相关论文: The Orbit-Sum Method for Higher Order Equations

Understanding the difference between group orbits and their closures is a key difficulty in geometric complexity theory (GCT): While the GCT program is set up to separate certain orbit closures, many beautiful mathematical properties are…

In the past fifteen years, the enumeration of lattice walks with steps takenin a prescribed set S and confined to a given cone, especially the firstquadrant of the plane, has been intensely studied. As a result, the generating functions…

An algorithm is proposed to calculate traveling dissipative solitons for the FitzHugh-Nagumo equations. It is based on the application of the steepest descent method to a certain functional. This approach can be used to find solitons…

Summation methods play a very important role in quantum field theory because all perturbation series are divergent and the expansion parameter is not always small. A number of methods have been tried in this context, most notably Pade…

We construct an integrable hierarchy of the Boussinesq equation using the Lie-algebraic approach of Holod-Flashka-Newell-Ratiu. We show that finite-gap hamiltonian systems of the hierarchy arise on coadjoint orbits in the loop algebra of…

We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…

Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…

We present a novel numerical method to calculate periodic orbits for dynamical systems by an iterative process which is based directly on the action integral in classical mechanics. New solutions are obtained for the planar motion of three…

We propose a new primal-dual splitting method for solving composite inclusions involving Lipschitzian, and parallel-sum-type monotone operators. Our approach extends the framework in \cite{Siopt4} to a more general class of monotone…

Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…

In this work a Green function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position dependent…

In this paper, we propose Riemannian conditional gradient methods for minimizing composite functions, i.e., those that can be expressed as the sum of a smooth function and a retraction-based convex function. We analyze the convergence of…

A new general and unified method of summation, which is both regular and consistent, is invented. It is based on the idea concerning a way of integers reordering. The resulting theory includes a number of explicit and closed form summation…

If we cannot obtain all terms of a series, or if we cannot sum up a series, we have to turn to the partial sum approximation which approximate a function by the first several terms of the series. However, the partial sum approximation often…

We present a finite-element approach for computing the aggregate scattering matrix of a network of linear coherent scatterers. These might be optical scatterers or more general scattering coins studied in quantum walk theory. While…

We reformulate quantum computation in terms of Lagrangian (sum-over-path) formalism, in contrast to the widely used Hamiltonian (unitary gate) formulation. We exemplify this formalism with some widely-studied models, including the standard…

Around 2000, Ira Gessel conjectured that the number of lattice walks in the quadrant N^2, starting and ending at the origin (0,0) and taking their steps in {E,NE,W,SW} had a simple hypergeometric form. In the following decade, this problem…

A new approach for trajectory optimization of musculoskeletal dynamic models is introduced. The model combines rigid body and muscle dynamics described with a Hill-type model driven by neural control inputs. The objective is to find input…

We give a precise estimate for the number of lattice points in certain bounded subsets of $\mathbb{R}^{n}$ that involve `hyperbolic spikes' and occur naturally in multiplicative Diophantine approximation. We use Wilkie's o-minimal structure…

The multistep solving strategy consists in a divide-and-conquer approach: when a multivariate polynomial system is computationally infeasible to solve directly, one variable is assigned over the elements of the base finite field, and the…