Research
Research
Research
Research
7,820+ open-access research outputs.
We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $\Omega(1/t)$ prim…
We investigate the lifetime of dynamical regimes under the impact of noise motivated by low-dimensional models of the atmosphere. One may expect that the inclusion of noise tends to make the system le…
We propose a regularized Hessian-free Newton-type method for minimizing smooth convex functions with Lipschitz continuous Hessians. The algorithm constructs an approximate Hessian by finite difference…
We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulat…
It is a fundamental question in epidemiology to estimate, model and predict the growth rate of a pandemic. Analogously, analysing the diffusion of innovation, (fake) news, memes, and rumours is of key…
This paper investigates the asymptotics of eigenstructure of sample covariance matrix under the spiked covariance matrix model in ultra-high-dimensional settings, where the dimensionality can grow muc…
We study the class of selfless C*-probability spaces introduced by Robert. It is known that a selfless tracial algebra has strict comparison and a unique trace. We prove that for separable tracial C*-…
We investigated the evolute of a space curve with singular points. As smooth curves with singular points, we apply the theory of framed curves. However, the involute corresponding to the evolute in th…
For a couple $\mathcal M$, $\mathcal N$ of Hilbert $C^*$-modules over a $C^*$-algebra $\mathcal A$, one has two notions of ``$\mathcal A$-rank 1 operators'': $\theta_{x,y}:\mathcal M\to\mathcal N$, $\…
We investigate the metric structure of nonassociative $\mathrm{L}^p$-spaces associated with tracial $\mathrm{JW}^*$-algebras. While noncommutative $\mathrm{L}^p$-spaces arising from von Neumann algebr…
This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of…
Let $X$ be a smooth complex projective curve. We prove that there exists a surjective commutative forgetful diagram from the chain of $\mathbb{C}^{*}$-flips of the moduli spaces of $\mathcal{O}_{X}$-t…
Ramsey-good graphs are graphs that contain neither a clique of size $s$ nor an independent set of size $t$. We study doubly saturated Ramsey-good graphs, defined as Ramsey-good graphs in which the add…
This paper presents the hybrid solver for a $CO_2$ sequestration problem. The solver uses the IGA-ADS (IsoGeometric Analysis Alternating Directions solver) to compute the saturation scalar field updat…
Understanding how biochemical systems settle into stable states, such as how protein concentrations reach equilibrium, is central to explaining cellular behavior and designing synthetic biological cir…
We establish the homogenization results for a class of nonlocal operators of convolution type with integrable jumping kernel $p$ multiplied by rapidly oscillating periodic or locally periodic coeffici…
We consider the Cauchy problem of the viscous $\beta$-plane equations. We first establish the global well-posedness of the system for the initial data sufficiently small compared to the Rossby paramet…
The multi-scale and non-linear nature of phase-field models of solidification requires fine spatial and temporal discretization, leading to long computation times. This could be overcome with artifici…
We prove a suitable fibration theorem over quasi-trivial tori that, through an approach developed by Harpaz and Wittenberg, implies so-called solvable descent. In particular, this gives a positive ans…
Approximation of functions satisfying partial differential equations (PDEs) is paramount for simulation of physical fluid flows and other problems in physics. Recently, physics-informed machine learni…
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