HelixFold-Single: MSA-free Protein Structure Prediction by Using Protein Language Model as an Alternative

AI-based protein structure prediction pipelines, such as AlphaFold2, have achieved near-experimental accuracy. These advanced pipelines mainly rely on Multiple Sequence Alignments (MSAs) as inputs to learn the co-evolution information from the homologous sequences. Nonetheless, searching MSAs from protein databases is time-consuming, usually taking dozens of minutes. Consequently, we attempt to explore the limits of fast protein structure prediction by using only primary sequences of proteins. HelixFold-Single is proposed to combine a large-scale protein language model with the superior geometric learning capability of AlphaFold2. Our proposed method, HelixFold-Single, first pre-trains a large-scale protein language model (PLM) with thousands of millions of primary sequences utilizing the self-supervised learning paradigm, which will be used as an alternative to MSAs for learning the co-evolution information. Then, by combining the pre-trained PLM and the essential components of AlphaFold2, we obtain an end-to-end differentiable model to predict the 3D coordinates of atoms from only the primary sequence. HelixFold-Single is validated in datasets CASP14 and CAMEO, achieving competitive accuracy with the MSA-based methods on the targets with large homologous families. Furthermore, HelixFold-Single consumes much less time than the mainstream pipelines for protein structure prediction, demonstrating its potential in tasks requiring many predictions. The code of HelixFold-Single is available at https://github.com/PaddlePaddle/PaddleHelix/tree/dev/apps/protein_folding/helixfold-single, and we also provide stable web services on https://paddlehelix.baidu.com/app/drug/protein-single/forecast

ObjSim: Lightweight Automatic Patch Prioritization via Object Similarity

In the context of test case based automatic program repair (APR), patches that pass all the test cases but fail to fix the bug are called overfitted patches. Currently, patches generated by APR tools get inspected manually by the users to find and adopt genuine fixes. Being a laborious activity hindering widespread adoption of APR, automatic identification of overfitted patches has lately been the topic of active research. This paper presents engineering details of ObjSim: a fully automatic, lightweight similarity-based patch prioritization tool for JVM-based languages. The tool works by comparing the system state at the exit point(s) of patched method before and after patching and prioritizing patches that result in state that is more similar to that of original, unpatched version on passing tests while less similar on failing ones. Our experiments with patches generated by the recent APR tool PraPR for fixable bugs from Defects4J v1.4.0 show that ObjSim prioritizes 16.67% more genuine fixes in top-1 place. A demo video of the tool is located at https://bit.ly/2K8gnYV.Comment: Proceedings of the 29th ACM SIGSOFT International Symposium on Software Testing and Analysis (ISSTA '20), July 18--22, 2020, Virtual Event, US

On Exact Poisson Structures

1991 Mathematics Subject Classification. 53D17, 37K10, 70G60, 70G45, 70G65.By studying the exactness of multi-linear vectors on an orientable smooth manifold M, we give some characterizations to exact Poisson structures defi ned on M and study general properties of these structures. Following recent works [12, 13, 15], we will pay particular attention to the classification of some special classes of exact Poisson structures such as Jacobian and quasihomogeneous Poisson structures. A characterization of exact Poisson structures which are invariant under the flow of a class of completely integrable systems will also be given.The rst author was partially supported by NSF grant DMS0204119. The second author is partially supported by NSFC grant 10231020 and Shuguang plan of Shanghai

Planar Analytic Nilpotent Germs Via Analytic First Integrals

1991 Mathematics Subject Classification. Primary: 34A25, 34A34, 37C10.We generalize the results of [6] by giving necessary and sufficient conditions for the planar analytic nilpotent germs to have an analytic first integral in (R[2], 0). The proof of our main result is based on a new method to compute the analytic first integrals of the nilpotent germs, the use of the weight homogeneous polynomials, and the method of characteristic curve for solving linear partial differential equations. Applications of our results to the Kukles-like cubic system are considered.The rst author is partially supported by NSF grant DMS0204119 and the second author is partially supported by NSFC grant 10231020 and Shuguang plan of Shanghai. This work is partially done when the second author was visiting the School of Mathematics and the Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology

First Integrals and Normal Forms for Germs of Analytic Vector Fields

1991 Mathematics Subject Classification. 34C20, 34K17, 34M35.For a germ of analytic vector fields, the existence of first integrals, resonance and the convergence of normalization transforming the vector field to a normal form are closely related. In this paper we first provide a link between the number of first integrals and the resonant relations for a quasi-periodic vector field, which generalizes one of the Poincaré’s classical results [18] on autonomous systems and Theorem 5 of [14] on periodic systems. Then in the space of analytic autonomous systems in C[2n] with exactly n resonances and n functionally independent first integrals, our results are related to the convergence and generic divergence of the normalizations. Lastly for a planar Hamiltonian system it is well known that the system has an isochronous center if and only if it can be linearizable in a neighborhood of the center. Using the Euler-Lagrange equation we provide a new approach to its proof.The second author was partially supported by NSF grant DMS0204119. The third author is partially supported by NSFC grant 10231020, Shuguang plan of Shanghai grant 03SG10 and NCET

FIRST INTEGRALS AND NORMAL FORMS FOR GERMS OF ANALYTIC VECTOR FIELDS

Abstract. For a germ of analytic vector fields, the existence of first integrals, resonance and the convergence of normalization transforming the vector field to a normal form are closely related. In this paper we first provide a link between the number of first integrals and the resonant relations for a quasi-periodic vector field, which generalizes one of the Poincaré’s classical results [18] on autonomous systems and Theorem 5 of [14] on periodic systems. Then in the space of analytic autonomous systems in C 2n with exactly n resonances and n functionally independent first integrals, our results are related to the convergence and generic divergence of the normalizations. Lastly for a planar Hamiltonian system it is well known that the system has an isochronous center if and only if it can be linearizable in a neighborhood of the center. Using the Euler-Lagrange equation we provide a new approach to its proof. 1. Introduction an

Soil Quality Evaluation of Typical Vegetation and Their Response to Precipitation in Loess Hilly and Gully Areas

The selection of suitable tree species and the reasonable allocation of planting areas are important measures for improving soil quality. This study aimed to investigate the characteristics of typical vegetation type soil quality differences and their dominant factors in loess hilly–gully areas after returning farmland to the forest (grassland). The soil quality status and dominant factors of arbors, shrubs and grasslands in the study area were comprehensively analyzed using the soil quality index (SQI) and structural equation modeling (SEM). The results showed the following: (1) In the study area, the shrub forest had a high capacity for air permeability, water retention and nitrogen fixation. (2) The soil quality of the three vegetation types improved with increasing precipitation, and the soil quality indicator of shrubs was the highest, indicating a better soil quality improvement. However, the soil quality of the arbors and grasslands showed a greater percentage increase. In the precipitation range of 400–410 mm, the soil quality of shrub forests was significantly higher than that of arbors and grasslands. (3) Structural equation modeling analysis indicated that precipitation, vegetation and soil factors are closely related to soil quality. Further analysis showed that soil bulk density, porosity, capillary water-holding capacity, soil organic carbon and total phosphorus were the dominant factors affecting the soil quality in the study area. The purpose of this study was to evaluate quantitatively the soil quality after different vegetation types under different precipitation gradients, to clarify the variation trend of soil quality at different vegetation types with different precipitation gradients and to provide a scientific basis and data support for the quantitative evaluation of vegetation restoration and selection of tree species and vegetation configuration within different precipitation gradients in loess hilly and gully regions in the future