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Let A be a Lebesgue measure space. We interpret measures on A×A×R{sup ×} as 'maps' from A to A, which 'spread' A along itself; their Radon-Nikodym derivatives are also spread. We discuss the basic properties of the semigroup of such maps and the action of this semigroup on the spaces L{sup p}(A). Bibliography: 26 titles.
The paper is concerned with a nonlinear system of partial differential equations with parameters. This system describes the two-layer quasi-solenoidal Lorenz model for a baroclinic atmosphere on a rotating two-dimensional sphere. The right-hand side of the system is perturbed by white noise. Sufficient conditions on the parameters and the right-hand side are obtained for the existence of a stationary measure. Bibliography: 25 titles.
The distribution of the zeros of the Hermite-Padé polynomials of the first kind for a pair of functions with an arbitrary even number of common branch points lying on the real axis is investigated under the assumption that this pair of functions forms a generalized complex Nikishin system. It is proved (Theorem 1) that the zeros have a limiting distribution, which coincides with the equilibrium measure of a certain compact set having the S-property in a harmonic external field. The existence problem for S-compact sets is solved in Theorem 2. The main idea of the proof of Theorem 1 consists in replacing a vector equilibrium problem in potential theory by a scalar problem with an external field and then using the general Gonchar-Rakhmanov method, which was worked out in the solution of the '1/9'-conjecture. The relation of the result obtained here to some results and conjectures due to Nuttall is discussed. Bibliography: 51 titles.
We use the notions of the Ω-function and functions suitable to it, to give a detailed proof of a decomposition theorem for the space of C{sup 1}-smooth skew products of interval maps whose quotient maps have complicated dynamics and satisfy the additional condition of Ω-stability with respect to the C{sup 1}-norm. In our theorem, the space of C{sup 1}-smooth skew products is decomposed into a union of four nonempty, pairwise disjoint subspaces. We give examples of maps contained in each of the four subspaces. Bibliography: 46 titles.
We solve a technical problem related to adeles on an algebraic surface. Given a finite set of natural numbers, one can associate with it an adelic group. We show that this operation commutes with taking intersections if the surface is defined over an uncountable field, and we provide a counterexample otherwise. Bibliography: 12 titles.
The El Soufi-Ilias theorem establishes a connection between minimal submanifolds of spheres and extremal metrics for eigenvalues of the Laplace-Beltrami operator. Recently, this connection was used to provide several explicit examples of extremal metrics. We investigate the properties of these metrics and prove that none of them is maximal. Bibliography: 24 titles.
In this paper, we prove the existence of a large set of Gram points t{sub n} such that the values ζ(0.5+it{sub n}) are 'anomalously' close to zero. A lower bound for the negative 'discrete' moment of the Riemann zeta-function on the critical line is also given. Bibliography: 13 titles.
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.