We study an open problem of understanding the effects of the minimum component separation on the convergence rates of parameter estimation in finite Gaussian mixtures. We address this by developing a unified geometric framework based on novel Hellinger lower bounds that directly relate discrepancies between mixture densities directly to Wasserstein distances between their underlying mixing measures, with explicit dependence on both the minimum separation and the minimum weight. Our approach combines carefully designed interpolation polynomials with confluent divided difference techniques to construct specialized moment-extraction test functions. When the number of components is known, these bounds uncover a localization phenomenon: the separation complexity is driven strictly by the spatial configuration of mixture components, namely, whether they are concentrated in a single cluster, partitioned into multiple clusters separated by a macroscopic gap, or arranged without any structural constraints. On the other hand, when the number of components becomes unknown and is over-specified, the separation complexity is slightly reduced, while the minimum mixture weight disappears entirely from the convergence rates due to a transition from first-order to second-order Wasserstein geometry. As a consequence, we obtain separation-dependent convergence rates that continuously interpolate between point-wise and uniform estimation regimes, thereby settling the fundamental limits of parameter recovery in finite Gaussian mixtures.

I know this is unconventional, but I'm going to start by telling you the ending. Or at least, the ending as it stands today. Most of the people involved in this story wind up either dead, maimed, spending months in a mental hospital, languishing in jail, or gone underground. It's a tragedy from almost any angle, especially because, at the outset, most of these people were idealists committed to doing as much good as possible in a world they saw as beset by existential threats. In spite of those aims, or perhaps in pursuit of them, over the course of this story their lives will devolve into senseless violence.

Target detection is a fundamental task in radar sensing, serving as the precursor to any further processing for various applications. Numerous detection algorithms have been proposed. Classical methods based on signal processing, e.g., the most widely used CFAR, are challenging to tune and sensitive to environmental conditions. Deep learning-based methods can be more accurate and robust, yet usually lack interpretability and physical relevance. In this paper, we introduce a novel method that combines signal processing and deep learning by unfolding the CFAR detector with a state space model architecture. By reserving the CFAR pipeline yet turning its sophisticated configurations into trainable parameters, our method achieves high detection performance without manual parameter tuning, while preserving model interpretability. We implement a lightweight model of only 260K parameters and conduct real-world experiments for human target detection using FMCW radars. The results highlight the remarkable performance of the proposed method, outperforming CFAR and its variants by 10X in detection rate and false alarm rate. Our code is open-sourced here: https://github.com/aiot-lab/NeuroDet.

Multiple events hosted at a historic former hotel in Berkeley, California, have brought together people from intellectual movements popular at the highest levels in Silicon Valley while platforming prominent people linked to scientific racism, the Guardian reveals. But because of alleged financial ties between the non-profit that owns the building – Lightcone Infrastructure (Lightcone) – and jailed crypto mogul Sam Bankman-Fried, the administrators of FTX, Bankman-Fried's failed crypto exchange, are demanding the return of almost 5m that new court filings allege were used to bankroll the purchase of the property. During the last year, Lightcone and its director, Oliver Habryka, have made the 20m Lighthaven Campus available for conferences and workshops associated with the "longtermism", "rationalism" and "effective altruism" (EA) communities, all of which often see empowering the tech sector, its elites and its beliefs as crucial to human survival in the far future. At these events, movement influencers rub shoulders with startup founders and tech-funded San Francisco politicians – as well as people linked to eugenics and scientific racism. Since acquiring the Lighthaven property – formerly the Rose Garden Inn – in late 2022, Lightcone has transformed it into a walled, surveilled compound without attracting much notice outside the subculture it exists to promote.

The parametric constant false alarm rate (CFAR) detection algorithms which are based on various statistical distributions, such as Gaussian, Gamma, Weibull, log-normal, G0 distribution, alpha-stable distribution, etc, are most widely used to detect the ship targets in SAR image at present. However, the clutter background in SAR images is complicated and variable. When the actual clutter background deviates from the assumed statistical distribution, the performance of the parametric CFAR detector will deteriorate. In addition to the parametric CFAR schemes, there is another class of nonparametric CFAR detectors which can maintain a constant false alarm rate for the target detection without the assumption of a known clutter distribution. In this work, the Wilcoxon nonparametric CFAR scheme for ship detection in SAR image is proposed and analyzed, and a closed form of the false alarm rate for the Wilcoxon nonparametric detector to determine the decision threshold is presented. By comparison with several typical parametric CFAR schemes on Radarsat-2, ICEYE-X6 and Gaofen-3 SAR images, the robustness of the Wilcoxon nonparametric detector to maintain a good false alarm performance in different detection backgrounds is revealed, and its detection performance for the weak ship in rough sea surface is improved to some extent. Moreover, the Wilcoxon nonparametric detector can suppress the false alarms resulting from the sidelobes at some degree and its detection speed is fast.