Related papers: Parallel Kac's Walk Generates PRU
We study the mixing time of a non-Markovian process, the step-reinforced random walk (SRRW) on a finite group. This process differs from a classical random walk in that at each integer time, with probability $\alpha$ the next step is chosen…
Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the…
In this article we present an effective Hamiltonian approach for Discrete Time Quantum Random Walk. A form of the Hamiltonian for one dimensional quantum walk has been prescribed, utilizing the fact that Hamiltonians are the generators of…
Fast dynamics and transient events are becoming more and more frequent in power systems, due to the high penetration of renewable energy sources and the consequent lack of inertia. In this scenario, Phasor Measurement Units (PMUs) are…
This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a…
Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional…
The advent of edge computing has enabled resource-constrained clients to delegate intensive computational tasks to distributed edge servers, especially within Internet of Things (IoT) environments. Among such tasks, Matrix Determinant…
Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify…
Random unitaries sampled from the Haar measure serve as fundamental models for generic quantum many-body dynamics. Under standard cryptographic assumptions, recent works have constructed polynomial-size quantum circuits that are…
This paper focuses on the Matrix Factorization based Clustering (MFC) method which is one of the few closed form algorithms for the subspace clustering problem. Despite being simple, closed-form, and computation-efficient, MFC can…
Unitary $k$-designs are probabilistic ensembles of unitary matrices whose first $k$ statistical moments match that of the full unitary group endowed with the Haar measure. In prior work, we showed that the automorphism group of classical…
Photonic integrated circuits (PICs) offer ultra-broad optical bandwidths that enable unprecedented data throughputs for signal processing applications. Dynamic reconfigurability enables compensation of fabrication flaws and fluctuating…
We consider the model of random walk on dynamical percolation introduced by Peres, Stauffer and Steif (2015). We obtain comparison results for this model for hitting and mixing times and for the spectral-gap and log-Sobolev constant with…
Secret Unknown Ciphers (SUC) have been proposed recently as digital clone-resistant functions overcoming some of Physical(ly) Unclonable Functions (PUF) downsides, mainly their inconsistency because of PUFs analog nature. In this paper, we…
We call progressive paths and rushed paths two families of Dyck paths studied by Asinowski and Jelinek, which have the same enumerating sequence (OEIS entry A287709). We present a bijection proving this fact. Rushed paths turn out to be in…
The key innovation of our analytical method, CaRT, lies in establishing a new hierarchical, distributed architecture to guarantee the safety and robustness of a given learning-based motion planning policy. First, in a nominal setting, the…
We develop a new framework that extends the quantum walk framework of Magniez, Nayak, Roland, and Santha, by utilizing the idea of quantum data structures to construct an efficient method of nesting quantum walks. Surprisingly, only…
This paper establishes a robust link between quantum dynamics and classical ones by deriving probabilistic representation for both continuous time and discrete time quantum walks. We first adapt Molchanov formula, originally employed in the…
We provide a new provably-secure steganographic encryption protocol that is proven secure in the complexity-theoretic framework of Hopper et al. The fundamental building block of our steganographic encryption protocol is a "one-time…
We introduce the pseudorandom quantum authentication scheme (PQAS), an efficient method for encrypting quantum states that relies solely on the existence of pseudorandom unitaries (PRUs). The scheme guarantees that for any eavesdropper with…