Luke Kuechly makes strong HOF case for Panthers teammate Cam Newton https://www.nytimes.com/athletic/7497532/2026/08/06/nfl-hall-of-fame-luke-kuechly-cam-newton-panthers/
AVFTCN 041 – 3 Weekend Long Reads About The Future of the Internet
What does the future of the Internet look like? What do we need to do differently? What could we do to bring about the Internet we want? What should we be concerned about with, for instance, the massive investment in AI infrastructure? Those are all questions that I've been focused on for years (well, except the last one... that's new), and I always seek out many other viewpoints as I ponder my own.
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From Flows to Maps: Sampling Laws for Attractor Intensity and Bounded-Noise Escape
Jiguang Yu, Louis Shuo Wang
https://arxiv.org/abs/2608.02933 https://arxiv.org/pdf/2608.02933 https://arxiv.org/html/2608.02933
arXiv:2608.02933v1 Announce Type: new
Abstract: Intensity of attraction quantifies the largest amplitude of a persistent bounded disturbance that an attractor can withstand without loss of controlled confinement in its basin. Although intensity has been formulated separately for flows and maps, its behavior under temporal sampling has remained unresolved. We establish an explicit correspondence between the intensity $\mu(A)$ of a continuous-time attractor and the intensity $\mu_h(A)$ of its exact time-$h$ map. For an $L$-Lipschitz vector field, \[ \frac{\mu(A)}{1 Lh} \leq \frac{\mu_h(A)}{h} \leq \mu(A)\frac{e^{Lh}-1}{Lh}, \] and hence $\mu_h(A)/h\to\mu(A)$. The resulting first-order rate is sharp in general, while smooth scalar escape geometries can exhibit second-order convergence. We extend the framework to one-step numerical methods through a stability theory for block intensity and to attracting invariant graphs over compact invertible nonautonomous bases, obtaining uniform sampling convergence over the forcing phase. For bounded-support random perturbations, normalized discrete intensity is identified with the pathwise safety threshold; above it, finite escape follows under an explicit finite-exit condition, while escape probabilities require additional assumptions on the noise law. We also show that the discrete state--normal boundary map converges to the normalized Pontryagin boundary system governing extremal reachable-set boundaries. Exact scalar benchmarks, a grazing resilience model, planar Duffing escape, anisotropic disturbances, periodic and quasiperiodic forcing, and transfer-operator computations illustrate the theory. These results give intensity estimated from discrete observations or simulations a sampling-independent continuous-time meaning.
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It'll be Carson Beck vs. Kenny Pickett when Cardinals-Panthers open the NFL's exhibition season https://www.foxsports.com/articles/nfl/itll-be-carson-beck-vs-kenny-pickett-when-cardinalspanthers-open-the-nfl…
Why you should watch Panthers-Cardinals in Hall of Fame Game, plus ranking the NFL's top 10 play-callers
https://www.cbssports.com/nfl/news/why-you…
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Panthers not ready to talk Bryce Young extension: 'His ceiling is currently unknown' https://www.nfl.com/news/panthers-not-ready-to-talk-bryce-young-extension-his-ceiling-is-currently-unknown