s****o
发帖数: 18 | 1 如果有N个相同维数的向量，how to efficiently find those subsets whose members
are all orthogonal to each other?
E.g. if we have vectors X_1, X_2, ..., X_n
we may find in (X_1, X_5, X_7) all vectors are orthogonal, and we need all
other subsets.
Any references?
Thank you in advance! |
|
m****a
发帖数: 132 | 2 【 以下文字转载自 EE 讨论区 】
发信人: muitta (muitta), 信区: EE
标 题: naive question on orthogonal functions
发信站: BBS 未名空间站 (Tue Mar 21 13:57:03 2006)
Two 2-D function, P1(x,y) and P2(x,y), what does "these functions are
orthogonal to each other mean"? and how to calculate , or
what is the definition of the operation? |
|
m****a
发帖数: 132 | 3 I need to have 64 orthogonal sequences, but when I use matlab as follow,
set_param('doc_ortho/Hadamard Code Generator', 'index', 'i');
the index can only be 1-63 (no matter what code generator is, hadamard,
walsh, or OVSF).
Is there any easy way to generate 64 different orthogonal sequence (not
sequence of period 64)?
Thanks in advance. |
|
s*******y
发帖数: 558 | 4 Let Y = R X, where X is an n-dimensional vector, and R is an nxn orthogonal
matrix.
My question is:
Given X and Y, can we compute the original R?
My thoughts:
If both X and Y are two-dimensional vectors, and R is a rotation matrix (
which is also an orthogonal matrix), then given Y and X, it seems we can
compute the original rotation matrix R by finding the angle between X and Y.
However, for other cases, I don't know whether we are able to find out the
original R. |
|
m****a
发帖数: 132 | 5 【 以下文字转载自 EE 讨论区 】
发信人: muitta (muitta), 信区: EE
标 题: naive question on orthogonal functions
发信站: BBS 未名空间站 (Tue Mar 21 13:57:03 2006)
Two 2-D function, P1(x,y) and P2(x,y), what does "these functions are
orthogonal to each other mean"? and how to calculate , or
what is the definition of the operation? |
|
m****a
发帖数: 132 | 6 I need to have 64 orthogonal sequences, but when I use matlab as follow,
set_param('doc_ortho/Hadamard Code Generator', 'index', 'i');
the index can only be 1-63 (no matter what code generator is, hadamard,
walsh, or OVSF).
Is there any easy way to generate 64 different orthogonal sequence (not
sequence of period 64)?
Thanks in advance. |
|
s*******y
发帖数: 558 | 7 Thank you very much.
What if I have many pairs X1, Y1; X2, Y2; ..., Xk, Yk
such that Y1 = R X1, Y2 = R X2, ..., Yk = R Xk, where
R is an ( n x n ) dimensional orthogonal matrix.
Then how many such pairs are needed in order to re-identify R?
Obviously, if I have n such pairs, I can compute the inverse
of matrix X and get R. But do I really need n pairs?
Thanks a lot |
|
s*******y
发帖数: 558 | 8 Thank you very much.
What if I have many pairs X1, Y1; X2, Y2; ..., Xk, Yk
such that Y1 = R X1, Y2 = R X2, ..., Yk = R Xk, where
R is an ( n x n ) dimensional orthogonal matrix.
Then how many such pairs are needed in order to re-identify R?
Obviously, if I have n such pairs, I can compute the inverse
of matrix X and get R. But do I really need n pairs?
Thanks a lot |
|
s*******y
发帖数: 558 | 9 给定一个矩阵 X_mxn, where n < m, 请问如何构建一个orthogonal
matrix Q such that QX = X.
如果rank(X) = m-1, 会有不同么?
谢谢了 |
|
s*******y
发帖数: 558 | 10 yes, this is obvious.
I am looking for other orthogonal matrices
that are not identity. |
|
m****n
发帖数: 45 | 11
If rank(X)=m-1, then n=m-1.
QX=X contains m*(m-1)independent equations for the entries of Q.
But a m-by-m orthogonal matrix only has m*(m-1)/2 freedom.
In this case, I think you probabily can't find a nontrivial Q as a solution. |
|
c*****a
发帖数: 49 | 12 假设随机产生两个2x2的矩阵（实数的），想找出一个标准，以判断哪一个矩阵的两行
更orthogonal。不知道有没有什么比较公认的标准。
诚心请教，多谢回答！ |
|
f**d
发帖数: 768 | 13 这是一本计算神经科学的优秀著作，全文拷贝这里（图和公式缺），有兴趣的同学可以
阅读
如需要，我可以分享PDF文件（－－仅供个人学习，无商业用途）
From Computer to Brain
William W. Lytton
From Computer to Brain
Foundations of Computational Neuroscience
Springer
William W. Lytton, M.D.
Associate Professor, State University of New York, Downstato, Brooklyn, NY
Visiting Associate Professor, University of Wisconsin, Madison
Visiting Associate Professor, Polytechnic University, Brooklyn, NY
Staff Neurologist., Kings County Hospital, Brooklyn, NY
In From Computer to Brain: ... 阅读全帖 |
|
t******n
发帖数: 6242 | 14 今天无聊，看到这篇无聊的文章，就给你无聊地翻译成英文吧。
探索星系的捷径
A Shortcut to Galaxy Exploration
1. 问苍天情为何物？
1. Ask what love is heaven?
有人类的历史以来，人类就不断地探索自然，扩展了解自然的疆界。哥伦布发现新大陆
就是最好的例子。人类探索自然的勇气是从哪儿来的呢？来自人类情感的力量。那么，
情感是什么东西呢？这是千万年来，文学家探索的主题。在有一些文学家的眼中，物理
学家是没有情感的冷血动物。我就是一个物理学家。但是，我一点也不埋怨这些文学家
。虽然物理学家在自然界的探索中做出了伟大的贡献，但是，物理学家从来就没有给出
情感的物理定义是什么，也没有找到自然界蕴含情感的丝毫证据。所以，虽然人类知道
自己的生存发展跟自然环境是密不可分的，但是，很少有人类表达出对自然环境感谢的
情感。在很多人的眼中，自然界是死亡无情的物质世界。中国有一句古语，叫做“天若
有情天亦老”。因为几乎所有人类相信天是不老的，所以，认为苍天是没有情感的，就
不足为奇了。我提出了一个宇宙生长衰老的模型。虽然这个模型及其简单，能解释大多
... 阅读全帖 |
|
t**********m
发帖数: 205 | 15 来自主题: Mathematics版 - 伟哥之乐 The joy of viXra
https://telescoper.wordpress.com/2011/05/19/
Posted in The Universe and Stuff with tags arXiv, astronomy, Cosmology,
Physics, scientific publishing, viXra on May 19, 2011 by telescoper
From time to time on this blog I post rants about the state of scientific
publishing, open access, the importance of the arXiv for astronomy and
cosmology, and so on.
This morning, however, I discovered an “alternative” side to the whole
business of online science, a site by the name of viXra. Mos... 阅读全帖 |
|
t**********m
发帖数: 205 | 16 The joy of viXra
https://telescoper.wordpress.com/2011/05/19/
Posted in The Universe and Stuff with tags arXiv, astronomy, Cosmology,
Physics, scientific publishing, viXra on May 19, 2011 by telescoper
From time to time on this blog I post rants about the state of scientific
publishing, open access, the importance of the arXiv for astronomy and
cosmology, and so on.
This morning, however, I discovered an “alternative” side to the whole
business of online science, a site by the name of viXra. Mos... 阅读全帖 |
|
g****t
发帖数: 31659 | 17 http://blogs.adventnet.com/svembu/2005/12/30/two-philosophies-in-cdma-a-stroll-down-memory-lane/
I have now worked a little over 10 years in the industry, after getting my
PhD. In my very first year of work at Qualcomm, I noticed how even when
speaking about the same subject, namely CDMA, academia and industry were on
totally different planets. When I was in Qualcomm, I co-authored a paper
with Dr. Viterbi, titled Two Different Philosophies in CDMA, A Comparison. I
still stand by the conclusions... 阅读全帖 |
|
b*s
发帖数: 82482 | 18 查imdb没有查到orthogonal来
里面的值是对应两个永远垂直的向量。有没有电影叫Orthogonal什么的？ |
|
k*********g
发帖数: 791 | 19 好好去翻翻书；
应用数学家、物理学家、力学家解偏微分方程；
用的是什么办法？
主要是“级数展开”；
采用的是什么级数？
一开始表面上看都是 polynomial of moments；
但是，这些 polynomial 重新排列组合后；
就成了各种各样的；
正交、完备函数；
如 legendre、bessel、hermite、fourier、、、
没有人在手工求解方程的时候采用有限元里面用的“拉格朗日多项式”
这给我们一点启示；
所以，在数值计算中；
也应该用 orthogonal complete polynomials；
藕门知道；
数值计算；
无非是 把未知的、想求出来的那个应变量 用 基函数的级数展开表示出来，其中的系
数未定；
然后藕门把 表达式代入 片微分方程；
藕门的目标是 找系数；
系数一搞定；
万事大捷；
完备性completeness，意味着你想要的东西都可以被它们轻松地表示出来；这些完备函
数的基好比是坐标系；系数好比是投影、坐标；
正交性orthogonality，意味着这些基函数之间有非常好的性能，产生的矩阵的每一行
非零元素非常少；
要知道；
线性方程迭代求... 阅读全帖 |
|
m******i
发帖数: 834 | 20 ☆─────────────────────────────────────☆
kennkqzhang (kenn) 于 (Mon Sep 27 16:20:44 2010, 美东) 提到:
即便在有限元擅长的regime、也恰好是性态很好的很容易求解的regime，如elliptic、
parabolic问题，也有一种数值方法比它快10~100倍；
让藕匪夷所思的是，为什么这么retard的东西会存在50+years。。。
☆─────────────────────────────────────☆
kennkqzhang (kenn) 于 (Sun Oct 31 06:47:05 2010, 美东) 提到:
一个产生的矩阵有几百个非零元素的数值方法；
比一个bandwidth只有几个元素的方法；
要慢10到100倍；
（一般来说）；
☆─────────────────────────────────────☆
kindlefan (maxwell) 于 (Sun Oct 31 14:34:49 2010, 美东) 提到:
请展开说说.
有限元的成熟... 阅读全帖 |
|
t**********m
发帖数: 205 | 21 The Structuring Force of Galaxies （3rd Version)
http://rxiv.org/pdf/1103.0110v3.pdf
The concept of rational structure was suggested in 2000. A flat material
distribution is called the rational structure if there exists a special net
of orthogonal curves on the plane, and the ratio of mass density at one side
of a curve (from the net) to the one at the other side is constant along
the curve. Such curve is called a proportion curve. Such net of curves is
called an orthogonal net of proportion curv... 阅读全帖 |
|
h*****x
发帖数: 1 | 22
明
I think you confused when you assume that "这个似乎是高中的知识，我觉得似乎应
该可以阿". As far as my memory goes, 高中的知识 says that you can simplify the
expression a*sin(w) + b*COS(w).
From another perspective, sin(m*w) and sin(n*w) are orthogonal to each other,
and for m =1, and n =1, as in your case, sin(w) and sin(2*w+c) (c can be
whatever constant) are orthogonal, and therefore linearly independent.
This is checks also. |
|
O**M
发帖数: 29 | 23 or, in MIMO, we can collect enough diversity in the spatial domain (too much
diversity may not be necessary as it kind of saturates in the end). Given t
hat OFDM is orthogonal in the freq. domain, the complexity of MIMO OFDM woul
d be much simpler than MIMO CDMA, which has non-orthogonality at both space
and freq domain. |
|
d***s
发帖数: 55 | 24 新手弱问，只是搜到了英文
Scalable Orthogonal Frequency Division Multiple Access
Orthogonal Frequency Division Multiplexing
但是有啥区别和联系？ |
|
e**t
发帖数: 6 | 25 什么叫orthogonal channel？是不是orthogonal channel之间通常可以假定没有干扰？
谢谢。 |
|
t**********m
发帖数: 205 | 26 The Structuring Force of Galaxies （3rd Version)
http://rxiv.org/pdf/1103.0110v3.pdf
The concept of rational structure was suggested in 2000. A flat material
distribution is called the rational structure if there exists a special net
of orthogonal curves on the plane, and the ratio of mass density at one side
of a curve (from the net) to the one at the other side is constant along
the curve. Such curve is called a proportion curve. Such net of curves is
called an orthogonal net of proportion curv... 阅读全帖 |
|
t**********m
发帖数: 205 | 27 The Structuring Force of Galaxies （3rd Version)
http://rxiv.org/pdf/1103.0110v3.pdf
The concept of rational structure was suggested in 2000. A flat material
distribution is called the rational structure if there exists a special net
of orthogonal curves on the plane, and the ratio of mass density at one side
of a curve (from the net) to the one at the other side is constant along
the curve. Such curve is called a proportion curve. Such net of curves is
called an orthogonal net of proportion curv... 阅读全帖 |
|
t********a
发帖数: 810 | 28 I cant remember the basic concepts, but I think it could. basically Garch
talks about the clustering of variance, which means non-linear correlation,
while white noise is mostly about linear correlation.
in other words, garch says the second moment of w_t and w_{t-1} are not
orthogonal, while white noise says the first moment of w_t and w_{t-1} are
orthogonal. these might not be contradictory. that's why you see flat acf
for garch at non-zero lags. |
|
r******r
发帖数: 138 | 29 is orthogonalizing Z & W the first step you want? and then check if the
orthogonal term significant? |
|
l******f
发帖数: 568 | 30 年代又早， 还是小日本的， 都找得绝望了， 到这里试试看， 或许有做 DOE的兄弟姐
妹熟悉这种骨灰级文献。
500伪币 ：）
Taguchi, G. (1959), "Linear Graphs for Orthogonal Arrays and
Their Application to Experimental Design, With the Aid of
Various Techniques," Reports of Statistical Application Research,
Japanese Union of Scientists and Engineers, 6, 4, 1-43.
Taguchi, G.(1960), "Table of Orthogonal Arrays and Linear Graphs,"
Reports of Statistical Applications Research, Union of Japanese
Scientists and Engineers, 6, 5, 1-52. |
|
q**j
发帖数: 10612 | 31 普通对付共线性把变量都orthogonalize就好了。所以觉得这些东西不是非常必要。另外
如书上所说，都是一些特殊的bayesian model estimator。我在bayesian model里面可
以找到比这些ridge, lasso之类合理的多的model。这次主要是碰上一个特殊问题，不能
够orthogonalize变量，也不能上model所以才看看的。
对了，如果1000个observation,estimate 12个参数。R^2只有5%-10%的时候，lasso比o
ls强多少？多谢了。
extension |
|
F******n
发帖数: 160 | 32 In that case, it is not a trivial problem, but it could be done by applying
the incremental SVD algorithm.
This efficient/adaptive algorithm was originally given by a guy (Matthew)
from Mitsubishi research lab. You can easily google that paper.
The main point relevant to the LS regression:
b = (X'X)^(-1) (X'y) (1)
is that, matrix inversion (X'X)^(-1) is essentially an SVD problem. As your
new data come in, you should sort of have an updated X and y, and
consequently an updated X'X. In abov... 阅读全帖 |
|
D**u
发帖数: 288 | 33 PCA,应该有两条线，呵呵，两个eigen vector,不过一般pca用来做reduction,所以这里
应该默认是value值最大的哪一条。
不同之处应该是point distance to the line (error) in linear regression is
measured orthogonal to the x axis, where in PCA the distance is measured
orthogonal to the eigen vector
呵呵，of course 一个是supervise一个是unsupervised，不过，问得是线为啥不同，
说一个是 supervise另一个是unsupervised跟没说一样 |
|
k***g
发帖数: 7244 | 34 呵呵，第一个你说的是Markov,不是martingale;
第二个，我们也没假设这些factor之间是orthogonal的，
最后 其实 forecasting (特别是计量上的)其实现在也挺普遍的。 |
|
u****n
发帖数: 7521 | 35 现在直接解Maxwell方程算出RCS（等效雷达反射面积），有一些文章。
有篇成都的文章：http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=825250
Jian Fang;
Southwest China Res. Inst. of Electron. Equipment, Chengdu, China
This paper appears in: Computational Electromagnetics and Its Applications,
1999. Proceedings. (ICCEA '99) 1999 International Conference
Abstract
A finite-surface method for the Maxwell equation is generalized to RCS
problems of an arbitrary cross-section PEC cylinder coated with a dielectric
medium. It directly app... 阅读全帖 |
|
|
d****o
发帖数: 32610 | 37 那个选项只是背景调查
跟前面是orthogonal的 |
|
c********e
发帖数: 4283 | 38 她英语口语很好了，肯定经过口音矫正训练的。
一个orthogonal observation, 她讲话（不单指英语）的方式是那种类似把舌头抵到上
下牙之间的，比较特别。
CCTV |
|
R***r
发帖数: 3519 | 39 妈的，又来了
只会极端思维
反共挺共只是两点，中间99.99%
对共态度只是一维
和其它100维orthogonal的概率小于e-9999
正负相关还看时间序列
too simple, sometimes naive |
|
M**S
发帖数: 3483 | 40 相关性如何？
大家来报一报自己的指标，用黑括号标出自己的取向，我老做个统计
我老的个人鉴定结果：
美新：左中【右】
军版：【老】中小 |
|
|
P**5
发帖数: 7467 | 42 美新被右派川粉霸占了，老将小将都有吧。左派声音太小。 |
|
|
|
i*****e
发帖数: 218 | 45 大家好：
因为不在学校里， 下载文章不容易。
请求几篇文章， 有谁可以帮忙下载一下吗 ？多谢
1. Keiper, J.B. (1992). "Power series expansions of Riemann's xi function".
Mathematics of Computation 58 (198): 765–773.
2. "The Riemann Hypothesis for Polynomials Orthogonal on the Unit Circle",
Mathematische Nachrichten 166:229-258 · December 1993
非常非常感谢。 |
|
l******r
发帖数: 18699 | 46 我们可以从一场数学史上极富盛名的挑战赛来比较一下牛顿和同时代其他数学家的水平。
约翰·伯努利在1696年提出最速降线的问题（problem of brachistochrone），向全欧
洲数学家征求解答。这个问题最早由伽利略在1630年提出：
“一个质点在只受重力的作用下，从一个给定点A到不在它垂直下方的另一点B，问沿着
什么曲线下滑所需时间最短？”
然而伽利略自己给出的答案是错误的：他认为这条曲线是过AB的圆弧。这条曲线也不是
连接AB两点的直线，尽管AB间线段最短，但小球滚下来的时间不是最短。
伯努利把此问题发布在Acta Eruditorum上，他还这么说：
“我，约翰·伯努利，想找到世界上最出色的数学家。对聪明人而言，没有什么能比一
道诚实而富有挑战性的难题更有吸引力，其可能的解决方案将会成为一个永恒的纪念碑
。按照帕斯卡，费马等人设定的例子，请允许我代表整个数学界将这个尤其能在今天考
验大家的数学技巧和思维耐力的问题展示在最优秀的数学家面前。如果有人能把答案递
交与我，我会将其公开，并授予其应得的奖赏。”
伯努利原定的截止期限是1696年年底，可是他只受到了一份来自他的老师... 阅读全帖 |
|
发帖数: 1 | 47 当人家Hinton老爷子几十年如一日的坚持神经网络的时候，也没看这些人跟着坚持。那
时候各个
都是SVM，kernel专家，等到deep learning 突然火了，一个个都想来分一杯，于是瞬
间就多了
那么多deep learning 专家。
如果中国科学家不改变这种跟风，赶潮流的态度，恐怕离科技强国还有很遥远的距离。
中国总是不缺乏获得自然科学一等奖却被发现什么鸟东西都不是的院士，和拿了诺贝尔
奖然而凭
不上院士的科学家。一个可以靠数数(论文)来评奖的体系，如何能期望鼓励产出原始创
新。
看他的论文，3-4年前还没有开始做deep learning，真正开始做deep learning来应用
到CV也就是
近2-3年的事情，2015年已经灌了101篇已发表论文了。就算说手底下有众多硕士博士，
但这
个频率也是够令人震惊(2天一篇?)，估计邮箱里光论文发表的相关邮件就能把他忙死吧
，还有什
么时间来研究deep learning？如果这都是2－3年就是专家，那专家的成本也未免太低
了点。
抛开民族仇恨不谈，中国的这些科学工作者真该向日本的科学家学习学习，能够耐的住
寂寞，
做些正真的... 阅读全帖 |
|
c********e
发帖数: 4283 | 48 不过这和你说的银行的安全问题是orthogonal的，这种保健品什么的都是现金支付的 |
|
g**1
发帖数: 10330 | 49 蝙蝠“百毒不侵” 清华团队发现蝙蝠身藏抑制剂
中国新闻组／北京1日电 2020年04月01日 06:06
6523
人气
小 中 大
研究人员从“百毒不侵”的蝙蝠身上，找到能有效抑制新冠病毒的基因。（新华社）
研究人员从“百毒不侵”的蝙蝠身上，找到能有效抑制新冠病毒的基因。（新华社）
清华大学与杜克-新加坡国立大学医学院等机构研究发现，多年来被视为“天然病毒蓄
水池”的蝙蝠，可能存在新型冠状病毒的解药。研究人员从蝙蝠“百毒不侵”的细胞全
基因组CRISPR筛选中，找到一个RNA病毒复制的关键宿主因子MTHFD1，其抑制剂
carolacton能有效抑制新冠病毒在灵长类动物细胞系中的复制。研究团队目前正进一步
进行临床前测试，希望能将其作为一种广谱抗病毒药物，早日推向临床。
澎湃新闻报导，研究团队由清华大学结构生物学高精尖创新中心、杜克-新加坡国立大
学医学院、中国疾控中心、中科院动物研究所、美国杜克大学组成，31日联合在论文预
印本网站BioRxiv在线发表了这项名为“Orthogonal genome-wide screenings in bat
cells identify MTH... 阅读全帖 |
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