Mixed Jacobi-Fourier spectral method for Fisher equation

In this paper, we propose a mixed Jacobi-Fourier spectral method for solving the Fisher equation in a disc. Some mixed Jacobi-Fourier approximation results are established, which play important roles in numerical simulation of various problems defined in a disc. We use the generalized Jacobi approximation to simulate the singularity of solution at the regional center. This also simplifies the theoretical analysis and provides a sparse system. The stability and convergence of the proposed scheme are proved. Numerical results demonstrate the efficiency of this new algorithm and coincide well with the theoretical analysis

Computing and Information MIXED SPECTRAL METHOD FOR NAVIER-STOKES EQUATIONS IN AN INFINITE STRIP BY USING GENERALIZED LAGUERRE FUNCTIONS

Abstract. In this paper, we propose a mixed spectral method for the Navier-Stokes equations in an infinite strip by using generalized Laguerre functions. We establish some results on mixed generalized Laguerre-Legendre approximation, which play important roles in spectral method for fourth order differential equations. A mixed spectral scheme is provided for stream function form of the Navier-Stokes equations. Its stability and convergence are proved. Numeric results demonstrate the efficiency of suggested algorithm. Key words. Mixed generalized Laguerre-Legendre spectral method, stream function form of Navier-Stokes equations in an infinite strip. 1

The complete mitochondrial genome of Sinopodisma hengshanica (Orthoptera: Acrididae) and its phylogenetic implication

The complete mitochondrial genome (mitogenome) of Sinopodisma hengshanica (Orthoptera: Acrididae) was firstly determined and analyzed in the present study. Assembled mitogenome sequence of S. hengshanica is 15,623 bp in size, containing 13 protein-coding genes (PCGs), two ribosomal RNA genes (rRNAs), 22 transfer RNA genes (tRNAs), as well as one A + T-rich region. Its gene component and arrangement are identical with other Acrididae species. The overall nucleotide composition is as follows: A (42.89%), G (10.34%), T (33.07%), and C (13.70%). All PCGs are initiated by typical ATN codons, and terminated with harboring complete stop codons TAA and TAG. Furthermore, phylogenetic trees were reconstructed based on 13 PCGs to validate the taxonomic status of S. hengshanica, exhibiting a close relationship with Sinopodisma rostellocerca

Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions

In this paper, a nonpolynomial-based spectral collocation method and its well-conditioned variant are proposed and analyzed. First, we develop fractional differentiation matrices of nodal Jacobi polyfractonomials [M. Zayernouri and G. E. Karniadakis, J. Comput. Phys., 252 (2013), pp. 495--517] and generalized Jacobi functions [S. Chen, J. Shen, and L. L. Wang, Math. Comp., 85 (2016), pp. 1603--1638] on Jacobi--Gauss--Lobatto (JGL) points. We show that it suffices to compute the matrix of order $\mu\in (0,1)$ to compute that of any order $k +\mu$ with integer $k \geq 0$. With a different definition of the nodal basis, our approach also fixes a deficiency of the polyfractonomial fractional collocation method in [M. Zayernouri and G. E. Karniadakis, SIAM J. Sci. Comput., 38 (2014), pp. A40--A62]. Second, we provide explicit and compact formulas for computing the inverse of direct fractional differential collocation matrices at “interior” points by virtue of fractional JGL Birkhoff interpolation. This leads to optimal integration preconditioners for direct fractional collocation schemes and results in well-conditioned collocation systems. Finally, we present a detailed analysis of the singular behavior of solutions to rather general fractional differential equations (FDEs). Based upon the result, we have the privilege to adjust an index in our nonpolynomial approximation. Furthermore, by using the result, a rigorous convergence analysis is conducted by transforming an FDE into a Volterra (or mixed Volterra--Fredholm) integral equation.MOE (Min. of Education, S’pore)Published versio

Dietary Shifts in the Adaptation to Changing Marine Resources: Insights from a Decadal Study on Greater Lizardfish (<i>Saurida tumbil</i>) in the Beibu Gulf, South China Sea

Understanding dietary behavior during the individual development of marine predators and its temporal variations elucidates how species adapt to changes in marine resources. This is crucial for predicting marine predators’ habitat selection and the natural population’s responses to environmental changes. The authors conducted a comparative analysis of dietary shift strategies and trophic level variations in Greater lizardfish (Saurida tumbil) in the Beibu Gulf during two distinct periods (2010 and 2020) using stomach content and stable isotope analysis methods. Possible driving factors for these changes were also explored. Changes in the fishery community structure and the decline in the abundance of primary prey resources have led the S. tumbil population to diversify their prey species, utilize alternative resources, and expand their foraging space. However, the species’ foraging strategy, characterized by chasing and preying on schooling and pelagic prey, promoted stability in their feeding behavior across spatial and temporal scales. The main prey items remained demersal and pelagic fish species, followed by cephalopods and crustaceans. Similar to other generalist fish species, ontogenetic dietary shifts (ODSs) indicated a partial transition towards larger prey items. However, the timing and magnitude of the ODSs varied between the two periods, reflecting life-history variations and adaptive adjustments to environmental changes. In comparison to 2010, the population’s mean body length (BL) increased in 2020, and the proportion of the population feeding on pelagic–neritic prey significantly increased. However, the δ15N values were lower, indicating that the shift in the ecological niche of preferred prey from demersal to pelagic–neritic was the primary cause of the decrease in trophic levels. In the future, we will conduct further quantitative research integrating the spatiotemporal data of both predators and prey to clarify the relationships between marine predators’ feeding behavior, trophic levels, and changes in prey community structure

Munc18-1 catalyzes neuronal SNARE assembly by templating SNARE association.

Sec1/Munc18-family (SM) proteins are required for SNARE-mediated membrane fusion, but their mechanism(s) of action remain controversial. Using single-molecule force spectroscopy, we found that the SM protein Munc18-1 catalyzes step-wise zippering of three synaptic SNAREs (syntaxin, VAMP2, and SNAP-25) into a four-helix bundle. Catalysis requires formation of an intermediate template complex in which Munc18-1 juxtaposes the N-terminal regions of the SNARE motifs of syntaxin and VAMP2, while keeping their C-terminal regions separated. SNAP-25 binds the templated SNAREs to induce full SNARE zippering. Munc18-1 mutations modulate the stability of the template complex in a manner consistent with their effects on membrane fusion, indicating that chaperoned SNARE assembly is essential for exocytosis. Two other SM proteins, Munc18-3 and Vps33, similarly chaperone SNARE assembly via a template complex, suggesting that SM protein mechanism is conserved