相关论文: The compensation approach for walks with small ste…
In this work, we develop a mathematical model to describe the local movement of individuals by taking into account their return to home after a period of travel. We provide a suitable functional framework to handle this system and study the…
The orbit-sum method is an algebraic version of the reflection-principle that was introduced by Bousquet-M\'{e}lou and Mishna to solve functional equations that arise in the enumeration of lattice walks with small steps restricted to…
In this article, a novel method to compute all discrete polyharmonic functions in the quarter plane for models with small steps, zero drift and a finite group is proposed. A similar method is then introduced for continuous polyharmonic…
A quantum walk model which reflects the $2$-cell embedding on the orientable closed surface of a graph in the dynamics is introduced. We show that the scattering matrix is obtained by finding the faces on the underlying surface which have…
We use a Hamiltonian (transition matrix) description of height-restricted Dyck paths on the plane in which generating functions for the paths arise as matrix elements of the propagator to evaluate the length and area generating function for…
Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta-analysis (NMA) is an active area of research. We extend this to the contributions of paths to NMA estimates. We present a general…
We present the method of walk-sum to study the real-time dynamics of interacting quantum many-body systems. The walk-sum method generates explicit expressions for any desired pieces of an evolution operator U independently of any others.…
This work presents algorithms for the feedback-stabilised walking of bipedal humanoid robotic platforms, along with the underlying theoretical and sensorimotor frameworks required to achieve it. Bipedal walking is inherently complex and…
A random walk generated by a sum of independent identity distributed random variables with positive expectation is considered. The limiting distributions for the first- passage -time of a step-function boundary are derived.
This paper considers the $1/\epsilon$ problem, which is the divergent behavior of the ground state energy of asymmetric potential in quantum mechanics, which is calculated with semi-classical expansion and resurgence technique. Using…
It is demonstrated that in gate-based quantum computing architectures quantum walk is a natural mathematical description of quantum gates. It originates from field-matter interaction driving the system, but is not attached to specific qubit…
We study quantum walk on a ladder with combination of conventional and split-step protocols. The two components of the walk resulting from periodic boundary conditions can be made to have three kinds of probability distributions. Two of…
Quantum walks have a host of applications, ranging from quantum computing to the simulation of biological systems. We present an intrinsically stable, deterministic implementation of discrete quantum walks with single photons in space. The…
We present an algorithm for receding-horizon motion planning using a finite family of motion primitives for underactuated dynamic walking over uneven terrain. The motion primitives are defined as virtual holonomic constraints, and the…
A branching random walk algorithm for the many-body Wigner equation and its numerical applications for quantum dynamics in phase space are proposed and analyzed. After introducing an auxiliary function, the (truncated) Wigner equation is…
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks…
We introduce a new approach to an enumerative problem closely linked with the geometry of branched coverings; that is, we study the number of ways a permutation can be decomposed into a product of a given number of 2-cycles, 3-cycles, etc.…
We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z…
In the context of lattice walk enumeration in cones, we consider the number of walks in the quarter plane with fixed starting and ending points, prescribed step-set and given length. After renormalization, this number may be interpreted as…
We develop walk-on-sphere for fractional Poisson equations with Dirichilet boundary conditions in high dimensions. The walk-on-sphere method is based on probabilistic represen tation of the fractional Poisson equation. We propose effcient…