Long-term lithium therapy remains the most effective maintenance treatment for bipolar disorder, yet it poses a significant risk of progressive renal impairment in a subset of patients. Early ...
The central limit theorem started as a bar trick for 18th-century gamblers. Now scientists rely on it every day.
Autoregressive LLMs generate text by sampling from estimated probability distributions over the next token, conditional on prior context. We use these probabilities to construct an entropy-based ...
Van Vleck’s largest lecture hall was filled to the brim for popular YouTuber Grant Sanderon’s talk on high-dimensional spheres.
ABSTRACT: Using the concept of quantum wave probability, combined with the identity principle, we can derive the Boltzmann distribution, Fermi distribution, and Bose distribution. Different ...
Interest Rate Probability Distributions Implied by Derivatives Prices is a daily measure of the distribution of future short-term interest rates, calculated from prices of fixed-income derivatives ...
With less than a month remaining before the 2026 College Scholastic Ability Test, concerns have been raised that online lectures from a well-known entrance exam academy are being distributed without ...
In this lecture we argue that the fluctuations of Dirac eigenvalues on the finest scale, i.e. on the scale of the average level spacing do not depend on the underlying dynamics and can be obtained ...
Plot A has higher entropy than Plot B. Plot A has higher variance than Plot B. Plot C has the highest possible variance amongst distributions with support {0, 1, 2, 3 ...
Life is uncertain. None of us know what is going to happen. We know little of what has happened in the past or is happening now outside our immediate experience. Uncertainty has been called the ...
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