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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 ...

For the C implementation on GPUs (recommended for benchmarking), please visit the following repository: $$ \begin{array}{ll} \underset{x \in \mathbb{R}^n}{\min} \quad & \langle c, x \rangle \\ \text{s ...

Standard computer implementations of Dantzig's simplex method for linear programming are based upon forming the inverse of the basic matrix and updating the inverse ...

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 ...

We study a class of integer bilevel problems, the so-called Integer Linear Multiplicative Bilevel Problem, ILMBP, where the constraints are linear and both the upper level problem and the lower level ...

Integer linear programming can help find the answer to a variety of real-world problems. Now researchers have found a much faster way to do it. The traveling salesperson problem is one of the oldest ...