DAILY KANSAN MONDAY, NOVEMBER 21. 2011 XAS A&M 61 PAGE 7 第十章 现代数学 一、基本概念 1. $\mathbb{P}$ 表示概率; 2. $\mathcal{E}$ 表示期望; 3. $\sigma$ 表示标准差。 4. $\mu$ 表示均值。 5. $X$ 表示随机变量。 6. $\rho$ 表示相关系数。 7. $\theta$ 表示模型参数。 二、数学方法 1. 线性回归: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 2. 线性拟合: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 3. 逻辑回归: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 4. 模糊推理: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 5. 支持向量机: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 6. 决策树: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 7. 集成学习: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 8. 强化学习: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 9. 神经网络: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 10. 卷积神经网络: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 11. 多层神经网络: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 12. 深度学习: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 13. 自然语言处理: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 14. 机器学习: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 15. 情感分析: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 16. 推荐算法: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 17. 文本分类: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 18. 词频统计: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 19. 句子拆分: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 20. 句子重构: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 21. 句子润泽: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 22. 句子紧凑: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 23. 句子流畅: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 24. 句子生动: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 25. 句子有趣: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 26. 句子简洁: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 27. 句子有创意: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 28. 句子有逻辑: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 29. 句子有意义: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 30. 句子有价值: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 31. 句子有创新: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 32. 句子有诗意: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 33. 句子有韵味: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 34. 句子有节奏: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 35. 句子有音调: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 36. 句子有语气: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 37. 句子有感情: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 38. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 39. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 40. 句子有灵感: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 41. 句子有动感: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 42. 句子有激情: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 43. 句子有活力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 44. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 45. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 46. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 47. 句子有创造性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 48. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 49. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 50. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 51. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 52. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 53. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 54. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 55. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 56. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 57. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 58. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 59. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 60. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 61. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 62. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 63. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 64. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 65. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 66. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 67. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 68. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 69. 句子有灵性: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 70. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 71. 句子有创造力: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 72. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 73. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 74. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 75. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 76. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 77. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 78. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 79. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 80. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 81. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 82. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 83. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 84. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 85. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 86. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 87. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 88. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 89. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 90. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 91. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 92. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 93. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 94. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 95. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 96. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 97. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 98. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 99. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 100. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 101. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 102. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 103. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 104. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 105. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 106. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 107. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 108. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 109. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 110. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 111. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 112. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 113. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 114. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ 115. 句子有智慧: $\hat{\beta}_0 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar.x)^2}$ $\hat{\beta}_1 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{\sum_{i=1}^{n} (x_i - \bar{x})^2}$ REWIND Texas A&M wastes no time MIKE VERNON mvernon@kansan.com Texas A&M punter Ryan Epperson had kicked 40 puns heading into Saturday's game against Kansas. He left with the same total, as the Kansas defense did not force one punt from the Aggies. Texas A&M had the ball for just 21 minutes and 43 seconds during Saturday's blowout. In that short time, the Aggies scored 61 points, as they knocked off Kansas 61-7. While Texas A&M coach Mike Sherman did say that time of possession should not be an indicator of what happened in the game, he did point out that the numbers were staggering. "I've never had that little time of possession with that many points," Sherman said. And while it was bad for a defense that had been improving in its last three games, the number of points Texas A&M scored did not properly portray the odds that were put against them. Giving up 469 yards like the Kansas defense did against Texas A&M is nothing to brag about. Yet the number is still similar to the amount of yards it had given up to Baylor and Iowa State in its previous two games, which were much closer contests. Against Baylor, Kansas gave up 505 yards and only 31 points. And against Iowa State the Jayhawks gave up 426 yards and only 10 points. The Jayhawks' defense was often put in poor field position as Texas A&M's 469 yards led to 61 points. "A lot of it was field position, they started on the 40 or they started on the 50," junior safety Bradley McDougald said. "Five or six of their starts were inside of our territory, so that definitely doesn't help when you have a high-powered running offense like they had and a lot of things they were doing." Texas A&M running back for Cyrus Gray ran the ball nine times in the first half for 95 yards for an average of 10.4 yards per carry. Gray did not play in the second half as a precautionary measure because of a shoulder injury. Kansas turned the ball over three times, which didn't help a defense that Texas A&M often bowled over. Senior linebacker Steven Johnson was visibly disappointed after a game in which the defense let up six touchdown plays of 25 yards or more. "You've got to make a play" Johnson said. "Everybody that we put on the field is capable of making plays, they've just got to hone in." Even though the 54-point loss was a staggering one, the Jayhawks defense did not quit on the field. As the team fell to 2-9 and 0-8 in Big 12 play, junior cornerback Greg Brown did not see any of his teammates' demeanor falter. "I really don't feel like anyone has quit, things just haven't been going the right way," Brown said. "I see everyone with their head up and still competing out there trying to make plays." Edited by Josh Kantor Texas A&M's junior wide receiver Brandal Jackson stiff-arms junior cornerback Greg Brown during the first half of Saturdays game in Texas. Jackson had two receptions for 33 yards for the Aggies. CHRIS NEAL/KANSAN ds. Cool Place. Smart Living 2, 3 & 4 Bedrooms • Private Shuttle to KU • Private Bathrooms 24 Hour Fitness Center • Pet Friendly 4101 W. 24th Place 785.856.KU4U (5848) For info text LEGENDS to <7464 www.LegendsPlace.com CHRIS NEAL/KANSAN Senior Cornerback Isiah Barfield makes a tackle on Texas A&M's sophomore running back Ben Malena during the second half of Saturday's game. Barfield had five solo tackles and two assists for the Jayhawks. Glass is half-full Only one game remains this miserable season. Glass is half-empty That game is against archival Mizzou which is set to leave for the SEC and might be the last Border Showdown for awhile, and the Jayhawks showed little life against Texas A&M, the other team departing for the SEC. Quote of the game "This game felt like a new low. This whole game is about life. When you get knocked down, you got to keep fighting. We came out flat and everything went wrong." Senior linebacker Steven Johnson Johnson } Game Balls Matthews Sophomore receiver Christian Matthews: For the first time all season, Matthews emerged as a viable receiving threat in addition to his use as a "Jayhawk" formation quarterback. Junior receiver Kale Pick: Pick led the Jayhawks in receiving, grabbing five passes for 46 yards, including a 16-yard completion on third and 14 in the first quarter. Pick Sophomore running back James Sims: Sims led the Jayhawks with 88 yards on the ground and scored the only touchdown on the day. Sims half. Delay of Games Webb Jordan Webb: Webb was under pressure by the Aggie defense and couldn't exploit them like other Big 12 quarterbacks have in the past. The pressure led to a lot of errant passing in the second Darrian Miller. Miller struggled to support the running game for Kansas, averaging just 1.5 yards per carry. Miller Kansas secondary: As a group, the entire secondary underperformed. They let receivers lose in coverage and missed too many tackles. Gill Hot Seat Watch To say Gill's seat is hot is an understatement, Odds that he will keep his job after this season appear slim. Still Questioning Why can't the Jayhawks play well in Texas? Thirty-eight Jayhawks hail from the Lone Star State. Yet all three times that Gill has taken the Jayhawks down to Texas, they have been demolished. Looking ahead Next up for the Jayhawks is the suddenly hot Missouri Tigers. It's the biggest game of the year, especially since it could be the last time these two teams meet on the football field for a long time. Final Thought Any improvement Kansas showed in losing late to Baylor and Iowa State was wiped away by this blowout defeat. This was the worst margin of defeat Turner Gill has had since taking over at Kansas last season. It's pretty hard to believe that just four years ago this team was playing in the Orange Bowl and competing for the Big 12 title. BRIEFING