Related papers: Higher-order Airy scaling in deformed Dyck paths
We consider the problem of enumerating Dyck paths staying weakly above the x-axis with a limit to the number of consecutive up steps, or a limit to the number of consecutive down steps. We use Finite Operator Calculus to obtain formulas for…
We develop the rough path counterpart of It\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\^o / forward) stochastic differential equations treatable…
We consider rough paths with jumps. In particular, the analogue of Lyons' extension theorem and rough integration are established in a jump setting, offering a pathwise view on stochastic integration against cadlag processes. A class of…
We develop a non-perturbative method for calculating partition functions of strongly coupled quantum mechanical systems with interactions between subsystems described by a path integral of a dual system. The dual path integral is derived…
We study sample-path large deviations for L\'evy processes and random walks with heavy-tailed jump-size distributions that are of Weibull type. Our main results include an extended form of an LDP (large deviations principle) in the $J_1$…
We formulate a new class of stochastic partial differential equations (SPDEs), named high-order vector backward SPDEs (B-SPDEs) with jumps, which allow the high-order integral-partial differential operators into both drift and diffusion…
The enumeration of k-Dyck paths ending at level j after m up-steps, where the last step is an up-step, is given as a sum, improving on a previous formula given by Deng and Mansour.
We introduce an extension of Dual Dynamic Programming (DDP) to solve convex nonlinear dynamic programming equations. We call Inexact DDP (IDDP) this extension which applies to situations where some or all primal and dual subproblems to be…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
We show that the dispersionless DKP hierarchy (the dispersionless limit of the Pfaff lattice) admits a suggestive reformulation through elliptic functions. We also consider one-variable reductions of the dispersionless DKP hierarchy and…
Distributed Arithmetic Coding (DAC) has emerged as a feasible solution to the Slepian-Wolf problem, particularly in scenarios with non-stationary sources and for data sequences with lengths ranging from small to medium. Due to the inherent…
Higher order coefficients of the inverse mass expansion of one--loop effective actions are obtained from a one--dimensional path integral representation. For the evaluation of the path integral with Wick contractions a suitable Green…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
We consider the problem of quickly computing shortest paths in weighted graphs given auxiliary data derived in an expensive preprocessing phase. By adding a fast weight-customization phase, we extend Contraction Hierarchies by Geisberger et…
In this paper, the recently developed differential homotopy approach is applied to the problem of disentangling dynamical and topological fields of the $3d$ higher-spin gauge theory at the linear level. This formalism allows us to reproduce…
We introduce a novel method for handling endpoint constraints in constrained differential dynamic programming (DDP). Unlike existing approaches, our method guarantees quadratic convergence and is exact, effectively managing rank…
Dynamic Movement Primitives (DMP) have found remarkable applicability and success in various robotic tasks, which can be mainly attributed to their generalization, modulation and robustness properties. Nevertheless, the spatial…
We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be…
Integrated task and motion planning has emerged as a challenging problem in sequential decision making, where a robot needs to compute high-level strategy and low-level motion plans for solving complex tasks. While high-level strategies…
Many numerical methods for multiscale differential equations require a scale separation between the larger and the smaller scales to achieve accuracy and computational efficiency. In the area of multiscale dynamical systems, so-called,…