ActTRANS: Functional classification in active transport proteins based on transfer learning and contextual representations

MotivationPrimary and secondary active transport are two types of active transport that involve using energy to move the substances. Active transport mechanisms do use proteins to assist in transport and play essential roles to regulate the traffic of ions or small molecules across a cell membrane against the concentration gradient. In this study, the two main types of proteins involved in such transport are classified from transmembrane transport proteins. We propose a Support Vector Machine (SVM) with contextualized word embeddings from Bidirectional Encoder Representations from Transformers (BERT) to represent protein sequences. BERT is a powerful model in transfer learning, a deep learning language representation model developed by Google and one of the highest performing pre-trained model for Natural Language Processing (NLP) tasks. The idea of transfer learning with pre-trained model from BERT is applied to extract fixed feature vectors from the hidden layers and learn contextual relations between amino acids in the protein sequence. Therefore, the contextualized word representations of proteins are introduced to effectively model complex structures of amino acids in the sequence and the variations of these amino acids in the context. By generating context information, we capture multiple meanings for the same amino acid to reveal the importance of specific residues in the protein sequence.ResultsThe performance of the proposed method is evaluated using five-fold cross-validation and independent test. The proposed method achieves an accuracy of 85.44 %, 88.74 % and 92.84 % for Class-1, Class-2, and Class-3, respectively. Experimental results show that this approach can outperform from other feature extraction methods using context information, effectively classify two types of active transport and improve the overall performance.     

d-Orthogonality via generating functions

In this paper, starting from a suitable generating function of a polynomial set, we show how to decide whether the considered polynomial set is d-orthogonal and, if it is so, how to determine the corresponding d-dimensional functional vector. Then, we apply the obtained results to some known and new d-orthogonal polynomial sets. For the known ones, we give new proofs for some already obtained results.     

A decomposition for invariant tests of uniformity on the sphere

We introduce a -statistic on which can be based a test for uniformity on the sphere. It is a simple function of the geometric mean of distances between points of the sample and consistent against all alternatives. We show that this type of -statistic, whose kernel is invariant by isometries, can be separated into a set of statistics whose limiting random variables are independent. This decomposition is obtained via the so-called canonical decomposition of a group representation. The distribution of the limiting random variables of the components under the null hypothesis is given. We propose an interpretation of Watson type identities between quadratic functionals of Gaussian processes in the light of this decomposition.

     

数论中三个著名级数定理的构造性证明及其推论

运用构造性方法,构建了一个确当的Gauss取整函数,使数论中的三个著名的级数公式,即Leibniz公式、Newton级数公式和Euler级数公式一举获证.并且还给出了四个漂亮的推论.     

Variationally complete representations are polar

A recent result of C. Gorodski and G. Thorbergsson, involving classification, asserts that a variationally complete representation is polar. The aim of this paper is to give a conceptual and very short proof of this fact, which is the converse of a result of Conlon.

     

Arithmetic Consequences of Jacobi's Two-Squares Theorem

There is a well-known formula due to Jacobi for the number r₂(n) of representations of the number n as the sum of two squares. This formula implies that the numbers r₂(n) satisfy elegant arithmetic relations. Conversely, these arithmetic properties essentially imply Jacobi's formula. So it is of interest to give direct proofs of these arithmetic relations, and this we do.     

Application of Analogues of General Kolosov–Muskhelishvili Representations in the Theory of Elastic Mixtures

The existence and uniqueness of a solution of the first, the second and the third plane boundary value problem are considered for the basic homogeneous equations of statics in the theory of elastic mixtures. Applying the general Kolosov–Muskhelishvili representations from [1], these problems can be split and reduced to the first and the second boundary value problem for an elliptic equation which structurally coincides with the equation of statics of an isotropic elastic body.     

New Bosonic Fock Representations of Affine-Virasoro Algebras

New bosonic Fock representations of the Virasoro algebra with nonzero centres are explicitly presented. Based on these, new Fock representations of affine-Virasoro algebras are constructed.