Research
Research
Research
Research
185+ 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 …
The minimum convex cover problem seeks to cover a polygon $P$ with the fewest convex polygons that lie within $P$. This problem is $\exists\mathbb R$-complete, and the best previously known algorithm,…
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 …
Grover's search algorithm is one of the basic building block in the world of quantum algorithms. Successfully applying it to combinatorial optimization problems is a subtle challenge. As a quadratic s…
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,…
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…
We compute numerically the dimensions of the graded quotients of the linearized Kashiwara-Vergne Lie algebra lkv in low weight, confirming a conjecture of Raphael-Schneps in those weights. The Lie alg…
We study the blow-up dynamics for the $L^2$-critical focusing half-wave equation on the real line, a nonlocal dispersive PDE arising in various physical models. As in other mass-critical models, the g…
We investigate the problem of finding the minimum number of pieces necessary for dividing a three-dimensional sphere or a ball and reassembling it to form $n$ congruent copies of the original object, …
In continuation of the study of the companion work, we prove the high-energy mode stability for linearized operator around self-similar profiles in [Bahri-Martel-Rapha\"el, 2021] for slightly mass-sup…
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