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This paper proposes a reformulation of the scenario-based two-stage unit commitment problem under uncertainty that allows finding unit-commitment plans that perform reasonably well both in expectation and for the worst case realization of…
Two-stage stochastic optimization is a framework for modeling uncertainty, where we have a probability distribution over possible realizations of the data, called scenarios, and decisions are taken in two stages: we make first-stage…
3D Gaussian Splatting (3DGS) has recently emerged as a pioneering approach in explicit scene rendering and computer graphics. Unlike traditional neural radiance field (NeRF) methods, which typically rely on implicit, coordinate-based models…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…
In this work, we attempt to solve the integer-weight knapsack problem using the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a well-known NP-complete problem in computer science, with applications in economics, business,…
Stochastic solutions provide new rigorous results for nonlinear PDE's and, through its local non-grid nature, are a natural tool for parallel computation. There are two different approaches for the construction of stochastic solutions:…
Cutting and packing problems arise in a large variety of industrial applications, where there is a need to cut pieces from a large object, or placing them inside a containers, without overlap. When the pieces or the containers have…
3D printing has long been a technology for industry professionals and enthusiasts willing to tinker or even build their own machines. This stands in stark contrast to today's market, where recent developments have prioritized ease of use to…
As high-performance computing (HPC) moves into the exascale era, computer scientists and engineers must find innovative ways of transferring and processing unprecedented amounts of data. As the scale and complexity of the applications…
We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the integrality gap of a "typical" knapsack problem is drastically smaller than the integrality…
Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of simulated models and morphologies have exceeded the capacity of any…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
Recent approaches representing 3D objects and scenes using Gaussian splats show increased rendering speed across a variety of platforms and devices. While rendering such representations is indeed extremely efficient, storing and…
A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real…
Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of…
The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…
3D Gaussian Splatting (3DGS) has demonstrated remarkable effectiveness in 3D reconstruction, achieving high-quality results with real-time radiance field rendering. However, a key challenge is the substantial storage cost: reconstructing a…
Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed…
In recent years, to sustain the resource-intensive computational needs for training deep neural networks (DNNs), it is widely accepted that exploiting the parallelism in large-scale computing clusters is critical for the efficient…
We illustrate the adiabatic quantum computing solution of the knapsack problem with both integer profits and weights. For problems with $n$ objects (or items) and integer capacity $c$, we give specific examples using both an Ising class…