ComputingNotes

Calculus – Initial Value Problems

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Book Calculus by Thomas/Finney, 9th Edition, Page 282 Understanding Initial Value Problems in Calculus When studying differential equations in calculus, we often encounter something called an Initial Value Problem (IVP). While differential equations describe entire families of functions, an initial value problem helps us find one specific solution that fits a given condition. What Is ... Read More

Channel Estimation and Prediction Datasets

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The four-dimensional array structure [n_ue, n_rx, n_tx, n_sub] represents the following: WAIR-D Wireless AI Research Datasethttps://arxiv.org/pdf/2212.02159https://www.viwi-dataset.net/ RadoML Datasethttps://github.com/radioML/dataset Raymodtimehttps://www.lasse.ufpa.br/raymobtime

Reconfigurable Intelligent Surface (RIS)

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https://www.etsi.org/technologies/reconfigurable-intelligent-surfaceshttps://www.rohde-schwarz.com/au/solutions/wireless-communications-testing/wireless-standards/6g/reconfigurable-intelligent-surfaces-ris/reconfigurable-intelligent-surfaces-ris_257043.htmlhttps://www.6gacademy.com/what-is-ris/https://wirelesspi.com/reconfigurable-intelligent-surfaces-ris-a-tutorial/ Reconfigurable Intelligent Surfaces (RIS) are physically placed to act as a bridge between the Base Station (BS) and the User Equipment (UE), particularly in scenarios where the direct path is obstructed. Physical Components of the Surface The physical layout of the surface itself is carefully engineered:

Wireless Systems – Terms

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MIMO- Multi input and multi output is wireless technology that multiplies the capcity of a radio link using multiple transmit and receive antennas.https://en.wikipedia.org/wiki/MIMO FDD (Frequency Division Duplex): A transmission mode where uplink and downlink channels operate on different frequency bands. In FDD systems, the base station typically relies on user feedback to obtain downlink CSI ... Read More

Calculus – Integration

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Book Calculus by Thomas/Finney, 9th Edition, Page 275 Differential Calculus to Integral Calculus. This is where we stop asking “how fast is it changing?” and start asking “how much have we accumulated?” Indefinite Integrals The chapter kicks off with a simple question: If I give you the answer (the derivative), can you tell me the ... Read More

What is quantum advantage actually?

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https://www.linkedin.com/posts/googleresearch_what-does-quantum-advantage-really-mean-activity-7411496236043808768-1fTo?utm_source=share&utm_medium=member_desktop&rcm=ACoAAFvtEp0B-fk768n2MQaWnQRVk0ixzjLJZV0 https://research.google/blog/a-verifiable-quantum-advantage/ https://www.nature.com/articles/s41586-025-09526-6 FUNDAMENTALS: Out-of-time-order correlators in quantummechanicshttps://arxiv.org/pdf/1703.09435

Various Bounds in Optimization

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Regret Bound:https://www.emergentmind.com/topics/cumulative-regret-analysishttp://sbubeck.com/LecturesALL_Bubeck.pdfhttps://www.jmlr.org/papers/volume11/jaksch10a/jaksch10a.pdfhttps://datascience.stackexchange.com/questions/62141/what-are-regret-boundshttps://arxiv.org/pdf/1403.5556 Lecture 1:Introduction to regret analysisS´ebastien BubeckMachine Learning and Optimization group, MSR AI

Assumptions and Their Meaning in Optimization Problems

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1. Lipschitz Continuity: The “Speed Limit”This assumption prevents the function from changing too rapidly over a certain distance. 2. 𝐿-Smoothness: The Curvature CeilingSmoothness ensures the gradient (slope) of the function doesn’t change abruptly. A function is 𝐿-smooth if its gradient is Lipschitz continuous. 3. 𝜇-Strong Convexity : The Curvature Floor – Bowl ShapeStrong convexity guarantees that ... Read More
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