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1. 发明申请

US20100262643A1 COMPUTING MINIMAL POLYNOMIALS 有权
标题翻译：计算最小多边形
公开(公告)号：US20100262643A1
公开(公告)日：2010-10-14
申请号：US12422315
申请日：2009-04-13
申请人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
发明人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
IPC分类号： G06F7/38 , G06F7/552
CPC分类号： G06F7/724 , G06F7/12 , G06F7/16
摘要： Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression over the ring Z of integer numbers or the ring Q of rational numbers. The levels of the radical are grouped into a level permutation group that is used to find a level permutation set. An annihilation polynomial is found based upon the level permutation set. The annihilation polynomial is factored, and a selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.
摘要翻译：描述了一种技术，例如在计算软件程序中实现的技术，通过该技术，对于整数的环Z或有理数的环Q，对于根基表达式有效地确定最小多项式。激进的级别被分组成用于找到级别置换集合的级别置换组。湮没多项式是基于层次排列集合找到的。湮灭多项式被考虑，选择机制根据湮灭多项式的因素选择最小多项式。

2. 发明授权

US09122563B2 Computing minimal polynomials 有权
标题翻译：计算最小多项式
公开(公告)号：US09122563B2
公开(公告)日：2015-09-01
申请号：US12422315
申请日：2009-04-13
申请人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
发明人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye , Dongmei Zhang
IPC分类号： G06F7/38 , G06F7/72 , G06F7/16 , G06F7/12
CPC分类号： G06F7/724 , G06F7/12 , G06F7/16
摘要： Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression over the ring Z of integer numbers or the ring Q of rational numbers. The levels of the radical are grouped into a level permutation group that is used to find a level permutation set. An annihilation polynomial is found based upon the level permutation set. The annihilation polynomial is factored, and a selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.
摘要翻译：描述了一种技术，例如在计算软件程序中实现的技术，通过该技术，对于整数的环Z或有理数的环Q，对于根基表达式有效地确定最小多项式。激进的级别被分组成用于找到级别置换集合的级别置换组。湮没多项式是基于层次排列集合找到的。湮灭多项式被考虑，选择机制根据湮灭多项式的因素选择最小多项式。

3. 发明申请

US20100198902A1 COMPUTING MINIMAL POLYNOMIALS OF RADICAL EXPRESSIONS 审中-公开
标题翻译：计算放射性表达的最小多边形
公开(公告)号：US20100198902A1
公开(公告)日：2010-08-05
申请号：US12364533
申请日：2009-02-03
申请人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye
发明人： Xu Yang , Zhouchen Lin , Sijun Liu , Tianjun Ye
IPC分类号： G06F7/552
CPC分类号： G06F17/10
摘要： Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression based upon its structure of the radical expression. An annihilation polynomial is found based upon levels of the radical to obtain roots of the radical. A numerical method performs a zero test or multiple zero tests to find the minimal polynomial. In one implementation, the set of roots corresponding to a radical expression is found. The annihilation polynomial is computed by grouping roots of the set according to their conjugation relationship and multiplying factor polynomials level by level. A selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.
摘要翻译：描述了一种技术，例如在计算软件程序中实现的技术，通过该技术，基于其基本表达式的结构，有效地确定基本表达式的最小多项式。基于获得根的根的自由基的水平找到湮灭多项式。数值方法执行零测试或多零测试以找到最小多项式。在一个实现中，找到与激进表达相对应的一组根。湮灭多项式通过根据它们的共轭关系和乘法因子多项式级别逐级分组的根来计算。选择机制根据湮灭多项式的因素选择最小多项式。

4. 发明授权

US07561739B2 Analyzing scripts and determining characters in expression recognition 有权
标题翻译：分析脚本并确定表达式识别中的字符
公开(公告)号：US07561739B2
公开(公告)日：2009-07-14
申请号：US11155748
申请日：2005-06-20
申请人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xianfang Wang , Xiaohui Hou , Dongmei Zhang , Zhouchen Lin , Jian Wang
发明人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xianfang Wang , Xiaohui Hou , Dongmei Zhang , Zhouchen Lin , Jian Wang
IPC分类号： G06K9/18
CPC分类号： G06K9/222
摘要： A mechanism for recognizing and inputting handwritten mathematical expressions into a computer by providing part of a multi-path framework is described. The part of the multi-path framework includes a subscript/superscript analysis and character determination component that is designed to identify subscript and superscript elements. A method for analyzing a handwritten mathematical expression includes receiving a symbols corresponding to handwritten mathematical expression input strokes, identifying subscript and/or superscript structures, and determining a character for each symbol of the set. A graph of vertexes and edges may be created based upon the set of symbols and the graph may be searched to determine optimized candidates.
摘要翻译：描述了通过提供一部分多路径框架来将手写数学表达式识别并输入计算机的机制。多路径框架的一部分包括下标/上标分析和字符确定组件，其被设计为识别下标和上标元素。一种用于分析手写数学表达式的方法包括接收对应于手写数学表达式输入笔画的符号，识别下标和/或上标结构，以及确定该组的每个符号的字符。可以基于符号集创建顶点和边缘的图形，并且可以搜索图形以确定优化的候选。

5. 发明申请

US20060062468A1 Analyzing scripts and determining characters in expression recognition 有权
公开(公告)号：US20060062468A1
公开(公告)日：2006-03-23
申请号：US11155748
申请日：2005-06-20
申请人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xianfang Wang , Xiaohui Hou , Dongmei Zhang , Zhouchen Lin , Jian Wang
发明人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xianfang Wang , Xiaohui Hou , Dongmei Zhang , Zhouchen Lin , Jian Wang
IPC分类号： G06K9/18
CPC分类号： G06K9/222
摘要： A mechanism for recognizing and inputting handwritten mathematical expressions into a computer by providing part of a multi-path framework is described. The part of the multi-path framework includes a subscript/superscript analysis and character determination component that is designed to identify subscript and superscript elements. A method for analyzing a handwritten mathematical expression includes receiving a symbols corresponding to handwritten mathematical expression input strokes, identifying subscript and/or superscript structures, and determining a character for each symbol of the set. A graph of vertexes and edges may be created based upon the set of symbols and the graph may be searched to determine optimized candidates.

6. 发明授权

US07929767B2 Analyzing subordinate sub-expressions in expression recognition 有权
标题翻译：分析表达式识别中的下级子表达式
公开(公告)号：US07929767B2
公开(公告)日：2011-04-19
申请号：US11155785
申请日：2005-06-20
申请人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xiaohui Hou , Zhouchen Lin , Dongmei Zhang , Jian Wang
发明人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xiaohui Hou , Zhouchen Lin , Dongmei Zhang , Jian Wang
IPC分类号： G06K9/18
CPC分类号： G06K9/00422 , G06K9/222 , G06K9/72 , G06K2209/01
摘要： A mechanism for recognizing and inputting handwritten mathematical expressions into a computer by providing part of a multi-path framework is described. The part of the multi-path framework includes a subordinate sub-expression analysis component. A method for analyzing a handwritten mathematical expression for a subordinate sub-expression includes identifying sub-expressions based on dominant symbols and determining a character for potential dominant symbols based upon sub-expression information. A determination may be made whether an expression structure candidate is valid and valid expression structure candidates may be stored in a parse tree.
摘要翻译：描述了通过提供一部分多路径框架来将手写数学表达式识别并输入计算机的机制。多路径框架的一部分包括从属子表达式分析组件。用于分析用于下级子表达式的手写数学表达式的方法包括基于主要符号识别子表达，并且基于子表达信息确定潜在的主要符号的字符。可以确定表达式结构候选是否是有效的，并且有效的表达式结构候选可以被存储在解析树中。

7. 发明申请

US20060062471A1 Analyzing subordinate sub-expressions in expression recognition 有权
标题翻译：分析表达式识别中的下级子表达式
公开(公告)号：US20060062471A1
公开(公告)日：2006-03-23
申请号：US11155785
申请日：2005-06-20
申请人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xiaohui Hou , Zhouchen Lin , Dongmei Zhang , Jian Wang
发明人： Mingqing Xu , Yu Zou , Lei Huang , Jian-Lai Zhou , Xiaohui Hou , Zhouchen Lin , Dongmei Zhang , Jian Wang
IPC分类号： G06K9/18
CPC分类号： G06K9/00422 , G06K9/222 , G06K9/72 , G06K2209/01
摘要： A mechanism for recognizing and inputting handwritten mathematical expressions into a computer by providing part of a multi-path framework is described. The part of the multi-path framework includes a subordinate sub-expression analysis component. A method for analyzing a handwritten mathematical expression for a subordinate sub-expression includes identifying sub-expressions based on dominant symbols and determining a character for potential dominant symbols based upon sub-expression information. A determination may be made whether an expression structure candidate is valid and valid expression structure candidates may be stored in a parse tree.
摘要翻译：描述了通过提供一部分多路径框架来将手写数学表达式识别并输入计算机的机制。多路径框架的一部分包括从属子表达式分析组件。用于分析用于下级子表达式的手写数学表达式的方法包括基于主要符号识别子表达，并且基于子表达信息确定潜在的主要符号的字符。可以确定表达式结构候选是否是有效的，并且有效的表达式结构候选可以被存储在解析树中。

8. 发明申请

US20080068386A1 Real-Time Rendering of Realistic Rain 有权
标题翻译：实时降雨的实时渲染
公开(公告)号：US20080068386A1
公开(公告)日：2008-03-20
申请号：US11532052
申请日：2006-09-14
申请人： Zhouchen Lin , Lifeng Wang , Tian Fang , Xu Yang , Xuan Yu , Jian Wang , Xiaoou Tang
发明人： Zhouchen Lin , Lifeng Wang , Tian Fang , Xu Yang , Xuan Yu , Jian Wang , Xiaoou Tang
IPC分类号： G06T13/00
CPC分类号： G06T13/60 , G06T2210/56
摘要： Real-time rendering of realistic rain is described. In one aspect, image samples of real rain and associated information are automatically modeled in real-time to generate synthetic rain particles in view of respective scene radiances of target video content frames. The synthetic rain particles are rendered in real-time using pre-computed radiance transfer with uniform random distribution across respective frames of the target video content.
摘要翻译：描述了实时降雨的实时渲染。在一个方面，根据目标视频内容帧的相应场景辐射，实时地自动建模真实雨和相关信息的图像样本以产生合成雨粒子。使用预先计算的辐射传输，通过目标视频内容的各个帧上的均匀随机分布实时地渲染合成雨粒子。

9. 发明授权

US07692647B2 Real-time rendering of realistic rain 有权
标题翻译：实时渲染逼真的雨
公开(公告)号：US07692647B2
公开(公告)日：2010-04-06
申请号：US11532052
申请日：2006-09-14
申请人： Zhouchen Lin , Lifeng Wang , Tian Fang , Xu Yang , Xuan Yu , Jian Wang , Xiaoou Tang
发明人： Zhouchen Lin , Lifeng Wang , Tian Fang , Xu Yang , Xuan Yu , Jian Wang , Xiaoou Tang
IPC分类号： G06T15/00 , G06T15/50 , G06T15/60 , G06T15/70 , G06T13/00 , G09G5/02 , G09G5/10
CPC分类号： G06T13/60 , G06T2210/56
摘要： Real-time rendering of realistic rain is described. In one aspect, image samples of real rain and associated information are automatically modeled in real-time to generate synthetic rain particles in view of respective scene radiances of target video content frames. The synthetic rain particles are rendered in real-time using pre-computed radiance transfer with uniform random distribution across respective frames of the target video content.
摘要翻译：描述了实时降雨的实时渲染。在一个方面，根据目标视频内容帧的相应场景辐射，实时地自动建模真实雨和相关信息的图像样本以产生合成雨粒子。使用预先计算的辐射传输，通过目标视频内容的各个帧上的均匀随机分布实时地渲染合成雨粒子。

10. 发明申请

US20100080450A1 CLASSIFICATION VIA SEMI-RIEMANNIAN SPACES 有权
标题翻译：通过SEMI-RIEMANNIAN SPACES分类
公开(公告)号：US20100080450A1
公开(公告)日：2010-04-01
申请号：US12242421
申请日：2008-09-30
申请人： Deli Zhao , Zhouchen Lin , Xiaoou Tang
发明人： Deli Zhao , Zhouchen Lin , Xiaoou Tang
IPC分类号： G06K9/62
CPC分类号： G06K9/6234 , G06K9/6252
摘要： Described is using semi-Riemannian geometry in supervised learning to learn a discriminant subspace for classification, e.g., labeled samples are used to learn the geometry of a semi-Riemannian submanifold. For a given sample, the K nearest classes of that sample are determined, along with the nearest samples that are in other classes, and the nearest samples in that sample's same class. The distances between these samples are computed, and used in computing a metric matrix. The metric matrix is used to compute a projection matrix that corresponds to the discriminant subspace. In online classification, as a new sample is received, it is projected into a feature space by use of the projection matrix and classified accordingly.
摘要翻译：描述了在监督学习中使用半黎曼几何学习学习用于分类的判别子空间，例如，标记的样本用于学习半黎曼子流形歧管的几何形状。对于给定的样本，该样本的K个最近类别以及其他类别中最近的样本以及该样本同一类中最近的样本进行确定。计算这些样本之间的距离，并用于计算度量矩阵。度量矩阵用于计算与判别子空间对应的投影矩阵。在线分类中，作为收到的新样本，通过使用投影矩阵将其投影到特征空间中并进行分类。

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