Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt found...
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Hybrid nonlinear conjugate gradient (CG) methods are known to be efficient and have less memory requirement for solving optimization problems in Euclidean spaces. The formulations strategically switch between two or m...
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The optimal tracking problem of the probability density function of a stochastic process can be expressed in terms of an optimal bilinear control problem for the Fokker-Planck equation, with the control in the coeffic...
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This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is...
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A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is a white-in-time random noise acting in a narrow band of high wavenumbers. The inverse-cascade process and the presence of the boundary lead ultimately to a pile-up of energy in the lowest wavenumber (Bose condensation). In the asymptotic limit where the enstrophy cascade range is negligible, Bose condensation is solely responsible for the generation of coherent vortices and intermittency in the system. We present the evolution of the velocity and vorticity fields through the later stages of the condensate state, and explore the possible implications for atmospheric turbulence constrained by the periodic domain about the earth.
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H2-regularity random attractor.
We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rati...
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We describe here a new technique and a package for rapid reconstruction of smooth surfaces from scattered data points. This method is based on a fast recurrent algorithm for the Delauney triangulation followed by rational interpolation inside triangles. Preprocessing of data includes sorting and takes N log(N) time. Afterwards the computational cost is a linear function of the amount of data. This technique enables a user to construct a surface of any class of smoothness and degree of convergence. Our package reconstructs surfaces that can be uniquely projected either on a plane or on a sphere. The graphical section of this package includes three dimensional transformations, shading, hidden surface removal, interactive adding points into triangulation by mouse, etc. The graphics has been implemented on Iris-4D, SUN-4 and IBM-5080.
In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly s...
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In this paper, a new kind of alternating direction implicit （ADI） Crank-Nicolson-type orthogonal spline collocation （OSC） method is formulated for the two-dimensional frac-tional evolution equation with a weakly singular kernel arising in the theory of linear viscoelas-ticity. The novel OSC method is used for the spatial discretization, and ADI Crank-Nicolson-type method combined with the second order fractional quadrature rule are considered for thetemporal component. The stability of proposed scheme is rigourously established, and nearlyoptimal order error estimate is also derived. Numerical experiments are conducted to supportthe predicted convergence rates and also exhibit expected super-convergence phenomena.
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then...
A new rotation symmetry for steady Hele-Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve L moving with constant velocity U is a solution to the Hele-Shaw problem, then the curve L obtained from a rotation of L about its center by an arbitrary angle is also a solution with the same velocity U. Similar results hold for the case with surface tension if and only if the Schwarz function of the curve L is regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.
By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid lim- it to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the soluti...
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By the uniform a priori estimate of solution about parameters, we prove the existence of global solution and inviscid lim- it to a generalized Ginzburg-Landau equations in two dimensions. We also prove that the solution to the Ginzburg-Landau equations converges to the weak solution to the derivative nonlinear Schrodinger equations.
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