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 ...

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 ...

Kamala Harris is camped out at a Pittsburgh hotel. Donald Trump is being peppered informally by aides. Both sides share the same belief about why the debate is so crucial. By Jonathan Swan Maggie ...

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 ...

Abstract: The Branch-and-Bound(B&B) algorithm is an effective method for solving the Mixed Integer Linear Programming (MILP) problem. Its performance significantly impacts the overall performance of ...