Related papers: Bounds on the number of time steps for simulating …
In literature, the cost of a partitioned fluid-structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the internal iterations within the nonlinear subproblems. In this…
The conventional spin dynamics simulations are performed in direct products of state spaces of individual spins. In a general system of n spins, the total number of elements in the state basis is >4^n. A system propagation step requires an…
Large molecular dynamics simulations (millions of atoms, tens of microseconds, thousands of processors) hit the strong scalability wall: simulation on twice as many processors does not take half the time. Inspired by large N-body space…
We pose a new and intriguing question motivated by distributed computing regarding random walks on graphs: How long does it take for several independent random walks, starting from the same vertex, to cover an entire graph? We study the…
We give faster algorithms for producing sparse approximations of the transition matrices of $k$-step random walks on undirected, weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of…
The physical processes at the interface of a low-temperature plasma and a solid are extremely complex. They involve a huge number of elementary processes in the plasma, in the solid as well as charge, momentum and energy transfer across the…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify…
The semi-random graph process is an adaptive random graph process in which an online algorithm is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the algorithm independently and uniformly at…
Graphical interaction models have become an important tool for analysing multivariate time series. In these models, the interrelationships among the components of a time series are described by undirected graphs in which the vertices depict…
An upper bound for the number of Hamiltonian cycles of symmetric diagraphs is established first in this paper, which is tighter than the famous Minc's bound and the Br$\acute{e}$gman's bound. A transformation on graphs is proposed, so that…
A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to…
We study hitting times in simple random walks on graphs, which measure the time required to reach specific target vertices. Our main result establishes a sharp lower bound for the variance of hitting times. For a simple random walk on a…
Level-sensitive latches are widely used in high- performance designs. For such circuits efficient statistical timing analysis algorithms are needed to take increasing process vari- ations into account. But existing methods solving this…
An algorithm observes the trajectories of random walks over an unknown graph $G$, starting from the same vertex $x$, as well as the degrees along the trajectories. For all finite connected graphs, one can estimate the number of edges $m$ up…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
Repulsive point processes arise in models where competition forces entities to be more spread apart than if placed independently. Simulation of these types of processes can be accomplished using dominated coupling from the past with a…
We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point…
We consider simulating an $n$-qubit Hamiltonian with nearest-neighbor interactions evolving for time $t$ on a quantum computer. We show that this simulation has gate complexity $(nt)^{1+o(1)}$ using product formulas, a straightforward…
Analog quantum simulations---simulations of one Hamiltonian by another---is one of the major goals in the noisy intermediate-scale quantum computation (NISQ) era, and has many applications in quantum complexity. We initiate the rigorous…