Related papers: Parallel Kac's Walk Generates PRU
We introduce a persistent random walk model with finite velocity and self-reinforcing directionality, which explains how exponentially distributed runs self-organize into truncated L\'evy walks observed in active intracellular transport by…
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph. We analytically prove that lackadaisical quantum walks can find a unique marked vertex on any regular…
Although a wide variety of handcrafted concurrent data structures have been proposed, there is considerable interest in universal approaches (henceforth called Universal Constructions or UCs) for building concurrent data structures. These…
Random walks are a series of up, down, and level steps that enumerate distinct paths from $(0,0)$ to $(2n,0)$, where $n$ is the semi-length of the path. We used these paths to analyze Catalan, Schr\"{o}der, and Motzkin number sequences…
This paper presents a symmetric stream cipher that utilizes the dynamic properties of random cubic mappings in the complex plane to generate pseudo-random key streams. The system is based on the iterations of the random cubic polynomial…
Physical Unclonable Functions (PUFs) leverage manufacturing process imperfections that cause propagation delay discrepancies for the signals traveling along these paths. While PUFs can be used for device authentication and chip-specific key…
Programmable photonic integrated circuits (PPICs) are an emerging technology recently proposed as an alternative to custom-designed application-specific integrated photonics. Light routing is one of the most important functions that need to…
The two major discrete time formulations for quantum walks, coined and scattering, are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology (PRA {\bf 80}, 052301 (2009)). Although the proof explicit…
Different flavors of quantum pseudorandomness have proven useful for various cryptographic applications, with the compelling feature that these primitives are potentially weaker than post-quantum one-way functions. Ananth, Lin, and Yuen…
Gluing theorem for random unitaries [Schuster, Haferkamp, Huang, QIP 2025] have found numerous applications, including designing low depth random unitaries [Schuster, Haferkamp, Huang, QIP 2025], random unitaries in ${\sf QAC0}$ [Foxman,…
This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. This is also posed as the dual control problem consisting of system identification and regulation. We…
Random walk algorithms are crucial for sampling and approximation problems in statistical physics and theoretical computer science. The mixing property is necessary for Markov chains to approach stationary distributions and is facilitated…
This paper introduces the batch-parallel Compressed Packed Memory Array (CPMA), a compressed, dynamic, ordered set data structure based on the Packed Memory Array (PMA). Traditionally, batch-parallel sets are built on pointer-based data…
The dynamical discrete web is a system of one-dimensional coalescing random walks that evolves in an extra dynamical time parameter. At any deterministic dynamical time, the paths behave as coalescing simple symmetric random walks. This…
There are various notions of quantum pseudorandomness, such as pseudorandom unitaries (PRUs), pseudorandom state generators (PRSGs) and pseudorandom function-like state generators (PRFSGs). Unlike classical pseudorandomness, where different…
Patankar schemes have attracted increasing interest in recent years because they preserve the positivity of the analytical solution of a production-destruction system (PDS) irrespective of the chosen time step size. Although they are now of…
Reinforcement learning (RL) methods have demonstrated their efficiency in simulation environments. However, many applications for which RL offers great potential, such as autonomous driving, are also safety critical and require a certified…
The involution walk is the random walk on $S_n$ generated by involutions with a binomially distributed with parameter $1-p$ number of $2$-cycles. This is a parallelization of the transposition walk. The involution walk is shown in this…
As NIST is putting the final touches on the standardization of PQC (Post Quantum Cryptography) public key algorithms, it is a racing certainty that peskier cryptographic attacks undeterred by those new PQC algorithms will surface. Such a…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…