Related papers: Parallel Kac's Walk Generates PRU
Our objective is to explore random walks on the general linear group, constrained to a specific domain, with a primary focus on establishing the conditioned local limit theorem. This paper marks the initial stride toward achieving this…
We introduce a continuous-time quantum walk on an ultrametric space corresponding to the set of p-adic integers and compute its time-averaged probability distribution. It is shown that localization occurs for any location of the ultrametric…
In this paper, we review and compare several velocity-level and acceleration-level Pseudo-Inverse-based Path Planning (PPP) and Pseudo-Inverse-based Repetitive Motion Planning (PRMP) schemes based on the kinematic model of robotic…
RC4 can be made more secured if an additional RC4-like Post-KSA Random Shuffing (PKRS) process is introduced between KSA and PRGA. It can also be made significantly faster if RC4 bytes are processed in a FPGA embedded system using multiple…
The continuous-time quantum walk is a particle evolving by Schr\"odinger's equation in discrete space. Encoding the space as a graph of vertices and edges, the Hamiltonian is proportional to the discrete Laplacian. In some physical systems,…
Recurrent neural networks (RNNs) are a popular choice for modeling sequential data. Modern RNN architectures assume constant time-intervals between observations. However, in many datasets (e.g. medical records) observation times are…
We introduce a new tool for quantum algorithms called quantum fast-forwarding (QFF). The tool uses quantum walks as a means to quadratically fast-forward a reversible Markov chain. More specifically, with $P$ the Markov chain transition…
In this paper we develop theory of sequential parametrized motion planning which generalises the approach of parametrized motion planning, which was introduced recently in [3]. A sequential parametrized motion planning algorithm produced a…
The parallel replica dynamics, originally developed by A.F. Voter, efficiently simulates very long trajectories of metastable Langevin dynamics. We present an analogous algorithm for discrete time Markov processes. Such Markov processes…
We develop a continuous time random walk (CTRW) approach for the evolution of Lagrangian velocities in steady heterogeneous flows based on a stochastic relaxation process for the streamwise particle velocities. This approach describes…
We provide a random walk in random scenery representation of a new class of stable self-similar processes with stationary increments introduced recently by Jung, Owada and Samorodnitsky. In the functional limit theorem they provided, only a…
Path homology proposed by S.-T.Yau and his co-workers provides a new mathematical model for directed graphs and networks. Persistent path homology (PPH) extends the path homology with filtration to deal with asymmetry structures. However,…
Constrained model predictive control (MPC) is a widely used control strategy, which employs moving horizon-based on-line optimisation to compute the optimum path of the manipulated variables. Nonlinear MPC can utilize detailed models but it…
Motion planning is a fundamental problem in robotics that involves generating feasible trajectories for a robot to follow. Recent advances in parallel computing, particularly through CPU and GPU architectures, have significantly reduced…
Continuous-time generative models, such as diffusion models, flow matching, and rectified flow, learn time-dependent vector fields but are typically trained with objectives that treat timesteps independently, leading to high estimator…
Recent optical flow methods are almost exclusively judged in terms of accuracy, while their robustness is often neglected. Although adversarial attacks offer a useful tool to perform such an analysis, current attacks on optical flow methods…
A self-avoiding walk (SAW) on the square lattice is prudent if it never takes a step towards a vertex it has already visited. Prudent walks differ from most classes of SAW that have been counted so far in that they can wind around their…
We study the ability of Transformer models to learn sequences generated by Permuted Congruential Generators (PCGs), a widely used family of pseudo-random number generators (PRNGs). PCGs introduce substantial additional difficulty over…
In the present paper, we construct QMCs associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution…
We consider a discrete time simple symmetric random walk on Z^d, d>=1, where the path of the walk is perturbed by inserting deterministic jumps. We show that for any time n and any deterministic jumps that we insert, the expected number of…