Separable polynomial constraints arise naturally in numerous engineering applications, including sensor positioning systems, robotic kinematics, and regularized optimization. While general-purpose iterative solvers are widely available, their computational overhead and non-deterministic convergence behavior can be limiting factors in real-time and resourceconstrained environments. This paper presents the Parametric K-Formula (PK-Formula), a straightforward closed-form method for solving a specific but practically important class of separable polynomial equations. The method achieves O(n) computational complexity through parametric decomposition, offering 50–120× speedups over Newton-Raphson […]

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I tend to spend a lot of time in the command-line tools when working with the public cloud computing providers. It is fast, scriptable, and… strangely empowering. Over the last year as a Product Manager on Google Cloud Platform, I have been thinking a lot about improving the developer experience. Obviously, one of the crucial parts of this experience is the command-line access to the cloud. To improve this experience, we have launched gcloud: a command-line tool for […]

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arXiv:2601.00141v1 Announce Type: new Abstract: The rapid development of generative AI has made AI-generated images increasingly realistic and high-resolution. Most AI-generated image detection architectures typically downsample images before inputting them into models, risking the loss of fine-grained details. This paper presents GLASS (Global-Local Attention with Stratified Sampling), an architecture that combines a globally resized view with multiple randomly sampled local crops. These crops are original-resolution regions efficiently selected through spatially stratified sampling and aggregated using attention-based scoring. GLASS […]

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Hey everyone, I’m currently an Applied Scientist II at Amazon working primarily with LLMs (in the speech domain, but open to other areas), and I’m considering applying to Google DeepMind for either Research Engineer or Research Scientist roles. For context on my background: AS II level at Amazon I do not have PhD, but 3+ years of experience I’d love to hear from anyone who has: Interviewed at DeepMind (especially for RE or RS roles) – what should […]

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What are techniques for writing maintainable Python code? How do you make your Python more readable and easier to refactor? Christopher Trudeau is back on the show this week, bringing another batch of PyCoder’s Weekly articles and projects. [ Improve Your Python With 🐍 Python Tricks 💌 – Get a short & sweet Python Trick delivered to your inbox every couple of days. >> Click here to learn more and see examples ]

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arXiv:2601.03368v1 Announce Type: cross Abstract: Natural languages exhibit striking regularities in their statistical structure, including notably the emergence of Zipf’s and Heaps’ laws. Despite this, it remains broadly unclear how these properties relate to the modern tokenisation schemes used in contemporary transformer models. In this note, we analyse the information content (as measured by the Shannon entropy) of various corpora under the assumption of a Zipfian frequency distribution, and derive a closed-form expression for the slot entropy expectation […]

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