving ST maps with the guidance of histology images. Specifically, we design a multi-modal disentangling network with cross-modal adaptive modulation to utilize complementary information from histology images and spatial gene expression. Moreover, we propose a dynamic cross-attention modelling strategy to extract hierarchical cell-to-tissue information from histology images. Lastly, we propose a co-expression-based gene-correlation graph network to model the co-expression relationship of multiple genes. Experiments show that our method outperforms other state-of-the-art methods in ST super-resolution on three public datasets.

Macro photography (MP) is a specialized field of photography that captures objects at an extremely close range, revealing tiny details. Although an accurate macro photography image quality assessment (MPIQA) metric can benefit macro photograph capturing, which is vital in some domains such as scientific research and medical applications, the lack of MPIQA data limits the development of MPIQA metrics. To address this limitation, we conducted a large-scale MPIQA study. Specifically, to ensure diversity both in content and quality, we sampled 2,000 MP images from 15,700 MP images, collected from three public image websites. For each MP image, 17 (out of 21 after outlier removal) quality ratings and a detailed quality report of distortion magnitudes, types, and positions are gathered by a lab study. The images, quality ratings, and quality reports form our novel multi-labeled MPIQA database, MMP-2k. Experimental results showed that the state-of-the-art generic IQA metrics underperform on MP images. The database and supplementary materials are available at this https URL