The Muromachi period is a division of Japanese history running from 1336 to 1573. The period marks the governance of the Muromachi or Ashikaga shogunate, established in 1338 by the first Muromachi shōgun, Ashikaga Takauji, two years after the brief Kenmu Restoration of imperial rule was brought to a close; the period ended in 1573 when the 15th and last shogun of this line, Ashikaga Yoshiaki, was driven out of the capital in Kyoto by Oda Nobunaga. From a cultural perspective, the period can be divided into the Higashiyama periods; the early years from 1336 to 1392 of the Muromachi period are known as the Nanboku-chō or Northern and Southern Court period. This period is marked by the continued resistance of the supporters of Emperor Go-Daigo, the emperor behind the Kenmu Restoration; the years from 1465 to the end of the Muromachi period are known as the Sengoku period or Warring States period. Emperor Go-Daigo's brief attempt to restore the imperial power in the Kenmu Restoration alienated the samurai class.
Ashikaga Takauji obtained the samurai's strong support, deposed Emperor Go-Daigo. In 1338 Takauji established his government in Kyoto. However, Emperor Go-Daigo revived his political power in Nara; the ensuing period of Ashikaga rule was called Muromachi from the district of Kyoto in which its headquarters – the Hana-no-gosho – were located by third shōgun Ashikaga Yoshimitsu in 1378. What distinguished the Ashikaga shogunate from that of Kamakura was that, whereas Kamakura had existed in equilibrium with the imperial court, Ashikaga took over the remnants of the imperial government; the Ashikaga shogunate was not as strong as that in Kamakura had been, was preoccupied with civil war. Not until the rule of Ashikaga Yoshimitsu did a semblance of order emerge. Yoshimitsu allowed the constables, who had had limited powers during the Kamakura period, to become strong regional rulers called daimyōs. In time, a balance of power evolved between the daimyōs. Yoshimitsu was successful in reunifying the Northern and Southern courts in 1392, despite his promise of greater balance between the imperial lines, the Northern Court maintained control over the throne thereafter.
The line of shoguns weakened after Yoshimitsu and lost power to the daimyōs and other regional strongmen. The shōgun's influence on imperial succession waned, the daimyōs could back their own candidates. In time, the Ashikaga family had its own succession problems, resulting in the Ōnin War, which left Kyoto devastated and ended the national authority of the bakufu; the power vacuum that ensued launched a century of anarchy. The Japanese contact with the Ming dynasty began when China was renewed during the Muromachi period after the Chinese sought support in suppressing Japanese pirates in coastal areas of China. Japanese pirates of this era and region were referred to as wokou by the Chinese. Wanting to improve relations with China and to rid Japan of the wokou threat, Yoshimitsu accepted a relationship with the Chinese, to last for half a century. In 1401 he restarted the tribute system, describing himself in a letter to the Chinese Emperor as "Your subject, the King of Japan". Japanese wood, copper ore and folding fans were traded for Chinese silk, porcelain and coins, in what the Chinese considered tribute but the Japanese saw as profitable trade.
During the time of the Ashikaga bakufu, a new national culture, called Muromachi culture, emerged from the bakufu headquarters in Kyoto to reach all levels of society influenced by Zen Buddhism. Zen played a central role in spreading not only religious teachings and practices but art and culture, including influences derived from paintings of the Chinese Song and Ming dynasties; the proximity of the imperial court to the bakufu resulted in a commingling of imperial family members, daimyō, Zen priests. Art of all kinds—architecture, Noh drama, Kyōgen, sarugaku, the tea ceremony, landscape gardening, flower arranging—all flourished during Muromachi times. There was renewed interest in Shinto, which had coexisted with Buddhism during the centuries of the latter's predominance. Shinto, which lacked its own scriptures and had few prayers, had, as a result of syncretic practices begun in the Nara period adopted Shingon Buddhist rituals. Between the eighth and fourteenth centuries, Shintoism was nearly absorbed by Buddhism, becoming known as Ryōbu Shinto.
The Mongol invasions in the late thirteenth century, evoked a national consciousness of the role of the kamikaze in defeating the enemy. Less than fifty years Kitabatake Chikafusa, the chief commander of the Southern Court forces, wrote the Jinnō Shōtōki; this chronicle emphasized the importance of maintaining the divine descent of the imperial line from Amaterasu to the current emperor, a condition that gave Japan a special national polity. Besides reinforcing the concept of the emperor as a deity, the Jinnōshōtōki provided a Shinto view of history, which stressed the divine nature of all Japanese and the country's spiritual supremacy over China and India; the Ōnin War led to serious political frag
Belief propagation known as sum-product message passing, is a message-passing algorithm for performing inference on graphical models, such as Bayesian networks and Markov random fields. It calculates the marginal distribution for each conditional on any observed nodes. Belief propagation is used in artificial intelligence and information theory and has demonstrated empirical success in numerous applications including low-density parity-check codes, turbo codes, free energy approximation, satisfiability; the algorithm was first proposed by Judea Pearl in 1982, who formulated it as an exact inference algorithm on trees, extended to polytrees. While it is not exact on general graphs, it has been shown to be a useful approximate algorithm. If X= is a set of discrete random variables with a joint mass function p, the marginal distribution of a single Xi is the summation of p over all other variables: p X i = ∑ x ′: x i ′ = x i p. However, this becomes computationally prohibitive: if there are 100 binary variables one needs to sum over 299 ≈ 6.338 × 1029 possible values.
By exploiting the polytree structure, belief propagation allows the marginals to be computed much more efficiently. Variants of the belief propagation algorithm exist for several types of graphical models. We describe here the variant. A factor graph is a bipartite graph containing nodes corresponding to variables V and factors F, with edges between variables and the factors in which they appear. We can write the joint mass function: p = ∏ a ∈ F f a where xa is the vector of neighboring variable nodes to the factor node a. Any Bayesian network or Markov random field can be represented as a factor graph by using a factor for each node with its parents or a factor for each node with its neighborhood respectively; the algorithm works by passing real valued functions called messages along with the edges between the hidden nodes. More if v is a variable node and a is a factor node connected to v in the factor graph, the messages from v to a, from a to v, are real-valued functions whose domain is Dom, the set of values that can be taken by the random variable associated with v.
These messages contain the "influence". The messages are computed differently depending on whether the node receiving the message is a variable node or a factor node. Keeping the same notation: A message from a variable node v to a factor node a is the product of the messages from all other neighboring factor nodes: ∀ x v ∈ D o m, μ v → a = ∏ a ∗ ∈ N ∖ μ a ∗ → v. where N is the set of neighboring nodes to v. If N ∖ is empty μ v → a is set to the uniform distribution. A message from a factor node a to a variable node v is the product of the factor with messages from all other nodes, marginalized over all variables except the one associated with v: ∀ x v ∈ D o m, μ a → v = ∑ x a ′: x v ′ = x v f a ∏ v ∗ ∈ N ∖ μ v ∗ → a. where N is the set of neighboring nodes to a. If
Cayman Islands bankruptcy law is principally codified in five statutes and statutory instruments: the Bankruptcy Law the Companies Law the Companies Winding Up Rules 2008 the Insolvency Practitioners' Regulations 2008 the Foreign Bankruptcy Proceedings Rules 2008These are supplemented by a number of practice directions of the Cayman Islands courts and a wide body of case law. Most of the recent emphasis of bankruptcy law reform in the Cayman Islands relates to corporate insolvency rather than personal bankruptcy; as an offshore financial centre, the Cayman Islands has more resident companies than citizens, accordingly the courts a large amount of time dealing with corporate insolvency and reorganisation. Because a large number of Cayman Islands are listed on stock exchanges in major financial centres, number of Cayman Islands corporate bankruptcies have generated a high profile internationally. Bankruptcy of individuals is referred to as "personal bankruptcy" in the Cayman Islands, whereas the bankruptcy of corporations is referred to as "corporate insolvency".
The relevant statutes deal with both separately, although there are some provisions which are common to both. A single creditor or two or more creditors who are owed an amount not less than CI$40 may present a petition to the court against a debtor for a declaration of bankruptcy if the debtor has committed one or more "acts of bankruptcy". An act of bankruptcy means: the debtor has made a general assignment of his property to a trustee or trustees for the benefit of creditors, but it is a requirement that: the alleged act of bankruptcy must have occurred within six months before the presentation of the petition. A company may enter winding up either voluntarily, or pursuant to an order of the court. If a company enters voluntary winding up the directors are required to make a determination of solvency. Any person may act as liquidator in a solvent voluntary winding up. However, if the directors are not able to make a determination of solvency, or if upon the application of a creditor to the court it is shown that either the company is or is to become insolvent.
In addition to voluntary liquidation, a company may be wound up by the court if: the company has passed a special resolution requiring the company to be wound up by the court. A company is deemed to be unable to pay its debts if: a creditor in a sum exceeding CI$100, has served a statutory demand on the company, the company has failed to pay the sum within 21 days.