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We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.
Let G be an arbitrary locally compact Abelian group and let C(G) be the space of all continuous complex-valued functions on G. A closed linear subspace H⊆C(G) is referred to as an invariant subspace if it is invariant with respect to the shifts τ{sub y}:f(x)↦f(xy), y∈G. By definition, an invariant subspace H⊆C(G) admits strict spectral synthesis if H coincides with the closure in C(G) of the linear span of all characters of G belonging to H. We say that strict spectral synthesis holds in the space C(G) on G if every invariant subspace H⊆C(G) admits strict spectral synthesis. An element x of a topological group G is said to be compact if x is contained in some compact subgroup of G. A group G is said to be element-wise compact if all elements of G are compact. The main result of the paper is the proof of the fact that strict spectral synthesis holds in C(G) for a locally compact Abelian group G if and only if G is element-wise compact. Bibliography: 14 titles.
We consider the lattice A(U(X)) of subalgebras of a semifield U(X) of continuous positive functions on an arbitrary topological space X and its sublattice A{sub 1}(U(X)) of subalgebras with unity. The main result of the paper is the proof of the definability of any semifield U(X) both by the lattice A(U(X)) and by its sublattice A{sub 1}(U(X)). Bibliography: 12 titles. (paper)
We calculate the Chern-Simons invariants of twist-knot orbifolds using the Schläfli formula for the generalized Chern-Simons function on the family of twist knot cone-manifold structures. Following the general instruction of Hilden, Lozano, and Montesinos-Amilibia, we here present concrete formulae and calculations. We use the Pythagorean Theorem, which was used by Ham, Mednykh and Petrov, to relate the complex length of the longitude and the complex distance between the two axes fixed by two generators. As an application, we calculate the Chern-Simons invariants of cyclic coverings of the hyperbolic twist-knot orbifolds. We also derive some interesting results. The explicit formulae of the A-polynomials of twist knots are obtained from the complex distance polynomials. Hence the edge polynomials corresponding to the edges of the Newton polygons of the A-polynomials of twist knots can be obtained. In particular, the number of boundary components of every incompressible surface corresponding to slope −4n+2 turns out to be 2. Bibliography: 39 titles. (paper)
Virtual 3-manifolds were introduced by Matveev in 2009 as natural generalizations of classical 3-manifolds. In this paper, we introduce a notion of complexity for a virtual 3-manifold. We investigate the values of the complexity for virtual 3-manifolds presented by special polyhedra with one or two 2-components. On the basis of these results, we establish the exact values of the complexity for a wide class of hyperbolic 3-manifolds with totally geodesic boundary. Bibliography: 24 titles. (paper)
As with all empirical sciences, nuclear physics operates in the virtuous cycle of the scientific method: observations inspire theoretical models; models lead to new predictions; predictions are tested in experiments; experiments lead to new observations; and so on. Evaluating what we are inferring, and how certain we are of it, is key to this process. These requirements, and a general interest in applying novel statistical, mathematical, and computational techniques, led to the formation of a dedicated research community entitled “Information and Statistics in Nuclear Experiment and Theory (ISNET)” (https://isnet-series.github.io/), which now includes more than 300 members. While the community’s interests lean toward nuclear theory, the unifying theme for this group is the inference of knowledge from data.
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Abstract Online, open access databases for biological knowledge serve as central repositories for research communities to store, find and analyze integrated, multi-disciplinary datasets. With increasing volumes, complexity and the need to integrate genomic, transcriptomic, metabolomic, proteomic, phenomic and environmental data, community databases face tremendous challenges in ongoing maintenance, expansion and upgrades. A common infrastructure framework using community standards shared by many databases can reduce development burden, provide interoperability, ensure use of common standards and support long-term sustainability. Tripal is a mature, open source platform built to meet this need. With ongoing improvement since its first release in 2009, Tripal provides full functionality for searching, browsing, loading and curating numerous types of data and is a primary technology powering at least 31 publicly available databases spanning plants, animals and human data, primarily storing genomics, genetics and breeding data. Tripal software development is managed by a shared, inclusive governance structure including both project management and advisory teams. Here, we report on the most important and innovative aspects of Tripal after 11 years development, including integration of diverse types of biological data, successful collaborative projects across member databases, and support for implementing FAIR principles.
Picking protein particles in cryo-electron microscopy (cryo-EM) micrographs is a crucial step in the cryo-EM-based structure determination. However, existing methods trained on a limited amount of cryo-EM data still cannot accurately pick protein particles from noisy cryo-EM images. The general foundational artificial intelligence–based image segmentation model such as Meta’s Segment Anything Model (SAM) cannot segment protein particles well because their training data do not include cryo-EM images. Here, we present a novel approach (CryoSegNet) of integrating an attention-gated U-shape network (U-Net) specially designed and trained for cryo-EM particle picking and the SAM. The U-Net is first trained on a large cryo-EM image dataset and then used to generate input from original cryo-EM images for SAM to make particle pickings. CryoSegNet shows both high precision and recall in segmenting protein particles from cryo-EM micrographs, irrespective of protein type, shape and size. On several independent datasets of various protein types, CryoSegNet outperforms two top machine learning particle pickers crYOLO and Topaz as well as SAM itself. The average resolution of density maps reconstructed from the particles picked by CryoSegNet is 3.33 Å, 7% better than 3.58 Å of Topaz and 14% better than 3.87 Å of crYOLO. It is publicly available at https://github.com/jianlin-cheng/CryoSegNet
Abstract Large language models (LLMs) are sophisticated AI-driven models trained on vast sources of natural language data. They are adept at generating responses that closely mimic human conversational patterns. One of the most notable examples is OpenAI's ChatGPT, which has been extensively used across diverse sectors. Despite their flexibility, a significant challenge arises as most users must transmit their data to the servers of companies operating these models. Utilizing ChatGPT or similar models online may inadvertently expose sensitive information to the risk of data breaches. Therefore, implementing LLMs that are open source and smaller in scale within a secure local network becomes a crucial step for organizations where ensuring data privacy and protection has the highest priority, such as regulatory agencies. As a feasibility evaluation, we implemented a series of open-source LLMs within a regulatory agency’s local network and assessed their performance on specific tasks involving extracting relevant clinical pharmacology information from regulatory drug labels. Our research shows that some models work well in the context of few- or zero-shot learning, achieving performance comparable, or even better than, neural network models that needed thousands of training samples. One of the models was selected to address a real-world issue of finding intrinsic factors that affect drugs' clinical exposure without any training or fine-tuning. In a dataset of over 700 000 sentences, the model showed a 78.5% accuracy rate. Our work pointed to the possibility of implementing open-source LLMs within a secure local network and using these models to perform various natural language processing tasks when large numbers of training examples are unavailable.
Abstract Cryo-electron microscopy (cryo-EM) has revolutionized structural biology by enabling the determination of high-resolution 3-Dimensional (3D) structures of large biological macromolecules. Protein particle picking, the process of identifying individual protein particles in cryo-EM micrographs for building protein structures, has progressed from manual and template-based methods to sophisticated artificial intelligence (AI)-driven approaches in recent years. This review critically examines the evolution and current state of cryo-EM particle picking methods, with an emphasis on the impact of AI. We conducted a comparative evaluation of popular AI-based particle picking methods, using both general machine learning metrics and specific cryo-EM structure determination metrics. This analysis involved constructing the 3D density map from the picked protein particles and assessing the obtained resolution and particle orientation diversity, underscoring the significant impact of AI on cryo-EM particle picking. Despite the advancements, we also identified key obstacles, such as handling complex micrographs with small proteins. The analysis provides insights into the future development of more sophisticated and fully automated AI methods in cryo-EM particle recognition.
Abstract The Maximally Informative Next Experiment or MINE is a new experimental design approach for experiments, such as those in omics, in which the number of effects or parameters p greatly exceeds the number of samples n (p > n). Classical experimental design presumes n > p for inference about parameters and its application to p > n can lead to over-fitting. To overcome p > n, MINE is an ensemble method, which makes predictions about future experiments from an existing ensemble of models consistent with available data in order to select the most informative next experiment. Its advantages are in exploration of the data for new relationships with n < p and being able to integrate smaller and more tractable experiments to replace adaptively one large classic experiment as discoveries are made. Thus, using MINE is model-guided and adaptive over time in a large omics study. Here, MINE is illustrated in two distinct multiyear experiments, one involving genetic networks in Neurospora crassa and a second one involving a genome-wide association study in Sorghum bicolor as a comparison to classic experimental design in an agricultural setting.
To address the need for improved phage annotation tools that scale, we created an automated throughput annotation pipeline: multiple-genome Phage Annotation Toolkit and Evaluator (multiPhATE). multiPhATE is a throughput pipeline driver that invokes an annotation pipeline (PhATE) across a user-specified set of phage genomes. This tool incorporates a de novo phage gene calling algorithm and assigns putative functions to gene calls using protein-, virus- and phage-centric databases. multiPhATE’s modular construction allows the user to implement all or any portion of the analyses by acquiring local instances of the desired databases and specifying the desired analyses in a configuration file. We demonstrate multiPhATE by annotating two newly sequenced Yersinia pestis phage genomes. Within multiPhATE, the PhATE processing pipeline can be readily implemented across multiple processors, making it adaptable for throughput sequencing projects. Software documentation assists the user in configuring the system.
Abstract Camelina is an annual oilseed plant from the Brassicaceae family that is gaining momentum as a biofuel winter cover crop. However, a significant limitation in further enhancing its utility as a producer of oils that can be used as biofuels, jet fuels or bio-based products is the absence of a repository for all the gene expression and regulatory information that is being rapidly generated by the community. Here, we provide CamRegBase (https://camregbase.org/) as a one-stop resource to access Camelina information on gene expression and co-expression, transcription factors, lipid associated genes and genome-wide orthologs in the close-relative reference plant Arabidopsis. We envision this as a resource of curated information for users, as well as a repository of new gene regulation information.
Abstract FatPlants, an open-access, web-based database, consolidates data, annotations, analysis results, and visualizations of lipid-related genes, proteins, and metabolic pathways in plants. Serving as a minable resource, FatPlants offers a user-friendly interface for facilitating studies into the regulation of plant lipid metabolism and supporting breeding efforts aimed at increasing crop oil content. This web resource, developed using data derived from our own research, curated from public resources, and gleaned from academic literature, comprises information on known fatty-acid-related proteins, genes, and pathways in multiple plants, with an emphasis on Glycine max, Arabidopsis thaliana, and Camelina sativa. Furthermore, the platform includes machine-learning based methods and navigation tools designed to aid in characterizing metabolic pathways and protein interactions. Comprehensive gene and protein information cards, a Basic Local Alignment Search Tool search function, similar structure search capacities from AphaFold, and ChatGPT-based query for protein information are additional features. Database URL: https://www.fatplants.net/
Abstract Ontologies are widely used in databases to standardize data, improving data quality, integration, and ease of comparison. Within ontologies tailored to diverse use cases, post-composing user-defined terms reconciles the demands for standardization on the one hand and flexibility on the other. In many instances of Breedbase, a digital ecosystem for plant breeding designed for genomic selection, the goal is to capture phenotypic data using highly curated and rigorous crop ontologies, while adapting to the specific requirements of plant breeders to record data quickly and efficiently. For example, post-composing enables users to tailor ontology terms to suit specific and granular use cases such as repeated measurements on different plant parts and special sample preparation techniques. To achieve this, we have implemented a post-composing tool based on orthogonal ontologies providing users with the ability to introduce additional levels of phenotyping granularity tailored to unique experimental designs. Post-composed terms are designed to be reused by all breeding programs within a Breedbase instance but are not exported to the crop reference ontologies. Breedbase users can post-compose terms across various categories, such as plant anatomy, treatments, temporal events, and breeding cycles, and, as a result, generate highly specific terms for more accurate phenotyping.
The Asian citrus psyllid ( Diaphorina citri Kuwayama) is the insect vector of the bacterium Candidatus Liberibacter asiaticus (CLas), the pathogen associated with citrus Huanglongbing (HLB, citrus greening). HLB threatens citrus production worldwide. Suppression or reduction of the insect vector using chemical insecticides has been the primary method to inhibit the spread of citrus greening disease. Accurate structural and functional annotation of the Asian citrus psyllid genome, as well as a clear understanding of the interactions between the insect and CLas, are required for development of new molecular-based HLB control methods. A draft assembly of the D. citri genome has been generated and annotated with automated pipelines. However, knowledge transfer from well-curated reference genomes such as that of Drosophila melanogaster to newly sequenced ones is challenging due to the complexity and diversity of insect genomes. To identify and improve gene models as potential targets for pest control, we manually curated several gene families with a focus on genes that have key functional roles in D. citri biology and CLas interactions. This community effort produced 530 manually curated gene models across developmental, physiological, RNAi regulatory and immunity-related pathways. As previously shown in the pea aphid, RNAi machinery genes putatively involved in the microRNA pathway have been specifically duplicated. A comprehensive transcriptome enabled us to identify a number of gene families that are either missing or misassembled in the draft genome. In order to develop biocuration as a training experience, we included undergraduate and graduate students from multiple institutions, as well as experienced annotators from the insect genomics research community. The resulting gene set (OGS v1.0) combines both automatically predicted and manually curated gene models.
Transcription factors (TFs) are an important class of regulatory molecules. Despite their importance, only a small number of genes encoding TFs have been characterized in Oryza sativa (rice), often because gene duplication and functional redundancy complicate their analysis. To address this challenge, we developed a web-based tool called the Rice Transcription Factor Phylogenomics Database (RTFDB) and demonstrate its application for predicting TF function. The RTFDB hosts transcriptome and co-expression analyses. Sources include high-throughput data from oligonucleotide microarray (Affymetrix and Agilent) as well as RNA-Seq-based expression profiles. We used the RTFDB to identify tissue-specific and stress-related gene expression. Subsequently, 273 genes preferentially expressed in specific tissues or organs, 455 genes showing a differential expression pattern in response to 4 abiotic stresses, 179 genes responsive to infection of various pathogens and 512 genes showing differential accumulation in response to various hormone treatments were identified through the meta-expression analysis. Pairwise Pearson correlation coefficient analysis between paralogous genes in a phylogenetic tree was used to assess their expression collinearity and thereby provides a hint on their genetic redundancy. Integrating transcriptome with the gene evolutionary information reveals the possible functional redundancy or dominance played by paralog genes in a highly duplicated genome such as rice. With this method, we estimated a predominant role for 83.3% (65/78) of the TF or transcriptional regulator genes that had been characterized via loss-of-function studies. In this regard, the proposed method is applicable for functional studies of other plant species with annotated genome.