We study a purely local inverse problem for non-reversible Randers metrics ( F = |cdot|_g + beta ) defined on smooth oriented surfaces. Using only the lengths of sufficiently small closed curves around a point ( p ), we prove that the exterior derivative ( dbeta(p) ) can be uniquely and stably recovered. Moreover, we establish that ( dbeta(p) ) is the only second-order local invariant retrievable from such local length measurements. Our approach is entirely metric-based, independent […]

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Missed a post last week due to the Thanksgiving long weekend :-). We had gone to San Francisco to see the city and try out a couple of hikes). Just FYI – strolling around SF is also as much a hike as any of the real trails at Mt Sutro – with all the uphill & downhill roads! As for Robotics, I am currently on Week 3 of the Mobility course, which is more of physics than ‘computer […]

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There are many obvious things that we humans do to a much larger degree than other animals. We construct great civilizations, we create advanced technology, we use complex language, we make art and tell stories. How do our unique capabilities guide us in figuring out how our brains are different from those of other animals, if they are? To me, the most revealing feature of human intelligence is that it is primarily societal, rather than individual. Most of […]

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Learn to visualize quasar redshift data by building an interactive marimo dashboard using Polars, pandas, and Matplotlib. You’ll practice retrieving, cleaning, and displaying data in your notebook. You’ll also build interactive UI components that live-update visualizations in the notebook. [ 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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Data engineering exists because production databases are built for fast transactions (rows), while analytics requires massive scans (columns); trying to do both on one system can crash your business and cost millions.

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Riyadh is quickly emerging into a dynamic hub of global influence and innovation. Guided by Vision 2030, Saudi Arabia is embracing forward-thinking policies, entrepreneurship, and technology to expand its economy and promote a creativity culture. Known for its commercial and political significance primarily, Riyadh now redefines its personality as an innovation center, attracting global startups, investors, and talent. Now, the city stands as a testament to the power of planning, progress, and ambition to shape a futuristic, dynamic […]

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Developers can now submit apps for review and publication in ChatGPT, with approved apps appearing in a new in-product directory for easy discovery. Updated tools, guidelines, and the Apps SDK help developers build powerful chat-native experiences that bring real-world actions into ChatGPT.

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