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We develop and counterfactually evaluate a resolution-aware risk-design framework (PIRAP) for perpetual futures whose underlying tracks a single binary prediction-market probability through resolution. The framework specifies six…
We establish four structural results for signature volatility models. First, we prove global existence and uniqueness of strong solutions to the signature SDE $dS_t = S_t \langle \ell, \widehat{W}_t \rangle \, dB_t$ on the weighted tensor…
We design and analyze an approximation method for advection-diffusion-reaction equations where the (generalized) degrees of freedom are polynomials of order $k\ge0$ at mesh faces. The method hinges on local discrete reconstruction operators…
We present a new meshless method for scalar diffusion equations which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of…
We evaluated the performance of the classical and spectral finite element method in the simulation of elastodynamic problems. We used as a quality measure their ability to capture the actual dispersive behavior of the material. Four…
The electric field grading of dielectric permittivity gradient devices is an effective way of enhancing their insulation properties. The in-situ electric field-driven assembly is an advanced method for the fabrication of insulation devices…
We couple a free solute diffusion model to a model of crystal surface growth represented by, but not limited to, a (2 + 1)-dimensional solid-on-solid (SOS) model confined by a flat surface. We use kinetic Monte Carlo (KMC) with dissolution…
Using extensive molecular dynamics simulation of a coarse-grained model, we demonstrate the possibility of sustained unidirectional motion (durotaxis) of droplets without external energy supply when placed on a polymer brush substrate with…
The present report describes a big data numerical study of crystal plasticity finite element (CPFE) modelling using static and grain-based meshing to investigate the dependence of the results on the discretization approach. Static mesh…
The most recent update of financial option models is American options under stochastic volatility models with jumps in returns (SVJ) and stochastic volatility models with jumps in returns and volatility (SVCJ). To evaluate these options,…
For elliptic interface problems in two- and three-dimensions, this paper establishes a priori error estimates for Crouzeix-Raviart nonconforming, Raviart-Thomas mixed, and discontinuous Galerkin finite element approximations. These…
A common problem when using model predictive control (MPC) in practice is the satisfaction of safety specifications beyond the prediction horizon. While theoretical works have shown that safety can be guaranteed by enforcing a suitable…
In post-quantum blockchain settings, objects that require validity proofs (e.g., blob roots, execution-layer or consensus-layer signature aggregates) must be broadcast through mempool and relay networks. Recursive STARKs have been proposed…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
Accurate free-energy estimation is essential in molecular simulation, yet the periodic boundary conditions (PBC) commonly used in computer simulations have rarely been explicitly exploited. Equilibrium methods such as umbrella sampling,…
We extend the notion of distributed decision in the framework of distributed network computing, inspired by recent results on so-called distributed graph automata. We show that, by using distributed decision mechanisms based on the…
Coherent potential approximation (CPA) has widely been used for studying residual resistivity of bulk alloys and electrical conductivity in inhomogeneous systems with structural disorder. Here we revisit the single-site CPA within the…
This paper is devoted to the non-asymptotic control of the mean-squared error for the Ruppert-Polyak stochastic averaged gradient descent introduced in the seminal contributions of [Rup88] and [PJ92]. In our main results, we establish…
Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…