{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"scicode","formal_name":"SciCode","introduction":"SciCode evaluates the ability to solve scientific research problems through code. Problems are decomposed into subproblems; this dev import preserves the relationships between 15 parent problems and 50 subproblems.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/SciCode1/SciCode","indexing_mode":"noindex","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[]}},"task_id":"35f45ae4-c416-5bfa-96eb-e9b73bfe3467","task_key":"dev--8d687b65-3840-5141-a0ef-5236e32ac9a0--47~2e4","task_revision_id":"3","upstream_id":"47.4","short_description":"Write a function to use Markov Chain Monte Carlo simulation to generate samples…","config":"","split":"dev","body":"{\"step_background\":\"Background:\\n\\nIn the canonical ensemble, we have to sample distribution. This can be done using the following scheme:\\nSelect a particle at random and calculate the energy of this configuration $\\\\mathcal{U}(0)$.\\n2. Give this particle a random displacement,\\n$$\\n\\\\mathbf{r}(\\\\mathbf{o}) \\\\rightarrow \\\\mathbf{r}(\\\\mathbf{0})+\\\\Delta(\\\\operatorname{Ranf}-0.5),\\n$$\\nwhere $\\\\Delta / 2$ is the maximum displacement. The value of $\\\\Delta$ should be chosen such that the sampling scheme is optimal. The new configuration is denoted $n$ and its energy $\\\\mathcal{U}(n)$.\\n\\n3. The move is accepted with a probability\\n$$\\n\\\\operatorname{acc}(o \\\\rightarrow \\\\mathfrak{n})=\\\\min (1, \\\\exp \\\\{-\\\\beta[\\\\mathcal{U}(\\\\mathfrak{n})-\\\\mathcal{U}(o)]\\\\})\\n$$\\nIf rejected, the old configuration is kept.\",\"step_description_prompt\":\"Write a function to use Markov Chain Monte Carlo simulation to generate samples energy of system of atoms interacting through Lennard Jones potential at temperature T, using Metropolis-Hasting Algorithm with Gaussian trial move. Assume that \\\"U_i\\\" is given, and it computes the total energy on a single stom. Also assume that \\\"U_system\\\" is given, and it computes the total energy of the entire system. The inputs of the resultant function contain a N by 3 float array init_posistion, a float sigma, a float epsilon, a float T, an integer MC_steps and a float dispSize. The output is a MC_steps by 1 float array.\"}","display_format":"scicode-step","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/SciCode1/SciCode","history":"initial import","indexing_mode":"noindex","subproblems":[],"grids":[]}