Daniel Zhao

Hi, I'm Daniel, a recent graduate from Harvard College in mathematics and statistics. I was previously a quantitative trader, and before that, I interned at SpaceX and NASA JPL.

Research

My interests include AI safety and its applications to the sciences. Some of my past research has been on MCMC, stochastic modeling, and computational biology

Journal Articles

Stopping time and return period figure
Calculations on stopping time and return period

Baiyu Chen, Yi Kou, Daniel Zhao, Fang Wu, Shaoxun Liu, Alvin Chia, Liping Wang

Natural Hazards, 2020

We study the stochastic characteristics of ocean environments and introduce stopping time into storm surge analysis.

Conference Proceedings and Presentations

Quantifying Mineral-ligand Structural Similarities

Daniel Zhao, Stuart Bartlett, Yuk Yung

American Geophysical Union, 2020

The geological world is closely associated with biological history and function. Here, we present a mathematical method for comparing structural and chemical similarities between mineral-ligand pairs using molecular similarity metrics.

Workshop Papers and Preprints

Policy Gradients for Optimal Parallel Tempering MCMC

Daniel Zhao and Natesh S. Pillai

ICML 2024 Workshop on Structured Probabilistic Inference & Generative Modeling, 2024

We introduce a policy-gradient algorithm for optimizing the temperature ladder in parallel tempering MCMC. Our method outperforms SoTA for benchmark distributions.

Puzzles and Paradoxes

A collection of my favorite puzzles.

Prisoners in Rainbow Hats

Seven prisoners are each assigned a hat of seven possible colors, with color repetitions allowed. Every prisoner can see the hat colors of the other six prisoners, but not their own. They cannot communicate with others in any form, or else they are immediately executed. Then each prisoner writes down his guess of his own hat color. If at least one prisoner correctly guesses the color of his hat, they all will be set free immediately; otherwise they will be executed. They are given the night to come up with a strategy. Is there a strategy that they can guarantee that they will be set free?

Ants on a Stick

One hundred ants are placed on a meter stick and simultaneously begin walking left or right at 1 cm/second. When two ants collide, they both reverse direction. If an ant reaches the end of the stick, it falls off. What arrangement of ants maximizes the time before all ants have fallen off? How long can they last?

Bertrand's Paradox

Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle?

The Devil's Chessboard

A jailer places a coin on each square of a chessboard, heads or tails as he pleases, then hides a key under one square, which he reveals to the first prisoner. The first prisoner must flip exactly one coin and leave. The second prisoner then enters, sees only the arrangement of coins, and must name the square hiding the key. The prisoners may agree on a strategy beforehand. Can they guarantee escape?

Conway's Soldiers

Checkers occupy every square below an infinite horizontal line. As in peg solitaire, a checker may jump horizontally or vertically over an adjacent checker into an empty square, removing the checker that was jumped. How far above the line can a checker advance?

Infinitely Many Hats

Countably many prisoners are each assigned a red or blue hat. Every prisoner can see the hats of all the others, but not their own, and no communication of any kind is allowed. All prisoners simultaneously guess their own hat color. They may agree on a strategy the night before. Is there a strategy under which only finitely many prisoners guess incorrectly?

Ten Dots, Ten Coins

Ten points are drawn on a table, arranged however an adversary likes. Show that they can always be covered using identical circular coins that do not overlap. (The coins may hang off the table, and fewer than ten may be used.)