Using an advanced Monte Carlo method, Caltech researchers found a way to tame the infinite complexity of Feynman diagrams and solve the long-standing polaron problem, unlocking deeper understanding of ...

$$ \begin{array}{ll} \underset{x \in \mathbb{R}^n}{\min} \quad & \langle c, x \rangle \\ \text{s.t.} \quad & L \leq A x \leq U, \\ & l \leq x \leq u . \end{array} $$ Before running the scripts, please ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

John C. Urschel is an assistant professor in the MIT Math Department and a Junior Fellow at the Harvard Society of Fellows. He previously played for the Baltimore Ravens. This interview has been ...

Abstract: This paper investigates the equivalence between a class of mixed-integer linear and linear programming prob-lems. By utilizing the addition of slack variables theorem, we demonstrate that ...

Many important practical computations, such as scheduling, combinatorial, and optimization problems, use techniques known as integer programming to find the best combination of many variables. In ...

Euler Method: The simplest numerical method for solving ODEs, which uses the derivative to project forward. [ y_{n+1} = y_n + h \cdot f(x_n, y_n) ] Heun's Method (Improved Euler Method): A two-step ...

Since the open-pit precedence-constrained production scheduling problem is an NP-hard problem, solving it is always a challenging task, especially from a long-term perspective because a mineral ...