Interactive walkthrough of the four-step martingale decomposition of an additive functional, with a CLT check.

This was one of my favourite during Empirical Analysis III course. ...

The most famous tango in concert music.

Jazz that behaves like Bach.

The Grant Park Music Festival’s outdoor venue is at the Jay Pritzker Pavilion, sitting in the heart of downtown Chicago around the skyscrapers. Your browser doesn't support the video tag. Tonight’s concert featured the Grant Park Orchestra, Carlos Kalmar and pianist Olga Kern, playing a magnificent program: Sergei Rachmaninov Piano Concerto No. 3 Igor Stravinsky Game of Cards Edward Elgar In the South The outdoor festival is exactly like the Frank Gehry architecture — it pierce through the air and stand firmly among the Chicago skyscrapers. You feel more the shape and less the nuance. Rachmaninoff carries through with Olga Kern’s powerful playing, very metallic, sculptured and sharp. She played the first original cadenza for mvt I written by Rachmaninoff. My pianist friend think it’s the best cadenza ever written and its early appearance even shadows rest of the concerto movements.

The same nocturne, the other temperament.

The Goldbergs returned to the instrument they were written for.

The idea originates in Milton Friedman’s essay “The Methodology of Positive Economics” (1953), the opening chapter of his book Essays in Positive Economics (University of Chicago Press, 1953, pp. 3–43). Basically, Friedman’s central idea is, a theory should be judged by the accuracy of its predictions within its intended domain — not by whether its assumptions are realistic or descriptively accurate. And further — “the more significant the theory, the more unrealistic the assumptions.” So we should use the “as if” method. Model agents as if the assumptions held. Three examples: the expert billiard player (plays as if solving the physics), leaves on a tree (arranged as if maximizing sunlight), the profit-maximizing firm (behaves as if optimizing; competition weeds out those that don’t). Tie-breakers. When theories predict equally well, prefer greater simplicity and fruitfulness (scope, precision, new research). Friedman’s original essay is ambiguous, contested but never settled. I printed it as part of my Price Theory I readings and it now lies with my Bach sonata sheets… ...

Conducted by Edwin Outwater, with soloist Sara Davis Buechner, the Grant Park Orchestra performed Tchaikovsky’s Piano Concerto No. 1. The evening also offered a pleasantly modern program: Jimmy López Loud Lou Harrison Symphony No. 2 (“Elegiac”) Amy Woodforde-Finden Kashmiri Song Pyotr Ilyich Tchaikovsky Piano Concerto No. 1 The orchestra has a lovely sound and plays as a tight, well-coordinated ensemble. The pieces are a nice surprise — very well-curated. Even so, I wasn’t especially looking forward to the Tchaikovsky — this is a festival, and a free concert at that (bravo!) — since the concerto’s solemnity asks for a certain seriousness rather than a cheerful summer spirit. But the first three pieces eased the audience nicely into the mood. ...

I participated in Model United Nations during high school — I was then lotteried to represent Antigua and Barbuda. For a 100% geography idiot, I am proud to say that I happen to know this country well — climate, economy, geography etc. Now the world seems to be doing the same thing with Cape Verde, according to Google Trend — the time line June 15 vs. Spain (0–0 Draw): Cape Verde kicked off their tournament by completely shocking heavyweights Spain, holding them to a scoreless draw. This was likely the first major spike where people collectively googled, “Where is Cape Verde?” June 21 vs. Uruguay (2–2 Draw): Proving the first game wasn’t a fluke, they went toe-to-toe with Uruguay in an absolute thriller. June 26 vs. Saudi Arabia (0–0 Draw): Tonight, they capped off their group stage with a gritty draw against Saudi Arabia in Houston. Soccer fans around the world realized this tiny team went undefeated against top-tier global talent, query (Google Trends) related to Cape Verde is skyrocketing right now. ...