Given two time series, can one faithfully tell, in a rigorous and quantitative way, the cause and effect between them? Based on a recently rigorized physical notion, namely, information flow, we solve an inverse problem and give this important and challenging question, which is of interest in a wide variety of disciplines, a positive answer. Here causality is measured by the time rate of information flowing from one series to the other. The resulting formula is tight in form, involving only commonly used statistics, namely, sample covariances; an immediate corollary is that causation implies correlation, but correlation does not imply causation. It has been validated with touchstone linear and nonlinear series, purportedly generated with one-way causality that evades the traditional approaches. It has also been applied successfully to the investigation of real-world problems; an example presented here is the cause-and-effect relation between the two climate modes, El Nio and the Indian Ocean Dipole (IOD), which have been linked to hazards in far-flung regions of the globe. In general, the two modes are mutually causal, but the causality is asymmetric: El Nio tends to stabilize IOD, while IOD functions to make El Nio more uncertain. To El Nio, the information flowing from IOD manifests itself as a propagation of uncertainty from the Indian Ocean.
For this book, the setting definitely came first! I knew I wanted to write something in that kind of Gossip Girl-esque private school environment, but with all the unique features of the international community in Beijing. I was also really interested in writing a protagonist who was more morally gray and struggled with feelings of self-worth and the weight of her own ambition, so once I had the general atmosphere, the character, and the invisibility element, the plot developed quite naturally from there!
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At the time, the warlord Liu Bei was living in Xinye County as a guest of Liu Biao, the governor of Jing Province. During this time, he met the hermit Sima Hui and consulted him on the affairs of their time. Sima Hui said, "What do Confucian academics and common scholars know about current affairs? Only outstanding talents have the best understanding of current affairs. In this region, there are two of such talents: Crouching Dragon and Young Phoenix." When Liu Bei asked him who "Crouching Dragon" and "Young Phoenix" were, Sima Hui replied, "Zhuge Kongming and Pang Shiyuan."[Sanguozhi zhu 8] Xu Shu, whom Liu Bei regarded highly, also recommended Zhuge Liang by saying, "Zhuge Kongming is the Crouching Dragon. General, don't you want to meet him?"[Sanguozhi 9] When Liu Bei asked Xu Shu if he could bring Zhuge Liang to meet him, Xu Shu advised him to personally visit Zhuge Liang instead of asking Zhuge Liang to come to him.[Sanguozhi 10]
The 14th-century historical novel Romance of the Three Kingdoms gives a romanticised account, spanning two chapters, of how Liu Bei met Zhuge Liang. After Xu Shu recommends Zhuge Liang to him, Liu Bei travels to Longzhong with his sworn brothers Guan Yu and Zhang Fei to find Zhuge Liang. When they reach Zhuge Liang's house (described as a "thatched cottage" ), a servant tells them that his master is out. Liu Bei then asks the servant to pass a message to Zhuge Liang that Liu Bei came to find him. Later during winter, Liu Bei and his sworn brothers brave heavy snowfall and travel to Longzhong again. Along the way, they meet Zhuge Liang's friends. This time, the servant leads them to his "master", who turns out to be Zhuge Liang's younger brother, Zhuge Jun. Just as they are about to leave, Liu Bei sees an older man approaching and thinks he is Zhuge Liang, but the man introduces himself as Huang Chengyan, Zhuge Liang's father-in-law. When spring arrives, Liu Bei decides to visit Zhuge Liang again, much to the annoyance of his sworn brothers. On this third occasion, Zhuge Liang is at home but is asleep. Liu Bei waits patiently for hours until Zhuge Liang wakes up.[17]
Tian Heng was nothing more than a mere warrior from Qi, yet he remained faithful and refused to surrender. Shouldn't we expect more from Liu Bei, scion of the royal house of Han? His heroism and talents are renowned throughout the world. Gentlemen and commoners alike honour and admire him. Like the rivers returning to the sea; like the upheavals in the affairs of our time, this is Heaven's doing. How could he turn his back on that and serve Cao Cao?[Sanguozhi 21]
After assuming governorship of southern Jing Province in 209,[14] Liu Bei appointed Zhuge Liang as Military Adviser General of the Household () and put him in charge of collecting tax revenue from Lingling, Guiyang and Changsha commanderies for his military forces.[Sanguozhi 26] During this time, Zhuge Liang was stationed in Linzheng County (; present-day Hengyang, Hunan) in Changsha Commandery.[Sanguozhi zhu 13]
Between late spring and early winter of 228,[25] Zhuge Liang directed his efforts towards reorganising the Shu military, strengthening discipline, and training the troops in preparation for another campaign.[Sanguozhi zhu 19] During this time, he received news that Shu's ally Wu had defeated Wei at the Battle of Shiting around September 228.[25] From this, he deduced that the Wei defences in the Guanzhong region must be weaker because Wei had mobilised its best troops to the eastern front to fight Wu.[Sanguozhi zhu 20]
In response to the Shu invasion, the Wei general Sima Yi led his forces and another 20,000 reinforcements to the Wuzhang Plains to engage the enemy. After an initial skirmish[Jin Shu 7] and a night raid on the Shu camp,[Jin Shu 8] Sima Yi received orders from the Wei emperor Cao Rui to hold his ground and refrain from engaging the Shu forces. The battle became a stalemate. During this time, Zhuge Liang made several attempts to lure Sima Yi to attack him. On one occasion, he sent women's ornaments to Sima Yi to taunt him. An apparently angry Sima Yi sought permission from Cao Rui to attack the enemy, but was denied. Cao Rui even sent Xin Pi as his special representative to the frontline to ensure that Sima Yi followed orders and remained in camp. Zhuge Liang knew that Sima Yi was pretending to be angry because he wanted to show the Wei soldiers that he would not put up with Zhuge Liang's taunting, and to ensure that his men were ready for battle.[Jin Shu 9][Sanguozhi zhu 35]
Pei Songzhi pointed out the problems in this anecdote. If this incident really happened, the assassin must be a great talent to be able to attract Liu Bei's attention and, in Liu Bei's opinion, worthy enough to serve as an assistant to Zhuge Liang. However, this was unlikely because assassins were typically rough and boorish men ready to sacrifice their lives to accomplish their mission. Besides, it did not make much sense for a man of such talent to be an assassin when he could be better off as an adviser to any of the great warlords. Moreover, as Cao Cao was known for respecting and cherishing talents, it was unlikely that he would willingly sacrifice someone of such talent by sending him on a risky mission. Furthermore, given the significance of this incident, it should be recorded in history, but there is no mention of it in the official histories.[Sanguozhi zhu 50]
Pei Songzhi pointed out that Zhuge Liang's goal of achieving a complete victory over Wei was already well known before he went on the first Northern Expedition, so it seemed very odd for Guo Chong to say that the people of Shu only realised it after Zhuge Liang came back from the first Northern Expedition. He also noted that the first Northern Expedition was an overall failure so the "successes" mentioned in this anecdote neither made sense nor were worthy of compliments. The reasons he gave were as such: Shu lost two battles against Wei in the first Northern Expedition and ultimately failed to conquer the three commanderies; Wei had nothing to lose from the defection of Jiang Wei, who at the time was a relative nobody; and the capture of the few thousand Wei families was insufficient to make up for the casualties the Shu forces suffered at Jieting and Ji Valley.[Sanguozhi zhu 53]
"When I can use one shot, I won't use a second one. But if you look closely, I often move the camera slightly, often when I'm following the characters. It does have to do with my theater training-there you don't have a camera and are dealing with real space and time issues which I've tried to carry over into my filmmaking."
One thing that I find really funny about the depiction of this campaign in fiction is that Zhuge Liang is always portrayed as rushing things and trying to work too fast. The reality, though, was quite the opposite. For once, Zhuge Liang made long-term preparations. He had his soldiers establish agricultural colonies so that they would be able to supply the army with food. He set about securing the friendship of the local populace, and his soldiers did not harass the civilians.
In this paper, the 1-D real-valued discrete Gabor transform (RDGT) proposed in the previous work and its relationship with the complex-valued discrete Gabor transform (CDGT) are briefly reviewed. Block time-recursive RDGT algorithms for the efficient and fast computation of the 1-D RDGT coefficients and for the fast reconstruction of the original signal from the coefficients are developed in both critical sampling and oversampling cases. Unified parallel lattice structures for the implementation of the algorithms are studied. And the computational complexity analysis and comparison show that the proposed algorithms provide a more efficient and faster approach to the computation of the discrete Gabor transforms.
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