Sheaf Hypergraph Networks

Higher-order relations are widespread in nature, with numerous phenomena involving complex interactions that extend beyond simple pairwise connections. As a result, advancements in higher-order processing can accelerate the growth of various fields requiring structured data. Current approaches typically represent these interactions using hypergraphs. We enhance this representation by introducing cellular sheaves for hypergraphs, a mathematical construction that adds extra structure to the conventional hypergraph while maintaining their local, higherorder connectivity. Drawing inspiration from existing Laplacians in the literature, we develop two unique formulations of sheaf hypergraph Laplacians: linear and non-linear. Our theoretical analysis demonstrates that incorporating sheaves into the hypergraph Laplacian provides a more expressive inductive bias than standard hypergraph diffusion, creating a powerful instrument for effectively modelling complex data structures. We employ these sheaf hypergraph Laplacians to design two categories of models: Sheaf Hypergraph Neural Networks and Sheaf Hypergraph Convolutional Networks. These models generalize classical Hypergraph Networks often found in the literature. Through extensive experimentation, we show that this generalization significantly improves performance, achieving top results on multiple benchmark datasets for hypergraph node classification

Sheaf Neural Networks for Graph-based Recommender Systems

Recent progress in Graph Neural Networks has resulted in wide adoption by many applications, including recommendation systems. The reason for Graph Neural Networks' superiority over other approaches is that many problems in recommendation systems can be naturally modeled as graphs, where nodes can be either users or items and edges represent preference relationships. In current Graph Neural Network approaches, nodes are represented with a static vector learned at training time. This static vector might only be suitable to capture some of the nuances of users or items they define. To overcome this limitation, we propose using a recently proposed model inspired by category theory: Sheaf Neural Networks. Sheaf Neural Networks, and its connected Laplacian, can address the previous problem by associating every node (and edge) with a vector space instead than a single vector. The vector space representation is richer and allows picking the proper representation at inference time. This approach can be generalized for different related tasks on graphs and achieves state-of-the-art performance in terms of F1-Score@N in collaborative filtering and Hits@20 in link prediction. For collaborative filtering, the approach is evaluated on the MovieLens 100K with a 5.1% improvement, on MovieLens 1M with a 5.4% improvement and on Book-Crossing with a 2.8% improvement, while for link prediction on the ogbl-ddi dataset with a 1.6% refinement with respect to the respective baselines.Comment: 9 pages, 7 figure

Renormalized Graph Neural Networks

Graph Neural Networks (GNNs) have become essential for studying complex data, particularly when represented as graphs. Their value is underpinned by their ability to reflect the intricacies of numerous areas, ranging from social to biological networks. GNNs can grapple with non-linear behaviors, emerging patterns, and complex connections; these are also typical characteristics of complex systems. The renormalization group (RG) theory has emerged as the language for studying complex systems. It is recognized as the preferred lens through which to study complex systems, offering a framework that can untangle their intricate dynamics. Despite the clear benefits of integrating RG theory with GNNs, no existing methods have ventured into this promising territory. This paper proposes a new approach that applies RG theory to devise a novel graph rewiring to improve GNNs' performance on graph-related tasks. We support our proposal with extensive experiments on standard benchmarks and baselines. The results demonstrate the effectiveness of our method and its potential to remedy the current limitations of GNNs. Finally, this paper marks the beginning of a new research direction. This path combines the theoretical foundations of RG, the magnifying glass of complex systems, with the structural capabilities of GNNs. By doing so, we aim to enhance the potential of GNNs in modeling and unraveling the complexities inherent in diverse systems

MiRNAs as Potential Prognostic Biomarkers for Metastasis in Thin and Thick Primary Cutaneous Melanomas.

Background/Aim: The identification of novel prognostic biomarkers for melanoma metastasis is essential to improve patient outcomes. To this aim, we characterized miRNA expression profiles in relation to metastasis in melanoma and correlated miRNAs expression with clinicalpathological factors. Materials and Methods: MiR-145-5p, miR-150-5p, miR-182-5p, miR-203-3p, miR-205-5p and miR211-5p expression levels were analyzed in primary cutaneous melanomas, including thin and thick melanomas, and in melanoma metastases by quantitative Real-Time PCR. Results: A significantly lower miR-205-5p expression was found in metastases compared to primary melanomas. Furthermore, a progressive down-regulation of miR-205-5p expression was observed from loco-regional to distant metastasis. Significantly lower miR-145-5p and miR-203-3p expression levels were found in cases with Breslow thickness >1 mm, high Clark level, ulceration and mitotic rate ≥1/mm2. Conclusion: Our findings point to miR-205-5p as potential biomarker of distant metastases and to miR-145-5p and miR-203-3p as markers of aggressiveness in melanoma

Magnetically Activated Stereoscopic Vision System for Laparoendoscopic Single-Site Surgery

n/

Metastases risk in thin cutaneous melanoma: Prognostic value of clinical-pathologic characteristics and mutation profile

Background: A high percentage of patients with thin melanoma (TM), defined as lesions with Breslow thickness ≤1 mm, presents excellent long-term survival, however, some patients develop metastases. Existing prognostic factors cannot reliably differentiate TM patients at risk for metastases. Objective: We aimed at characterizing the clinical-pathologic and mutation profile of metastatic and not-metastatic TM in order to distinguish lesions at risk of metastases. Methods: Clinical-pathologic characteristics were recorded for the TM cases analyzed. We used a Next Generation Sequencing (NGS) multi-gene panel to characterize TM for multiple somatic mutations. Results: A statistically significant association emerged between the presence of metastases and Breslow thickness ≥0.6 mm (p=0.003). None of TM with lymph-node involvement had Breslow thickness < 0.6 mm. Somatic mutations were identified in 19 of 21 TM analyzed (90.5%). No mutations were observed in two not-metastatic cases with the lowest Breslow thickness (≤0.4 mm), whereas mutations in more than one gene were detected in one metastatic case with the highest Breslow thickness (1.00 mm). Conclusion: Our study indicates Breslow thickness ≥0.6 mm as a valid prognostic factor to distinguish TM at risk for metastases

Propuesta de plan estratégico de la empresa Nica Beauty Brand

La investigación presenta un diseño de planificación estratégica que tiene como objetivo determinar las acciones estratégicas que faciliten el cumplimiento de las metas establecidas por la empresa para los próximos cinco años

Effects of excitation light polarization on fluorescence emission in two-photon light-sheet microscopy

Light-sheet microscopy (LSM) is a powerful imaging technique that uses a planar illumination oriented orthogonally to the detection axis. Two-photon (2P) LSM is a variant of LSM that exploits the 2P absorption effect for sample excitation. The light polarization state plays a significant, and often overlooked, role in 2P absorption processes. The scope of this work is to test whether using different polarization states for excitation light can affect the detected signal levels in 2P LSM imaging of typical biological samples with a spatially unordered dye population. Supported by a theoretical model, we compared the fluorescence signals obtained using different polarization states with various fluorophores (fluorescein, EGFP and GCaMP6s) and different samples (liquid solution and fixed or living zebrafish larvae). In all conditions, in agreement with our theoretical expectations, linear polarization oriented parallel to the detection plane provided the largest signal levels, while perpendicularly-oriented polarization gave low fluorescence signal with the biological samples, but a large signal for the fluorescein solution. Finally, circular polarization generally provided lower signal levels. These results highlight the importance of controlling the light polarization state in 2P LSM of biological samples. Furthermore, this characterization represents a useful guide to choose the best light polarization state when maximization of signal levels is needed, e.g. in high-speed 2P LSM.Comment: 16 pages, 4 figures. Version of the manuscript accepted for publication on Biomedical Optics Expres