Small Representations Research Articles

DeepRSMA: a cross-fusion based deep learning method for RNA-small molecule binding affinity prediction.

RNA is implicated in numerous aberrant cellular functions and disease progressions, highlighting the crucial importance of RNA-targeted drugs. To accelerate the discovery of such drugs, it is essential to develop an effective computational method for predicting RNA-small molecule affinity (RSMA). Recently, deep learning based computational methods have been promising due to their powerful nonlinear modeling ability. However, the leveraging of advanced deep learning methods to mine the diverse information of RNAs, small molecules and their interaction still remains a great challenge. In this study, we present DeepRSMA, an innovative cross-attention-based deep learning method for RSMA prediction. To effectively capture fine-grained features from RNA and small molecules, we developed nucleotide-level and atomic-level feature extraction modules for RNA and small molecules, respectively. Additionally, we incorporated both sequence and graph views into these modules to capture features from multiple perspectives. Moreover, a Transformer-based cross-fusion module is introduced to learn the general patterns of interactions between RNAs and small molecules. To achieve effective RSMA prediction, we integrated the RNA and small molecule representations from the feature extraction and cross-fusion modules. Our results show that DeepRSMA outperforms baseline methods in multiple test settings. The interpretability analysis and the case study on spinal muscular atrophy (SMA) demonstrate that DeepRSMA has the potential to guide RNA-targeted drug design. The codes and data are publicly available at https://github.com/Hhhzj-7/DeepRSMA. Supplementary data are available at Bioinformatics online.

Word Measures on Unitary Groups: Improved Bounds for Small Representations

Abstract Let $F$ be a free group of rank $r$ and fix some $w\in F$. For any compact group $G$ we can define a measure $\mu _{w,G}$ on $G$ by (Haar-)uniformly sampling $g_{1},...,g_{r}\in G$ and evaluating $w(g_{1},...,g_{r})$. In [23], Magee and Puder study the behavior of the moments of $\mu _{w,U(n)}$ as a function of $n$, establishing a connection between their asymptotic behavior and certain algebraic invariants of $w$, such as its commutator length. We employ geometric insights to refine their analysis, and show that the asymptotic behavior of the moments is also governed by the primitivity rank of $w$. Additionally, we also apply our methods to prove a special case of a conjecture of Hanany and Puder [13, Conjecture 1.13] regarding the asymptotic behavior of expected values of irreducible characters of $U(n)$ under $\mu _{w,U(n)}$.

Real‐time topology optimization via learnable mappings

AbstractIn traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering contexts. This work proposes a multi‐stage machine learning strategy that aims to predict an optimal topology and the related stress fields of interest, either in 2D or 3D, without resorting to any iterative analysis and design process. The overall topology optimization is treated as regression task in a low‐dimensional latent space, that encodes the variability of the target designs. First, a fully‐connected model is employed to surrogate the functional link between the parametric input space characterizing the design problem and the latent space representation of the corresponding optimal topology. The decoder branch of an autoencoder is then exploited to reconstruct the desired optimal topology from its latent representation. The deep learning models are trained on a dataset generated through a standard method of topology optimization implementing the solid isotropic material with penalization, for varying boundary and loading conditions. The underlying hypothesis behind the proposed strategy is that optimal topologies share enough common patterns to be compressed into small latent space representations without significant information loss. Results relevant to a 2D Messerschmitt‐Bölkow‐Blohm beam and a 3D bridge case demonstrate the capabilities of the proposed framework to provide accurate optimal topology predictions in a fraction of a second.

Transfer of Highest Weight Modules and Small Unipotent Representations

Transfer of Highest Weight Modules and Small Unipotent Representations

Finite Multiplicities Beyond Spherical Spaces

Abstract Let $G$ be a real reductive algebraic group, and let $H\subset G$ be an algebraic subgroup. It is known that the action of $G$ on the space of functions on $G/H$ is “tame” if this space is spherical. In particular, the multiplicities of the space ${\mathcal {S}}(G/H)$ of Schwartz functions on $G/H$ are finite in this case. In this paper, we formulate and analyze a generalization of sphericity that implies finite multiplicities in ${\mathcal {S}}(G/H)$ for small enough irreducible representations of $G$.

From intuition to AI: evolution of small molecule representations in drug discovery.

Within drug discovery, the goal of AI scientists and cheminformaticians is to help identify molecular starting points that will develop into safe and efficacious drugs while reducing costs, time and failure rates. To achieve this goal, it is crucial to represent molecules in a digital format that makes them machine-readable and facilitates the accurate prediction of properties that drive decision-making. Over the years, molecular representations have evolved from intuitive and human-readable formats to bespoke numerical descriptors and fingerprints, and now to learned representations that capture patterns and salient features across vast chemical spaces. Among these, sequence-based and graph-based representations of small molecules have become highly popular. However, each approach has strengths and weaknesses across dimensions such as generality, computational cost, inversibility for generative applications and interpretability, which can be critical in informing practitioners' decisions. As the drug discovery landscape evolves, opportunities for innovation continue to emerge. These include the creation of molecular representations for high-value, low-data regimes, the distillation of broader biological and chemical knowledge into novel learned representations and the modeling of up-and-coming therapeutic modalities.

On the spectrum of exterior algebra, and generalized exponents of small representations

We present some results about the irreducible representations appearing in the exterior algebra Λg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \\mathfrak {g}$$\\end{document}, where g\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathfrak {g}$$\\end{document} is a simple Lie algebra over C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {C}}$$\\end{document}. For Lie algebras of type B, C or D we prove that certain irreducible representations, associated to weights characterized in a combinatorial way, appear as irreducible components of Λg\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \\mathfrak {g}$$\\end{document}. Moreover, we propose an analogue of a conjecture of Kostant, about irreducibles appearing in the exterior algebra of the little adjoint representation. Finally, we give some closed expressions, in type B, C and D, for generalized exponents of small representations that are fundamental representations and we propose a generalization of some results of De Concini, Möseneder Frajria, Procesi and Papi about the module of special covariants of adjoint and little adjoint type.

Benchmarking of Small Molecule Feature Representations for hERG, Nav1.5, and Cav1.2 Cardiotoxicity Prediction.

In the field of drug discovery, there is a substantial challenge in seeking out chemical structures that possess desirable pharmacological, toxicological, and pharmacokinetic properties. Complications arise when drugs interfere with the functioning of cardiac ion channels, leading to serious cardiovascular consequences. The discontinuation and removal of numerous approved drugs from the market or at late development stages in the pipeline due to such inhibitory effects further highlight the urgency of addressing this issue. Consequently, the early prediction of potential blockers targeting cardiac ion channels during the drug discovery process is of paramount importance. This study introduces a deep learning framework that computationally determines the cardiotoxicity associated with the voltage-gated potassium channel (hERG), the voltage-gated calcium channel (Cav1.2), and the voltage-gated sodium channel (Nav1.5) for drug candidates. The predictive capabilities of three feature representations─molecular fingerprints, descriptors, and graph-based numerical representations─are rigorously benchmarked. Additionally, a novel training and evaluation data set framework is presented, enabling predictive model training of drug off-target cardiotoxicity using a comprehensive and large curated data set covering these three cardiac ion channels. To facilitate these predictions, a robust and comprehensive small molecule cardiotoxicity prediction tool named CToxPred has been developed. It is made available as open source under the permissive MIT license at https://github.com/issararab/CToxPred.

Left-symmetric superalgebras on special linear Lie superalgebras

In this paper, we study the existence and classification problems of left-symmetric superalgebras on special linear Lie superalgebras sl(m|n) with m≠n. The main three results of this paper are: (i) a complete classification of the left-symmetric superalgebras on sl(2|1), (ii) sl(m|1) does not admit left-symmetric superalgebras for m≥3, and (iii) sl(m+1|m) admits a left-symmetric superalgebra for every m≥1. To prove these results we combine previous results on the existence and classification of left-symmetric algebras on the Lie algebras glm with a detailed analysis of small representations of the Lie superalgebras sl(m|1). We also conjecture that sl(m|n) admits left-symmetric superalgebras if and only if m=n+1.

Multi-label classification of chest X-ray images with pre-trained vision Transformer model

目的 基于计算机的胸腔X线影像疾病检测和分类目前存在误诊率高，准确率低的问题。本文在视觉Transformer（vision Transformer，ViT）预训练模型的基础上，通过迁移学习方法，实现胸腔X线影像辅助诊断，提高诊断准确率和效率。方法 选用带有卷积神经网络（convolutional neural network，CNN）的ViT模型，其在超大规模自然图像数据集中进行了预训练；通过微调模型结构，使用预训练的ViT模型参数初始化主干网络，并迁移至胸腔X线影像数据集中再次训练，实现疾病多标签分类。结果 在IU X-Ray数据集中对ViT迁移学习前、后模型平均AUC（area under ROC curve）得分进行对比分析实验。结果表明，预训练ViT模型平均AUC得分为0.774，与不使用迁移学习相比提升了0.208。并针对模型结构和数据预处理进行了消融实验，对ViT中的注意力机制进行可视化，进一步验证了模型有效性。最后使用Chest X-Ray14和CheXpert数据集训练微调后的ViT模型，平均AUC得分为0.839和0.806，与对比方法相比分别有0.014～0.031的提升。结论 与其他方法相比，ViT模型胸腔X线影像的多标签分类精确度更高，且迁移学习可以在降低训练成本的同时提升ViT模型的分类性能和泛化性。消融实验与模型可视化表明，包含CNN结构的ViT模型能重点关注有意义的区域，高效获取胸腔X线影像的视觉特征。;Objective The chest X-ray-relevant screening and diagnostic method is essential for radiology nowadays. Most of chest X-ray images interpretation is still restricted by clinical experience and challenged for misdiagnose and missed diagnoses. To detect and identify one or more potential diseases in images automatically，it is beneficial for improving diagnostic efficiency and accuracy using computer-based technique. Compared to natural images，multiple lesions are challenged to be detected and distinguished accurately in a single image because abnormal areas have a small proportion and complex representations in chest X-ray images. Current convolutional neural network（CNN）based deep learning models have been widely used in the context of medical imaging. The structure of the CNN convolution kernel has sensitive to local detail information，and it is possible to extract richer image features. However，the convolution kernel cannot be used to get global information，and the features-extracted are restricted of redundant information like its relevance of background， muscles，and bones. The model’s performance in multi-label classification tasks are affected to a certain extent. At present，the vision Transformer（ViT）model has achieved its priorities in computer vision-related tasks. The ViT can be used to capture information simultaneously and effectively for multiple regions of the entire image. However，it is required to use large-scale dataset training to achieve good performance. Due to some factors like patient privacy and manual annotate costs，the size of the chest X-ray image data set has been limited. To reduce the model's dependence on data scale and improve the performance of multi-label classification，we develop the CNN-based ViT pre-training model in terms of the transfer learning method for diagnosis-assisted of chest X-ray image and multi-label classification. Method The CNN-based ViT model is pre-trained on a huge scale ground truth dataset，and it is used to obtain the initial parameters of the model. The model structure is fine-tuned according to the features of chest X-ray dataset. A 1×1 convolution layer is used to convert the chest X-ray images channels between 1 to 3. The number of output nodes of the linear layer in the classifier is balanced from 1 000 to the number of chest X-ray classification labels，and the Sigmoid is used as an activation function. The parameters of the backbone network are initialized in terms of the pre-trained ViT model parameters，and it is trained in the chest X-ray dataset after that to complete multi-label classification. The experiment is configured of Python3. 7 and PyTorch1. 8 to construct the model and RTX3090 GPU for training. Stochastic gradient descent（SGD）optimizer，binary cross-entropy（BCE）loss function，an initial learning rate of 1E-3，the cosine annealing learning rate decay are used. For training，each image is scaled to a size of 512×512 pixels，and a 224×224 pixels area and it is then cropped in random as the model input，and data augmentation is performed randomly by some of the flipping，perspective transformation， shearing，translation，zooming，and changing brightness. For testing，the chest X-ray image is scaled to 256×256 pixels and center crop a 224×224 area to input the trained model. Result The experiment is performed on the IU X-Ray，which is a small-scale chest X-ray dataset. This model is evaluated in quantitative using the average of area under ROC curve （AUC）scores across all classification labels. The results show that the average AUC score of the pre-trained ViT model is 0. 774. The accuracy and training efficiency of the non-pre-trained ViT model is dropped significantly. The average AUC score is reached to 0. 566 only，which is 0. 208 lower. In addition，the attention mechanism heat map is generated based on the ViT model，which can strengthen the interpretability of the model. A series of ablation experiments are carried out for data augmentation，model structure，and batch size design. The fine-tuned ViT model is trained on the Chest-Ray14 and CheXpert dataset as well. The average AUC score is reached to 0. 839 and 0. 806，which is optimized by 0. 014 and 0. 031. Conclusion A pre-trained ViT model is used for the multi-label classification of chest X-ray images via transfer learning. The experimental results illustrate that the ViT has its stronger multi-label classification performance in chest Xray images，and its attention mechanism is beneficial for lesions precision-focused like the interior of the chest cavity and the heart. Transfer learning is potential to improve the classification performance and model generalization of the ViT in small-scale datasets，and the training cost is reduced greatly. Ablation experiments demonstrate that the incorporated model of CNN and Transformer has its priority beyond single-structure model. Data enhancement and the batch size cutting can improve the performance of the model，but smaller scale of batch is still interlinked to longer training span. To improve the model's ability，we predict that future research direction can be focused on the extraction for complex disease and highlevel semantic information，such as their small lesions，disease location，and severity.

DrugTax: package for drug taxonomy identification and explainable feature extraction

DrugTax is an easy-to-use Python package for small molecule detailed characterization. It extends a previously explored chemical taxonomy making it ready-to-use in any Artificial Intelligence approach. DrugTax leverages small molecule representations as input in one of their most accessible and simple forms (SMILES) and allows the simultaneously extraction of taxonomy information and key features for big data algorithm deployment. In addition, it delivers a set of tools for bulk analysis and visualization that can also be used for chemical space representation and molecule similarity assessment. DrugTax is a valuable tool for chemoinformatic processing and can be easily integrated in drug discovery pipelines. DrugTax can be effortlessly installed via PyPI (https://pypi.org/project/DrugTax/) or GitHub (https://github.com/MoreiraLAB/DrugTax).Graphical

Deep attentive convolutional neural network for automatic grading of imbalanced diabetic retinopathy in retinal fundus images.

Automated fine-grained diabetic retinopathy (DR) grading was of great significance for assisting ophthalmologists in monitoring DR and designing tailored treatments for patients. Nevertheless, it is a challenging task as a result of high intra-class variations, high inter-class similarities, small lesions, and imbalanced data distributions. The pivotal factor for the success in fine-grained DR grading is to discern more subtle associated lesion features, such as microaneurysms (MA), Hemorrhages (HM), soft exudates (SE), and hard exudates (HE). In this paper, we constructed a simple yet effective deep attentive convolutional neural network (DACNN) for DR grading and lesion discovery with only image-wise supervision. Designed as a top-down architecture, our model incorporated stochastic atrous spatial pyramid pooling (sASPP), global attention mechanism (GAM), category attention mechanism (CAM), and learnable connected module (LCM) to better extract lesion-related features and maximize the DR grading performance. To be concrete, we devised sASPP combining randomness with atrous spatial pyramid pooling (ASPP) to accommodate the various scales of the lesions and struggle against the co-adaptation of multiple atrous convolutions. Then, GAM was introduced to extract class-agnostic global attention feature details, whilst CAM was explored for seeking class-specific distinctive region-level lesion feature information and regarding each DR severity grade in an equal way, which tackled the problem of imbalance DR data distributions. Further, the LCM was designed to automatically and adaptively search the optimal connections among layers for better extracting detailed small lesion feature representations. The proposed approach obtained high accuracy of 88.0% and kappa score of 88.6% for multi-class DR grading task on the EyePACS dataset, respectively, while 98.5% AUC, 93.8% accuracy, 87.9% kappa, 90.7% recall, 94.6% precision, and 92.6% F1-score for referral and non-referral classification on the Messidor dataset. Extensive experimental results on three challenging benchmarks demonstrated that the proposed approach achieved competitive performance in DR grading and lesion discovery using retinal fundus images compared with existing cutting-edge methods, and had good generalization capacity for unseen DR datasets. These promising results highlighted its potential as an efficient and reliable tool to assist ophthalmologists in large-scale DR screening.

Multiplicity in restricting small representations

We give a geometric criterion for the bounded multiplicity property of “small” infinite-dimensional representations of real reductive Lie groups in both induction and restrictions. In particular, for a reductive symmetric pair $(G,H)$, we determine the reductive subgroups $G'$ having the property that any irreducible $H$-distinguished admissible representations of $G$ are of bounded multiplicity when restricted to $G'$.

Lift of the Trivial Representation to a Nonlinear Double Cover

Abstract Let $\widetilde G$ be the nonlinear double cover of the real points of a connected, simply connected, semisimple complex group. In [16], we introduce a set of genuine small representations of $\widetilde G$ with infinitesimal character $\lambda $, denoted $\prod _\lambda ^s (\widetilde G)$. In this paper, we show that $\prod _{\rho /2} ^s (\widetilde G)$ is precisely the set of genuine irreducible representations arising from the Kazhdan–Patterson lifting of the trivial representation, when $\widetilde G$ is simply laced and split.

Review of: <em>A Geography of the Hutterites of North America</em>—Simon M. Evans

Imagine a complex academic book without a subtitle: straightforward, lucid, accessible. These qualities describe Simon Evans’ final word on Hutterites of the western plains of Canada and the United States. It’s an historical geography, distinctive from the more numerous social scientific studies of the Hutterites. It methodically traces the dispersion of an 1870s Dakota settlement into Manitoba and Alberta during World War I, and then into Montana and Saskatchewan after World War II, with small representations in Washington State and British Columbia. Along the way, Evans deepens his analysis and interlaces theological consideration, demographic change, ecological intrusion, marketplace engagement, political interaction, gender relations, and internecine differences with the geographer’s craft, spatial arrangement. Indeed, these various intersections make for a richly textured historical geography that no subtitle could capture. And they rely on Evans’ own expansive on-colony ethnography, rich map collections, and broad engagement with a multi-disciplinary secondary literature. In the process Evans gives us a fresh look at the Hutterites and produces a historical geography that does much more than document the Hutterite diaspora in the North American grassland. [First paragraph.]

Moduli-dependent KK towers and the swampland distance conjecture on the quintic Calabi-Yau manifold

We use numerical methods to obtain moduli-dependent Calabi-Yau metrics and from them the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their K\"ahler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods and compare the results. Finally, we fit the moduli-dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order one, as suggested by the swampland distance conjecture. We also observe level-crossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations.

Lumbar Canal Stenosis: Pre and Post Decompression laminectomy Outcomes in a Single Neurosurgery Private Practice

Lumbar canal stenosis (LCS) or Lumbar Spinal Stenosis (LSS) is the most common degenerative condition affecting older adults. The clinical presentation of LCS includes lower back pain, radiating pain, tingling sensation, and numbness in the lower limbs, as well as nocturnal leg cramps, and bladder dysfunction due to neurological compression. Laminectomy is one of the most common procedures performed for the treatment of LCS. This study aimed to examine the pre-surgical presentations and post-surgical outcomes based on the available clinical records from a single neurosurgeon private practice based in Melbourne, Victoria, Australia. The clinical records of 166 patients were extracted and reviewed for clinical presentation notes, surgical notes, post-surgery follow-up letters between 2010 and 2019. Records without follow-up notes were excluded. The presurgical presentation symptoms included lower back pain, weakness, neurogenic claudication, pins and needles, and sensory and motor deficits. Post-surgical outcomes were evaluated based on the 1-month, 3-month, and 1-year follow up based on the notes and letters. Many patients mentioned significant improvement in symptoms immediately after the decompressive laminectomy. Descriptive analysis was performed; the results have been presented as percentages and charts. Post- laminectomy results reported that 87% improvement in back pain and 85% people reported improvements in neurogenic claudication. This study suggested that decompressive laminectomy was effective in the management of LCS. However, further studies are required due to the limitations, such as small population size, data availability, multiple re-presentations, and lack of proper follow-up.

Heuristic Methods for Updating Small World Representations in Strategic Situations of Knightian Uncertainty

Recent studies on the construction and use of “small world representations” in strategic decision-making under Knightian uncertainty say little about how such representations should be updated over...

Hyperoperations defined on sets of S -helix matrices

A hyperproduct on non-square ordinary matrices can be defined by using the helix-hyperoperation. Therefore, the helix-hyperoperation (abbreviated hope ) is based on a classical operation and was introduced in order to overcome the non-existing cases. We study the helixhyperstructures on the special type of matrices, the Shelix matrices, used on the small dimension representations. In this paper, we introduce and focus our study on the class of S-helix matrices called k-overlap helix matrices. The reason is that their hyper-vector spaces can represent n-dimensional spaces which have independent both, single valued dimensions and multivalued dimensions.

Using small world toys for research: a method for gaining insight into children’s lived experiences of school

ABSTRACT The importance of children’s perspectives is now well-established and there has been much attention afforded to appropriate methods for listening to children within the research. Whilst language-based research methods, such as interview, remain commonplace, children’s representations are increasingly included as data in educational research. Photographs, drawings and tours have been used alongside the traditional tools of observation and interview to illuminate children’s understanding of their school experiences but more are needed. This paper reports on an addition to this repertoire of tools, small world toys, and finds that valuable insight can be gained through using them as a data collection method. Drawing on research into children’s lived experiences of school, it outlines the affordances and key principles of this method. It argues that capturing the process as well as the outcome is key in using small world toy representations and that using them in collaboration with other methods is needed in order to gain rich, reliable data. It concludes that whilst ethical praxis is key in using any method to research children’s perspectives, crafting new and bespoke methods to more authentically hear and take account of children’s perspectives should be an important and ongoing endeavour of researchers in this field.