“李约瑟Needham难题”并不存在? 李约瑟难题,由英国学者李约瑟(Joseph Needham,1900-1995)提出,他在其编著的15卷《中国科学技术史》中正式提出此问题,其主题是:“尽管中国古代对人类科技发展做出了很多重要贡献,但为什么科学和工业革命没有在近代的中国发生?”1976年,美国经济学家肯尼思·博尔丁称之为李约瑟难题。 https://baike.baidu.com/item/%E6%9D%8E%E7%BA%A6%E7%91%9F%E9%9A%BE%E9%A2%98 The “Needham Question” or “Needham Problem,” also misleadingly called “the Needham Paradox,”: (1) “the essential problem why modern science had not developed in Chinese civilization (or Indian) but only in Europe.” (2) “why, between the first century BC and the fifteenth century AD, Chinese civilization was much more efficient than occidental in applying human natural knowledge to practical human needs” https://www.oxfordbibliographies.com/view/document/obo-9780199920082/obo-9780199920082-0006.xml 席泽宗 http://casad.cas.cn/sourcedb_ad_cas/zw2/ysxx/ygysmd/200906/t20090624_1809635.html ( 1) 席泽宗先生《关于“李约瑟难题”和近代科学源于希腊的对话》里提出:“‘李约瑟难题’可以研究,但不必大搞”。近代当代欧美世界的“科技中心”也在不停地转移。 ( 2) 传闻有人用“科技大事”进行定量计量,结果发现:古代中国科技在贡献并不比国外更大。要是按照“人均”,就更小了。 这就是说:“李约瑟难题”中的“管中国古代对人类科技发展做出了很多重要贡献”并不是很肯定的存在。 可惜一时没有找到出处。感谢您的指教! ( 3) 2004年艾萨克·牛顿页告诉我:“不要研究李约瑟难题。因为李约瑟难题根本就不存在!” 现代人的统计表明:中国古代影响力大。 但是在地理大发现(15世纪到17世纪)之前,地球七大洲上的人类之间来往不多。五大文明古国(或许有更多个)大都自生自灭,老死不相往来(只有欧洲和北非还算有点来往)。只有我中华文明数千年绝绵延不绝。 谁能保证美索不达米亚、古埃及、古印度、古希腊在自己的兴旺时期,不是世界领先? 现在谁还记得“古希腊”?假如没有伟大的阿拉伯文明把“古希腊”给传承下来的话? 参考资料: 席泽宗. 关于“李约瑟难题”和近代科学源于希腊的对话 . 科学,1996-07-25,48(4): 32-3432-34. http://www.cnki.com.cn/Article/CJFDTotal-KXZZ199604011.htm 李约瑟难题究竟问什么?2016年08月23日 15:26 来源:《自然辩证法通讯》 作者:桂质亮. http://www.cnki.com.cn/Article/CJFDTotal-ZRBT199706008.htm http://www.cssn.cn/zhx/zx_kxjszx/201608/t20160823_3173098_5.shtml?COLLCC=1519144518 European exploration - The Age of Discovery | Britannica https://www.britannica.com/topic/European-exploration/The-Age-of-Discovery In the 100 years from the mid-15th to the mid-16th century, a combination of circumstances stimulated men to seek new routes, and it was new routes rather than new lands that filled the minds of kings and commoners, scholars and seamen. Age of Exploration https://dictionary.cambridge.org/us/dictionary/english/age-of-exploration a period from 1400 to 1600 in which Europeans traveled the rest of the world in search of goods, raw materials, land, and trade partners What Was The Age Of Exploration Or The Age Of Discovery? https://www.worldatlas.com/articles/what-was-the-age-of-exploration-or-the-age-of-discovery.html This era began in the late 1400’s and lasted through the 1700’s. 感谢您的指教! 感谢您指正以上任何错误! 感谢您提供更多的相关资料!
Happened to read a blog for poincare conjecture and its prove. This remind me of first impression of this conjecture long time ago, and think that this conjecture was not proved. Yes, this is right, it is not proved, even its definition has some problem. For example, three dimension objects should have its correspoding surface defined as three dimensions as well, just as one dimension and two dimensions space define their surfaces as the same dimensions of their correspoding space dimensions. This will lead to the right connection definition. Connection problem is the core problem that need to be proved in the poincare conjecture. Wrong definition will lead to wrong conception of prove. The torus connection should change its definition and the band should go around the hollow circle which is the condition of violation. This can be the definition for axiomatized topological solid ball. Other topology connections should also be changed. So, poincare conjecture could not have been proved. At least not properly proved. I also read some Hamilton, and don't think he is a great mathematician. It seemed that he lacked the basic knowledge to be a mathematician. Other mathematicians like Hilbert etc. are not much qualified either. Thanks everyone.
Title:Spectral Ensemble Clustering 整体聚类的谱方法 ABSTRACT Ensemble clustering, also known as consensus clustering, is emerging as a promising solution for multi-source and/or heterogeneous data clustering. The co-association matrix based method, which redefines the ensemble clustering problem as a classical graph partition problem, is a landmark method in this area. Nevertheless, the relatively high time and space complexity preclude it from real-life large-scale data clustering. We therefore propose SEC, an efficient Spectral Ensemble Clustering method based on co-association matrix. We show that SEC has theoretical equivalence to weighted K-means clustering and results in vastly reduced algorithmic complexity. We then derive the latent consensus function of SEC, which to our best knowledge is among the first to bridge co-association matrix based method to the methods with explicit object functions. The robustness and generalizability of SEC are then investigated to prove the superiority of SEC in theory. We finally extend SEC to meet the challenge rising from incomplete basic partitions, based on which a scheme for big data clustering can be formed. Experimental results on various real-world data sets demonstrate that SEC is an effective and efficient competitor to some state-of-the-art ensemble clustering methods and is also suitable for big data clustering. 摘要:整体聚类,也叫一致聚类,是一个多源异构数据聚类的新的很有希望的解决办法。基于联合矩阵的方法,重新定义了作为一个图划分问题的整体聚类,是该领域的标志性的方法。然而高时间和空间复杂性妨碍了它应用 于现实大规模数据聚类中。我们因此提出了SEC,一个有效的基于联合矩阵谱整体聚类方法。我们证明SEC和K均值聚类理论上是等价的,也会大量减少计算复杂度。然后我们产生了SCE的潜在一致方程,这是我们所知的联合矩 阵的第一个明确的目标方程。我们研究了SEC的理论上的稳定性和一般性。我们最后将SEC扩展到满足不完全基础划分,基于此可以形成大数据策略。基于实际数据集的实验结果证明了SEC是一个有效又有效率的方法,可以和 state-of-the-art(最好的)整体方法PK一下,而且他还适用与大数据。 这篇文章研究整体聚类。整体聚类是什么意思呢。就是你有多个数据源,你在利用每个数据源都可以得到一个聚类,然后你将这些聚类综合起来得到一个综合的,整体的,最靠谱的聚类。得到广大人民群众真心拥护的聚类就 是好聚类嘛。哈哈。怎么才能得到广大人民群众的真心拥护呢,呵呵。这是商业秘密,我就不告诉你把它嵌入到推荐系统中就行。哈哈。搞个AB测试就行。哈哈。那么问题来了,这哥儿们干了个什么事情呢。很简单,他用谱 聚类的方法给整体聚类重要方法降低了一下复杂度,然后可以使这个方法应用与大数据。这也是不错的贡献嘛。所以总结起来,这哥们大概有三点贡献:(1)我们提出了SEC方法,证明了他和K均值(越来越觉得这个简单的东 西吊炸天了)的理论等价性,同时该方法可以大大降低co-association matrix based method的复杂度。(2)我们研究了SEC的稳定性和普遍性,将SEC推展到可以满足非完全的划分方法上,可以被应用于大数据。(3)我们 做了大量的实验,结果和state-of-the-art还有得一拼呢。
This problem has confused me for several months. In the figure, the GEOTIFF file can be loaded as a layer, and then called ’china’ shapefile was read and overlay on the GEOTIFF, but the figure cannotbe saved perfectly, excluding the GEOTIFF layer, how I can? The code and results is following. %Read .shp s=shaperead('china'); %Read .tiff =geotiffread('EA.tif'); h=figure; clf; worldmap( , ); setm(gca,'mapprojection','mercator'); geoshow(A,R); geoshow( , ,'Color', ./255,'linewidth',1.5); Figure as Final result as jpg
There are no new difficulties in nonlocal equations and everything is proved analogously as in the classical case Unfortunately, this is a common misconception. Nonlocal equations is a much richer class than the usual PDEs involving (local) differential operators of second order. Just look at the class of differential operators of order 2 with constant coefficients and the corresponding class of integro-differential operators of differentiability order 3/2 with constant coefficients (whatever this is). Predictably, there are some intrinsic difficulties. A common difficulty comes from the fact that fractional order operators have different scaling properties and therefore interact differently with other terms. Moreover, in certain cases there are some surprising results which do not match what one would expect from local PDE intuition. We have a list of results that are fundamentally different to the local case . Nonlocal equations is a field in which one replaces the Laplacian by the fractional Laplacian in whatever equation and writes a paper One can certainly do this. In some cases the classical methods would work after a simple adaptation. In other cases there is a significant difference either in the methods or in the results. Naturally, the good papers are the ones that fit into the second category. This wiki should help people learn to differentiate one from the other. Nonlocal equations are bizarre and unnatural objects The Starting page of this wiki should clarify the importance of nonlocal equations. Most equations in nature are local In fact the opposite is true. In many cases local PDEs are a good simplification though. All statements and proofs in nonlocal equations involve gigantic formulas Nonlocal equations usually involve integral quantities that are larger to write than usual derivatives. This is a notation problem to a large extent. Many proofs in nonlocal equations deal with long integral quantities that come from the nonlocal character of the equation. These features are there, but are rarely at the essence of the arguments. Most statements and proofs are just as conceptual as in usual PDEs. Retrieved from http://www.ma.utexas.edu/mediawiki/index.php/Myths_about_nonlocal_equations Nonlocal equations wiki . http://www.ma.utexas.edu/mediawiki/index.php/Starting_page Obstacle problem for the fractional Laplacian http://www.ma.utexas.edu/mediawiki/index.php/Fractional_obstacle_problem Fractional Laplacian - Mwiki Lecture notes on nonlocal equations - http://www.ma.utexas.edu/mediawiki/index.php?title=Lecture_notes_on_nonlocal_equationsoldid=1130 Regularity results for fully nonlinear integro - differential equations Luis Silvestre University of Chicago - Mathematics department http://www.math.uchicago.edu/~luis/ Non-local operators and applications Raffaella's home page https://www.mat.unical.it/~servadei/ http://www.aimsciences.org/AIMS-Conference/conf-reg2012/ss/detail-ss.php?id=32
【这是自己在2012年5月16日随手记录的,一直没想过与大家分享。一方面 觉得自己研究水平还比较初级,似乎都是大牛才有资格介绍这种话题;另一方面,觉得自己的很多见解也是比较肤浅,而英语写作水平也不高,公开出来很可能会贻笑大方。但昨天看到一篇文章,忽然心中顿悟,觉得自己这个阶段更需要与其他人交流分享。 】 My Story at Princeton I just completed the PARSEC project and started to look for new research projects. I came up with an idea that I planned to work on for 2~3 years with a group of 3~5 students. I discussed the idea with Prof. Kai Li and asked for his advice. I originally thought that Kai would like the idea, but he gave me unexpected feedback. He said that the project is too ambitious to be finished by just one person in a short time. Furthermore, from the methodology perspective, u sually, there is only one best solution for one specific goal. My idea violated the natural rule that achieving three goals by doing just one thing. He suggested me to firstly look for an idea that I can make progress on in three months. I had to admit that I was stunned by hearing the comment that was not supposed to be spoken out from Kai's mouth. I used to hear him talk about how to identify a research topic when I was in ICT several years ago. He disagreed with the way ICTers do research projects whose goals are to prudently complete the requirements of proposals. He told ICTers that you need to setup ambitious research projects aiming at global demands and you also want to tolerate failure since good research implies high risk. In his office, he kept talking about his opinion, experience as well as some concrete examples. He said, if you devote yourself on a long-term project when you are just a junior faculty, you would probably not get any publications for a while, then some issues will show off. You might encounter doubt. People will doubt you. Especially in China, there is performance review every year. So you need to escalate your confidence through the progress of a series of short-term projects.. He added, this proposal is sort of inappropriate but I'm not gonna to criticize you. Actually this is a good exercise. You can learn how to identify proper projects from these lessons. After I walked out from Kai's office, I reflected on my original way of doing research. It seems that I always come up with a bunch of rough ideas but never refine those ideas to several concrete challenges. Thus, I always propose kind of big projects. H ow to identify a proper idea? In fact, finding an idea means finding a good problem. I think there should be several common steps. An overview of Research Flow The following chart illustrates my understanding of how to carry on research. Case Studies Let's look at two case studies. 1. Dr. Xinyu Zhang wrote an article on how he did the research that ended up with ACM MobiCom 2011 best paper award ( 获得ACM MobiCom 2011 最佳论文奖 ,科学网 ). I drew the diagram to describe his experience according to the article. In 2008, Xinyu took a course on real system and learned the idea of DVFS that is widely used in microprocessor. He asked a question that why not apply DVFS to wireless receiver?. After doing survey and thinking, he found the reason that wireless receiver is required to obey Nyquist-Shannon Sampling Theorem in order to correctly receive and decode signals. It seems impossible to break the theorem, so he thought the idea was not doable. But in 2010, one day when he was reading papers, he suddenly came up with a solution that receiving and decoding can be decoupled. Then, he quickly implemented his idea and verified its feasibility. Finally, t his work won the ACM Mobicom 2011 best paper award which led him to be a faculty of University of Wisconsin Madison. In Xinyu's story, I think the key reason he succeeded is that he had distilled the key challenge in 2008. 2. Prof. Kai Li was elected as a member of the National Academy of Engineering in 2012 for his contributions in the fields of data storage and distributed computer systems. Kai pioneered the distributed shared memory (DSM) techniques that allow users to program using a shared-memory programming model on clusters of computers. I used to ask Kai how he came up with the great idea, and he answered that originally he was working on implementing a message-based programming model by RPC that was just proposed in the early 1980s. But he struggled with handling pointers between different machines. So he asked a question that why not use global address space in the distributed system?. He delved into the question and found that the key challenge was how to maintain data coherence among multiple machines. He borrowed the idea of CPU cache coherence protocol and applied it to DSM. Actually, his prestigious paper on DSM is entitled memory coherence in shared virtual memory systems, which has been cited by more than 1600 times. Kai's story exemplifies the importance of distilling key challenges after coming up with a rough new idea. Actually, how to do good research? Perhaps this is the question that every researcher used to ask himself or herself. This article presents my thought and understanding on how to do good research. Be cautious that I am a good researcher yet but just a junior guy. You comments are welcome.
https://trac.macports.org/ticket/22992 Oh, and I guess it goes without saying that you need to have dbus running. Make sure that you have done as the dbus port notes suggest % port notes dbus dbus has the following notes: ############################################################################ # Startup items have been generated that will aid in # starting dbus with launchd. They are disabled # by default. Execute the following command to start them, # and to cause them to launch at startup: # # sudo launchctl load -w /Library/LaunchDaemons/org.freedesktop.dbus-system.plist # launchctl load -w /Library/LaunchAgents/org.freedesktop.dbus-session.plist ############################################################################ If all is well you should see % ps ax | grep dbus 95394 ?? Ss 0:00.03 /opt/local/bin/dbus-daemon --system --nofork 95397 ?? S 0:00.03 /opt/local/bin/dbus-daemon --nofork --session
什么是教育不公?下面的一段话也许会给出一些答案,字虽少,但句句入理: “Educational disadvantage is a complex, multi-faceted problem but at its heart lies a simple truth: a child born into a less-affluent family is statistically less likely to do well at school. That sad fact will, in turn, mean that their choices and future will be limited in ways that are deep, lasting and unjust.” 我想读完这句话,大多数的人都会深有感触,不知道什么时候才能让每个人都能有机会得到公平的受教育机会和环境,也不知道是否有正开会的“代表”们想到了这件事并递交了提案?估计是指望不上他们了,因为这么多年了,这个问题依然屹立不倒。。。
Iman Marvian1, 2 and Robert W. Spekkens1 1Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5 2Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 (Dated: May 11, 2011) The asymmetry properties of a state relative to some symmetry group specify how and to what extent the given symmetry is broken by the state. Characterizing these is found to be surprisingly useful for addressing a very common problem: to determine what follows from a systems dynamics (possibly open) having that symmetry. We demonstrate and exploit the fact that the asymmetry properties of a state can also be understood in terms of information-theoretic concepts. We show that for a pure state and a symmetry group G, they are completely specified by the characteristic function of the state, defined as (g) ≡ h |U(g)| i where g ∈ G and U is the unitary representation of interest. Based on this observation, we study several important problems about the interconver- sion of pure states under symmetric dynamics such as determining the conditions for reversible transformations, deterministic irreversible transformations and asymptotic transformations. 1105 1816v1
It's not really a problem if it just drizzles, but it's hard to go out when the strong wind blows the raindrops all over the place. the drizzles may come down at 45-deg angle, or travel horizontally. Many people seems to be taking today off, since the parking lot at the mall is more than full, with cars waiting for spaces. I will just walk over to see The Hobbit.
coarse: GL fine: partical Lifshiz-Slyozov, Ohta-Kawasaki, Swift-Hohenberg barrier problem, intrinsically slow process, downhill but small Onsager coefficient, and vastly different time scales (stiff equations) Coupling between particle model and continuum description. Free energy from restraint simulations. field-theoretic umbrella sampling, field-theoretic force matching. on the fly string method,
http://lammps.sandia.gov/threads/msg30102.html From : Steve Plimpton sjplimp@gmail.com Date : Thu, 26 Jul 2012 09:21:59 -0600 Please keep the list in the loop. I don't have any further suggestions. Maybe someone else on the mail list can comment. Steve On Wed, Jul 25, 2012 at 10:12 AM, hossein hossein408@gmail.com wrote: Dear Steve, Thank you very much for your comments. The pressure that I calculate is the pressure of both liquid and vapor regions (L_V group) not pressure of just vapor region. Unfortunately, the pressure of system is not correct in step 1 and 2 (before starting heating) and as you saw in the figures its value is very high. I used exactly the same procedure that you mentioned in the manual of LAMMPS. I cannot use "Compute pressure" for calculating pressure of Liquid and vapor Argon because the group ID in this command MUST be "all" while I just want to calculate the pressure of Liquid+vapor region(L_V). Therefore, I used the procedure that you mentioned in the manual of "compute stress/atom". Concerning density calculation, the results of vapor density have very good agreement with experimental data for vapor Argon. For liquid Ar , there is an error of 15% between experimental data and my data which i think it is satisfactory. Regarding the temperature of Argon(liquid+vapor), I think it is not physical because the temperature of Ar MUST not be higher than solid wall. I read some related papers similar to my problem. In all of them, the temperature of Ar was lower than the one for Solid. On Wed, Jul 25, 2012 at 7:55 AM, Steve Plimpton sjplimp@gmail.com wrote: Couple of comments below. Steve On Tue, Jul 24, 2012 at 12:48 PM, hossein hossein408@gmail.com wrote: Hello LAMMPS-Users I am performing evaporation simulation on a flat copper surface. I constructed seven layers of copper atoms to form bottom solid wall, and different layers match with different functions. From outside to inside, the first layer of copper atoms stayed still as a boundary wall to keep the volume of the system constant (fix wall); the following inside three layers were set as heat source from which heat flux was generated (phantom atoms), the last three layers (wall atoms) were set as solid walls through which heat conducted to argon fluids. Above the solid surfece, there is a thin film of liquid and above the liquid region there is vapor region with approximately 250 atoms. The procedure that I used in my problem is 1- Carried out an EMD simulation at T=90K for whole system to achieve a system with constant temperature. Is the pressure of the vapor in this system correct, before you start heating? 2- Change the NVT ensemble to NVE ensemble for fluid domain while the temperature of the solid wall was still fixed at 90 K by the thermostat. Ditto for this step? 3- Increased the solid wall temperature to T=140 K for evaporation. I have not any problem with step 1 and 2. My problems and questions are related to step 3: 1- In a short interval after equilibration period the temperature of argon get higher than temperature of solid substrate which is not realistic. I played with different parameters such as time step and height of computational domain but I couldn't fix the problem. When you spike the substrate temperature, the vapor may take a while to re-equilibrate. That's what your T plot seems to be doing - why is this bad? 2- The result of pressure is not realistic. Due to fix volume of system, the pressure should increase during evaporation period but it just fluctuates. Even in equilibration period the average value of pressure doesn't have good agreement with saturation pressure of Argon at T=90K which is nearly 1.35 bar. Is the method that I used for calculating pressure correct? I attached the plots of temperature and pressure with respect to time to this email. Your plot is 100 bar, not 1 bar. Hence the questions as to whether P is correct in steps 1 and 2, before heating. You can use the compute pressure command or compute stress/atom to look at the virial vs kinetic component. So you can see which component you think is off. I presume you are calculating the pressure of the gas with respect to its volume. 250 atoms is not a lot to compute a pressure on. Do you have the density of the gas correct? #=================================================================== # wall_fix------ first layer of solid substrate which should be fix during the simulation to keep the volume of system constant # wall_phantom ------- next three layers of solid substrate which their function is adding heat to the system # wall_free -------- solid walls through which heat conducted to argon fluid. # L_V-------- Liquid+Vapor region # solid ------ wall_phantom+wall_free # whole 1 ----- all the atoms of computational domain except the first layer of solid substrate # whole 2 ----- all the atoms of computational domain except the phantoms layer of solid substrate #=================================================================== units metal dimension 3 boundary p sf p atom_style atomic neighbor 2 bin neigh_modify delay 5 #==================================================== # Geometry of system and lattice structure #==================================================== region box block 0 72 0 800 0 72 units box ### simulation box create_box 4 box lattice fcc 3.61 ### lattice for solid region region 1 block 0 72 0 1 0 72 units box ### fix solid atoms region region 2 block 0 72 1 4.9 0 72 units box ### phantom solid atoms region region 3 block 0 72 4.9 12 0 72 units box ### free solid atoms region create_atoms 1 region 1 create_atoms 2 region 2 create_atoms 3 region 3 lattice none lattice fcc 5.76 ### lattice for liquid region region 4 block 0 72 12 32 0 72 units box ### liquid atoms region create_atoms 4 region 4 lattice none lattice fcc 32.86 ### lattice for vapor region region 5 block 0 72 32 800 0 72 units box ### vapor atoms region create_atoms 4 region 5 lattice none group wall_fix region 1 group wall_phantom region 2 group wall_free region 3 group liquid region 4 group vapor region 5 group L_V union vapor liquid group solid union wall_phantom wall_free group whole1 subtract all wall_fix ### group all - wall_fix group whole2 subtract all wall_phantom ### group all - wall_phantom mass 1 63.5463 ### mass of fix solid atoms mass 2 63.5463 ### mass of phantom solid atoms mass 3 63.5463 ### mass of free solid atoms mass 4 39.948 ### mass of liquid and vapor atoms set group wall_fix type 1 set group wall_phantom type 2 set group wall_free type 3 set group liquid type 4 set group vapor type 4 #============================================================================ # Potential calculation L---- Liquid , V----- Vapor , S----Solid #============================================================================ pair_style lj/cut 11.9 pair_coeff 4 4 0.0104233 3.40 11.9 ### L-L, L-V and V-V pair_coeff 3 4 0.065007161 2.8689 11.9 ### L-S and V-S(free layers) pair_coeff 1 *3 0.409598855 2.34 11.9 ### S-S (first layer with all solid atoms) pair_coeff 2 2*3 0.409598855 2.34 11.9 ### S-S (phantom with itself and free atoms) pair_coeff 3 3 0.409598855 2.34 11.9 ### S-S (free layer with itself) compute T wall_free temp ### wall free compute_modify T dynamic yes compute T_LV L_V temp ### Liquid+vapor compute_modify T_LV dynamic yes compute S L_V stress/atom compute pLV L_V reduce sum c_S c_S c_S ### summation of diagonal components of per atom stress variable Pres equal -(c_pLV +c_pLV +c_pLV )/(3*4084992) ### 2011392 is the volume of L_V region min_style cg minimize 1.0e-6 1.0e-8 10000 10000 reset_timestep 0 velocity wall_fix set 0.0 0.0 0.0 units box velocity whole1 create 90 482748 units box fix 1 wall_fix setforce 0.0 0.0 0.0 fix 2 all nve fix 3 solid temp/rescale 100 90 90 0.01 1 fix 4 L_V temp/rescale 100 90 90 0.01 1 fix 5 solid spring/self 6.2415e-2 ### spring constant of solid material,6.2415e-2 correspond to 46.7 N/m fix 6 all wall/reflect yhi EDGE units box ### Mirror boundary condition at upper wall of computational domain fix c all ave/time 10000 1 10000 v_Pres ave one file flat.average thermo 1000 thermo_style custom step c_T c_T_LV v_Pres thermo_modify line one lost error norm no dump 1 all atom 500 Cu-flat.vmd timestep 0.001 run 500000 #============================================================================ # Equlibration/relaxation period #============================================================================ unfix 2 unfix 3 unfix 4 fix 7 all nve run 500000 #============================================================================ # Evaporation and boiling period #============================================================================ unfix 7 fix 8 wall_phantom nvt temp 140 140 0.1 fix 9 whole2 nve run 1000000 ------------------------------------------------------------------------------ Live Security Virtual Conference Exclusive live event will cover all the ways today's security and threat landscape has changed and how IT managers can respond. Discussions will include endpoint security, mobile security and the latest in malware threats. http://www.accelacomm.com/jaw/sfrnl04242012/114/50122263/ _______________________________________________ lammps-users mailing list lammps-users@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/lammps-users
Nature的“道歉”发表后,科学网可说是“举网欢腾”。但是读了原文之后,不禁心生疑惑,Nature 的“道歉”究竟说了些什么?下面是Nature的原文,我的翻译和评论。 EDITORS’ NOTE (updated 6 August 2012) This article has drawn an extraordinary level of outraged response. The volume of comments has been so great that our online commenting system is unable to cope: it deletes earlier posts as new ones arrive. We much regret this ongoing problem. The disappearance of some cogent responses to the story has fuelled suspicions that Nature is deliberately censoring the strongest criticisms. This is absolutely not the case: Nature welcomes critically minded discussion of our content. (We intentionally removed only a few comments that violated our Community Guidelines by being abusive or defamatory, including several that offensively stereotyped the many Chinese readers who commented on the story.) 本文引来了异乎寻常之多的义愤填膺的回应。评论的数量是如此之大以至于我们的在线评论系统难以承受,在新的评论涌入时删除了旧的评论。对这个仍然存在的问题我们非常抱歉。一些很有说服力的对原文的批评的消失引起了怀疑:Nature有意删除了最强烈的批评意见。这绝对不是事实:Nature 欢迎对我们文章内容的批判性讨论。(我们有意删除了一些辱骂和诽谤性的评论,包括几个令人厌恶的对中国读者怀有偏见的评论) *** 博主评论: Nature 对于一个技术问题表示了歉意,顺便表扬了一下自己的公正性,同时澄清了对Nature公正性的怀疑。 *** Many of the commenters have questioned why we changed the original subtitle of the story from “‘Performance profiling’ could help catch sports cheats” to “‘Performance profiling’ could help dispel doubts”. The original version of the title was unfair to the swimmer Ye Shiwen and did not reflect the substance of the story. We regret that the original appeared in the first place. We also regret that the original story included an error about the improvement in Ye’s time for the 400-metre individual medley: she improved by 7 seconds since July 2011, not July 2012. We have corrected the error. 许多评论者问我们为什么把原来的新闻标题“‘成绩曲线’能够帮助我们发现体育运动中的欺骗行为”改成了“‘成绩曲线’能够帮助我们驱散怀疑”。原来的标题对游泳选手叶诗文是不公平的,也没有反映新闻的实质内容。首先,我们为原来的标题表示道歉。我们也为原来的新闻中包含的一个错误about the improvement in Ye’s time for the 400-metre individual medley: she improved by 7 seconds since July 2011, not July 2012表示道歉。我们已经改正了这个错误。 *** 博主评论: Nature承认新闻中有一个数据错误,并为此表示道歉;除此之外,Nature暗示新闻的实质内容并不错,只是原始的标题有不公正的地方,也为此道歉。Nature的道歉就这么多了。 *** We apologize to our readers for these errors, and for the unintended removal of comments because of technical issues with our commenting system. Below we reproduce one of the most thorough and thoughtful of the hundreds of responses we received. Beneath it, we continue with our response. 。。。。。。(无需翻译)。。。。 EDITORS’ NOTE (continued) The news story was triggered by a debate that was already active, concerning the scale of Ye Shiwen’s victory. Such debates have arisen over many outstanding feats in the past, by athletes from many countries, and it is wrong to suggest, as many of the critics do, that we singled her out because of her nationality. 关于叶诗文的胜利的争论早已非常活跃,此新闻的灵感就是由此来的。来自许多国家的表现特别突出的许多运动员早就引起了这样的争论。许多批评者认为我们单单选择了叶诗文是因为她的民族,这种观点是错误的。 *** Nature说,虽然我们提到叶诗文,但并不是因为她是中国人,所以这篇新闻与种族和政治无关,请不要对号入座。 *** The story’s intention as an Explainer was to examine how science can help resolve debates over extraordinary performances, not to examine those performance statistics in detail. Several analyses done by others convinced us that it was fair to characterize Ye’s performance as ‘anomalous’ — in the sense that it was statistically unusual. But we acknowledge that the combination of errors discussed above and the absence of a more detailed discussion of the statistics (which with hindsight we regret) gave the impression that we were supporting accusations against her, even though this was emphatically not our intention. For that, we apologize to our readers and to Ye Shiwen. 本新闻的意图是考察科学怎样能帮助解决关于非同寻常的运动成绩的争论,而不是详细考察这些成绩的统计学。其他人做的几个分析使我们确信,用“反常”-统计上非同寻常-来描述叶诗文的表现是公正的。但是我们认识到,由于上面提到的几个错误的组合,以及缺少统计学上更加详细的讨论(事后我们很抱歉),此事给了大家我们支持指控叶诗文的印象,虽然这绝不是我们的本意。对此我们向读者和叶诗文表示道歉。 *** Nature说,本新闻在科学上是正确的,叶诗文的表现就是科学上的“反常”。不过“反常”不等于“兴奋剂指控”,你们理解错了。无论如何,我向你们表示道歉。 *** 博主后记: 我没有读过Nature那篇令国人如此激动的原文,不敢妄评。 这次风波唯一能够证明的,就是Nature在许多国人特别是科学网的许多博主的心目中,有很崇高的地位。国内外媒体上天天都有成千上万篇大骂中国人的文章,从来没有引起科学网的签名抗议。
Non-professionals are required to write their stories with each word starting with a letter "N", whileprofessionalsare required towrite their stories with each word starting with a letter "P". Is there any surprise that the NP problem is leftunsolvable?
Can the complex motions in fluid, such as Brownian motion and diffusion, be described with the exact solution of the motion equations of fluid? This problem is closely related to the famous " Millennium Prize Problems " established by the Clay Mathematics Institute of Cambridge, Massachusetts,for celebrating mathematics of new millennium. One of them is about the Navier-Stokes equation. This problem was introduced shortly and vividly in the website of the Clay Institute as follows: Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. Although these equations were written down in 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations. Obviously, one of the possible explorations to the this problem is to try to give an exact solution to the Euler equation (which is the simplest case of Navier-Stokes equations) for describing some complex fluid motions. In the past thirty years, several exact solutions of such kind were given, such as in , , and . But these solutions usually need some complex and unnatural external force in the Euler equation, i.e., the corresponding complex motions were driven by the complex and unnatural external force (here, the "unnatural external force" means a non-potential force). So, these solutions are somehow not quite satisfactory. From 2006 to 2008, this problem was also studied by me and my graduate students Weiwei Yu and Minghui Liu. Based on the "pseudo-potential" conception proposed by Weiwei Yu, a kind of exact solution of the Euler equation was found out. This kind of exact solution contains two arbitrary given functions and three arbitrary given parameters, and the external force of the corresponding Euler equation could be zero or any given potential force. Based on the choice of the two functions and three parameters contained in the solution, and based on the KAM theory and Melnikov Method, it is proven that the Brownian motion and diffusion of the fluid can described by the chosen exact solution. The concrete exact solutions and the sketch of the related proofs are introduced in my blog paper A Series along the Nature and Beauty in Chinese. The exact solutions and the obtained second order Melnikov function are also listed on the attached pdf file Main Mathematical Formulae in English. Main Mathematical Formulae.pdf To show the complex motion (diffusion), an animation (click on the animation to watch it) was made with the software Mathematica. In this animation, 40000 fluid particles are initially distributed to four small circles, and the four groups of particles are each dyed with a different color, so that each circle has their own unified color. The animation shows how the 40000 particles move according to the chosen exact solution, and how the four colored circles develop into four different closed curves following the fluid particles on it. It is a well known fact that if infinitely many particles are continuously distributed on the four circles, following the motions of the fluid particles, the shapes of the four circles will develop into four closed curves (homotopic to the original four circles), while the areas surrounded by them are maintained respectively, and the four closed curves will never intersect each other. This means the true diffusion (or osmosis) can not really happen if the continuity of the curves is not destroyed. However, for a practical fluid, the fluid particles are always with finite number, no matter how large the number is. So, each circles are formed with only a finite number fluid particles. When the "pseudo-continuous" curves are stretched and deformed drastically, the "continuity" of these curves will be destroyed, obviously, and the diffusion (or osmosis) will really happen between the particles distributed on the four closed curves, shown this way by the animation. The velocity field described by the chosen exact solution used for the animation is periodic both in time and in the coordinates of the two dimensional plane. It is proven by calculation that the mean value of the velocity over time and over space is zero, while the mean value of the square of the velocity is a positive number if the motion exists. Clearly, the larger the mean value of the square of the velocity is, the stronger the complex motion of the fluid is. Therefore, if the period of time and period of space are small from the view point of macro-scope, then the exact solution obtained can be treated as a module of static water with temperature which is proportional the mean value of the square of the velocity. References: T.H.Solomon and J.P. Gollub, Chaotic particle transport in time-dependent Rayleigh-Benard convection , Physical Review A. Vol.38 No. 12, (1988) 6280-6286 S. Wiggins, The dynamical systems approach to Lagrangian transport in oceanic flows , Annu. Rev. Fluid Mech. 37, (2005) 295–328. N. Malhotra and S. Wiggins, Geometric Structures, Lobe Dynamics, and Lagrangian Transport in Flows with Aperiodic Time-Dependence, with Applications to Rossby Wave Flow ,J. Nonlinear Sci. Vol. 8: pp. 401–456 (1998) Author: Keying Guan (Science College, Beijing Jiaotong University) email: keying.guan@gmail.com
题材如下,写议论文。 美国老师以为大多会选择继续手术,因为上英语课的多是东亚几个非英语国家的学生。 确实算不错的论题。 你是怎么想的呢? ----------- The Twin Problem... You are a highly skilled surgeon with a flourishing practice. You know you are very good at what you do and have earned the respect of your patients. ne day a Mr. and Mrs. Waterhouse come to see you. They are obviously very upset, and tell you they have a problem of life and death and need your help. The Waterhouses explain that they are the parents of 14-year-old twin girls named Irene and Meg. Some years ago Irene contracted a disease of the kid- neys, and she has been seriously ill ever since. Her kidneys are now so badly damaged that unless she receives a kidney transplant she will surely die within three months. Irene is a charming and open girl, full of vitality and intelligence. She is studying piano, and is so good that her teacher feels sure she will have a most successful professional career—if she lives. The parents tell you—as you already know—that the only kidney transplant which will be successful is one from Irene’s identical twin. All other kidney transplants are universally unsuccessful because of rejection by the recipients of the “foreign” tissue. Only Meg’s kidney can save Irene’s life. You also know that a kidney transplant between twins is a relatively safe operation. There is some risk, of course, as there is with any major surgery, but it is minimal. Both the donor and the recipient can get along on one kidney apiece. The obvious solution is for you to transplant one of Meg’s kidneys to Irene, and that is what Mr. and Mrs. Waterhouse ask you to do. But, they tell you, there is a serious problem. Meg has flatly refused to agree to the operation. Unlike her sister, Meg is depressed, socially backward, and shy. Her parents have focused on Irene’s illness and her musical achievements, and Meg feels profoundly rejected. Meg’s parents have told her about the urgent need for the transplant. They have explained that Irene will die unless she is given one of Meg’s kidneys. But Meg says she has always hated Irene, who has received much more love and attention than she has, and she—Meg—will certainly do nothing whatsoever to prevent Irene from dying. Every possible device has been used to make Meg change her mind, including extensive psychiatric treatment, but without success. In desperation, say the Waterhouses, they have come to you for help. In the state in which you practice you are permitted to operate on a person under the age of 18 if his or her parents consent to the operation. The patient, as a minor, has no legal rights in the matter. Mr. and Mrs. Waterhouse say they have decided to ask you to go ahead and perform the operation over Meg’s objections in order to save Irene’s life. They know you are the best possible surgeon, and say they will do whatever you decide—but they plead with you to decide to operate.
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For what the UW charges each out-of-state student, it ought to provide better services. It messed up two out of three bills, and ended up charging the student the so-called LTF (late transaction fee?) each time. Look, there is room to spell out LTF, unless you intend to fool the recipient, which apparently worked.
汉语是联合国官方正式使用的 6 种同等有效语言之一。请不要歧视汉语! Chinese is one of the six equally effective official languages of the United Nations. Not to discriminate against Chinese, please! P对NP:请郝克刚教授等专家指教(一) ( 一般背景知识汇报 , 无穷化版本下的“P 对 NP” ) 求教心切,由于种种原因,下文里面错误难免。 请您不吝批评与指教!衷心感谢! 主要相关数学分 支:公理集合论,图论, 概率论 ;以及理论计算机科学。 一、术语的缩写、相关数学知识简介 NDTM ( NTM ), non-deterministic Turing machine ,非确定型图灵机; DTM ( TM ), deterministic Turing machine ,确定型图灵机; NPC , NP-complete , NP- 完全; NPI , NP-Intermediate , NP里 不属于 P 类且不属于 NP- 完全问题,早期指“人们 不知道是属于 P 类还是属于 NP- 完全类,还有待于证明其归属”; CH , continuum hypothesis , 连续统假设 ; TSP , traveling salesman problem , 旅行推销员问题 ; SAT , Boolean satisfiability problem, Boolean 逻辑可满足性,是由 Cook 证明的第一个 NPC 问题 。 ZF , Zermelo–Fraenkel set theory , 策梅洛 - 弗伦克尔公理系统; ZFC , Zermelo–Fraenkel set theory with the axiom of choice ,承认选择公理的 策梅洛 - 弗伦克尔公理系统 ; NBG 或 GB , NBG of Neumann–Gdel–Bernays , 冯 · 诺伊曼、 P. 贝尔奈斯、 K. 哥德尔 集合论公理系统 。 a ,可数无穷基数; c ,连续统的基数(全体实数集的基数); f ,全体几何曲线集合的 基数 。 CH 的基本含义: The hypothesis, due to G. Cantor (1878), stating that every infinite subset of the continuum R is either equivalent to the set of natural numbers or to R itself. 目前已知“ 连续统假设在 ZF (或 GB )中是不可判定的,它即不能被证明,也不能被否证。 ” 换言之,在著名的集合论公理系统中,都不足以解决连续统假设。这正是人们不断地寻求新公理系统的主要原因。人们总希望能找到科学的为大家所能接受的公理系统,并且得以解决著名的未解决的问题。 “ Formal unsolvability is understood in the sense that there does not exist a formal derivation in the Zermelo–Fraenkel system ZF either for the continuum hypothesis or for its negation. ” 阿列夫 Aleph 是个有争议的问题。据说有人认为 阿列夫 2 与连续统的基数相等,还有人认为 阿列夫 可数无穷 仍然小于连续统的基数。所以,我不采用 阿列夫 来研究“ P 对 NP ”,而是采用数学意义更为直观明确的 Cantor 无穷级数第二序列( a , c , f , h , i , 等等)来表述。在 1997 年《百科知识》、 1999 年《哲学研究》等文章里开始使用。 二、本人相关背景简介 我是一名普通的基础课教师,天生的笨傻。每年能用于真正“科研”的时间,十分有限。为了完成岗位职责,要花去大量的时间。 上帝啊! 我太累了 ! 我没有时间 ! 因此推出“ P 对 NP ”完全证明的个人观点,肯定是十分艰难和缓慢的。 本文博文作为正式的介绍材料之一 。 期待有关专家指导俺修改之! 1993 年暑假,某天夜里后半夜,想到在“ 有穷情况” 下的 P 和 NP 关系。 这个发现,是以生命为代价换来的! 大约到 1995 年初,真傻又做出“ 无穷版本” 下的 P 和 NP 关系:是一个著名数学问题的特定解释。 2011 年 3 月,给出概率意义下的有穷直接证明。 本人专业背景简介 我目前是天津大学( 985 大学)在岗的“ 模式识别与智能系统”和“软件工程” 2 个专业的硕士生导师,工学博 士学位。曾经开设硕士生选修课《人工智能专题》多年,以史忠植先生的《高级人工智能》为主要参考书。 从2002年开始 主讲硕士生选修课《模糊理论及应用》至今。 我 1988 年硕士入学后不久,就听说了“ P 对 NP ”问题。该问题的核心,数次被两位教授重复。一位教授开设硕士生《数据结构与算法》多年,俺跟该教授上过这门课;该教授在 1980 年代,就指导过东欧来天津大学的访问学者。另一位教授在图论方面有较深的造诣,曾经对两个经典问题做出世界最好结果。由于未征求这两位教授的意见,此处只能隐去他们的姓名,以避免可能对他们产生的某种不必的负面影响。 其中的图论教授,数次向我们讲解“ P 对 NP ”的核心,并推荐了名著《 GAREY M R, JOHNSON D S. Computers and Intractability: A Guide to the Theory of NP-Completeness . New York: W. H. Freeman, 1979. 》。我从系资料室(现更名为学院资料室)借阅该书的汉译本 20 余年。由本学院上届领导批准,几年前将该书赠送给我。 感谢这位好心的领导!礼轻情意重! 因此,“ P 对 NP ”是属于我专业背景的科学问题(数学 - 计算机科学)。 三、 对“ P 对 NP ”核心的个人理解 3.1 “ P 对 NP ”定义的核心 P 是 DTM (确定型图灵机)在多项式时间内的可判定问题类。 这里的“问题类”,常被记为“语言类”。“可判定”是可计算性、计算复杂性里面使用的术语。可判定的一个通俗理解,就是可以求解,可以得到正确的答案。典型的 P 问题,有常见的排序 sorting ,数值矩阵的乘法。 NP 是 DTM (确定型图灵机)在多项式时间内的可验证问题类。 NP 是 NDTM ( NTM ,非确定型图灵机)在多项式时间内的可判定问题类。 DTM 与 NDTM 关系的一个直观解释: 非确定型图灵机是一种能够同时进行多路计算的“并行”的图灵机,并且限制这些并行的图灵机之间不能相互通讯。 A nondeterministic Turing machine is a "parallel" Turing machine that can take many computational paths simultaneously, with the restriction that the parallel Turing machines cannot communicate. 3.2 “ P 对 NP ”的有关主流看法 显然, P 包含在 NP 里面。是否所有的 P 都是 NP ,是“ P 对 NP ”的表述方式之一。 NP 里面最难的称为 NPC ( NP 完备的)。 NP 里面的任何问题,都可以在多项式时间内归约为 NPC 。 如果 NPC 找到了多项式时间求解算法,则证明 P=NP 。 如果证明 NPC 必须使用指数时间,则证明 P ¹ NP ( P 不等于 NP,也有人记为 P ! =NP )。 如果 P ¹ NP ,则可能存在“不是 P ,又不是 NPC ”的中间类型 NPI 。找到一个 NPI ,则等效于证明 P ¹ NP 。 NPC 的例子很多。第一个 NPC 是 SAT ,常见的自然问题有 TSP 等。 到目前为止,“ P 对 NP ”未见主流承认的答案。 Clearly, is contained in . However , it is not known whether or not the containment is proper . The problem of whether or not equals ( ?) can justly be called the most celebrated open problem in the theory of computation. The significance of this question is due to the fact that many practically important problems are known to be in , whereas it is not known whether or not they are in . In fact, all known deterministic algorithms for these problems are exponential as far as time is concerned. Thus, a proof of would make all of these problems tractable. Most exponential time algorithms are marely variations on exhaustive search, whereas polynomial time algorithms generally are possible only through the gain of some deeper insight into the structure of a problem. 大多数指数时间算法只是穷举搜索的变种,而多项式时间算法通常只有在对问题的结构有了某些比较深入的理解之后才有可能给出。 现有的研究与证明方法主要有三大类:对角化 diagonalization 、电路复杂性 circuit complexity 、证明复杂性 proof complexity 。但国际学术界普遍的看法是这些方法都不能得到彻底的结果。一般认为,“不同数学领域的意外结合”、“ P 或 NP 新特征的使用”、“新的电路复杂性下界证明方法”以及“对角化的新变形”等是可能获得新结果的途径。 3.3 对“ P 对 NP ”的一些个人看法 由于“重复发表”、“首次发表”等现行科技规范问题,这里只能就我的某些看法想有关老师汇报。其余的看法,希望能在“有同行评审的期刊”发表。敬请您的指教! ( 1 )“ P 对 NP ”的难度(为什么该问题如此难?) ① 由 NP 定义可知“对于 NDTM , P=NP ”,因此 “对于 DTM , P ¹ NP ”才是研究的重点 。这十分类似希尔伯特第四问题,“ P 对 NP ”问题描述的不确定性,误导了人们的研究。造成了 “ P 对 NP ”研究额外的困难性。 缺少对 DTM 和 NDTM 结构差异的充分使用,是导致“ 对于 DTM , P ¹ NP ”长期缺乏明确结论的原因之一。 ② 目前的以及历史上出现的各种主流研究方法,都集中在 P 或 NP 问题类的数量性质研究上。 从问题类角度看,由于 NPC 类、 P 类只是在 DTM 上计算“速度”的差异,只是一种“量”的区分,而不像“可计算性”是一种质的区分,这是引起 “ P 对 NP ”困难性的 原因之二。因为证明所采用的“逻辑”,通常是成立、不成立两种明确状态(质)划分的。 ③ 如果能证明对于 DTM , P 不等于 NP ,则无穷版本下的 NPI 就是 Cantor 原本意义下连续统假设的关系。预计可以得出不接受连续统假设的结论。 ( 2 )“ P 对 NP ”完全证明的结论 “ P 对 NP ”实际上是三个更具体问题的合成: ① 在 NDTM 中 P 等于 NP ; For a NDTM, P=NP; ② 在 DTM 中 P 不等于 NP ; For a DTM, P ¹ NP; ③ 没有关于所采用的理论计算机模型的必要说明,则具有独立性。 从形式语言的表示看, 郝克刚 老师《纠正对 NP 问题的错误理解( 3 ) -- 对一位网友文章的评论》( http://blog.sciencenet.cn/home.php?mod=spaceuid=506146do=blogid=530828 ) 表述是很准确的。 这里仍然采用“ 没有 …… 必要说明 ”,基本意图是想提供多的信息:命题对公理系统的独立性,除了该命题对证明所采用的公理系统“独立”外(直观“独立”的意思),公理系统的信息量不够,也可能造成独立。例如实系数一元二次方程,当根的判别式小于 0 时,在实数域是没有解的。这是由公理系统信息量不够引起独立的直观类比或解释。 参见 1974 年的 Chaitin 定理。一般认为, Chaitin 的三条定理,是对 Kurt Friedrich Gdel 的 哥德尔 第一不完全定理( Gdel's first incompleteness theorem )的信息论意义下的具体化 。( Gdel incompleteness theorem 在《苏联数学百科全书 Encyclopedia of Mathematics》扩展版, http://www.encyclopediaofmath.org/index.php/G%C3%B6del_incompleteness_theorem 。 Kurt Gdel 在《Stanford Encyclopedia of Philosophy》, http://plato.stanford.edu/entries/goedel/ ) ( 3 )“ P 对 NP ”完全证明结论的三类证明 ① 有穷形式下形转化的直接证明; ② 无穷形式 / 版本下的证明,直接否证 Cantor 原本意义下的“连续统假设”; ③ 概率形式、有穷形式下的直接证明。 其中“ ③ 概率形式、有穷形式下的直接证明”,还未公开过。计划争取英文文章。 在 2011 年初夏,以文字形式,向党组织汇报过(党员创优活动的汇报,一个笔记本。 恳请党组织保留该笔记本一些时间 ,感谢党的指导与关怀!) 。 上面的“ ① 有穷形式下形转化的直接证明; ② 无穷形式 / 版本下的证明,直接否证 Cantor 原本意义下的‘连续统假设’”, 1995 年以《 从 NP 结构到超级计算机分类理论》为题目,在天津大学百年校庆研究生院研究生学术报告会(1 995 年 10 月初)公开讲解过。可惜没有录音或录像,希望有人愿意证明我讲过。 “ ① 有穷形式下形转化的直接证明”的细节,计划争取英文文章。 因此,本博文主要汇报“ ② 无穷形式 / 版本下的证明,直接否证 Cantor 原本意义下的‘连续统假设’”。 ( 4 )无穷形式 / 版本下的证明,直接否证 Cantor 原本意义下的“连续统假设” 该证明发表在 2011 年 TTU 的《 A non-canonical example to support that P is not equal to NP 》,其核心在 2008 年《 密码学与非确定型图灵机 》里扼要介绍过。 “无穷形式 / 版本”的基本意思,是将 DTM 、 NDTM 的运行时间取为无穷大(可数无穷步。接受“实无穷”,令字母表、状态数为可数无穷即可,这很自然;坚定的“潜无穷”论者可能提出怀疑。)。 DTM 此时只有一个新状态、一共生成 a 个状态;而 NDTM 此时产生 | Q-F | a 新状态,以及指数界数目的总状态。 直观地说:限制 NDTM 的转移函数每次只产生一个转移状态,则该最小的 NDTM 就退化为一个 DTM 。所以,容易证明, DTM 至多用指数时间就可以模拟一个对应的 NDTM 。这等价于“ P 包含在 NP 里面”。 如果证明“ DTM 必须用指数时间就才能模拟一个对应的 NDTM ”,则从某种意义上讲,就等价地证明的“ P 不等于 NP ”。而这并不容易,所以 2011 年 TTU 的文章采用“支持 P 不等于 NP ”的说法( A non-canonical example to support that P is not equal to NP )。 演绎证明的实质,是将“公理”包含的信息,以某种方式显示出来,所以“演绎证明的结论是前提蕴含的”。假如不是前提蕴含的,就是“独立的”。 假如找到 NPI ,则在其无穷化版本下,等价于否证 Cantor 原本意义下的连续统假设。 目前众所周知的康托三分集( Cantor ternary set ),显然与连续统假设( continuum hypothesis )的研究有直接的关系。 ( 5 )关于“ P 对 NP ”的独立性 ① 如果没有明确是用 DTM 或 NDTM 求解,则 “ P 对 NP ” 具有独立性。 这是说 “ P 对 NP ”对“用 DTM 或 NDTM 求解 ”独立,而不是对现有的公理集合论系统( ZF、NGB 等 )独立 。 这类似:实系数一元二次方程,当根的判别式小于 0 时,在实数域无解;在复数域有解。 又如, 1975 年 Baker 、 Gill 和 Solovay 报道的“存在不同的计算模型 A 、 B ,使得 P A =NP A 、 P B ¹ NP B 分别成立。” ② 承认“对 DTM , P 不等于 NP ”,则 无穷版本下的 NPI ,就是的 Cantor 原本意义下的连续统假设 CH 。 无穷版本下 NPI 的存在性,对 目前现有的公理集合论系统( ZF、NBG 等 )独立。 所以 1975 年 Ladner 证明“如果 P ¹ NP ,则 NPI=(NP - P) 不是空集”以及 1993 年 Zimand 证明如果 NP - P 不空则很大( If not empty, NP - P is topologically large ),都不能给出确定的结果。 假如 P 不等于 NP ,则 NPI 对应一种介于多项式和指数之间的时间增长方式。由于 Cantor 没有构造出这样的增长方式,所以才在 1878 年提出连续统假设:连续统子集的基数,要么是自然数,要么还是连续统的基数。康托三分集的基数还是连续统的基数 c ;可以从连续线段中抽取有穷或无穷个离散点(自然数集的基数,有穷基数,或可数无穷基数 a )。 四、请教 4.1 关于 真傻 的叙述 ( 1 )以上关于无穷化版本下的“ P 对 NP ”问题的看法是否介绍清楚? ( 2 )关于“ P 对 NP ”问题难度的解释,《 A non-ca nonical example to support that P is not equal to N P 》的介绍是否清楚? 4.2 创新性小结与说明 我的方法基本没有创新:属于“不同数学领域的意外结合”和“P或NP新特征的使用”,并没有超出主流的预期。 主要创新: (1)提出“完全证明Full proof”作为数学证明的新标准; (2)建立无穷版本下的NPI与Cantor原本意义下连续统假设的关系。 其它的都是主流预期的,没什么让人耳目一新的。惭愧! 4.3 有关的问题请教 ( 1 ) “ 2TSP 是 P , 3TSP 是 NPC ”的证明,还有在 SCI、EI 期刊发表的可能性吗? ( 2 ) “ P 对 NP ”相关问题对 ZF 的独立性,是否有进一步研究的必要和可能? 真诚期待有关专家的批评与指教。 衷心感谢! 主要参考文献: COOK S. The P versus NP Problem, official problem description , . http://www.claymath.org/millennium/P_vs_NP/pvsnp.pdf ALLENDER E. A status report on the P Versus NP question . Advances in Computers , 2009, 77: 117-147. FORTNOW L. The Status of the P versus NP Problem . Communications of the ACM , 2009, 52(9): 78-86. SIPSER M. The history and status of the P versus NP question . Proceedings of the 24th Annual ACM Symposium on the theory of Computing’ 92 (Canada) , 1992, pp 603–618. COOK S. The importance of the P versus NP question . Journal of the ACM , 2003, (50)1: 27-29. HAZEWINKEL M. Encyclopaedia of mathematics: an updated and annotated translation of the Soviet “Mathematical encyclopaedia” . Dordrecht: Kluwer Academic Publishers, 2001. HOPCROFT J E, MOTWANI R M, ULLMAN J D. Introduction to automata theory, languages, and computation (Third edition) . New Jersey: Ad dison Wesley , 2006. GAREY M R, JOHNSON D S. Computers and Intractability: A Guide to the Theory of NP-Completeness . New York : W. H. Freeman, 1979. Nondeterministic Turing Machine . http://mathworld.wolfram.com/NondeterministicTuringMachine.html CHAITIN G J. Information-theoretic computational complexity . IEEE Transactions on Information Theory , 1974, 20(1): 10-15. 中国大百科全书•数学 . 北京 : 中国大百科全书出版社 , 1988. BAKER T, GILL J, SOLOVAY R. Relativizations of the P =? NP question . SIAM Journal on Computing , 1975, 4(4): 431-442. LADNER R E. On the structure of polynomial time reducibility . Journal of the ACM , 1975, 22(1): 155-171. ZIMAND M. If not empty, NP - P is topologically large . Theoretical Computer Science, 1993, 119: 293-310. Weisstein, Eric W. "Nondeterministic Turing Machine." From MathWorld--A Wolfram Web Resource . http://mathworld.wolfram.com/NondeterministicTuringMachine.html 杨正瓴 . 从 NP 结构到超级计算机分类理论 . 天津大学百年校庆研究生院研究生学术报告会(一等奖论文),和天津大学百年校庆自动化系学术报告会, 1995 年 10 月 . 杨正瓴 . 人脑有多复杂? . 百科知识, 1997 , 7 (总第 216 期): pp39 – 40. 杨正瓴 . 人脑复杂性的估计及其哲学意义 ,《中国新时期社会科学成果荟萃》, 1999 ,第 1 卷 p296 。卢继传 主编,中国经济出版社,北京, ISBN 7 – 5017 – 4100 – X/G. 374 , (第 2 编,哲学,第 4 章,自然辩证法) . 杨正瓴,林孔元 . 人类智能模拟的“第 2 类数学(智能数学)”方法的哲学研究 . 哲学研究, 1999, (4): 44-50. 杨正瓴 . 密码学与非确定型图灵机 . 中国电子科学研究院学报 , 2008, 3(6): 558-562. 杨正瓴 . 第二类计算机构想 . 中国电子科学研究院学报 , 2011, 6(4): 368-374. YANG Zhengl ing ( 杨正瓴 ). A non-canonical example to support that P is not equal to NP . Transactions of Tianjin University, 2011, 17(6): 446-449. 相关链接: 郝克刚 教授《纠正对NP 问题的错误理解(3)-- 对一位网友文章的评论》 http://blog.sciencenet.cn/home.php?mod=spaceuid=506146do=blogid=530828 徐建良 教授《P对NP -- 与杨正瓴老师商榷》 http://blog.sciencenet.cn/./home.php?mod=spaceuid=66861do=blogid=551309 《A FULL PROOF to the P versus NP problem》 http://bbs.sciencenet.cn/home.php?mod=spaceuid=107667do=blogid=486692 里面有一些全文可以下载。 您有兴趣,可以直接跟我要相关的论文全文。 《 “P对NP(P versus NP, P vs NP)”问题的描述、难度、可能的答案》 http://bbs.sciencenet.cn/forum.php?mod=viewthreadtid=266338 《 Vinay Deolalikar宣称自己证明了“P!= NP”(P 不等于 NP)》 http://bbs.sciencenet.cn/forum.php?mod=viewthreadtid=106360
Abstract: hort-term earthquake prediction has always been a very difficult problem in geology, 15 this article pre-displacement, pre-established short-term break for the earthquake prediction based on the theory becomes completely abandoned to form the basis of earthquake prediction method, short-term earthquake prediction is a theoretical breakthrough. Key words: Mechanics; earthquake,;short-term forecasting,;pre-displacement; pre-fracture 摘要: 地震短期预报历来是一个十分困难的地质学问题,本文以预位移预断裂为依据对于短期地震预报进行了理论思考,一旦该理论被实践所证明,将会是地震短期预报的一次理论突破。 关键词 :固体力学;地震;短期预报;预位移;预断裂 预位移预断裂短期地震预报数学方法探析.pdf
My reportand papers on "the P versus NP problem" (P vs NP) 杨正瓴, Zheng-Ling YANG, YANG Zhengling Abbreviations: NDTM, non-deterministic Turing machine; DTM, deterministic Turing machine; NPC, NP-complete; NPI, NP-Intermediate; CH, continuum hypothesis; TSP, traveling salesman problem. The FULL PROOF: The mathematical proofs of a proposition must give the following three cases: (1) The proposition is valid, under some certain axiomatic systems; (2) The proposition is not valid, under other axiomatic systems; (3) The proposition can not be proved/decided, without the necessary designating axiomatic systems. A FULL PROOF requires that the three cases are all identified definitely, because "Any proof is relative, since it is based on certain unprovable assumptions." http://eom.springer.de/P/p075420.htm (Encyclopaedia of Mathematics, Edited by Michiel Hazewinkel, an updated and annotated translation of the Soviet "Mathematical encyclopaedia") The essence of "the P versus NP problem": ① P = NP for a NDTM; ② P ≠NP for a DTM; ③ The “P vs NP problem” can not be proved/decided, without the necessary designating of a NTM or DTM. The keys of two sufficientproofs of "P ≠NP for a DTM": (1) 2SAT is a planar graph; 3SAT can be a non-planar graph, since it can have the Kuratowski graph K3,3. (2) Non-canonically, a maximal NDTM is the power set of DTM. If the "Axiom of power set" in ZFC (Zermelo–Fraenkel set theory with the axiom of choice) is accepted, then P ≠NP for a DTM. My relative report and papers: 从NP结构到超级计算机分类理论 . 天津大学百年校庆研究生院学术报告会(一等奖论文), 和天津大学百年校庆自动化系学术报告会, 1995年10月. From the hierarchy of NP to a classification of supercomputer. The Student Academic Symposium of Graduated School to Celebrate the 100th Anniversary of the Founding of Tianjin University, October, 1995. (An oral report in Chinese) 人类智能模拟的“第2类数学(智能数学)”方法的哲学研究 . 哲学研究, 1999, 4: 44-50. Philosophical research on "the second class mathematics (intelligent mathematics)" for simulations of human intelligence. Philosophical Research, 1999, 4: 44-50. (in Chinese) 密码学与非确定型图灵机 . 中国电子科学研究院学报, 2008, 3(6): 558-562. Cryptology and non-deterministic turing machine. Journal of China Academy of Electronics and Information Technology, 2008, 3(6): 558-562. (in Chinese) 第二类计算机构想 . 中国电子科学研究院学报, 2011, 6(4): 368-374. Conception of the second class computer. Journal of China Academy of Electronics and Information Technology, 2011, 6(4): 368-374. (in Chinese) A non-canonical example to support that P is not equal to NP . Transactions of Tianjin University, 2011, 17(6): accepted. 支持 P 不等于 NP 的一个非规范例子(英文稿) . YANG Zhengling (杨正瓴). A non-canonical example to support that P is not equal to NP . Tra nsactions of Tianjin University, 2011, 17(6): 446-449. 现在已经刊出,2011-12-05后记。 “P对NP”难题研究的形转换新思路 ,中科院在线《科学智慧火花》,2011-08-30, http://idea.cas.cn/viewdoc.action?docid=1275 。 拟投英文稿2个,正在写作。 相关链接: 真傻 对 “ P 对NP(P versus NP, P vs NP) ”问题的思考,请看: “P对NP(P versus NP, P vs NP)”问题的描述、难度、可能的答案: http://bbs.sciencenet.cn/forum.php?mod=viewthreadtid=266338 Vinay Deolalikar宣称自己证明了“P!= NP”(P 不等于 NP): http://bbs.sciencenet.cn/forum.php?mod=viewthreadtid=106360
《How To Choose a Good Scientific Problem》 Abstract: Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out on their own and through the observation of their teachers. This lack of explicit discussion leaves a vacuum that can lead to approaches such as choosing problems that can give results that merit publication in valued journals, resulting in a job and tenure. 个人点评: 我认为此文精华在下图 a rule for new students and postdocs: Do not commit to a problem before 3 months have elapsed.
For new readers and those who request to be “ 好友 good friends”please read my 公告 栏 first. First of all, a word of explanation about the title: 1. Decentralized – By this word, I mean the absence of an all wise and all knowing supreme being which governs everything that go around in an idealized world for the best of all possible purposes. In this real world, events take place via the interactions of individuals, organizations, and countries each pursuing their own agenda and interest. 2. Control and Optimization – By these two words which I use in the colloquial sense to mean that human civilization always strive for “improvement” though not always successfully. This is a fundamental desire. #1 and #2 certainly reflect the situation in the real world. . Now I want to explain conceptually why this is hard, very hard, to do. In the process I hope to explain using very simple terms as to the “what” and “why that constitute an impossibility theorem. In my earlier blogs you may have read my mention of the so-called “Witsenhausen Problem”. This is a problem made famous by Hans Witsenhausen, a Bell Laboratory researcher in 1968 to illustrate the difficulty with information and coordination (the issue of who know what when and dynamic team theory. If you google or bing it you will get over 1000 reference to this problem ). It is a problem of the SIMPLEST kind with all the right mathematical assumptions such as linearity, convexity, Gaussian noise, etc. involving only two decision variables. You have a constant (which is a sample of a gaussian random variable) to eliminate or cancel. The first decision maker, DM1, knows exactly the value of this constant, but his action is costly. Thus, it costs something for him to eliminate the constant (reduce it to zero). The second decision maker, DM2, who acts after the first decision maker incurs no cost to act, but he does not know what DM1 knows. He only has a noisy observation of the resultant value of the unknown (to him) constant value plus any effort on the part of DM1’s attempt to cancel this constant. Thus he cannot cancel what remains exactly if he uses the noisy observation. The un-canceled leftover will incur a cost. The problem is what should the two decision maker jointly do so that resultant performance (cost to cancel in part or in whole by DM1 plus the leftover un-canceled portion due to uncertainty and the action of DM2) is at a minimum . Note the problem will be trivial not even qualify to be an exercise in an undergraduate control/optimization course if the two decisions are under the control of one decision maker – the centralized case (we can even let the first decision’s information be noisy also. The optimal solution is well known to every student in such courses). But this simple change of different decision maker having different and non-inclusive information made all the difference. Witsnehausen did not solve the problem he thus posed. But showed a number of surprising things. Among them: What everyone expect to be the answer – a linear proportional solution- is not optimal A much better nonlinear solution, though still not optimal, exists. This is highly surprising at the time. In the ensuing 40+ years (1968-2009), a large number of people, including myself spend enormous number of hours using rather advanced technical theory trying to advance the solution to this so-called W-problem resulting in many published papers on different aspects of this simplest problem. In 2002, my student and I finally published a numerical solution of the Witsenhausen problem with a conceptual explanation that captures the essence of the problem. We claimed that we have exhausted all the ideas associated this problem and any further improvement can only be numerical (for example using more significant number of digits in computation, or a better search algorithm). Since 2002, several other people have worked on this problem (including someone just last month) but no one has invalidated our claim. Thus, you can say that the last word probably has been said on it. But why such an apparently simple problem took 40+ years and many scholars’ time? Now let me explain the essence of this simple problem in an even simpler way without any advanced mathematics. Once understood, readers will begin to appreciate why decentralized control and optimization (in plain language – coordinate actions to work for the common good) is very hard in the best of circumstances. Once you add in human frailties, politics, and other vices, a perfect world is impossible for all practical purposes. Think back to the W-problem.as described above. It is clear unilateral action by either decision maker (for DM1 to simply cancel out the constant regardless of the cost or for DM2 to treat the noisy observation as true value and cancel accordingly) is not going to be the best course of action. Thus, they need to cooperate and each does a bit of work. The expected linear solution simply does a proportional compromise which is better than unilateral action by either one. But you can do better. The following are clear: For DM1 you wish to use as small an effort as possible in changing (canceling in whole or in part) the value of the constant since it is costly for him to act. If the constant is either one of two possible known values separated far apart comparing to the size of the noise, then canceling by the DM2 should be easy. Because even with noise, you can be very certain which one of the two values the constant has and cancel with no cost accordingly. From these two considerations, a nonlinear scheme emerges. Let DM1 observe the constant exactly and then proceed to change (cancel) the value of the constant to either one of two pre-agreed-on positive or negative value, say +or – C. DM2 then observes with noise either plus or minus C and can be pretty certain even under noise which one it is and cancel it out completely. Now of course when the particular noise sample is very large, mistake in cancellation can still occur. Similarly, when the value of the constant is very different from + or – C, the cost of moving to these values can be high. But the probability of these rare event happening are very small. Thus, on expected value basis, this nonlinear scheme works better than any sort of compromise using linear proportional methods. In effect, DM1 is signaling to DM2 (Nobel economics prize 2002 to Michael Spence on market signaling is based on similar idea). Finally, once you can use one pair of pre-agreed-on values, there is nothing wrong and every thing to gain by considering more than one pair of pre-agree-on values. More values will enable DM1 to choose the nearest value in order to minimize the cost moving the value of the constant. However, more pre-agreed-on values will complicate the problem for the DM2. He will have more chance of making mistakes because of observation noise when trying to guess which one of the many possible values DM1 has move the constant value to. Thus, there is a limit and tradeoff on the number and value of these pre-agreed-on points. For any given numerical example, we can perform a brute force search to solve the problem which is still computational intensive but doable (Note 1). This was what we did in 2002. It took 30-40 years before we realized the simple insight in this paragraph . Anyway, the above discussion points out the complexity of coordination even in the simplest problem between two decision makers. When you come to the real world where there are many interacting decision makers and vairables, much more complex dynamics and uncertainties, the resultant exponential growths adds MANY MORE ORDERS of difficulty and complexity. Thus, the popular slogan of think globally and act locally is much easily said than done . So far our discussion of complexity and difficulty is purely technical. We have not brought in other non-quantifiable and softer issues such as human frailty, emotion, nationalism, and politics that always intrude in the real world. What we generally do instead is iteratively tries to improve locally in the short term, and hope for the best globally and for the long term. You can also say that throughout history human beings by way of different types of government and systems try to solve or improve on the solution to this basically impossible dream. It is actually relatively amazing we do as well as we have done so far. But can our luck hold forever? Don’t you sometime wish for an all wise and benevolent dictator to decide everything? (Note 1. Actually because of the quadratic nature of the formula used to measure cost, there is an additional bit of extra that can be squeezed out of the problem by introducing a very small perturbation on the various pre-agreed-on points. But this is conceptually a detail dependent on the particular criterion used and not central to the major points of the discussion. Mathematically, however, such issues confused the research in earlier years which emphasized analytics of rather than the physical insight of the problem as explained above)
The Traveling Salesman Problem and Its Variations Series: Combinatorial Optimization , Vol. 12 Gutin, Gregory; Punnen, Abraham P. (Eds.) 2007, XVIII, 830 p., Softcover ISBN: 978-0-387-44459-8 Springer出版,非常全面系统地介绍了旅行商问题及其各种研究技术,下面是该书的About。后面有免费下载网址。 This volume, which contains chapters written by reputable researchers, provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, thorough computational analysis of heuristic and metaheuristic algorithms, theoretical analysis of approximation algorithms, including the emerging area of domination analysis of algorithms, discussion of TSP software and variations of TSP such as bottleneck TSP, generalized TSP, prize collecting TSP, maximizing TSP, orienteering problem http://www.ebookee.com.cn/The-Traveling-Salesman-Problem-and-Its-Variations_147149.html