Interestingly, when using implicit updating to solve a continuous time system (of a certain structure), it coincide with Newton’s Method Setup Consider a household with state $(a, z) \in \mathcal{A} \times \mathcal{Z}$, where $a$ denotes assets and $z$ follows a Poisson process with intensity matrix $\Lambda$. Hamilton-Jacobi-Bellman Equation: $$ \rho v(a,z) = \max_c \left \lbrace u(c) + \partial_a v(a,z) \cdot s(a,z) + \sum_{z'} \lambda_{zz'} v(a,z') \right\rbrace $$where savings $s(a,z) = ra + wz - c(a,z)$. ...

Wolfgang Amadeus Mozart (Jan 27 1756 - Dec 5 1791) was born today 270 years ago! (But remember, he was still actively publishing in 2024…) Ganz kleine Nachtmusik (KV 648): Some prev posts about mozart: A Little Mozart Wisdom Mozart K.314 Movt. 3 | 2001 Europakonzert Istanbul Series Catalog | Glenn Gould vs. Mozart’s Greatest Concerto Glenn Gould vs. Mozart’s Greatest Concerto | IV. the piano sonata that Glenn recommends (K.333) Glenn Gould vs. Mozart’s Greatest Concerto | III. the piano concerto that Glenn dislikes for being too ‘boring’ (K.491) Mozart K.550, Symphony No.40 Mozart’s Requiem at the CSO Cosi Fan Tutte, by the LA Opera mozart stories

It’s just January, but there’s good news already! There are possibly hundreds of dishes. My favourites is the Pineapple Bun. (This one’s probably larger than my face…) Guangzhou, my hometown, is the origin of Canton Morning Tea (or dimsum, see leadtochina’s Canton Morning Tea for a crisp and very accurate introduction). But lately as the popularization of pre-made food, some restaurants start to microwave frozen food and put them in steaming plates as if they’re fresh made. It’s cheaper, and not everyone can tell the difference. People who love morning tea are scared that the market might get screwed up — so here comes regulation: ...

Meet my new PR Sleepingbot, an intelligent assistant that answers questions about all my historical blogposts. Its high-level architecture is: ┌─────────────────┐ ┌─────────────────┐ ┌─────────────────┐ │ Hugo Blog │────▶│ Railway API │────▶│ Anthropic API │ │ (GitHub Pages) │ │ (server.py) │ │ (Claude) │ └─────────────────┘ └─────────────────┘ └─────────────────┘ 1. Two-Stage (Retrieval-Augmented Generation) RAG Chatbot Stage 1: Send all post titles to Claude → “Which posts are relevant to this question?” Stage 2: Send full content of relevant posts + question → Get answer This is smarter than simple keyword search, and cheaper than sending all posts every time. ...

The Thaïs Méditation was originally an Entr’acte from the opera Thaïs by Jules Massenet. The opera itself is set in Roman-era Egypt and centers on a monk named Athanaël who tries to convert the courtesan Thaïs to Christianity. The Méditation occurs in Act II between two scenes, at a moment when Thaïs is wrestling with her worldly life and the possibility of spiritual change. It was originally for orchestra plus solo violin. The piece has long line melody that pierce through your heart. ...

Today Chicago is 3 degrees warmer than the North Pole… Preposterous (In Celsiu) A warm winter Largo for my fellow in the cold:

As the title suggests, this short and sweet piece is a love song: Elgar finished the piece in July 1888, when he was romantically involved with Caroline Alice Roberts, and he called it “Liebesgruss” (‘Love’s Greeting’) because of Miss Roberts’ fluency in German. On their engagement she had already presented him with a poem “The Wind at Dawn” which he set to music and, when he returned home to London on 22 September from a holiday at the house of his friend Dr. Charles Buck in Settle, he gave her Salut d’Amour as an engagement present. (Wikipedia) ...

Sometimes I embed music playing links onto my website. The workflow is as follows: Create assets/css/extended/custom.css and paste: /* Apple Music Embed */ .music-embed { max-width: 660px; border-radius: 12px; overflow: hidden; box-shadow: 0 4px 20px rgba(0, 0, 0, 0.15); } .music-embed iframe { display: block; width: 100%; border: none; } /* Alignment */ .music-embed.left { margin-right: auto; } .music-embed.center { margin-left: auto; margin-right: auto; } .music-embed.right { margin-left: auto; } /* Width modifiers */ .music-embed.small { max-width: 400px; } .music-embed.full { max-width: 100%; } I am ok with directly writing html code in markdown files (if you prefer another layer of abstraction, you can create an .html file in layouts so that embedding is more straightforward) ...

Mean reversion is a property some models have and some data exhibits. It’s not a law. It’s a useful lens but requires specifying the mechanism and checking whether it actually holds. So let’s check the conditions. In our Macroeconomics with Heterogeneous Households class, for the continuous-time model of an individual household with (Poisson) income shock, consumption follows the following dynamic: Courtsey to Professor Kaplan’s Course material… If you’re interested in more about the math/model. ...

The Grand Budapest Hotel (2014) written and directed by Wes Anderson was inspired by Zweig’s Die Welt von Gestern. It’s the pinnacle of color grading and metaphors. The film got 9 academy award nominations and won 4. The movie’s intrinsic core is quite obvious. To be frank, i think his world had vanished long before he even entered it. but i will say, he certainly sustained the illusion with a marvelous grace. ...