Under investigation in this paper is a (3+1)-dimensional nonlinear evolution equation, which was proposed and analyzed to study features and properties of nonlinear dynamics in higher dimensions. ...Using the Hirota bilinear method, we construct a bilinear Bäcklund transformation, which consists of four equations and involves six free parameters. With test function method and symbolic computation, three sets of lump–kink solutions and new types of interaction solutions are derived, and figures are presented to reveal the interaction behaviors. Setting constraints to the new interaction solution via the test function expressed by “polynomial-cos-cosh,” we simulate the periodic interaction phenomenon. Pfaffian solutions to the (3+1)-dimensional nonlinear evolution equation are obtained based on a set of linear partial differential conditions. According to our results, the diversity of solutions to the (3+1)-dimensional nonlinear evolution equation is revealed.
In this paper, we focus on the inverse problem study of nonlinear Schrödinger (NLS) typed equations in optical fiber communicaitons. As an extension of the physics-informed neural network (PINN), ...multi-parallelized PINNs are constructed and trained for the discovery of diverse high-order terms and variable coefficients. We firstly study various constant-coefficient combinations of a generalized high-order NLS typed equation, where the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation and the Kundu-Eckhaus equation are included. With small amount of exact solutions available to us, we predict the value of multiple coefficients under different cases to deduce the undetermined terms of the generalized equation based on the multi-parallelized PINN. Different categories of NLS typed equations are then inferred. In the meantime, high accuracy numerical solutions on localized regions can be accordingly obtained.
The parameter discovery of NLS typed equations with variable coefficients has also been carried out based on the extended network, including analysis on interaction behaviors and the periodic phenomenon of solutions. According to outputs of multi-parallelized PINNs, we compare the numerical solutions and the predicted variable coefficients with exact results. Error analysis are then performed to check the accuracy of prediction, where both the absolute error and the mean squared error are given. Compared with the traditional PINN, our model exerts its state-of-art power in the inverse problem study of nonlinear systems, where different high-order terms and variable-coefficient terms can be clearly predicted while deducing diverse types of localized numerical solutions with lower fitting error and less data consumption. As the self-steepening pulses without self-phase modulation and the Raman effect are closely related to the inferred high-order terms of NLS typed equations, our research will serve as experimental basis in the field of optical fiber communications.
•Multi-parallelized PINNs are constructed for the study of inverse problem.•With small data available, we can deduce undetermined terms of a generalized NLS typed equation.•Nonlinear analysis are provided based on the parameter discovery of variable coefficients.•Compared with traditional PINNs, lower fitting error of solutions and parameters can be achieved.
Improved durability, enhanced interfacial stability, and room temperature applicability are desirable properties for all‐solid‐state lithium metal batteries (ASSLMBs), yet these desired properties ...are rarely achieved simultaneously. Here, in this work, it is noticed that the huge resistance at Li metal/electrolyte interface dominantly impeded the normal cycling of ASSLMBs especially at around room temperature (<30 °C). Accordingly, a supramolecular polymer ion conductor (SPC) with “weak solvation” of Li+ was prepared. Benefiting from the halogen‐bonding interaction between the electron‐deficient iodine atom (on 1,4‐diiodotetrafluorobenzene) and electron‐rich oxygen atoms (on ethylene oxide), the O‐Li+ coordination was significantly weakened. Therefore, the SPC achieves rapid Li+ transport with high Li+ transference number, and importantly, derives a unique Li2O‐rich SEI with low interfacial resistance on lithium metal surface, therefore enabling stable cycling of ASSLMBs even down to 10 °C. This work is a new exploration of halogen‐bonding chemistry in solid polymer electrolyte and highlights the importance of “weak solvation” of Li+ in the solid‐state electrolyte for room temperature ASSLMBs.
PEO‐based electrolytes suffer from huge interfacial resistance, poor Li+ transport, and Li dendrite formation in all‐solid‐state lithium metal batteries (ASSLMBs) operating at around room‐temperature. This work proposes the regulation of the Li+ solvation environment through halogen‐bonding interaction and highlights the importance of “weak solvation” of Li+ in solid electrolytes for room temperature ASSLMBs.
In this paper, a
(
3
+
1
)
-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, ...which consists of six bilinear equations and involves nine arbitrary parameters. With multiple exponential function method and symbolic computation, nonresonant-typed one-, two-, and three-wave solutions are obtained. Furthermore, two classes of lump solutions to the dimensionally reduced cases with
y
=
x
and
y
=
z
are both derived. Finally, some figures are given to reveal the propagation of multiple wave solutions and lump solutions.
In this paper, a (3+1)-dimensional nonlinear evolution equation and its reduction is studied by use of the Hirota bilinear method and the test function method. With symbolic computation, diversity of ...exact solutions is obtained by solving the under-determined nonlinear system of algebraic equations for the associated parameters. Finally, analysis and graphical simulation are given to reveal the propagation and dynamical behavior of the solutions.
We describe the identification and characterization of circular intronic long noncoding RNAs in human cells, which accumulate owing to a failure in debranching. The formation of such circular ...intronic RNAs (ciRNAs) can be recapitulated using expression vectors, and their processing depends on a consensus motif containing a 7 nt GU-rich element near the 5′ splice site and an 11 nt C-rich element close to the branchpoint site. In addition, we show that ciRNAs are abundant in the nucleus and have little enrichment for microRNA target sites. Importantly, knockdown of ciRNAs led to the reduced expression of their parent genes. One abundant such RNA, ci-ankrd52, largely accumulates to its sites of transcription, associates with elongation Pol II machinery, and acts as a positive regulator of Pol II transcription. This study thus suggests a cis-regulatory role of noncoding intronic transcripts on their parent coding genes.
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•Circular intronic RNAs accumulate in human cells owing to escape from debranching•Their processing depends on RNA motifs near 5′ splice site and branchpoint•ciRNAs regulate parent gene expression by modulating elongation Pol II activity
Small nucleolar RNAs (snoRNAs) are a new type of functional small RNAs involved in the chemical modifications of rRNAs, tRNAs, and small nuclear RNAs. It is reported that they play important roles in ...tumorigenesis via various regulatory modes. snoRNAs can both participate in the regulation of methylation and pseudouridylation and regulate the expression pattern of their host genes. This research investigated the expression pattern of snoRNAs in eight major cancer types in TCGA via several machine learning algorithms. The expression levels of snoRNAs were first analyzed by a powerful feature selection method, Monte Carlo feature selection (MCFS). A feature list and some informative features were accessed. Then, the incremental feature selection (IFS) was applied to the feature list to extract optimal features/snoRNAs, which can make the support vector machine (SVM) yield best performance. The discriminative snoRNAs included HBII-52-14, HBII-336, SNORD123, HBII-85-29, HBII-420, U3, HBI-43, SNORD116, SNORA73B, SCARNA4, HBII-85-20, etc., on which the SVM can provide a Matthew's correlation coefficient (MCC) of 0.881 for predicting these eight cancer types. On the other hand, the informative features were fed into the Johnson reducer and repeated incremental pruning to produce error reduction (RIPPER) algorithms to generate classification rules, which can clearly show different snoRNAs expression patterns in different cancer types. The analysis results indicated that extracted discriminative snoRNAs can be important for identifying cancer samples in different types and the expression pattern of snoRNAs in different cancer types can be partly uncovered by quantitative recognition rules.
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