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We derive explicit distance bounds for Stratonovich iterated integrals along two Gaussian processes (also known as signatures of Gaussian rough paths) based on the regularity assumption of their covariance functions. Similar estimates have…
We introduce new hybridizable discontinuous Galerkin (HDG) methods for solving the two-dimensional vector Laplacian equation under three types of boundary conditions: electric, magnetic, and Dirichlet. The method is formulated on a…
In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow…
We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to…
While deep learning has expanded the possibilities for highly expressive variational families, the practical benefits of these tools for variational inference (VI) are often limited by the minimization of the traditional Kullback-Leibler…
This paper presents novel method for distribution-free robust trajectory optimization and control of discrete-time, nonlinear, and non-Gaussian stochastic systems, with closed-loop guarantees on chance constraint satisfaction. Our framework…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens &…
A new method ( PI-DFT ) which combines path integrals and density functional theory is proposed as a pathway to many fields of physics. Within path integral theory it is possible to construct particle densities without explicitly…
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals $X$ which are not semimartingales and whose $p$-variation is finite only for large values of $p$. In this context, rough…
Slender structures are ubiquitous in biological and physical systems, from bacterial flagella to soft robotic arms. The Cosserat rod provides a mathematical framework for slender bodies that can stretch, shear, twist and bend. In viscous…
This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
We extend unsteady thin aerofoil theory to model aerofoils with generalised chordwise porosity distributions. The analysis considers a linearised porosity boundary condition where the seepage velocity through the aerofoil is related to the…
A self-consistent mode-coupling theory is presented for the viscosity of solutions of charged rod-like polymers. The static structure factor used in the theory is obtained from polymer integral equation theory; the Debye-H\"{u}ckel…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to…
We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…
This paper presents a total Lagrangian mixed Petrov-Galerkin finite element formulation that provides a computationally efficient approach for analyzing Cosserat rods that is free of singularities and locking. To achieve a singularity-free…
Stochastic iterative algorithms, including stochastic gradient descent (SGD) and stochastic gradient Langevin dynamics (SGLD), are widely utilized for optimization and sampling in large-scale and high-dimensional problems in machine…