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Ray tracing algorithm simulates the physical movements of a huge amount of rays to render a high quality image, in which the tracing procedure for each ray can be implemented in parallel. By leveraging the inherent parallelism of quantum…
A numerical method is developed for solving a system of partial differential equations modeling the flow of a nematic liquid crystal fluid with stretching effect, which takes into account the geometrical shape of its molecules. This system…
We design a lightweight beam-searching algorithm for mobile millimeter-wave systems. We construct and maintain a set of path skeletons, i.e., potential paths between a user and the serving base station to substantially expedite the…
A Dyson map explicitly determines the appropriate basis of electromagnetic fields which yields a unitary representation of the Maxwell equations in an inhomogeneous medium. A qubit lattice algorithm (QLA) is then developed perturbatively to…
Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…
Evolving trees arise in many real-life scenarios from computer file systems and dynamic call graphs, to fake news propagation and disease spread. Most layout algorithms for static trees do not work well in an evolving setting (e.g., they…
The performance of modern algorithms on certain computer vision tasks such as object recognition is now close to that of humans. This success was achieved at the price of complicated architectures depending on millions of parameters and it…
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…
The electromagnetic behavior of plasmonic structures can be predicted after discretizing and solving a linear system of equations, derived from a continuous surface integral equation (SIE) and the appropriate boundary conditions, using a…
In this paper, we propose a sampling-based motion planning algorithm that finds an infinite path satisfying a Linear Temporal Logic (LTL) formula over a set of properties satisfied by some regions in a given environment. The algorithm has…
We review recent results and present new ones on a deterministic follow-the-leader particle approximation of first and second order models for traffic flow and pedestrian movements. We start by constructing the particle scheme for the first…
We study the pedestrian escape from an obscure corridor using a lattice gas model with two species of particles. One species, called passive, performs a symmetric random walk on the lattice, whereas the second species, called active, is…
We present the quantum algorithm for the Longest Trail Problem. The problem is to search the longest edge-simple path for a graph with $n$ vertexes and $m$ edges. Here edge-simple means no edge occurs in the path twice, but vertexes can…
The computational complexity of classical numerical methods for solving Partial Differential Equations (PDE) scales significantly as the resolution increases. As an important example, climate predictions require fine spatio-temporal…
In this paper, we propose an approach for solving PDEs on evolving surfaces using a combination of the trace finite element method and a fast marching method. The numerical approach is based on the Eulerian description of the surface…
In the context of PDE-constrained optimization theory, source identification problems traditionally entail particles emerging from an unknown source distribution inside a domain, moving according to a prescribed stochastic process,…
Classically, the time complexity of a first-order method is estimated by its number of gradient computations. In this paper, we study a more refined complexity by taking into account the `lingering' of gradients: once a gradient is computed…
We propose a multi-stage learning approach for pruning the search space of maximum clique enumeration, a fundamental computationally difficult problem arising in various network analysis tasks. In each stage, our approach learns the…
We introduce two types of estimators of the finite-dimensional parameters in the case of observations of inhomogeneous Poisson processes. These are the estimators of the method of moments and multi-step MLE. It is shown that the estimators…
Consider the model where particles are initially distributed on $\mathbb{Z}^d, \, d\geq 2$, according to a Poisson point process of intensity $\lambda>0$, and are moving in continuous time as independent simple symmetric random walks. We…