[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M6XGP5GAC81SK2AT8YA1XT6T":3,"skill-same:01M6XGP5GAC81SK2AT8YA1XT6T":72},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":16,"categories":17,"keywords":18,"publishedAt":39,"linkOnly":40,"markdownContent":41,"markdownBody":42,"frontMatter":43,"refName":52,"commitSha":53,"skillDirectory":54,"forksCount":14,"repositoryHtmlUrl":55,"repositoryHomepageUrl":6,"ownerHtmlUrl":56,"ownerBlogUrl":6,"ownerDescription":6,"updatedAt":57,"install":58,"resources":71},"01M6XGP5GAC81SK2AT8YA1XT6T","statistical-mechanics",null,"Monte Carlo simulation for statistical mechanics — Ising model, Metropolis-Hastings, Wolff cluster algorithm, observables (magnetization, susceptibility, specific heat), finite-size scaling, and critical phenomena analysis.","fadrienne\u002FMyGitHub","fadrienne","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F197874571?v=4","01M6X64V8VWCRSMFZ4EPS2BWXG","Francesca Adrienne","01M6X64VD5MW4F9PHDWQKS7ZAF",0,"MIT","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fopenscience\u002Fbackend\u002Fcli\u002Fskills\u002Fphysics\u002Fstatistical-mechanics\u002FSKILL.md",[],[19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38],"statistical mechanics","mechanics","synthetic","Critical Phenomena","Phase Transition","Ising Model","Monte Carlo","phase","transition","for","size","cluster","analysis","critical","scaling","physics","scipy","numpy","model","simulation","2026-11-10 10:12:30",false,"---\nname: statistical-mechanics\ndescription: Monte Carlo simulation for statistical mechanics — Ising model, Metropolis-Hastings, Wolff cluster algorithm, observables (magnetization, susceptibility, specific heat), finite-size scaling, and critical phenomena analysis.\ncategory: physics\nversion: 1.0.0\nauthor: Synthetic Sciences\nlicense: MIT\ntags: [Statistical Mechanics, Monte Carlo, Ising Model, Phase Transition, Critical Phenomena]\ndependencies: [\"numpy>=1.24.0\", \"scipy>=1.11.0\", \"matplotlib>=3.7.0\"]\n---\n\n# Statistical Mechanics (Monte Carlo)\n\n## Overview\n\nMonte Carlo simulation of classical statistical mechanics models. Metropolis-Hastings and cluster algorithms for spin models, with tools for measuring observables, detecting phase transitions, and finite-size scaling analysis.\n\n## When to Use\n\n- Simulating spin models (Ising, Potts, XY, Heisenberg)\n- Finding critical temperatures and exponents\n- Computing thermodynamic observables (energy, magnetization, susceptibility, specific heat)\n- Finite-size scaling analysis\n- Any equilibrium statistical mechanics simulation\n\n## Core Workflows\n\n### 1. 2D Ising Model (Metropolis)\n\n```python\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nclass IsingModel:\n    def __init__(self, L, T, J=1.0):\n        self.L = L\n        self.T = T\n        self.J = J\n        self.beta = 1.0 \u002F T\n        self.spins = np.random.choice([-1, 1], size=(L, L))\n\n    def energy(self):\n        \"\"\"Total energy: H = -J Σ s_i s_j (nearest neighbors).\"\"\"\n        s = self.spins\n        E = -self.J * np.sum(\n            s * np.roll(s, 1, axis=0) +\n            s * np.roll(s, 1, axis=1)\n        )\n        return E\n\n    def magnetization(self):\n        return np.sum(self.spins)\n\n    def metropolis_step(self):\n        \"\"\"Single Metropolis sweep (L² spin flip attempts).\"\"\"\n        L = self.L\n        for _ in range(L * L):\n            i, j = np.random.randint(0, L, size=2)\n            s = self.spins[i, j]\n            # Sum of nearest neighbors\n            nn = (self.spins[(i+1)%L, j] + self.spins[(i-1)%L, j] +\n                  self.spins[i, (j+1)%L] + self.spins[i, (j-1)%L])\n            dE = 2 * self.J * s * nn\n            if dE \u003C= 0 or np.random.rand() \u003C np.exp(-self.beta * dE):\n                self.spins[i, j] *= -1\n\n    def wolff_step(self):\n        \"\"\"Wolff cluster flip (much faster near T_c).\"\"\"\n        L = self.L\n        p_add = 1 - np.exp(-2 * self.beta * self.J)\n\n        i, j = np.random.randint(0, L, size=2)\n        cluster_spin = self.spins[i, j]\n        stack = [(i, j)]\n        visited = set()\n        visited.add((i, j))\n\n        while stack:\n            ci, cj = stack.pop()\n            for di, dj in [(1,0),(-1,0),(0,1),(0,-1)]:\n                ni, nj = (ci+di)%L, (cj+dj)%L\n                if (ni, nj) not in visited and self.spins[ni, nj] == cluster_spin:\n                    if np.random.rand() \u003C p_add:\n                        visited.add((ni, nj))\n                        stack.append((ni, nj))\n\n        for ci, cj in visited:\n            self.spins[ci, cj] *= -1\n\ndef simulate(L, T, n_equil=1000, n_measure=5000, algorithm='metropolis'):\n    \"\"\"Run simulation and collect observables.\"\"\"\n    model = IsingModel(L, T)\n\n    # Equilibration\n    for _ in range(n_equil):\n        if algorithm == 'wolff':\n            model.wolff_step()\n        else:\n            model.metropolis_step()\n\n    # Measurement\n    E_samples = []\n    M_samples = []\n    N = L * L\n\n    for _ in range(n_measure):\n        if algorithm == 'wolff':\n            model.wolff_step()\n        else:\n            model.metropolis_step()\n        E_samples.append(model.energy() \u002F N)\n        M_samples.append(abs(model.magnetization()) \u002F N)\n\n    E = np.array(E_samples)\n    M = np.array(M_samples)\n\n    return {\n        'E_mean': np.mean(E),\n        'E_std': np.std(E) \u002F np.sqrt(len(E)),\n        'M_mean': np.mean(M),\n        'M_std': np.std(M) \u002F np.sqrt(len(M)),\n        'C': N * np.var(E) \u002F T**2,           # specific heat\n        'chi': N * np.var(M) \u002F T,             # susceptibility\n        'spins': model.spins.copy(),\n    }\n```\n\n### 2. Phase Transition: Temperature Sweep\n\n```python\nfrom scipy import constants as const\n\nT_c_exact = 2 \u002F np.log(1 + np.sqrt(2))  # ≈ 2.269 (Onsager)\nprint(f\"Exact T_c = {T_c_exact:.4f}\")\n\nL = 32\ntemperatures = np.linspace(1.5, 3.5, 30)\nresults = []\n\nfor T in temperatures:\n    res = simulate(L, T, n_equil=2000, n_measure=5000, algorithm='wolff')\n    results.append(res)\n    print(f\"T={T:.3f}: \u003CE>={res['E_mean']:.4f}, \u003C|M|>={res['M_mean']:.4f}, \"\n          f\"C={res['C']:.4f}, χ={res['chi']:.4f}\")\n\n# Plot\nfig, axes = plt.subplots(2, 2, figsize=(12, 10))\n\nE_vals = [r['E_mean'] for r in results]\nM_vals = [r['M_mean'] for r in results]\nC_vals = [r['C'] for r in results]\nchi_vals = [r['chi'] for r in results]\n\nfor ax, vals, ylabel, title in zip(\n    axes.flat,\n    [E_vals, M_vals, C_vals, chi_vals],\n    [r'$\\langle E \\rangle \u002F N$', r'$\\langle |M| \\rangle \u002F N$',\n     r'$C_v \u002F N$', r'$\\chi \u002F N$'],\n    ['Energy', 'Magnetization', 'Specific Heat', 'Susceptibility']\n):\n    ax.plot(temperatures, vals, 'bo-', markersize=4)\n    ax.axvline(T_c_exact, color='red', linestyle='--', label=f'$T_c$ = {T_c_exact:.3f}')\n    ax.set_xlabel('Temperature $T$ [$J\u002Fk_B$]')\n    ax.set_ylabel(ylabel)\n    ax.set_title(title)\n    ax.legend()\n    ax.grid(True, alpha=0.3)\n\nplt.tight_layout()\nplt.savefig('ising_phase_transition.png', dpi=150, bbox_inches='tight')\n```\n\n### 3. Finite-Size Scaling\n\n```python\ndef finite_size_scaling(sizes, temperatures, n_equil=3000, n_measure=10000):\n    \"\"\"Run simulations for multiple L to extract critical exponents.\"\"\"\n    all_results = {}\n\n    for L in sizes:\n        all_results[L] = []\n        for T in temperatures:\n            res = simulate(L, T, n_equil=n_equil, n_measure=n_measure, algorithm='wolff')\n            all_results[L].append(res)\n        print(f\"L={L} done\")\n\n    # Find T_c from susceptibility peak for each L\n    for L in sizes:\n        chi = [r['chi'] for r in all_results[L]]\n        T_peak = temperatures[np.argmax(chi)]\n        print(f\"L={L:3d}: χ peak at T = {T_peak:.3f}\")\n\n    return all_results\n\n# sizes = [8, 16, 32, 64]\n# T_range = np.linspace(2.0, 2.6, 20)\n# results = finite_size_scaling(sizes, T_range)\n```\n\n### 4. Autocorrelation and Error Estimation\n\n```python\ndef autocorrelation_time(data):\n    \"\"\"Estimate integrated autocorrelation time.\"\"\"\n    n = len(data)\n    mean = np.mean(data)\n    var = np.var(data)\n    if var == 0:\n        return 1.0\n\n    acf = np.correlate(data - mean, data - mean, mode='full')[n-1:]\n    acf \u002F= acf[0]\n\n    # Integrate until first negative value\n    tau = 0.5\n    for k in range(1, n \u002F\u002F 4):\n        if acf[k] \u003C 0:\n            break\n        tau += acf[k]\n\n    return tau\n\n# Effective number of independent samples = N \u002F (2 * tau)\n# True standard error = std(data) * sqrt(2 * tau \u002F N)\n```\n\n## Critical Exponents (2D Ising, Exact)\n\n| Exponent | Symbol | Value | Relation |\n|---|---|---|---|\n| Specific heat | α | 0 (log) | C ~ |T - T_c|^(-α) |\n| Order parameter | β | 1\u002F8 | M ~ |T_c - T|^β |\n| Susceptibility | γ | 7\u002F4 | χ ~ |T - T_c|^(-γ) |\n| Correlation length | ν | 1 | ξ ~ |T - T_c|^(-ν) |\n| Critical isotherm | δ | 15 | M ~ H^(1\u002Fδ) at T_c |\n\n## Troubleshooting\n\n| Symptom | Fix |\n|---|---|\n| Very long equilibration | Use Wolff algorithm near T_c (no critical slowing) |\n| Noisy observables | Increase measurement sweeps, check autocorrelation time |\n| Wrong T_c | Finite-size effect — run larger L or use scaling |\n| Magnetization doesn't go to 0 | Take |M| (absolute), not M (which fluctuates around 0) |\n| Metropolis too slow near T_c | Switch to Wolff cluster algorithm |\n","# Statistical Mechanics (Monte Carlo)\n\n## Overview\n\nMonte Carlo simulation of classical statistical mechanics models. Metropolis-Hastings and cluster algorithms for spin models, with tools for measuring observables, detecting phase transitions, and finite-size scaling analysis.\n\n## When to Use\n\n- Simulating spin models (Ising, Potts, XY, Heisenberg)\n- Finding critical temperatures and exponents\n- Computing thermodynamic observables (energy, magnetization, susceptibility, specific heat)\n- Finite-size scaling analysis\n- Any equilibrium statistical mechanics simulation\n\n## Core Workflows\n\n### 1. 2D Ising Model (Metropolis)\n\n```python\nimport numpy as np\nimport matplotlib.pyplot as plt\n\nclass IsingModel:\n    def __init__(self, L, T, J=1.0):\n        self.L = L\n        self.T = T\n        self.J = J\n        self.beta = 1.0 \u002F T\n        self.spins = np.random.choice([-1, 1], size=(L, L))\n\n    def energy(self):\n        \"\"\"Total energy: H = -J Σ s_i s_j (nearest neighbors).\"\"\"\n        s = self.spins\n        E = -self.J * np.sum(\n            s * np.roll(s, 1, axis=0) +\n            s * np.roll(s, 1, axis=1)\n        )\n        return E\n\n    def magnetization(self):\n        return np.sum(self.spins)\n\n    def metropolis_step(self):\n        \"\"\"Single Metropolis sweep (L² spin flip attempts).\"\"\"\n        L = self.L\n        for _ in range(L * L):\n            i, j = np.random.randint(0, L, size=2)\n            s = self.spins[i, j]\n            # Sum of nearest neighbors\n            nn = (self.spins[(i+1)%L, j] + self.spins[(i-1)%L, j] +\n                  self.spins[i, (j+1)%L] + self.spins[i, (j-1)%L])\n            dE = 2 * self.J * s * nn\n            if dE \u003C= 0 or np.random.rand() \u003C np.exp(-self.beta * dE):\n                self.spins[i, j] *= -1\n\n    def wolff_step(self):\n        \"\"\"Wolff cluster flip (much faster near T_c).\"\"\"\n        L = self.L\n        p_add = 1 - np.exp(-2 * self.beta * self.J)\n\n        i, j = np.random.randint(0, L, size=2)\n        cluster_spin = self.spins[i, j]\n        stack = [(i, j)]\n        visited = set()\n        visited.add((i, j))\n\n        while stack:\n            ci, cj = stack.pop()\n            for di, dj in [(1,0),(-1,0),(0,1),(0,-1)]:\n                ni, nj = (ci+di)%L, (cj+dj)%L\n                if (ni, nj) not in visited and self.spins[ni, nj] == cluster_spin:\n                    if np.random.rand() \u003C p_add:\n                        visited.add((ni, nj))\n                        stack.append((ni, nj))\n\n        for ci, cj in visited:\n            self.spins[ci, cj] *= -1\n\ndef simulate(L, T, n_equil=1000, n_measure=5000, algorithm='metropolis'):\n    \"\"\"Run simulation and collect observables.\"\"\"\n    model = IsingModel(L, T)\n\n    # Equilibration\n    for _ in range(n_equil):\n        if algorithm == 'wolff':\n            model.wolff_step()\n        else:\n            model.metropolis_step()\n\n    # Measurement\n    E_samples = []\n    M_samples = []\n    N = L * L\n\n    for _ in range(n_measure):\n        if algorithm == 'wolff':\n            model.wolff_step()\n        else:\n            model.metropolis_step()\n        E_samples.append(model.energy() \u002F N)\n        M_samples.append(abs(model.magnetization()) \u002F N)\n\n    E = np.array(E_samples)\n    M = np.array(M_samples)\n\n    return {\n        'E_mean': np.mean(E),\n        'E_std': np.std(E) \u002F np.sqrt(len(E)),\n        'M_mean': np.mean(M),\n        'M_std': np.std(M) \u002F np.sqrt(len(M)),\n        'C': N * np.var(E) \u002F T**2,           # specific heat\n        'chi': N * np.var(M) \u002F T,             # susceptibility\n        'spins': model.spins.copy(),\n    }\n```\n\n### 2. Phase Transition: Temperature Sweep\n\n```python\nfrom scipy import constants as const\n\nT_c_exact = 2 \u002F np.log(1 + np.sqrt(2))  # ≈ 2.269 (Onsager)\nprint(f\"Exact T_c = {T_c_exact:.4f}\")\n\nL = 32\ntemperatures = np.linspace(1.5, 3.5, 30)\nresults = []\n\nfor T in temperatures:\n    res = simulate(L, T, n_equil=2000, n_measure=5000, algorithm='wolff')\n    results.append(res)\n    print(f\"T={T:.3f}: \u003CE>={res['E_mean']:.4f}, \u003C|M|>={res['M_mean']:.4f}, \"\n          f\"C={res['C']:.4f}, χ={res['chi']:.4f}\")\n\n# Plot\nfig, axes = plt.subplots(2, 2, figsize=(12, 10))\n\nE_vals = [r['E_mean'] for r in results]\nM_vals = [r['M_mean'] for r in results]\nC_vals = [r['C'] for r in results]\nchi_vals = [r['chi'] for r in results]\n\nfor ax, vals, ylabel, title in zip(\n    axes.flat,\n    [E_vals, M_vals, C_vals, chi_vals],\n    [r'$\\langle E \\rangle \u002F N$', r'$\\langle |M| \\rangle \u002F N$',\n     r'$C_v \u002F N$', r'$\\chi \u002F N$'],\n    ['Energy', 'Magnetization', 'Specific Heat', 'Susceptibility']\n):\n    ax.plot(temperatures, vals, 'bo-', markersize=4)\n    ax.axvline(T_c_exact, color='red', linestyle='--', label=f'$T_c$ = {T_c_exact:.3f}')\n    ax.set_xlabel('Temperature $T$ [$J\u002Fk_B$]')\n    ax.set_ylabel(ylabel)\n    ax.set_title(title)\n    ax.legend()\n    ax.grid(True, alpha=0.3)\n\nplt.tight_layout()\nplt.savefig('ising_phase_transition.png', dpi=150, bbox_inches='tight')\n```\n\n### 3. Finite-Size Scaling\n\n```python\ndef finite_size_scaling(sizes, temperatures, n_equil=3000, n_measure=10000):\n    \"\"\"Run simulations for multiple L to extract critical exponents.\"\"\"\n    all_results = {}\n\n    for L in sizes:\n        all_results[L] = []\n        for T in temperatures:\n            res = simulate(L, T, n_equil=n_equil, n_measure=n_measure, algorithm='wolff')\n            all_results[L].append(res)\n        print(f\"L={L} done\")\n\n    # Find T_c from susceptibility peak for each L\n    for L in sizes:\n        chi = [r['chi'] for r in all_results[L]]\n        T_peak = temperatures[np.argmax(chi)]\n        print(f\"L={L:3d}: χ peak at T = {T_peak:.3f}\")\n\n    return all_results\n\n# sizes = [8, 16, 32, 64]\n# T_range = np.linspace(2.0, 2.6, 20)\n# results = finite_size_scaling(sizes, T_range)\n```\n\n### 4. Autocorrelation and Error Estimation\n\n```python\ndef autocorrelation_time(data):\n    \"\"\"Estimate integrated autocorrelation time.\"\"\"\n    n = len(data)\n    mean = np.mean(data)\n    var = np.var(data)\n    if var == 0:\n        return 1.0\n\n    acf = np.correlate(data - mean, data - mean, mode='full')[n-1:]\n    acf \u002F= acf[0]\n\n    # Integrate until first negative value\n    tau = 0.5\n    for k in range(1, n \u002F\u002F 4):\n        if acf[k] \u003C 0:\n            break\n        tau += acf[k]\n\n    return tau\n\n# Effective number of independent samples = N \u002F (2 * tau)\n# True standard error = std(data) * sqrt(2 * tau \u002F N)\n```\n\n## Critical Exponents (2D Ising, Exact)\n\n| Exponent | Symbol | Value | Relation |\n|---|---|---|---|\n| Specific heat | α | 0 (log) | C ~ |T - T_c|^(-α) |\n| Order parameter | β | 1\u002F8 | M ~ |T_c - T|^β |\n| Susceptibility | γ | 7\u002F4 | χ ~ |T - T_c|^(-γ) |\n| Correlation length | ν | 1 | ξ ~ |T - T_c|^(-ν) |\n| Critical isotherm | δ | 15 | M ~ H^(1\u002Fδ) at T_c |\n\n## Troubleshooting\n\n| Symptom | Fix |\n|---|---|\n| Very long equilibration | Use Wolff algorithm near T_c (no critical slowing) |\n| Noisy observables | Increase measurement sweeps, check autocorrelation time |\n| Wrong T_c | Finite-size effect — run larger L or use scaling |\n| Magnetization doesn't go to 0 | Take |M| (absolute), not M (which fluctuates around 0) |\n| Metropolis too slow near T_c | Switch to Wolff cluster algorithm |\n",{"name":5,"tags":44,"author":46,"license":15,"version":47,"category":34,"description":7,"dependencies":48},[45,25,24,23,22],"Statistical Mechanics","Synthetic Sciences","1.0.0",[49,50,51],"numpy>=1.24.0","scipy>=1.11.0","matplotlib>=3.7.0","main","4aa39efd1cdab0b4657ecee16c92a92011a5b10f","openscience\u002Fbackend\u002Fcli\u002Fskills\u002Fphysics\u002Fstatistical-mechanics","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub","https:\u002F\u002Fgithub.com\u002Ffadrienne","2026-10-28 00:43:09",{"source":8,"skillName":5,"commands":59,"prompt":69,"zipAvailable":70},[60,63,66],{"tool":61,"command":62},"npx","npx skills add fadrienne\u002FMyGitHub --skill statistical-mechanics",{"tool":64,"command":65},"bunx","bunx skills add fadrienne\u002FMyGitHub --skill statistical-mechanics",{"tool":67,"command":68},"pnpm","pnpm dlx skills add fadrienne\u002FMyGitHub --skill statistical-mechanics","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fopenscience\u002Fbackend\u002Fcli\u002Fskills\u002Fphysics\u002Fstatistical-mechanics\u002FSKILL.md",true,[],[73,102,128,162,189,216],{"skillNo":74,"name":75,"nameZh":6,"description":76,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":77,"categories":78,"keywords":84,"publishedAt":39},"01M7167B28PK20HP7R7ZED2DY0","statistical-power","Sample size calculation, power analysis, and effect size conversion for scientific studies. Use BEFORE data collection (a priori) to determine required N, or after (post-hoc) to compute achieved power. Covers parametric tests (t-test, ANOVA, chi-square, proportions, correlation, regression), simulation-based power for complex\u002Fclustered\u002Fnested designs, and power curves. Use this skill when someone asks 'how many samples do I need', 'what is my power', 'what effect size can I detect', or any variant. Pairs with \u002Fexperimental-design (choose design first, then compute power) and \u002Fstatistical-analysis (analyze data after collection).","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fscientific-agent-skills\u002Fskills\u002Fstatistical-power\u002FSKILL.md",[79],{"categoryNo":80,"categoryName":81,"taxonomyType":82,"taxonomyTypeDesc":83},"01JBSEEDCAT000000000000023","Skill与智能体开发","SCENARIO","使用场景",[85,86,87,35,88,89,90,91,92,93,94,31,95,96,97,98,99,100,38,101],"power","statistical power","effect","regression","choose","design","uv","when","Bash","collection","calculation","ANOVA","conversion","analyze","t-test","chi-square","sample",{"skillNo":103,"name":104,"nameZh":6,"description":105,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":106,"categories":107,"keywords":111,"publishedAt":39},"01M71677EBCM8EPCE9BZCK8505","statistical-analysis","Guided statistical analysis with test selection and reporting. Use when you need help choosing appropriate tests for your data, assumption checking, power analysis, and APA-formatted results. Best for academic research reporting, test selection guidance. For implementing specific models programmatically use statsmodels.","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fscientific-agent-skills\u002Fskills\u002Fstatistical-analysis\u002FSKILL.md",[108],{"categoryNo":109,"categoryName":110,"taxonomyType":82,"taxonomyTypeDesc":83},"01JBSEEDCAT000000000000008","测试与质量",[31,112,85,113,114,115,92,116,117,118,28,119,120,121,122,123,124,125,126,127],"statistical analysis","academic research","implementing","selection","you","reporting","data","tests","use","with","test","research","results","statsmodels","models","help",{"skillNo":129,"name":130,"nameZh":6,"description":131,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":132,"categories":133,"keywords":143,"publishedAt":39},"01M71673R93XAHFH81DBNVNG7H","scientific-writing","Core skill for the deep research and writing tool. Write scientific manuscripts in full paragraphs (never bullet points). Use two-stage process with (1) section outlines with key points using research-lookup then (2) convert to flowing prose. IMRAD structure, citations (APA\u002FAMA\u002FVancouver), figures\u002Ftables, reporting guidelines (CONSORT\u002FSTROBE\u002FPRISMA), for research papers and journal submissions.","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fscientific-agent-skills\u002Fskills\u002Fscientific-writing\u002FSKILL.md",[134,137,138],{"categoryNo":135,"categoryName":136,"taxonomyType":82,"taxonomyTypeDesc":83},"01JBSEEDCAT000000000000018","写作与文案",{"categoryNo":80,"categoryName":81,"taxonomyType":82,"taxonomyTypeDesc":83},{"categoryNo":139,"categoryName":140,"taxonomyType":141,"taxonomyTypeDesc":142},"01JBSEEDCAT000000000000036","内容创作者","PROFESSION","适用职业",[144,145,146,147,148,149,150,151,152,153,93,154,155,156,157,158,159,160,117,161],"writing","scientific","scientific writing","Citations","deep","deep research","never","papers","journal","false","api","prisma","structure","openrouter","Outlines","core skill","read","features",{"skillNo":163,"name":164,"nameZh":6,"description":165,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":166,"categories":167,"keywords":172,"publishedAt":39},"01M7166ZPKXBF4EBPHVTJPQBB1","scientific-visualization","Meta-skill for publication-ready figures. Use when creating journal submission figures requiring multi-panel layouts, significance annotations, error bars, colorblind-safe palettes, and specific journal formatting (Nature, Science, Cell). Orchestrates matplotlib\u002Fseaborn\u002Fplotly with publication styles. For quick exploration use seaborn or plotly directly.","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fscientific-agent-skills\u002Fskills\u002Fscientific-visualization\u002FSKILL.md",[168,171],{"categoryNo":169,"categoryName":170,"taxonomyType":82,"taxonomyTypeDesc":83},"01JBSEEDCAT000000000000013","分析与可视化",{"categoryNo":80,"categoryName":81,"taxonomyType":82,"taxonomyTypeDesc":83},[173,145,174,175,176,177,178,179,180,152,92,181,182,183,184,185,186,187,28,188],"visualization","scientific visualization","error","ready","quick","exploration","meta-skill","Meta","safe","plotly","annotations","formatting","Publication","figures","panel","submission",{"skillNo":190,"name":191,"nameZh":6,"description":192,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":15,"licenseFileUrl":6,"sourceHtmlUrl":193,"categories":194,"keywords":201,"publishedAt":39},"01M7166VXJWQSSC3RQZP60WBGR","research-code","Debug, profile, review, and restructure Python research and analysis code. Use when analysis scripts crash, produce wrong results, run too slowly, or need a correctness review. Covers: reading tracebacks and diagnosing root causes, hypothesis-driven debugging, reviewing code for common statistical\u002Fnumerical errors, profiling data pipelines, improving reproducibility (seeds, environments, determinism), and structuring analysis scripts for sharing. Distinct from \u002Fexploratory-data-analysis (which understands data) and \u002Fstatistical-analysis (which chooses and runs tests) — this skill focuses on the code itself.","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fscientific-agent-skills\u002Fskills\u002Fresearch-code\u002FSKILL.md",[195,198],{"categoryNo":196,"categoryName":197,"taxonomyType":82,"taxonomyTypeDesc":83},"01JBSEEDCAT000000000000021","资料检索与研究",{"categoryNo":199,"categoryName":200,"taxonomyType":141,"taxonomyTypeDesc":142},"01JBSEEDCAT000000000000030","开发工程师",[202,203,123,204,205,206,207,91,208,92,93,31,209,210,211,212,213,214,160,215],"code","research code","which","memory","data-analysis","errors","debugging","common","review","data pipelines","run","scripts","line","write",{"skillNo":217,"name":218,"nameZh":6,"description":219,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":12,"repositoryNo":13,"starsCount":14,"licenseSpdxId":220,"licenseFileUrl":6,"sourceHtmlUrl":221,"categories":222,"keywords":229,"publishedAt":39},"01M7166CF5HSR7SVZYZFWTDX55","markdown-mermaid-writing","Comprehensive markdown and Mermaid diagram writing skill. Use when creating any scientific document, report, analysis, or visualization. Establishes text-based diagrams as the default documentation standard with full style guides (markdown + mermaid), 24 diagram type references, and 9 document templates.","Apache-2.0","https:\u002F\u002Fgithub.com\u002Ffadrienne\u002FMyGitHub\u002Fblob\u002Fmain\u002Fscientific-agent-skills\u002Fskills\u002Fmarkdown-mermaid-writing\u002FSKILL.md",[223,226,227,228],{"categoryNo":224,"categoryName":225,"taxonomyType":82,"taxonomyTypeDesc":83},"01JBSEEDCAT000000000000002","文档处理",{"categoryNo":135,"categoryName":136,"taxonomyType":82,"taxonomyTypeDesc":83},{"categoryNo":80,"categoryName":81,"taxonomyType":82,"taxonomyTypeDesc":83},{"categoryNo":139,"categoryName":140,"taxonomyType":141,"taxonomyTypeDesc":142},[144,230,231,232,233,234,173,235,236,92,93,31,237,238,239,240,241,242,145,160],"markdown mermaid writing","mermaid","markdown","community","diagrams","project","default","team","guides","text","documentation","references","diagram"]