Ah, the sweet smell of competition: Freebies are flying on campus. Verified US students can snag two free months of ChatGPT Plus from March 31 to May 31, 2025 (chatgpt.com/students). And Google’s Gemini Advanced become freely available to US college students all the way through finals 2026 from April 17, 2025 (gemini.google/students/). Why Tech Giants Love Students (and Their Data)? Discounts to college students are the cheapest brand loyalty booster. By getting students accustomed to their ecosystem and tools (AI, cloud services, productivity apps), tech companies help shape the default workflows and preferences of the future workforce, creating built-in demand and fashion. ...

It’s a gift to have sharp music memories—the kind that catch a familiar vibe in something new. The two pieces below don’t share the same melody, but there’s something in the way the instruments blend, the vocals drift, the atmosphere builds. Hit play and feel the resemblance for yourself:

Scoring rules are really cool, and useful. This seminal survey paper has over 6k citations as of April 2025 :o Strictly proper scoring rules, prediction, and estimation tandfonline [pdf] Scoring rules assess the quality of probabilistic forecasts, by assigning a numerical score based on the predictive distribution and on the event or value that materializes. A scoring rule is proper if the forecaster maximizes the expected score for an observation drawn from the distribution F if he or she issues the probabilistic forecast F, rather than G ≠ F. It is strictly proper if the maximum is unique. In prediction problems, proper scoring rules encourage the forecaster to make careful assessments and to be honest. In estimation problems, strictly proper scoring rules provide attractive loss and utility functions that can be tailored to the problem at hand. This article reviews and develops the theory of proper scoring rules on general probability spaces, and proposes and discusses examples thereof. Proper scoring rules derive from convex functions and relate to information measures, entropy functions, and Bregman divergences. In the case of categorical variables, we prove a rigorous version of the Savage representation. Examples of scoring rules for probabilistic forecasts in the form of predictive densities include the logarithmic, spherical, pseudospherical, and quadratic scores. The continuous ranked probability score applies to probabilistic forecasts that take the form of predictive cumulative distribution functions. It generalizes the absolute error and forms a special case of a new and very general type of score, the energy score. Like many other scoring rules, the energy score admits a kernel representation in terms of negative definite functions, with links to inequalities of Hoeffding type, in both univariate and multivariate settings. Proper scoring rules for quantile and interval forecasts are also discussed. We relate proper scoring rules to Bayes factors and to cross-validation, and propose a novel form of cross-validation known as random-fold cross-validation. A case study on probabilistic weather forecasts in the North American Pacific Northwest illustrates the importance of propriety. We note optimum score approaches to point and quantile estimation, and propose the intuitively appealing interval score as a utility function in interval estimation that addresses width as well as coverage. ...

Didn’t know calculating expectation would take this long… Consider $n$ i.i.d. random variables $X_i$ drawn from Power Law distribution with support lowerbound $x_\text{min} = 1$ and the shape parameter $\alpha > 2$—in other words, the pdf of $X_i$ being $$ f_{X_i}(x) = (\alpha - 1) x^{-\alpha }, $$ and $$ F_{X_i}(x) =1 - x^{-(\alpha - 1)} \quad \text{ for }x \ge 1. $$ Btw, for the heavy-tailed distribution family, it can be more comfortable (and general) to understand random variable $X$ as $$ \Pr[X > x] \sim x^{-\alpha}. $$ see Ibragimov and Walden (MS'10)’s Section 3 “Heavy-Tailed Distributions” for a cooler, less intuitive way of seeing it. ...

So are advertisement good or bad? There’s no fixed answer. One view says it’s great cause advertisers have to pay for ads—so only sellers who believe that their own products/services are of good quality will use ads (if ads price and the ads market adjust appropriately)—then ads become informative and useful signals, and they would help consumers distinguish valuable products out of the sea of alternatives. Another view is that ads are more like competitors for attention—and it becomes a bad equilibrium now when seller would have to buy ads to at least get any attention. ...

Four papers (topic) from the C&A (complexity & algorithms) workshop 2025 that I personally found interesting (or, perhaps, just understood), hosted by Sun Yat-Sen University, Guangzhou China. Two EconCS papers: Persuasive Calibration Yiding Feng and Wei Tang, 2025 (Arxiv link) The paper studies a persuasion problem consisting of an information sender and a receiver. It’s somewhat like information design—but calibration replaced commitment to an information policy. The model is restricted to a state in [0, 1] (unknown success probability of a Bernoulli experiment). Calibration means when the sender sends an signal $q$ it’s close to the expected value of the real state. ...

I’ve blogged about Mendelssohn’s Scherzo from a A Midsummer Night’s Dream previously (two interesting Mendelssohn paraphrases—Rachmaninoff’s genius piano transciption of Mendelssohn’s incidental music). But today let’s talk about the piece itself, in its most authentic orchestral form. Mendelssohn is a big fan of Shakespeare and particular the Midsummer play. The composer’s sister Fanny explained it this way. “From our youth on we were entwined in A Midsummer Night’s Dream, and Felix [Mendelssohn] particularly made it his own. He identified with all the characters. He re-created them, so to speak, every one of those whom Shakespeare produced in the immensity of his genius.” ...

My undergraduate advisor Pinyan Lu has published a special introductory column for theoretical computer science in the Communication of CCF (China Computer Federation). The Chinese version is available here. TCS field is not only home to many powerful tools (and brilliant minds), but it also boasts a beautiful, elegant philosophical methodology—a way of thinking that is deeply fundamental. Snippets from the article: [TCS has] its unique internal way of thinking. I believe that most work in theoretical computer science follows a three-step pattern: ...

See previous post for the idea: My Ex, Apple PR, and the Economics of (Not) Buying an iPhone — for iteratively updated products like iPhone, do consumers strategically decide on Wait-to-Buy? It turns out that the market does anticipate upcoming product and update expectations w.r.t. new information. When Trump first announced the Tariff raise, Apple Pro Fans quickly reacts and adjusted their policy for iPhone Purchase: Should you buy an iPhone right now? Chance Miller 9to5mac ...

Companies react strategically to tariff raise: Apple transported five planes full of iPhones and other products from India to the US in just three days during the final week of March. The urgent shipments were made to avoid a new 10% reciprocal tariff. Gadgets Now Although Apple’s headquater is in California, iPhones are manufactured overseas—China, India. Apple currently assembles the entire iPhone 15 and iPhone 16 lineups in India as well as China. A 10% baseline tariff on all imports into the United States kicked in on Saturday. On April 9, the tariffs that Trump has falsely labeled as “reciprocal” will kick in. This will raise the tariff rate on imports from China to 54% and imports from India to 27%. ...