Research
Research
Research
Research
375+ open-access research outputs.
In 1963, Rapha\"el Salem concluded his highly influential book ``Algebraic Numbers and Fourier Analysis'' with a list of four unsolved problems. The first two problems remain wide open while the last …
Very-low-Earth orbit drag uncertainty quantification in the rarefied/transitional Knudsen-number regime requires estimating not only the mean drag coefficient but also higher-order moments under atmos…
We present CapBench, a fully reproducible, multi-PDK dataset for capacitance extraction. The dataset is derived from open-source designs, including single-core CPUs, systems-on-chip, and media acceler…
A new radiation solver, RAPRAL (RAdiation Prediction based on RAy tracing and Line-by-line) implemented in C++, is developed for simulating high-temperature thermochemical nonequilibrium radiative pro…
Let $\Lambda$ be a set and $\mathbb{F}$ a field, and suppose that $K,Q:\Lambda^2\to\mathbb{F}$ are two functions such that for any $n\in\mathbb{N}$ and $x_1,x_2,\ldots,x_n\in\Lambda$, the determinants…
In this paper, we investigate a universal blow-up bound for the focusing mass-critical nonlinear Schr\"odinger equation for general initial data in $L^2(\mathbb R^d)$, extending previous knowledge for…
For the mass-critical generalized Korteweg-de Vries equation, $$ \partial_{t}u+\partial_{x}\left( \partial_{x}^{2}u+u^{5}\right)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}.$$ We prove the existence …
Alp\"oge--Bhargava--Shnidman showed that even a strengthened \emph{no local obstruction} condition for monogenicity does not force a global power integral basis: in the full spaces of cubic and quarti…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact thr…
In this work we study the mean-field description of Consensus-Based Optimization (CBO), a derivative-free particle optimization method. Such a description is provided by a non-local SDE of McKean-Vlas…
Consensus-based optimization (CBO) is a multi-agent metaheuristic derivative-free optimization algorithm that has proven to be capable of globally minimizing nonconvex nonsmooth functions across a div…
Voice cloning technology poses significant privacy threats by enabling unauthorized speech synthesis from limited audio samples. Existing defenses based on imperceptible adversarial perturbations are …
This paper documents Project Rachel, an action research study that created and tracked a complete AI academic identity named Rachel So. Through careful publication of AI-generated research papers, we …
For the quintic, mass critical generalized Korteweg-de Vries equation, for any $\nu \in (\frac{1}{2}, 1)$, we prove the existence of solutions in the energy space that blow up in finite time $T>0$ wit…
Monte Carlo random walk methods are widely used in capacitance extraction for their mesh free formulation and inherent parallelism. However, modern semiconductor technologies with densely packed struc…
Collaborative machine learning enables multiple data owners to jointly train models for improved predictive performance. However, ensuring incentive compatibility and fair contribution-based rewards r…
In this brief article, we present the formula created by Rafael Barrett in 1903 in a note to Henri Poincar\'e, which remained unknown for decades. Discovered in the 1930s by a Uruguayan mathematician,…
We derive the asymptotic behaviour of the genealogy of a logistic branching process in the setting where the equilibrium population size is large. In three regimes on the tail of the offspring distrib…
This paper presents a comprehensive refurbishment of the interactive robotic art installation Standards and Double Standards by Rafael Lozano-Hemmer. The installation features an array of belts suspen…
My findings show what causes loss of awareness, anesthesia, memory replay, opioid induced respiratory depression (OIRD), and slow-wave sleep (SWS). Opiates are fast pain relievers and anesthetics that…
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