**High** **order** asymptotic expansion for Wiener functionals

**high**-

**order**asymptotic expansion theory for a sequence of vector-valued random variables. Expand abstract.

**high**-

**order**asymptotic expansion theory for a sequence of vector-valued random variables. Our asymptotic expansion formulas give the development of the characteristic functional and of the local density of the random vectors up to an arbitrary

**order**. We analyzed in details an example related to the wave equation with space-time white noise which also provides interesting facts on the correlation structure of the solution to this equation.

10/10 relevant

arXiv

Resonant Laplace-Lagrange theory for extrasolar systems in mean-motion resonance

**high**

**order**in the eccentricities of the resonant Hamiltonian both at

**orders**one and two in the masses. Expand abstract.

**order**resonant Hamiltonian expansion is unfit to describe the long-term evolution of these systems. We extend the Laplace-Lagrange secular approximation for coplanar systems with two planets by including (near-)resonant harmonics, and realize an expansion at

**high**

**order**in the eccentricities of the resonant Hamiltonian both at

**orders**one and two in the masses. We show that the expansion at first

**order**in the masses gives a qualitative good approximation of the dynamics of resonant extrasolar systems with moderate eccentricities, while the second

**order**is needed to reproduce more accurately their orbital evolutions. The resonant approach is also required to correct the secular frequencies of the motion given by the Laplace-Lagrange secular theory in the vicinity of a mean-motion resonance. The dynamical evolutions of four (near-)resonant extrasolar systems are discussed, namely GJ 876 (2:1 resonance), HD 60532 (3:1), HD 108874 and GJ 3293 (close to 4:1).

4/10 relevant

arXiv

Efficient **high**-**order** singular quadrature schemes in magnetic fusion

**high**-

**order**accurate convergence. Expand abstract.

**order**accurate, and therefore requires a dense computational mesh in

**order**to obtain sufficient accuracy. In this work, we present a fast,

**high**-

**order**quadrature scheme for the efficient computation of these integrals. Several numerical examples are provided demonstrating the computational efficiency and the

**high**-

**order**accurate convergence. A corresponding code for use in the community has been publicly released.

9/10 relevant

arXiv

High-level cognition during story listening is reflected in **high**-**order** dynamic correlations in neural activity patterns

**high**er-

**order**patterns of dynamic network interactions throughout the brain. Expand abstract.

**High**-

**order**dynamic correlations in neural activity patterns reflect different subgraphs of the brain's connectome that display homologous lower-level dynamic correlations. We tested the hypothesis that

**high**-level cognition is supported by

**high**-

**order**dynamic correlations in brain activity patterns. We developed an approach to estimating

**high**-

**order**dynamic correlations in timeseries data, and we applied the approach to neuroimaging data collected as human participants either listened to a ten-minute story, listened to a temporally scrambled version of the story, or underwent a resting state scan. We trained across-participant pattern classifiers to decode (in held-out data) when in the session each neural activity snapshot was collected. We found that classifiers trained to decode from

**high**-

**order**dynamic correlations yielded the best performance on data collected as participants listened to the (unscrambled) story. By contrast, classifiers trained to decode data from scrambled versions of the story or during the resting state scan yielded the best performance when they were trained using first-

**order**dynamic correlations or non-correlational activity patterns. We suggest that as our thoughts become more complex, they are supported by higher-

**order**patterns of dynamic network interactions throughout the brain.

10/10 relevant

bioRxiv

Analysis of corneal real astigmatism changes and **high** **order** aberration after lower eyelid epiblepharon repair surgery

**high**

**order**aberrations (LOA and HOA), which cause visual disturbances after lower eyelid epiblepharon repair surgery. Expand abstract.

**high**

**order**aberrations (LOA and HOA), which cause visual disturbances after lower eyelid epiblepharon repair surgery. Methods and analysis: This was a retrospective, cross-sectional study, which included 108 eyes from 54 patients. Wavefront analyses for calibrated LOAs and HOAs (root mean square, coma, three-piece aberrations [Trefoil], secondary astigmatisms, and spherical aberrations [SA]) were performed via a Galilei G4 Dual Scheimpflug Analyzer preoperatively, at the first and second follow-ups (f/u), and at G1, G2, and G3 (

10/10 relevant

medRxiv

Improvement for Color Glass Condensate factorization: single hadron
production in pA collisions at next-to-leading **order**

**order**(NLO) result to have a smaller theoretical uncertainty comparing with LO result, which makes

**high**order calculation in CGC factorization to be useful. Expand abstract.

**High**

**order**calculation at semi-hard scale is very important, but a satisfactory calculation framework is still missing. We propose a systematic method to regularize rapidity divergences in the CGC factorization, which makes higher

**order**calculation rigorous and straight forward. By applying this method to single hadron production in pA collision, we find the kinematic constraint effect introduced by hand in previous works comes out automatically, but with different values. The difference is crucial for our next-to-leading

**order**(NLO) result to have a smaller theoretical uncertainty comparing with LO result, which makes

**high**

**order**calculation in CGC factorization to be useful. As a byproduct, the negativity problem found in literature can also be overcome in our framework by a proper choosing of factorization scale.

7/10 relevant

arXiv

Analysis of **high** **order** dimension independent RBF-FD solution of
Poisson's equation

**orders**of RBF-FD approximation, which are further combined with theoretical complexity analyses and experimental execution time measurements into a study of accuracy vs. execution time trade-off. Expand abstract.

**orders**of RBF-FD approximation, which are further combined with theoretical complexity analyses and experimental execution time measurements into a study of accuracy vs. execution time trade-off. The study clearly demonstrates regimes of optimal setups for target accuracy ranges. Finally, the dimension independence is demonstrated with a solution of Poisson's equation in an irregular 4D domain.

8/10 relevant

arXiv

High-**order** partitioned spectral deferred correction solvers for
multiphysics problems

**high**-

**order**partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves. Expand abstract.

**high**-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1, 2], which used implicit-explicit Runge-Kutta methods (IMEX) to build

**high**-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily

**high**-

**order**partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-

**order**partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems including a simple linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design

**order**of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1, 2] on this suite of test problems. The results suggest that the

**high**-

**order**partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

10/10 relevant

arXiv

Photon vortex generation in quantum level by **high**-**order** harmonic
synchrotron radiations from spiral moving electrons in magnetic fields

**high**-

**order**harmonic radiations. Expand abstract.

**high**-

**order**harmonic radiations. We also calculate the decay widths and the energy spectra. Under strong magnetic fields as 10^13 G, which are found in astrophysical objects such as magnetars, photon vortices are predominantly generated.

10/10 relevant

arXiv

Solution of Stokes flow in complex nonsmooth 2D geometries via a
linear-scaling **high**-**order** adaptive integral equation scheme

**high**-

**order**accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. Expand abstract.

**high**-

**order**accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of evaluating weakly-singular, nearly-singular and hyper-singular integrals to

**high**accuracy. Near-singular integral evaluation, in particular, is done using an extension of the scheme developed in J.~Helsing and R.~Ojala, {\it J. Comput. Phys.} {\bf 227} (2008) 2899--2921. The boundary of the given geometry is ``panelized'' automatically to achieve user-prescribed precision. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy.

10/10 relevant

arXiv