In such settings, the inverse scattering transform (IST) of Ablowitz, Kaup, Newell, and Segur [2] has enjoyed a rich and successful history, and is now the standard theoretical framework for deriving reduced-order evolution equations for soliton dynamics. Although these derivations are traditionally of an analytical - rather than data-driven - nature, recent work has employed the IST formalism as a tool for experimental data analysis, using the technique to analyze soliton content from empirical measurements [8, 15, 24]. Moreover, recent approaches using alternative parameterization techniques have demonstrated that the learning of reduced-order, interpretable equations of motion for solitons is tenable in a data-driven setting [6, 26, 27]. Despite the success of this recent work, however, little effort has been devoted to developing a data-driven modeling approach based on the IST itself, most likely due to the fact that the framework is fundamentally problem-specific. In this paper, we address the question of whether effective soliton dynamics can be inferred directly from observed scattering data (as opposed to being derived or approximated analytically).

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Flock cameras track more than your license plate, and they're spreading fast Flock cameras track more than your license plate, and they're spreading fast You can't get a breath of fresh air ... without us knowing. Thanks to the rise of AI, a new kind of surveillance camera has rapidly proliferated across the United States. Typically referred to as automated license plate readers, or ALPRs, they're most often mounted along roadways, where they log the movements of cars which pass through their field of vision. Though various companies offer them, the most well known come from Flock Security, and the company has consequently been a lightning rod for public opinion. Shocking exactly nobody, there has been widespread public backlash to cameras that track everyone, whether or not they've been suspected of a crime.

We study the sublinear multivariate mean estimation problem in d-dimensional Euclidean space. Specifically, we aim to find the mean µ of a ground point set A, which minimizes the sum of squared Euclidean distances of the points in Ato µ. We first show that a multiplicative (1 + ε) approximation to µ can be found with probability 1 δ using O(ε 1 logδ 1)many independent uniform random samples, and provide a matching lower bound. Furthermore, we give two estimators with optimal sample complexity that can be computed in optimal running time for extracting a suitable approximate mean: 1.

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The arachnids have multiple layers of retinas in each eye. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy . Technological advancements sometimes feel like a perpetual fight against nature itself, with scientists working out how to do things faster, more powerfully, and more efficiently.

Portions of the rock date back billions of years to when the moon was molten rock. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. NWA 12593 was discovered in Mali in 2017. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .

Background on Principal Component Analysis Principal component analysis (PCA) is a method widely used by practitioners for learning features of high-dimensional data [15]. It is a dimension reduction technique that represents the data in lower dimensions, often with the aim of exploratory analysis or visualization. PCA can also be used as a data preprocessing step, for instance in regression analysis. While PCA is familiar and commonplace for understanding behavior in the data's'bulk', only recently have similar methods been proposed for understanding high-dimensional extremes. The aim of this chapter is to review and compare recent approaches for extremal PCA. 1

Plus: The EU has proposed new legislation to end its Big Tech dependence. Most days in her chambers, Judge Maritza Braswell, a federal magistrate judge in Colorado, sifts through stacks of documents written by people without a lawyer. The number of these filings has more than doubled compared to before 2023. She puts that jump down to AI. But while AI appears to be expanding access to justice, it doesn't seem to be improving people's chances of winning. Judges are starting to question what rights and duties chatbots should have as they stand in for lawyers.

The world's first'hovertrain' could reach speeds of 270 mph in the 1960s But the futuristic Aérotrain never saw the light of day. More information Adding us as a Preferred Source in Google by using this link indicates that you would like to see more of our content in Google News results. This cancelled Mongolian postage stamp shows the Aérotrain Orleans, circa 1979. Breakthroughs, discoveries, and DIY tips sent six days a week. By signing up, you confirm you are 16+, will receive newsletters and promotional content and agree to our Terms of Use and acknowledge the data practices in our Privacy Policy .