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California officials on Friday broke ground on Caltrain's nearly $2 billion electrification project.
California’s High Speed Rail Authority got clearance to proceed with a plan to electrify Caltrain tracks between San Francisco's 4th and King Station to San Jose's Tamien Station. The first electric train is expected to start running in late 2020 or 2021.
Friday's ceremony was attended by Gov. Jerry Brown, House Democratic Leader Nancy Pelosi, San Francisco Mayor Ed Lee and other leaders.
The state Department of Finance approved the expenditure of $600 million in voter-approved bond money. The approval follows the Trump administration’s decision to fully fund a $650 million grant for the project.
The peninsula section is the northernmost piece of the $64 billion bullet train that will link San Francisco and Los Angeles.
Caltrain runs diesel locomotives that are more than 30 years old and need to be replaced, officials say.
An estimated 65,000 people ride Caltrain every day, which is more than double the number of commuters in 2005. With its new electric trains, Caltrain can increase capacity by adding up to six new trains in each direction during peak hours. The new cars will still top out at 79 mph, but will be quieter and less polluting.
High-speed rail opponents have filed a lawsuit challenging the electrification project. They argue that state legislation unconstitutionally allows high-speed rail bonds to be spent on Caltrain, violating promises made to voters in 2008.
A number of people with property along the tracks might be forced to give up some or all of their land to make way for the project. Some of them have also raised safety and health concerns about the electromagnetic field that this project will create. |
Since Leng‑chia Shzh‑tzu Chi was discovered,1) Seng‑ts'an's authorship of the Hsin‑hsin Ming has been doubted, because of the remark that Seng ts'an did not put any writings into circulation. Ui 2) proposed that Seng ts'an, perhaps, only recited the text, otherwise written by someone else. Nishitani and Yanagida3) added some further arguments, considering that the text was written in the eighth century, two centuries after Seng‑ts'an. This was accepted as valid by other authors.4)
CONTRIBUTIONS OF THE HSIN‑HSIN MING
Dumoulin5) was among the first to recognize that in many passages the composition of Hsin‑hsin Ming isakin to the Avatamsaka sutra, especially the closing stanzas (30‑36).
Actually, there is some resemblance between the concepts of one mind (stanza 123, oneness (stanzas 5,6,7) and one vehicle (stanza 19) in Hsin‑hsin Ming, and equivalent concepts developed in Hua‑yen. However, the obviously common subjects of Hsin‑hsin Ming and Hua‑yen are relativity and interpenetration of time and space dimensions (in stanzas 32‑33), equality of things (st. 33) and the famous "one is all, all is one" principle (st. 35), which are explained later in detail (in "Analysis of the text" - related to sections VII and VIII of the Hsin-hsin Ming). On such grounds we can conclude that this text should be - at least partly - related also with the Hua‑yen tradition (i.e., not exclusively with Ch’an).
We can outline two significant contributions of the Hsin‑hsin ming to the overall tradition of Chinese Buddhism.
a) The first is "faith in mind", which could be considered as a "Ch’anist" response to the Buddhism of faith (Pure Land), since the object of faith is not Amitabha, but mind as a means of awakening.
b) The second contribution is the principle of oneness (i‑chung). It is particularly mentioned in stanzas 5, 6 and 7. Otherwise, it is the running idea of the whole text, continually warning against various dualities: liking‑disliking (stanzas 1, 19, 21), grasping‑rejecting (st. 3), conditions/form‑emptiness (qt. 5, 14), motion‑rest (st. 6, 21, 26), truth‑views (st. 10), right‑wrong (st. It, 23), things/dharmas‑mind (st. 123, subject‑object (st. 133), coarse‑fine (st. 15), strange‑familiar (st. 18), sense‑objects/awakeness (st. 19), things/dharmas‑suchness (st. 24), profit-loss (st. 23) other‑self (st. 25, 30), moment‑eon (st. 32), here‑there (st. 32), small‑large (st. 33), one‑all (st. 35). These dualities should be refuted or transcended with the perspective of one mind - in emptiness and real suchness.
Broadly speaking, Hsin‑hsin Ming is an elegant exposition of prajna (principles), and dhyana (practice). With approximation, we can say that sections I, V, and VI mostly deal with principles (oneness, one mind, emptiness, suchness), sections II. III, and IV mostly expose practice, while sections VII, and VIII describe the results of such practice, and applied principles.
PROBLEMS OF TRANSLATING
In translating ancient religious and philosophical texts, one of the major problems is to decide - in case it is not a terminus technicus per se - whether a certain word (in our case, a Chinese character) is used colloquially, or as a terminus technicus. On such a decision sometimes depends not only the appropriate translation of a particular word, but the proper understanding of the whole passage, as well. To decide, we should know the tradition of the text and have in mind the context, as well as previous commentaries, if such exist (nevertheless, these can also be misleading, since in many cases they are comments, not for the sake of interpreting, but in order to give support and authority of the tradition to the thoughts of their respective authors).
The second problem is that the translator uses a language the words of which have the same ambiguity (colloquial‑technical) as the original language, or a vocabulary which (itself) lacks the necessary technical terms. This can be solved by using capitals, italics, etc. Also, one of the solutions for translating Chinese Buddhist texts was to use the Sanskrit terms as technical, in the same manner as in European philosophy one would use Greek or Latin, instead of native words, in order to convey the technical meaning and avoid ambiguity.
Meaning is developed through use. For example, for "awakening" or "enlightenment" no one uses capitals; through lengthy use it is supposed that these will not be misunderstood (that they will be understood as technical terms in a Buddhist context, and not in colloquial meaning). But some terms (One, Way, Void, Suchness) are still written with capitals. For translations from Chinese it is still customary to use Sanskrit equivalents to pinpoint the meaning, or when the terms from European languages are not good enough. For example, Chinese fa is better translated with Sanskrit dharma, than with "things" (as was done in this translation - but, to use "dharma" supposes that the reader is more familiar with Sanskrit, than with the Chinese, which, for the average person is not the case).
Wing‑tsit Chan remarked that "Without adequate tools to help them, many translators have rendered technical terms in their popular meanings".6) Fortunately, some sixty years ago, Soothill and Hodous,7) filled the gap for Chinese Buddhist terms with their dictionary. However, their dictionary was possible thanks to the work done some 1500 years ago, by generations of Chinese Buddhists, who translated Sanskrit Buddhist texts into Chinese, using and standardizing certain Chinese characters as technical terms (equivalents) for Sanskrit terms.
In order to proceed with the analysis of the Hsin‑hsin Ming, and its general meaning in the context of Chinese Buddhism, particularly Ch’an, we propose a new translation. Originally, the text, as presented in Taisho (Taisho shinshu daizokyo) No. 2010, was not divided in stanzas. The translators, excepting Suzuki, were faithful to this form. In the second version of his translation Suzuki has added numbers to the stanzas, in which he grouped the lines of the poem (his first translation, let it be remarked, omits four verses of stanza 6).10) In order to make possible easy reference for the analysis we have also divided the poem in stanzas, but this "versification" differs from Suzuki's version. However, in the right hand row we have given the numbers of his stanzas in brackets (for those who want to compare the translations). For easy reference we also suggest a division of the text into eight (principal) parts, notated with Roman numerals (I-VIII)..
INSCRIPTION ON FAITH IN MIND
I) l) The best way is not difficult (1)
It only excludes picking and choosing
Once you stop loving and hating
It will enlighten itself.
2) Depart for a hairbreadth
And heaven and earth are set apart,
If you want it to appear
Do not be for or against.
3) To set longing against loathing (2)
Makes the mind sick,
Not knowing the deep meaning (of the way)
It is useless to quiet thoughts.
4) Complete it is like great vacuity (3)
With nothing lacking, nothing in excess.
When you grasp and reject
There is no suchness.
II) 5) Do not follow conditions, (4)
Do not dwell in emptiness.
Cherishing oneness in the hearth,
Everything will stop by itself.
6) Rest to stop motion, (5)
And rest will move you again.
If you are merely in either,
How will you know oneness?
7) Not understanding oneness (6)
You will miss in two ways.
Expelling being you will be without it,
Following emptiness you are always behind it.
8) The more words and thoughts (7)
The more you will go astray
Stop speaking, stop thinking
And there is nothing you cannot understand.
9) Return to the root and obtain the purport. (8)
Following the outcome you lose the source.
For a moment turn inward,
And surpass the emptiness of things.
Changes that go on in emptiness (9)
All have their cause in ignorance.
III) 10) Do not seek the true,
Only abstain from views.
Do not dwell in dual views, (10)
Be careful not to pursue them.
11) The slightest trace of right and wrong
And mind is lost in confusion.
One being is the source of the two (11)
However, do not even maintain the one.
12) With one mind there is no arising,
Then everything is without blame.
No blame, no things. (12)
No arising, no mind.
13) The subject follows when the object ceases
The object is expelled when the subject sinks.
The object is related to the subject (13)
The subject is related to the object.
14) If you want to know these two
Their origin is one emptiness.
In one emptiness both are equal (14)
Evenly containing innumerable forms.
IV ) 15) Do not differentiate coarse and fine
And you will not be for or against.
The great way is all‑embracing (15)
Neither easy nor difficult.
16) Small views are irresolute, full of doubt,
Now in haste, then too late.
Grasp beyond measure (16)
And you will go astray.
Now we shall proceed with the analysis of the text, section by section (I‑VIII), explaining technical terms, their meaning in the context of Chinese Buddhism, and the main ideas of the text. When necessary we shall also reach for the wider context of Indian Buddhism, in order to explain the history of certain concepts.Hsin‑hsin Ming mentions faith (hsin) in its title and in the concluding stanza (36). We know that faith (Skt. sraddha) in Buddhism is one of the five qualities for making progress on the path (Skt. marga). Various texts speak of faith in Buddha (Tathagata), the Buddhist doctrine (Dharma), as well as Buddhist community, or assembly (Sangha). In certain Mahayanic texts (Sukhavativyuha, Mahayanasraddhotpada, Amitayurdhyana) faith has been promoted as a principal quality, and an agent of salvation. K.N. Jayatilleke11) has indicated three aspects of faith in early Buddhism: affective, conative and cognitive. In later Buddhism a theistic aspect of faith is introduced, and faith is redefined. Sakyamuni as a historical person is enveloped by a deified transhistorical Buddha. The faith that Sakyamuni attained at awakening, (which is - under certain conditions and precepts - repeatable for other Buddhists), has been transformed into a faith (related to worship and reverence) that salvation is based on a transcendental, omnipotent, transhistorical principle (Adi-Buddha), and bestowed to the faithful, with compassion, as grace from his emanations (other Buddhas, and bodhisattvas).
With this background, "faith in mind" is an original contribution of Hsin‑hsin Ming. It introduces the meditative aspect of faith, based on mind-doctrine affirmed in Ch’an. To have “faith in mind” means to have faith that awakening will follow when the mind "returns to the root (or source)" and stops discriminating (realizes one-ness). It is based on a common denominator present in all sects of Ch'an tradition: "Mind is the root of the myriad phenomena... If you can completely comprehend mind, the myriad practices are completed".12)
In the first stanza of Hsin‑hsin Ming we encounter the refutation of dualities. Perhaps, the author—whoever he was—was aware of the paradox, rather common in Taoism and Ch'an, when he said that the best way is not difficult, under the condition which is most difficult for humans: to stop loving and hating, picking and choosing.
The first four stanzas bear a definitely Taoist influence (compare Lao‑tzu, I). They banish feelings and duality, connecting the way with vacuity (hsu) and deep meaning (hsuan chih). In relation to vacuity (hsu) we should emphasize the difference in meaning between this character in Taoism and the meaning of emptiness (k'ung ) in Buddhism. Lao‑tzu (Ch. II) proposes the ideal of a "vacuous" (hsu) heart for man, that is, of peace and purity of mind, freedom from worry and egoism. To maintain this vacuity (according to Lao‑tzu, Ch. 15‑16) is to be open for the tao and its way, "open and broad, like a valley". It means to keep the receptive, feminine aspect of mind, in order to be able to accord with the tao. Emptiness (k'ung) willbe explained later in relation to stanzas 5, 7, 9 and 14.
In the first line (st. 1) we decided to translate chih‑tao as "the best way". Blyth13) has suggested "great way" which is not wrong per se, but since in stanza 15 we already have ta tao, which must be "great tao", it was unreasonable to use the same word for different characters. In this translation we have been—as far as possible—faithful to the principle that the same character should be translated with the same word and vice versa - a different character with a different word. Other translators decided to use "perfect way" as equivalent for chih‑tao. This is not wrong, but "perfect" also denotes something that has been brought to the end, finished. However, speaking of the way, we have something that has yet to be threaded. That is why we made an option for the "best way". On the other hand we have reserved "perfect" as equivalent for cheng, which appears in stanza 19. We understand that the "way" (which is spoken of in the first four stanzas) is not the Taoist tao, but the way of Buddhism (Skt. marga). With stanza 4 we leave the Taoist meanings, since the "great vacuity", which is a Taoist expression, is related to a peculiarly Buddhist term ("suchness"). In the fourth line of stanza 4 Waley missed the meaning of ju. He takes the colloquial meaning (so), instead of the technical, Buddhist meaning - suchness, thatness (Skt. tathata).
II
Stanza 5, and the last two lines of stanza 4 are important because they introduce several terms and ideas of overall importance for the whole text. First is grasping (ch'ui, Skt. upadana).14)With grasping and rejecting suchness cannot appear. The same goes for the duality of “following conditions” and “dwelling in emptiness.” Conditions (yuan, Skt. pratyaya), or conditioning factors, are mental activity and external objects. Not to dwell in emptiness means that practice of meditation can become one‑sided if attachment is developed for emptiness, peace and purity of meditative absorption. This is a recurrent warning, in all schools of Ch'an. That is why our text puts an accent on oneness (i‑chung), which is also the main subject in stanzas 6 and 7.
Stanzas 5 and 7 (in contrast to stanzas 9 and 14) speak about emptiness (k'ung) in practice of meditation, which can become a pitfall. In stanzas 9 and 14 emptiness is considered from the prajna‑perspective, as an essential trait of the world and connecting principle of all opposites, all dualities. On the other hand, one should not dwell and abide in emptiness during meditation (stanza 5). "When working on Zen, the worst thing is to become attached to quietness, because this will unknowingly cause you to be engrossed in dead stillness. Then you will develop an inordinate fondness for quietness and at the same time an aversion for activity of any kind''.15) Stanza 6 accentuates the overcoming of duality between rest and motion which is a subtle obstacle. "If one abandons deconcentration in order to seek concentration, what he will attain is the deconcentration but not concentration. If one turns back on impurity in order to get purity, he will get impurity but not purity".16) It is interesting to note the fourth line of stanza 7, which expresses that emptiness (in prajna‑sense) is definitely out of reach from the dhyana‑perspective. This has to do with the dynamics of meditation. If one seeks emptiness trying to reach rest, he always seems one step behind, until he realizes that emptiness is the common and connecting principle of rest and motion, being and nothingness.
In Hsin‑hsin Ming there is no explicit mentioning of meditation. However, sections II and III can be considered as "meditation sections". They contain admonitions on correct meditation practice, its possible mistakes and pitfalls. Stanzas 8 and 10 speak of stopping the internal monologue and the related thinking. Returning to the root and turning inward are related with such stoppage - otherwise they would just be an introversion.
III
The first two lines of stanza 10 introduce two important technical characters: chen (which also appears in stanza 18), meaning true, real, and chien, meaning view (Skt. drsti). The course toward awakening is not related with a mind in search of new truths. Such a search only multiplies (dual) views, leading to a road without end. That is why the admonition "abstain from views" is given as one of the main principles of the meditative via negativa.
Stanzas 11‑14 return to the themes of oneness and duality. The first line of stanza 12 focuses oneness of mind, or one‑mind (i‑hsin, Skt. eka‑citta). We find that eka‑citta is mentioned back at the time of Asanga, who speaks about it in the context of the fifth perfection (dhyana‑paramita) of the paramita‑yana.17)
One Mind is also mentioned in the Surangama as a doctrine which enables one to overcome dualities, understand senses as a part of bodhi, and attain imperturbability (acala).18) In Chinese Buddhism the one‑mind concept is exposed by Hui‑ssu (sixth century) in "The Method of Concentration and Insight", which belongs to the T’ien‑t’ai school: "...All dharmas are but one mind. Therefore there is no differentiation in itself, for differentiation is the one mind. As the mind involves all functions, the one mind is differentiation. They are always the same and always different".19)
The one mind doctrine was especially elaborated in the Awakening of Faith in the Mahayana.20)Here, one mind appears as suchness (tathata), in its pure form, and as samsara when it falls under conditions. Fa‑tsang has written a commentary on the Awakening of Faith. For him, one mind is the unchanging, undifferentiated, non‑dual basis of all experience: deluded and awakened.
In Hsin‑hsin Ming one mind is considered in a meditative context (rather than as a metaphysical concept). It is a state of mind free of duality.
IV
In the second line21) in stanza 17 we encounter the character t'i (essence, substance) which is usually paired with yung (function, application). It is an important concept in Buddhism, and other schools of Chinese philosophy. The character yang appears also in our text (in Stanzas 18 and 21), but the context suggests a colloquial rendering: "to use". Peculiar for our text is that (in stanza 12) it focuses blame (chin) as a factor that binds mind to things and arising (sheng). This relatedness of the subject and object is underlined in verse 13.
In order to avoid duality, Hsin‑hsin Ming once more (in stanza 14) focuses emptiness as origin of both. Now comes the second stage of cultivating the mind: it consists in applying (yung) which is now changed through this “meeting” with t'i. This means that yung itself would be different after its “meeting” with t'i (the “meeting” is expressed by the "one‑mind"). That is, yung is changed when mind understands its relation with things (fa - Skt. dharma) - how is it influenced by things, and how it influences things. Then the mind is free from things, as well as from its previous yung (function, application); it now functions in the world, but is not influenced and affected by the world. The new functioning in the world is exposed in part IV (stanzas 15‑18) of the Hsin‑hsin Ming; there we find what is, and what is not peculiar to such free functioning.
In the third line of stanza 17 we encounter a Taoist maxim of according with tao, but we should give it a Buddhist reading: accord your nature with the way (tao), i.e. accord with the Buddhist path (Skt. marga).
V
The fifth part opens introducing the One‑vehicle (i‑ch'eng, Skt. eka‑yana).22)
In China we encounter the subject of One vehicle (i‑ch'eng) in the Hua‑yen school. As in other teachings in that school, it calls upon the authority of the Avatamsaka sutra However, here we have an interpretation differing from Mahayana. In Fa‑tsang's Treatise on the Golden Lion we find an exposition of various schools and Buddhist doctrines in a five‑level gradation. The Hinayana doctrine includes all Theravada schools, the initial doctrine of Mahayana includes Madhyamaka and Yogacara, the final doctrine of Mahayana is given by the T'ien‑t'ai school, the Mahayana doctrine of sudden awakening is given by Ch’an, and the Yuan (rounded, complete, all‑inclusive) doctrine (yuan chiao) of the One vehicle is given by the Hua‑yen school. What is this all‑inclusive teaching of the One vehicle? "When the feelings have been eliminated and true substance (t’i) revealed, all becomes an undifferentiated mass. Great functions (yung) arise in abundance, and whatever it does is real (or absolute, chen). The myriad manifestations, despite their variety, interfuse without disarray. The all is the one, for both are similar, being empty in nature. And the one is the all for cause and effect clearly take course. In their power and functions each implies the other. They spread out and roll up freely. This is called the all‑inclusive doctrine of the One vehicle" (compare slight variations in translations of this passage—because of its importance it was quoted by various authors).23)
Now, how does this Hua‑yen understanding of the One vehicle stand in relation to Hsin‑hsin Ming?
We find this "one is all, all is one" principle, and the Hua‑yen teaching of mutual penetration and identity, in stanzas 33, 34, and 35. Therefore, the One vehicle in Hsin‑hsin Ming is open toward six sense‑objects (luchan, Skt. sad guna), six qualities (or "six dusts"), that appear in the conjunction of objects and sense organs, including reason. Perhaps, it is the "dust" which was supposed to be wiped from the “bright mirror of the mind” in the verse by Shen‑hsiu (composed in competition for the successor of the fifth patriarch of the Ch’an school), while Hui‑neng said that Buddha‑nature is forever pure and cannot be defiled by "dust".
The integrative, monistic standpoint—similar to Hua‑yen—is obvious from the third and fourth lines of stanza 19. This is where the One vehicle and the one mind doctrine meet, because one mind has two aspects: one is suchness (seen in perfect awakeness), the other is origination and cessation with six sense‑objects.
Stanza 21 speaks of possible mistakes related with meditative practice. One can find similar instructions in earlier texts, as in the Surangama sutra. Surangama and Hsin‑hsin Ming are cautious and give warnings against the possible misuse of meditative process. With the first two lines of stanza 21 compare two lines from Surangama:
If mind be set on searching for the mind, that which
At heart is not illusion, becomes illusory.24)
This subtle obstacle was a matter of special attention in Buddhism, especially Ch'an. For example, a text with a similar title (HsinMing), attributed to Fa-jung,25) besides other points in common with the Hsin‑hsin Ming, has an admonition similar
to stanza 21.
If you wish to attain purity of mind,
then make effort (in the context of) no‑mind (...)
To maintain tranquillity with the mind is
still not to transcend the illness (of ignorance)".26)
It is worth mentioning that in Hsin‑hsin Ming we do not find one of the common technical terms of Ch'an—especially of the Southern school—namely, wu‑hsin (no-mind). The author of our text had much more affinity for one‑mind (i-hsin), and wu‑wei (non‑action - in stanza 20), which is part of the Taoist legacy ("no mind", which is found in stanza 12, is actually pu‑hsin). With respect to the Taoist legacy we should say that besides the general influence felt in part I of the poem, it is also present in using the typical Taoist term: non‑action (wu‑wei). We also find tzu‑jan (spontaneity) in stanza 17 (which has a completely Taoist meaning), and in stanza 25. This is in line with the Ch'an principle, developed under the Taoist influence - to stress spontaneity, at the expense of rules, or discipline.
In Hsin‑hsin Ming we cannot find any trace of the debate between the concepts of gradual and sudden awakening. We know that the concept of sudden awakening was already present in Indian Buddhism - “one-moment” (eka-kshana) awakening. However it seems that this concept was not concurrent, or opposed, to the idea of gradualness in Indian Buddhism.27) In China the debate lasted several centuries - from the beginning of the fifth, until the end of the eighth century, with certain lapses. It started before Ch'an was recognized as a separate school but was most fervently pursued in Ch’an, especially after the division between the Northern and the Southern schools.
The first person in Ch’an who confronted sudden with gradual awakening, was Tao‑sheng (ca. 360‑434).28) This aroused the opposition of Hui‑kuan, who, like Tao‑sheng, was also a disciple of Kumarajiva. The debate continued through the fifth century. We will skip over the fine arguments of this debate and pay attention to only one remark, relevant for our inquiry. That is the difference between faith and understanding, in terms of "gradual" and "sudden". One of the arguments in favor of the doctrine of sudden awakening was as follows: "Enlightenment (ming) is not to be gradually reached, whereas faith (hsin) arises (gradually) from instruction. What do I mean by this? Faith arises and is strengthened in daily progress, but enlightenment is not gradual" (The Discussion of Essentials).29)
The fundamental and obvious argument in favor of suddenness is that the awakening is one: non‑dual and non‑divisible. This would mean that faith‑in‑mind (hsin‑hsin), appearing in stanza 36 as non‑dual, is not the same as divisible (and gradual) faith mentioned in this debate (the character hsin is the same). Hsin‑hsin Ming mentions neither sudden awakening (tun‑wu), nor gradual awakening (chien‑wu), which were already in use at the time of Tao‑sheng (i.e. three centuries before the supposed time of Hsin‑hsin Ming). Its author deemed as unnecessary to specify (in terms of gradual or sudden) complete awakenness (cheng‑chüeh), and awakening (wu).
The sixth century was an intermezzo. In the seventh century the debate between the doctrines of gradual and sudden awakening burst with new strength in an encounter between Shen‑hsiu and Hui‑neng, and in the division of Ch'an (into Northern and Southern sects).
By the end of the eighth century, in 794 A.D., there was also a recorded debate on the international level (held in Tibet), between Kamalasila from India, who was representing the orthodox gradual doctrine, and the exponents of Ch’an from China, who argued in favor of the doctrine of sudden enlightenment.30)
It should be noted that in Hsin‑hsin Ming wefind altogether two terms related with awakening - cheng-chüeh (stanza 19) and wu (stanza 21). In Chinese Buddhism ming (enlightenment) was used at least from the time of Tao‑sheng (c. 400 A.D.), as a synonym for wu. This means that during the Indian history of Buddhism the basic term was “awakening” (Skt. bodhi), and that Chinese Buddhism introduced the term "enlightenment" (ming)31) into Buddhism (one should not be confused with the fact that, for separate reasons, in western writings the term “enlightenment” was used more often - it is more popular - then “awakening”). We also encounter this character (ming) in Hsin‑hsin Ming, although not in a noun‑sense (enlightenment). In stanza 1 (fourth line) it is used as a verb (enlighten), and in stanza 29 as an attribute (enlightened) - “ming” appearing in the tittle of the text is a different character, which means “inscription.”
Chüeh means "to awaken," "completely understand", or "awakenness" as a permanent accomplishment, while wu means "awakening". It is obvious that these two were used as technical terms - cheng‑chüeh meaning “perfect awakenness” (Skt. sambodhi), and wu, meaning “awakening” (bodhi). Concerning these matters, Garma C.C. Chang remarks that wu "as shown in the Zen tradition, to denote the inner experience of the awakening to the prajna‑truth (the truth realized through transcendental wisdom), is not the same as that of cheng‑teng‑chüeh (Skt. samyaksambodhi),which is the final and perfect Enlightenment of Buddhahood. Ch'an Buddhists seldom talk of cheng‑chüeh (sambodhi), or speak of their Ch’an experience as chüeh (bodhi). Although chüeh and wu are veryclose, adifference still exists between them. Wu refers more to the awakening experience in its immediate sense, while chüeh denotes permanent and complete Enlightenment (...). However, these experiences are different only in degree of profundity, not in essence, or in basic principle".32)
It is also worth noting that in Hsuan‑tsang's doctrine of Mere Ideation (seventh century), in Fa‑tsang's Hua‑yen, and in T'ien‑t'ai we find chüeh rather than wu.33)
VI
In stanza 24 we encounter two important terms—one suchness (i‑ju) and conditions (yüan). We have already mentioned the second term, which is also found in stanza 5 with the same meaning (Skt. pratyaya; Pali, paccaya — root‑conditions: greed, hate, delusion, etc.). Concerning suchness, we find altogether three variations of this term in Hsin‑hsin Ming. In stanza 4 we find "suchness" (ju), in stanza 24 "one suchness", and in stanza 30 "real suchness" (chen‑ju - Skt. bhutatathata). The first and the third are well known in Mahayana tradition, but the second seems to be an innovation of the author of Hsin‑hsin Ming.
Stanzas 28‑29 can be compared with Seng‑chao: "Sage harbors (no desires, his mind is like an) empty hole: there are no perceptions nor thoughts. Indeed, though living in the midst of our ever‑changing world, he remains completely detached..."
In the first line of stanza 30 we find two technical terms: real suchness (chen‑ju), and thing‑realm, or totality of dharmas, fa-chieh (Skt. dharma-dhatu). These concepts have been used in Mahayana, and also in the Mind‑only school, T'ien‑t'ai, and Hua‑yen. In Ch'eng Wei‑shih Lun Hsuan‑tsang gives the following definitions. "Chen means genuine and real. It indicates that it is not baseless and false. Ju means constantly thus. The meaning is that this genuine reality remains, under all conditions, constantly thus in its nature".35)
The T'ien‑t'ai school gives a slightly different meaning: "Further as to chen‑ju: it is that of all things which, being genuinely and really thus, consists of the single mind only. This single mind is therefore called chen‑ju (genuinely thus). Anything external to it is neither genuine nor thus,: but consists only of false and: diverse appearances".36)
In stanza 30 and the first two lines of stanza 31, we find the relation between real suchness (chen‑ju), non‑duality (pu‑erh), equality (t'ung),37) and totality (nothing is left out) of the thing (dharma) realm (fachieh). The connecting experience between the "meditative" (dhyana) and "wisdom" (prajna) aspects is the negation of the difference between “other” (t'a) and “self” (tzu). In meditation this is the experience of non‑obstruction between ego and non‑ego, when “all is free of marks” - and therefore, “not-different” (in a Buddhist context it would not be consistent to say that the ego has become all‑inclusive with the falling off of the ego boundaries, because ego is also without marks). In the “wisdom" sense this means that in real suchness it is not possible to make any distinction ‑ therefore, the realm of things (fa chieh), where nothing is left out, is experienced as non‑distinctive totality, or oneness. This can remind someone of postmodern debate on “difference”, and “other”, but this is a different context, and should not be meddled with postmodern debate.
Stanza 32 expands (makes explicit) this experience with interpenetration (and transcendence) of time (urgent, moment, eon) and space dimensions (extensive, here, there, nowhere, everywhere). This has also been explained by Fa‑tsang in Hua‑yen Yi‑hai Pai‑men: "Since a single moment has no substance of its own it becomes interchangeable with the great eons. Because the great eons have no substance they also embrace the single moment".38)
Non‑duality (pu‑erh) deserves separate comment. We find it in several stanzas (30, 31 and 36). It is also related to oneness (i‑chung—one kind), in stanzas 5, 6 and 7. Non‑duality (Skt. advaya, advaita) was the favorite principle in many schools of Indian philosophy, including Buddhism. In Buddhism this has been exposed in various texts, mostly of Mahayanic origin.
In Ashtasahasrika-prajnaparamita (Ch. XVI) it is said that the "suchness of the Tathagata and of all dharmas is one suchness, non‑dual (advaya), not divided (advaidhikara)".
In Abhisamayalamkara (Ch. VII) we find the: "momentary intuition of non‑duality". The commentary says: "This form of momentary intuition represents the state when the bodhisattva, having during a long period of time made it his habit to negate the double aspect of the elements (as subjective and objective), has this double representation completely removed".39)
In Gandavyuha, when Sudhana reaches Maitreya, he is introduced to a dwelling place of those who delight in emptiness and in experiencing: the interpenetration of all the ages of the universe; the entrance (anupravesa) of one into all, and all into one; the non‑obstruction (anavarana) of all phenomena; the non‑duality (advaya) of all Buddhas.
At the climax of Vimalikirtinirdesa-sutra, thirty‑two bodhisattvas explain in words the principle of non‑duality, each one setting forth the solution of apair of opposites ("coming" and "going", purity and impurity, samsara and nirvana). Finaly, Manjusri states that non‑duality can be entered only by abstaining from words and thoughts, and the same advice is given in Hsin-hsin Ming, in stanza 8..
Stanza 33 extends the principle of non‑duality to large and small. On this subject Fa‑tsang says in Hua‑yen Huan‑yüan Kuan: "When we see, for example, the height and width of a mountain, it is mind that manifests this largeness; there is no largeness apart (from mind). Or when we see the utter tinynes ofa particle of matter (guna), here again it is mind that manifests this tinyness..." 40)
With regards to influences between Hua‑yen and Ch'an, Suzuki has long ago remarked: "While scholars of the Avatamsaka school (Hua‑yen, D.P.) were making use of the intuitions of Zen in their own way, the Zen masters were drawn towards the philosophy of Identity and Interpenetration, advocated by the Avatamsaka, and attempted to incorporate it into their own discourses. (...) The influence of Avatamsaka philosophy on Zen masters grew more and more pronounced as time went on, and reached its climax in the tenth century after the passing of Tsung‑mi, the fifth patriarch of the Avatamsaka school in China".41)
In Hsin‑hsin Ming we can also find traces of this syncretism, especially in the last seven stanzas. The relationship between Hua‑yen and Ch'an has been sensed by contemporary authors like Gimello, who remarks: "One frequently encounters in Hua‑yen thought difficult issues which might better be understood if only one knew their true relationship to meditative cultivation".42) The same remark stands for many stanzas in the Hsin‑hsin Ming. In our opinion, the following stanzas are especially related to meditative cultivation: 6, 8, 10, 12; 13, 19, 21, 24, 25, 26, 28, 29, 30, 33, 35.
In Ta‑ch'eng Chih‑kuan Fa‑men of the T'ien‑t'ai school we can find similar ideas on large and small as in stanza 33. "The mind, being single, has neither largeness nor smallness. The hair‑pore and the city both embody the single total mind as their substance. From this we should realize that the hair‑pore and the city are integrated in substance and everywhere the same. For this reason the small admits of the large; thus there is nothing large that is not small. The large integrates the small: thus there is nothing small that is not large. Because there is nothing small that is not large, the large may enter the small, yet is not diminished. Because there is nothing large that is not small, the small may contain the large, yet is not increased".43)
However, the idea of relativity of small and large has been introduced to the context of Chinese philosophy some thousand years before, by Chuang‑tzu and Hui‑shih. Chuang‑tzu (in ch. XVII, "Autumn Floods") observes that "From the point of view of differences, if we regard a thing as big because there is a bigness to it, then among all the ten thousand things there are none that are not big. If we regard a thing as small because there is a certain smallness to it, then among the ten thousand things there are none that are not small".44)
The other concept that connects Hsin‑hsin Ming and Chuang‑tzu is equality (t’ung). Chuang‑tzu speaks of equality of things in ch. II: "Whether you point to a little stalk or a great pillar, a leper or the beautiful Hsi‑shih, things ribald and shady, or things grotesque and strange, the Way makes them all into one. Their dividedness is their completeness, their completeness is their impairment. No thing is either complete or impaired, but all are made into one again".45) And then he adds: "There is nothing in the world bigger than the tip of an autumn hair, and Mount T’ai is tiny. No one has lived longer than a dead child, and P'eng‑tsu died young".46)
Nevertheless, we should note the difference between Chuang‑tzu and Hsin‑hsin Ming. For Chuang‑tzu everything is equal, because: (a) tao is the equalizer of everything, and (b) everything is appropriate in relation to its kind, environment and context. In Hsin‑hsin Ming everything is equal because of emptiness and suchness.
In stanzas 34 and 35 Hsin‑hsin Ming exposes the interpenetration of being (yu ) and non‑being (wu),47) of one (i ) and all (i‑chien).
With stanza 36 the discourse is brought to the end, because the subject is pronounced as beyond time (past, present, or future).
NOTES
1. Leng‑chia Shih-tzu Chi is one of the Tun Huang manuscripts (Pelliot 3436, and Stein 2054). It was discovered in 1926, and later included in Taisho, 85. 1283-1290. Seizan Yanagida has published a critically edited version with a Japanese translation in Shoki no Zenshi I, Zen no Goroku, 2 (Tokyo, 1971) pp. 49‑326.
8. To our knowledge, there already exist five translations of the Hsin‑hsin Ming in English. The first translator, D. T. Suzuki, has published two versions of his translation—one in D.T. Suzuki, Essays in Zen Buddhism, First series (London: Rider, 1970), pp. 196‑201, and the other in Buddhist Scriptures, trans. and ed. by Edward Conze (Harmondsworth: Penguin, 1969), pp. 171‑175. His first translation was published in 1949. The second translation was done by A. Waley, in Buddhist Texts Through the Ages (Oxford: Bruno Cassirer, 1954), pp. 295‑8. The third is by R. H. Blyth, Zen and Zen Classics, Vol. I, (Tokyo: The Hokuseido Press, 1960), pp. 5~99. The fourth is by Lu K'uan Yu, Practical Buddhism (London: Rider, 1971), pp. 34‑8. The fifth, anonymous translation, can be found in a manual, Daily Chants (Rochester: Zen Center, 1985).
At first it seemed that we could use one of these as the basis for a new analysis of the poem, but after closer scrutiny it was obvious that none of the existing translations were adequate for the purpose. The fifth translation is a rather free rendering made for immediate purposes in a Zen Center. Of the other four, some are inconsistent in translating Buddhist technical terms (translations by Blyth and Yu, while Suzuki's translation occasionally introduces terms which seem to be part of a technical vocabulary (Absolute Reason), but actually belong to Hegelian philosophy, rather than Chinese Buddhism. Waley’s translation is faithful except in technical terms. Perhaps he lacked the knowledge of Buddhist tradition and therefore translated technical terms as quasi‑technical (in stanza 19, True Perception, instead of perfect awakeness; in stanza 21, Wisdom instead of awakening).
21. In the second line of stanza 17 we also find the character chu, which is a technical term for stages (Skt. bhumi) on the bodhisattva path. If we read it in this sense it would mean that the essence is not related to stages, and that is in accordance with the concept of awakening which refutes stages. However, since Hsin‑hsin Ming gives no special attention to sudden awakening, we have chosen a colloquial reading to abide, dwell. Blyth (Zen p. 79) has misunderstood the second line of stanza 17, translating t'i as activity.
22. One vehicle has an interesting history in Indian Mahayana, which has been lately exposed by D.S. Ruegg in "The gotra, ekayana and tathagatagarbha theories of the Prajnaparamita according to Dharmamitra and Abhyakaragupta", and A. Kunst in "Some Aspects of the Ekayana" - both papers published in Prajnaparamita and Related Systems, ed. by L. Lancaster (Berkeley Buddhist Studies Series), 1977.
In various Mahayana texts the subject of One vehicle is interpreted differently. In Sri‑Mala (The Lion's Roar of Queen Srimala), trans. by Wayman, A. and H., (New York: Columbia University Press, 1974), and the Lotus sutra, Ekayana is identified with Mahayana as a vehicle (yana) that incorporates all vehicles. It also takes tathagatagarbha as an explanation for the thesis of One vehicle: an embryo of the Tathagata is present in every sentient being, and (potentially) they are all Buddhas, which means that tathagatagarbha isthe basis of only one vehicle—the vehicle of the tathagatas. Finally, samyaksambodhi is one, not various, or different, in relation to various vehicles - yana-s.
The gist of the interpretation in various sutras or their commentaries is that the three yanas, pertaining to sravakas, pratyekabuddhas and bodhisattvas isfundamentally Eka‑yana pertaining to Buddhahood. The basis for this is that all‑aspiring Buddhists are of one gotra (lineage), and all have tathagatagarbha (embryo of tathagatha). "No system postulating (different) vehicles indeed exists (in a certain meaning): I teach that the vehicle is one (ultimately). [But] in order to attract the childish I speak of different vehicles" (Lankavatara-sutra, cf. Ruegg, in Lancaster, Prajnaparamita, p. 295).
One vehicle doctrine in the context of Japanese Buddhist thought was reviewed by M. Kiyota, “The presupposition to the understanding of Japanese Buddhist thought", Monumenta Nipponica vol. X~11, no. 34 pp. 251‑9, 1967.
25. For John R McRae, Hsin‑ming is falsely attributed to Fa-jung. See his article, "The Ox‑head School of Chinese Ch’an Buddhism", eds., R. N. Gimello and P.N. Gregory, Studies in Ch'an and Hua‑yen (Honolulu: University of Hawaii Press, 1986), p. 208. On the other hand, Henrik H. Sorensen, commenting on the authorship and contents of the Hsin‑ming, says: "All in all, we must conclude that there are a number of important points such as style, and contents which clearly allow us to associate the text with Fa-jung and the Niu‑t'ou School... Interestingly, the 'Hsin‑hsin Ming'... has many points in common with the 'Hsin‑ming', both as regards contents and style", H.H. Sorensen, "The 'Hsin‑ming' attributed to Niu‑t’ou Fa-jung", Journal of Chinese Philosophy, 13: 105 (1986).
27. We know that Indian Buddhism has elaborated a broad spectrum of ideas on these matters. We find altogether some six Sanskrit terms related to this subject.
(a) Bodhi‑citta designates the cognition of the necessity to step on the path (marga) and the decision/will to tread it. It is the power needed to tread the path, whether it is defined in terms of an arhat or a bodhisattva. However, these are supposed to differ—the first one is bent on attaining an awakening for himself, while the other is supposed to attain it in order to lead others to the path, and awakening.
(b) Bodhi isawakening. It means the full understanding (what was previously an aspiration) of the Buddhist truths (whether in Theravada, Mahayana or Tantrayana tradition), inner transformation of cognitive, emotional and volitional faculties, and a transition to unconditioned (not bound by karma) existence. It is sometimes described as "reaching the other shore", or "turning about in the deepest seat of consciousness", or "breaking through" the bondage of ignorance and karma. Bodhi is derived from the root budh, which means to awake; therefore it is correct to translate it as awakening, and less correct as enlightenment. However, light is related with awakening in some sutras and tantras, principally in two forms. First is the light of the all‑powerful! Buddha, which enlightens and awakes sentient beings. Second is the individual, inner light of the mind. Under delusion it appears as false thinking, but after awakening it turns into the true light, radiant wisdom.
(c) Sambodhi (supposedly) means complete awakening.
(d) Samyak‑sambodhi is "right complete awakening".
(e) Anuttara‑samyak‑sambodh is "ultimate right complete awakening".
However, these terms were not used consistently. For example, (b) and (c) were sometimes used as synonyms, as well as (d) and (e). Perhaps we can better understand this from the point of actual practice of meditation. There existed a practical need for terms which would designate experiences of various quality. Besides, it was supposed that the awakening of a Buddha is somewhat different in relation to the awakening of aspirants (Arahants, Bodhisattvas). For example, samyak‑sambodhi (Pali, samma‑sambodhi) was in Theravada a designation for the awakening of a Buddha; later it was anuttara‑samyak‑sambodhi. In Mahayana there was a tendency to use different terms for awakening of a Sravaka, Pratyekabuddha, Bodhisattva and Buddha, in order to underline the supposed difference in kind and quality.
However, divisions of the path, meditation, insight and of awakening, provoked a reaction, which derived its reasons partly from theory, and partly from practice. From the theoretical standpoint it was considered that awakening - after all - must be "in one piece", apart from the preceding "not yet complete" forms; otherwise, it would fall under ordinary undertakings, which are conditioned, relative, and a matter of accumulation. From the practical point it seemed that the practicing Buddhist is lost in a complex maze of an endless accumulation of merits, insights, wisdoms, samadhis and awakenings. One could expect a reaction to this in order to put things back in pristine simplicity and proclaim that there is, after all, an only One vehicle (Eka‑yana), one germ of the thus‑come (tathagata‑garbha), one nirvana, and one awakening, which is spontaneous, instant and sudden. As Lankavatara puts it: "It is reached suddenly and intuitively as the 'turning about' in the deepest seat of consciousness; it neither enters, nor goes out—it is like moon seen in water".
Thus, sudden awakening, that caused so much turbulence in Ch’an, was already at stake in Indian Buddhism (see: L.O. Gomez, "Indian Materials on the Doctrine of Sudden Enlightenment," in Lai and Lancaster, Early Ch'an in China awl Tibet). The Sanskrit term, introduced in Abhisamayalamkara, was eka‑ksana‑abhisambodha - “complete‑awakening‑in‑one‑moment”, a final removal of even the subtlest defilement and ignorance, attained in a thunderbolt‑like (vajropama) samadhi (E. Obermiller, “The Doctrine of Prajnaparamita as Exposed in the Abhisamayalamkara of Maitreya", ActaOrientalia, XI, 1933, p. 44). This momentary intuition is said to be the end of the bodhisattva path. It is an intuition of ultimate non‑duality (advaya). It is supposed to be the end of a progressive (gradual) process of intuition (anupurva‑abhisamaya). In such a context "gradualness" and "suddenness" were not concurrent, but compatible parts of the same (and one) process. The final realization is a matter of moment, but this moment and suddenness have to be prepared through a gradual building up. This can be seen even in Ch'an of the Southern school. Sometimes, decades of training were necessary for "sudden attainment", and integrating t'i (essence) with yung (function) - which followed “sudden attainment” in everyday life and experience - was (for the most part) a gradual process.
28. That is one of the reasons for Fung Yu‑Lan to say: "Ideologically speaking, the origin of the Ch’an school goes back to Tao‑sheng" - A History of Chinese Philosophy, II, 388.
29. Compare the translation of this passage from Pieh Tsung Lun in Walter Liebenthal, The Book of Chao - Peking: The Catholic University 1948 p. 187; also, Fung Yu‑Lan, A History of Chinese Philosophy, II, p. 278.
31. This character (ming) has a long history in Chinese philosophy. It was introduced back at the time of Lao tzu: "All things, howsoever they flourish, return to their root. This return to the root is called quiescence, which is called the invariable. To know this invariable is called enlightenment (ming)" - Tao Te Ching, XVI.
32. Chang, The Practice of Zen, p. 162‑3.
33. See Fung Yu‑Lan, A History of Chinese Philosophy, II, pp. 337, 356 and 381. In time, Chinese Buddhism developed the whole specter of technical equivalents for Sanskrit terms (either in meaning, or as transliterations). For example, for bodhi, beside wu, and chüeh, we find a transliteration p’u-t'i. For sambodhi, beside cheng‑chüeh, we find a transliteration san-p'u-t'i. For samyak‑sambodhi we find teng cheng‑chüeh, and for anuttara‑samyak‑sambodhi, there is cheng-teng cheng‑chüeh.
34. The Book of Chao, p. 109.
35. Fung yu‑Lan, A History of Chinese Philosophy, II, p. 331.
36. Ibid. p. 361.
37. Equality, or sameness (t'ung - Skt. samata), of all things is one of the favorite subjects in Hsin‑hsin Ming. Some authors observed that equality of things was attained in Indian Buddhism primarily by reducing all things to the common level of insignificance, and in Hua‑yen by raising all things to the common level of supreme value. We cannot say that Hsin‑hsin Ming applies either of these standpoints. In stanza 14 we see that dualities are equal on the basis of emptiness, which is their common "ground". In stanzas 30-31 equality is based on suchness and non‑duality. In stanza 33 equality appears when boundaries and limits are seen as conventions. Thus, equality is here neither equality in insignificance, nor in value. |
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E chega o empate! Arango desmarca-se no limite do fora de jogo e faz um chapéu ao guardião Rui Vieira. |
On Sunday evening, May 31, executives of Environmental Resources Management (ERM), a British research consultancy, joined the principals of the HKND Group, a Hong Kong-based development group set on building a canal across Nicaragua, in a private ceremony in Managua. The event was held to formally submit a 14-volume study to Nicaraguan authorities on the environmental and social consequences of constructing a new and mammoth shipping corridor across Central America.
The following day, in a made-for-television press event, a copy of the 14-volume Environmental and Social Impact Assessment of the proposed Nicaragua Canal was displayed on a small table for news photographers. Though the study is not available for public review, ERM and HKND executives joined government authorities in asserting that the canal construction is safe and feasible, and they defended the quality of the environmental assessment, which the government and HKND say is central to the case for starting excavation, perhaps before the end of the year.
“The purpose of the study is to provide an objective, current assessment based on science,” Manuel Coronel Kautz, the president of Nicaragua’s Grand Canal Authority, told reporters.
Edwin Castro, a senior Sandanista official, added that “this is the work of more than two years by ERM, with all the scientific means and serious business of ERM.”
The quality of ERM’s data, though, and the accuracy of its conclusions about the potential harms from canal construction and operation, are not nearly as airtight as Nicaraguan authorities and HKND affirm. In March, ERM invited 15 environmental scientists and project experts to Miami to spend two days reviewing four chapters of the environmental assessment. In an 11-page evaluation obtained by Circle of Blue, the panel’s members concluded this spring that ERM’s environmental study is rife with significant flaws.
Panel members expressed frustration at what they said was insufficient data collection on water quality, geology, sediments, species, erosion, and fisheries. They complained about the pedestrian quality of ERM’s analysis of the data that it did collect. At various points in their report, the panel castigated ERM for what they called “indefensible,” “implausible,” “wrong,” and “not realistic” scientific conclusions.
The special panel’s members, most from US universities, also raised penetrating questions about whether building and operating the proposed $US 50 billion, 278-kilometre (173-mile) canal is even feasible. The gravest areas of concern, said panel members, involved understanding the geology beneath Lake Nicaragua, the disposal of 1.1 billion metric tons of silt that would be dredged from the lake for shipping channels nearly 28 meters (91 feet) deep and up to 520 meters (1,700 feet) wide, and whether there would be sufficient supplies of water to operate two sets of locks in the event of deep and prolonged droughts that are anticipated in the region due to climate change.
“It seemed to me that the environmental impact assessment process was to create the illusion of science,” said Michael T. Brett, a professor in the Department of Civil and Environmental Engineering at the University of Washington in Seattle, during an interview with Circle of Blue. “I had the impression that most of the sections presented to us were of the quality of a weak Master’s thesis at any major research university. We kept asking, ‘Couldn’t this have been done better?’ It’s not very good work.”
Panel members also said in interviews that they wondered if the study’s weaknesses would jeopardise ERM’s global reputation for thorough and first-rate work.
When asked about that concern, David Blaha, a principal partner at London-based ERM, emailed this response to Circle of Blue:
“As you may know, ERM sponsored the expert panel. We did not need to do this but we believed a project of this magnitude deserved this level of review. ERM was very appreciative of the comments we received from the panel and we responded to all of their comments in the Environmental and Social Impact Assessment (ESIA). We believe the ESIA is a robust document and objectively evaluates the effects of the project. I encourage you to review the ESIA (or at least the executive summary), once it is available, before reaching any conclusions about the document.”
ERM Responds
Circle of Blue also obtained a copy of ERM’s 16-page response to the special panel, which is the only portion of the 14-volume study that has been made public. In its response, ERM generally agreed with the weaknesses in the work that the panel illustrated and said that some analysis had been reworked.
In most cases, said ERM, the tight two-year deadline for completing the assessment for HKND meant its researchers often did not have sufficient time to conduct more thorough data gathering. ERM recommended that HKND and Nicaragua authorities pursue research that responds to the concerns raised by the special panel and by several other science and environmental organizations, which have produced evaluations that are critical of the potentially grave consequences to water, forests, coastal regions, wildlife, and human communities from building the canal.
As proposed by HKND, the Nicaragua Canal would be more than three times longer than the Panama Canal; include two sets of monumental locks, larger than those currently under construction at the Panama Canal; require the construction of a 395 square kilometre (152 square mile) artificial lake; and force thousands of people from their homes.
As noted in the special panel’s report, the entire corridor proposed for construction — and the coastal marine environments in close proximity to the canal’s Pacific and Caribbean entrances — supports strong fisheries, is a storehouse of exotic tropical plant and animal species, and is home to dozens of indigenous human communities.
Learn more about the proposed route of the Nicaragua Canal below. To view full screen click here
Safety of Canal Project Far From Assured
The panel found that the four chapters of the environmental assessment they reviewed contained what members called “limited” data on forest habitat and other essential resources that would be affected by the canal.
“We were most concerned about the lack of information collected and presented,” said Sudeep Chandra, an associate professor of biology at the University of Nevada in Reno, during an interview with Circle of Blue. “It wasn’t just about the impact on the environment. It’s also about the feasibility of the project. There didn’t seem to be enough due diligence to see whether the project was even feasible. We were just so surprised by the lack of response to each of our points. I would suggest it is one of the most mismanaged environmental reviews I have ever read.”
One of the panel’s deepest concerns is the safety of Lake Nicaragua, Central America’s largest lake and a relatively shallow, clean, and oxygen-rich source of fresh water for thousands of people and a thriving fishery. HKND proposes to cut a 105 kilometre (40 mile) channel across the lake so deep and wide that it would require a wet-excavation project of silt and mud five times larger than constructing the offshore airport in Hong Kong, which is the largest such wet-excavation project ever conducted.
HKND proposes to build three islands in the lake to dispose a portion of the dredge spoils. The rest would be dumped into the lake to settle to the bottom in 3 metre high berms that would run the length of both sides of the dredged channel.
The panel found that the data for understanding the consequences on fisheries and water quality from dumping that much fine silt into the lake was “limited.” That did not stop ERM researchers from arguing in their draft environmental assessment that “the magnitude of the impact is considered small.”
The 15-member panel found that conclusion absurd.
“This finding of moderate significance of dredging impact simply is scientifically indefensible,” the panel concluded in their report. Pouring so much fine silt into a shallow lake would cloud the water, cause oxygen-starved conditions, introduce nutrients that lead to dense algae blooms, dramatically damage the lake’s important fisheries, and seriously degrade the lake as a source of drinking water.
“This fine-grained clay will likely have a large impact on the in-lake sediment disposal plan and result in severe water quality impairment,” said the panel report.
Sea Turtles At Risk
The panel also criticised ERM surveys of existing plant and animal life in the canal corridor, calling the consultancy’s data gathering “brief and incomplete.” Panel members noted that little attention was paid by ERM researchers to the effect that the canal would have on the ability of animals to migrate freely, because the proposed canal would form a new terrestrial barrier.
Another of the panel’s concerns was large gaps in the environmental subjects that ERM researchers chose to address. For instance, ERM did not consider the canal’s potential to affect the Pacific Coast of Nicaragua, which is one of the world’s most important habitats and nesting beaches for four of the seven species of sea turtles.
The Nicaraguan government has not made the ERM study public, nor has it indicated when it will do so. Panel members said it is imperative that the 14-volume study be available for public review.
“That is the most urgent short-term concern with the process,” said Ryan Stoa, a lawyer and senior scholar at Florida International University who helped to organise the independent review panel. “The government is holding it back. It’s hard for anyone to judge the merits of the study without seeing the research in its entirety. It’s troubling for us that the government has not publicly released the report or even indicated when they will do so. While the science we reviewed was problematic, I expect the final ESIA will raise serious concerns about the impacts of the canal. It’s imperative that the public have access to that research sooner rather than later.”
“It’s safe to say that all of us are very concerned about the potential environmental impacts of a project of this scale,” added Adam Henson, a member of the panel and technical director with Fauna & Flora International, a respected international conservation organization that has worked in Nicaragua since 1998. “We are most interested in a scientifically robust, publicly transparent environmental assessment process. At this stage, we hope the ESIA will be released for public comment to ensure a robust scientific review and wide consultation with the Nicaraguan scientific community and civil society in general.” |
/* Copyright (c) 2012 The Chromium Authors. All rights reserved.
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
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/**
* This file defines the <code>PPB_BrowserFont_Trusted</code> interface.
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label Chrome {
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PP_BROWSERFONT_TRUSTED_FAMILY_DEFAULT = 0,
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PP_BROWSERFONT_TRUSTED_FAMILY_SERIF = 1,
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PP_BROWSERFONT_TRUSTED_WEIGHT_900 = 8,
PP_BROWSERFONT_TRUSTED_WEIGHT_NORMAL =
PP_BROWSERFONT_TRUSTED_WEIGHT_400,
PP_BROWSERFONT_TRUSTED_WEIGHT_BOLD =
PP_BROWSERFONT_TRUSTED_WEIGHT_700
};
[assert_size(48)]
struct PP_BrowserFont_Trusted_Description {
/**
* Font face name as a string. This can also be an undefined var, in which
* case the generic family will be obeyed. If the face is not available on
* the system, the browser will attempt to do font fallback or pick a default
* font.
*/
PP_Var face;
/**
* When Create()ing a font and the face is an undefined var, the family
* specifies the generic font family type to use. If the face is specified,
* this will be ignored.
*
* When Describe()ing a font, the family will be the value you passed in when
* the font was created. In other words, if you specify a face name, the
* family will not be updated to reflect whether the font name you requested
* is serif or sans serif.
*/
PP_BrowserFont_Trusted_Family family;
/**
* Size in pixels.
*
* You can specify 0 to get the default font size. The default font size
* may vary depending on the requested font. The typical example is that
* the user may have a different font size for the default monospace font to
* give it a similar optical size to the proportionally spaced fonts.
*/
uint32_t size;
/**
* Normally you will use either normal or bold.
*/
PP_BrowserFont_Trusted_Weight weight;
PP_Bool italic;
PP_Bool small_caps;
/**
* Adjustment to apply to letter and word spacing, respectively. Initialize
* to 0 to get normal spacing. Negative values bring letters/words closer
* together, positive values separate them.
*/
int32_t letter_spacing;
int32_t word_spacing;
/**
* Ensure that this struct is 48-bytes wide by padding the end. In some
* compilers, PP_Var is 8-byte aligned, so those compilers align this struct
* on 8-byte boundaries as well and pad it to 16 bytes even without this
* padding attribute. This padding makes its size consistent across
* compilers.
*/
int32_t padding;
};
[assert_size(20)]
struct PP_BrowserFont_Trusted_Metrics {
int32_t height;
int32_t ascent;
int32_t descent;
int32_t line_spacing;
int32_t x_height;
};
[assert_size(24)]
struct PP_BrowserFont_Trusted_TextRun {
/**
* This var must either be a string or a null/undefined var (which will be
* treated as a 0-length string).
*/
PP_Var text;
/**
* Set to PP_TRUE if the text is right-to-left.
*/
PP_Bool rtl;
/**
* Set to PP_TRUE to force the directionality of the text regardless of
* content
*/
PP_Bool override_direction;
};
/**
* Provides an interface for native browser text rendering.
*
* This API is "trusted" not for security reasons, but because it can not be
* implemented efficiently when running out-of-process in Browser Client. In
* this case, WebKit is in another process and every text call would require a
* synchronous IPC to the renderer. It is, however, available to native
* (non-NaCl) out-of-process PPAPI plugins since WebKit is available in the
* plugin process.
*/
interface PPB_BrowserFont_Trusted {
/**
* Returns a list of all available font families on the system. You can use
* this list to decide whether to Create() a font.
*
* The return value will be a single string with null characters delimiting
* the end of each font name. For example: "Arial\0Courier\0Times\0".
*
* Returns an undefined var on failure (this typically means you passed an
* invalid instance).
*/
PP_Var GetFontFamilies(
[in] PP_Instance instance);
/**
* Returns a font which best matches the given description. The return value
* will have a non-zero ID on success, or zero on failure.
*/
PP_Resource Create(
[in] PP_Instance instance,
[in] PP_BrowserFont_Trusted_Description description);
/**
* Returns PP_TRUE if the given resource is a Font. Returns PP_FALSE if the
* resource is invalid or some type other than a Font.
*/
PP_Bool IsFont(
[in] PP_Resource resource);
/**
* Loads the description and metrics of the font into the given structures.
* The description will be different than the description the font was
* created with since it will be filled with the real values from the font
* that was actually selected.
*
* The PP_Var in the description should be of type Void on input. On output,
* this will contain the string and will have a reference count of 1. The
* plugin is responsible for calling Release on this var.
*
* Returns PP_TRUE on success, PP_FALSE if the font is invalid or if the Var
* in the description isn't Null (to prevent leaks).
*/
PP_Bool Describe(
[in] PP_Resource font,
[out] PP_BrowserFont_Trusted_Description description,
[out] PP_BrowserFont_Trusted_Metrics metrics);
/**
* Draws the text to the image buffer.
*
* The given point represents the baseline of the left edge of the font,
* regardless of whether it is left-to-right or right-to-left (in the case of
* RTL text, this will actually represent the logical end of the text).
*
* The clip is optional and may be NULL. In this case, the text will be
* clipped to the image.
*
* The image_data_is_opaque flag indicates whether subpixel antialiasing can
* be performed, if it is supported. When the image below the text is
* opaque, subpixel antialiasing is supported and you should set this to
* PP_TRUE to pick up the user's default preferences. If your plugin is
* partially transparent, then subpixel antialiasing is not possible and
* grayscale antialiasing will be used instead (assuming the user has
* antialiasing enabled at all).
*/
PP_Bool DrawTextAt(
[in] PP_Resource font,
[in] PP_Resource image_data,
[in] PP_BrowserFont_Trusted_TextRun text,
[in] PP_Point position,
[in] uint32_t color,
[in] PP_Rect clip,
[in] PP_Bool image_data_is_opaque);
/**
* Returns the width of the given string. If the font is invalid or the var
* isn't a valid string, this will return -1.
*
* Note that this function handles complex scripts such as Arabic, combining
* accents, etc. so that adding the width of substrings won't necessarily
* produce the correct width of the entire string.
*
* Returns -1 on failure.
*/
int32_t MeasureText(
[in] PP_Resource font,
[in] PP_BrowserFont_Trusted_TextRun text);
/**
* Returns the character at the given pixel X position from the beginning of
* the string. This handles complex scripts such as Arabic, where characters
* may be combined or replaced depending on the context. Returns (uint32)-1
* on failure.
*
* TODO(brettw) this function may be broken. See the CharPosRTL test. It
* seems to tell you "insertion point" rather than painting position. This
* is useful but maybe not what we intended here.
*/
uint32_t CharacterOffsetForPixel(
[in] PP_Resource font,
[in] PP_BrowserFont_Trusted_TextRun text,
[in] int32_t pixel_position);
/**
* Returns the horizontal advance to the given character if the string was
* placed at the given position. This handles complex scripts such as Arabic,
* where characters may be combined or replaced depending on context. Returns
* -1 on error.
*/
int32_t PixelOffsetForCharacter(
[in] PP_Resource font,
[in] PP_BrowserFont_Trusted_TextRun text,
[in] uint32_t char_offset);
};
|
Waffles Lovers Guide to Lajpat Nagar-Delhi
April 3, 2018
Share and Spread Ideas:
If Lajpat Nagar Market in South Delhi is your next abode girls, we have brought some best Waffles shops there to quench your chocolaty- thirst. Here is a post about some of the best and easily accessible shops in the market or on the way for it/ quiet nearby, that you must give a try once.
1. The Belgian Waffle Co.
The Belgian Waffle Co. lies on the way to the Lajpat Nagar Central market from the Metro station provided you take a simple walk once you deboard Metro. About 200 mtrs walk down the lane, this shop specializes in making waffles as the name suggests. It’s a fairly small and cozy outlet with comfortable seating arrangements. They freshly prepare the batter as per the order and an excellent choice for Vegetarian folks. Waffles are Eggless but taste no short of it. Their menu also offers a variety of Shakes, coolers and Ice-creams with waffles. You can also customize your waffle with additional toppings of extra chocolate, oreos, fresh cream, banana, nutella and almonds. Prices are pocket-friendly too for all that YUMmm…
2. 24 Seven Store
24 Seven Store is actually a convenience store and not a restaurant per se. This also lies on the same way towards the market a few steps further down the Belgian Waffle Co. This shop stocks a large variety of knick-knacks – perfect on the go food and snacking options like burgers, poha, wraps, shakes, sandwiches, coffees and teas. All these snacks are freshly stocked & packed daily and heated in an oven or microwave when you order. But they make gooey Chocolate Waffles freshly, right in front of you. These are priced about Rs250 and the portion is fairly big for 2 friends on the go. If you wish to pick some international grocery like sauces and condiments for your cooking experiments, they are available handy in this store too. Well Air-conditioned, the only downside is that there is no seating arrangements.
3. The Waffles Point
Once you enter the market (Metro side Entry), traverse through the central square to reach the lane on the other side (exactly parallel) to find The Waffles Point. This is situated near Golden Fiesta Birthday Cakes shop and is surrounded by a number of tiny food joints- Momo joints, tikki chaat, steamed corn and golgappa corners. They make Both Eggless and Non-veg options and Sweet and Salty varieties in waffles. Prices are mostly upto Rs 200. The stall gets busier in the evenings, so order in the daytime to avoid the rush. |
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Posts Tagged ‘Predictably Irrational’
In February, John Tierney wrote a great column in February for the New York Times about Dan Ariely’s new book, Predictably Irrational. We already posted about Ariely’s book last week (see here). In this post, we simply wanted to highlight Tierney’s excellent summary of some of Ariely’s experiments.
* * *
In a series of experiments, hundreds of students could not bear to let their options vanish . . . .
* * *
They played a computer game that paid real cash to look for money behind three doors on the screen. . . . After they opened a door by clicking on it, each subsequent click earned a little money, with the sum varying each time.
As each player went through the 100 allotted clicks, he could switch rooms to search for higher payoffs, but each switch used up a click to open the new door. The best strategy was to quickly check out the three rooms and settle in the one with the highest rewards.
Even after students got the hang of the game by practicing it, they were flummoxed when a new visual feature was introduced. If they stayed out of any room, its door would start shrinking and eventually disappear.
They should have ignored those disappearing doors, but the students couldn’t. They wasted so many clicks rushing back to reopen doors that their earnings dropped 15 percent. Even when the penalties for switching grew stiffer — besides losing a click, the players had to pay a cash fee — the students kept losing money by frantically keeping all their doors open.
Why were they so attached to those doors? The players . . . say they were just trying to keep future options open. But that’s not the real reason, according to Dr. Ariely and his collaborator in the experiments, Jiwoong Shin, an economist who is now at Yale.
They plumbed the players’ motivations by introducing yet another twist. This time, even if a door vanished from the screen, players could make it reappear whenever they wanted. But even when they knew it would not cost anything to make the door reappear, they still kept frantically trying to prevent doors from vanishing.
Apparently they did not care so much about maintaining flexibility in the future. What really motivated them was the desire to avoid the immediate pain of watching a door close.
“Closing a door on an option is experienced as a loss, and people are willing to pay a price to avoid the emotion of loss,” Dr. Ariely says.
Dan Ariely, Professor of Economics at Duke University, has an article in the UK publication “The Independant,” in which he details some of the scenarios his team studied that show how people can behave irrationally in various situations. Part of the article is excerpted below.
* * *
Relativity
Next time you hit the town in search of a date, take a friend who looks similar to you, but is slightly less attractive. We presented participants with two portraits – Mike and John – and asked them to choose whom they’d rather date. For half the participants we distorted the picture of Mike and added it to the set, so they had John, Mike and an ugly version of Mike to choose from. For the other half of the students, we distorted John, so they had Mike, John and an ugly John.
When the ugly version of Mike was presented, the attractive version of Mike became the most desirable date. And when the ugly version of John was presented, John’s attractive version became the most desirable.
It is very hard for us to evaluate things in absolute terms. So, we evaluate products and people in relative terms, which makes us vulnerable to this kind of trap, called the asymmetric dominance effect.
Spending power
We asked a group of MBA students to write down the last two digits of their Social Security number next to the descriptions of a few products. We then asked them if they would pay the amount of money indicated by these numbers (79 became $79 and so on) for each of the products.
We then asked them to bid on the items in an auction. It turned out that people with higher Social Security numbers were willing to pay more.
What was going on? It’s not that people with high Social Security numbers are willing to pay more for everything in general. Instead, it is what’s known as the power of first decision. Once people start thinking of something as having a specific value, they do so not just once, but repeatedly.
So we live in two worlds: one characterized by social exchanges and the other characterized by market exchanges. And we apply different norms to these two kinds of relationships. Moreover, introducing market norms into social exchanges, as we have seen, violates the social norms and hurts the relationships. Once this type of mistake has been committed, recovering a social relationship is difficult. Once you’ve offered to pay for the delightful Thanksgiving dinner, your mother-in-law will remember the incident for years to come. And if you’ve ever offered a potential romantic partner the chance to cut to the chase, split the cost of the courting process, and simply go to bed, the odds are that you will have wrecked the romance forever.
My good friends Uri Gneezy (a professor at the University of California at San Diego) and Aldo Rustichini (a professor at the University of Minnesota) provided a very clever test of the long-term effects of a switch from social to market norms. A few years ago, they studied a day care center in Israel to determine whether imposing a fine on parents who arrived late to pick up their children was a useful deterrent. Uri and Aldo concluded that the fine didn’t work well, and in fact it had long-term negative effects. Why? Before the fine was introduced, the teachers and parents had a social contract, with social norms about being late. Thus, if parents were late — as they occasionally were — they felt guilty about it — and their guilt compelled them to be more prompt in picking up their kids in the future. (In Israel, guilt seems to be an effective way to get compliance.) But once the fine was imposed, the day care center had inadvertently replaced the social norms with market norms. Now that the parents were paying for their tardiness, they interpreted the situation in terms of market norms. In other words, since they were being fined, they could decide for themselves whether to be late or not, and they frequently chose to be late. Needless to say, this was not what the day care center intended.
But the real story only started here. The most interesting part occurred a few weeks later, when the day care center removed the fine. Now the center was back to the social norm. Would the parents also return to the social norm? Would their guilt return as well? Not at all. Once the fine was removed, the behavior of the parents didn’t change. They continued to pick up their kids late. In fact, when the fine was removed, there was a slight increase in the number of tardy pickups (after all, both the social norms and the fine had been removed).
This experiment illustrates an unfortunate fact: when a social norm collides with a market norm, the social norm goes away for a long time. In other words, social relationships are not easy to reestablish. Once the bloom is off the rose — once a social norm is trumped by a market norm — it will rarely return.
* * *
To listen to an interesting, nine-minute All Things Considered interview of Dan Ariely, click here. In addition, a podcast with an interview of Professor Ariely and describing more of his research can be found at Open Source, while an interview with him from ABC Radio National can be heard by clicking here. Image from Harper Collins. We’ll have another post on Ariely’s book later this week. |
‘I don’t think I knew how sick I was:’ Troup County COVID-19 patient tells her story
Gayle Marie Truitt is not just a statistic on a report from the Georgia Department of Public Health.
She is one of the people those numbers represent who has been diagnosed with a confirmed case of COVID-19 in Troup County.
Truitt is 45 years old, an elementary school teacher, a mother and a grandmother. However, in three weeks, COVID-19 hit her so hard that she didn’t have the energy to lift a fork to eat despite extreme hunger.
Truitt is recovering at her LaGrange home, waiting on April 2 for her self-quarantine to end so she can see her sons, grandchildren, mother-in-law and church family. But for now, she’s focusing on achieving everyday goals like unloading the dishwasher or folding laundry without running out of breath or avoiding a coughing fit.
Truitt’s life came to a screeching halt once she started getting sick at the end of February. She had gotten married right out of high school and worked for Milliken for 18 years. She endured a divorce, went back to school at 32 years old to obtain an early childhood education degree from LaGrange College and struggled to find a full-time job while substitute teaching at George E. Washington in Meriwether County to support her children.
Luckily, in 2012, she landed her dream job as an elementary school teacher at George E. Washington in Meriwether County.
“I wanted to be a teacher for as long as I can remember,” Truitt said.
COVID-19 has thrown a slight wrench into her life. However, slowly but surely, Truitt said she’s recovering with some good days and some bad.
First signs
of sickness
It was Friday, Feb. 28, when Truitt felt a mild cough start to develop. There were 16 cases of COVID-19 in the U.S. total and zero cases in Georgia. Truitt said she wasn’t experiencing a dry cough and didn’t have a fever or shortness of breath, which were the symptoms health officials were saying could be a sign of coronavirus.
Truitt said on that following Monday, her health started to go downhill, but like many Americans, she continued to work because she didn’t think it was that bad.
However, on Thursday, March 5, she said she “felt like death warmed over.”
She worked that day but felt she would most likely call in sick that Friday. But, when she woke up, she said she was fine. She went to work and felt fine all day. She even went to dinner with her friend. The next day, she picked up her grandchildren and had them all weekend, went to church on Sunday morning and participated in her small-group church session Sunday night.
All this time, she said she continued to take her temperature just to be sure she was OK, and it was usually about 97 or 98 degrees.
She went to work that following Monday again and was fine once again, so she thought whatever was ailing her was over. However, when she woke up on Tuesday, March 10, she had a 101-degree fever.
On March 10, there were 937 cases of COVID-19 in the U.S. There were 15 cases in Georgia. None of those cases were in Troup County.
She went to Summit Urgent Care in LaGrange, where they treated her for bronchitis. She said she had a bout with it in the past, so they gave her a breathing treatment and sent her home. Truitt said she was given instructions she could return to work on Thursday, March 12.
After considering her options, she emailed her principal and said it would probably be best if she stayed home throughout the week because she wasn’t sure how productive she could be. That Thursday night, she awoke once again with a fever.
The next morning, on Friday, March 13, something happened that Truitt said most likely led to her getting the care she needed to treat the virus.
While in her bedroom Friday morning, she hit the center of her eye on her bedroom door handle. She said she was bending over to grab something while it was dark, and the door must not have been shut all the way.
“I don’t know what would have happened if I hadn’t hit that door,” Truitt said.
Her mother-in-law came over and took her back to Summit, but once again, she said she wasn’t feeling ill and didn’t have a fever or cough.
She was instructed to return to the office on Saturday to ensure the eye was healing, but while being examined, she said she wasn’t feeling well.
“The second the doctor put the stethoscope up to my back, she kind of stepped back and was like, I think you need to be tested,” Truitt said.
This was Saturday, March 14. Truitt said she tried to get tested at WellStar West Georgia Medical Center and in Newnan but couldn’t get anyone to test her.
Health officials in the area during that time were admitting that test supplies were extremely limited and were only testing very high-risk people. The number of cases in the U.S. had reached more than 4,000 cases. Georgia had 66 confirmed cases and was one day removed from reporting its first death. Troup County still had zero cases.
After failing to get tested, Truitt went home but refused to let anybody stay with her and she also refused to stay with anybody else.
“I couldn’t take that chance, so I came home and I went to sleep,” she said.
Getting tested
On the night of Saturday, March 14, Truitt was awakened by the sound of her mother-in-law banging on her front door to take her to the emergency room. She had emailed the governor’s office about Truitt’s story, and within 15 minutes, she got a call from the state health department, according to Truitt.
The mother-in-law was instructed to take Truitt to the emergency room, get a mask on her and WellStar was expecting her.
At first, Truitt said health officials were still reluctant to test her but did learn she had pneumonia. However, Truitt said because the public health department was involved, the hospital was mandated to test her.
After her test, she was isolated to the intensive care unit and eventually moved to another wing of the hospital for patients under investigation, or PUIs. It would be another week before she learned of the test results.
She was in the hospital from that Saturday night until Thursday, March 19.
“I don’t think I knew how sick I was,” Truitt said. “I guess you can get to that point where exhaustion takes over. There were days that all I would do is sleep. People were bringing me food, but even eating was so exhausting at that point.”
While waiting for results, she thought there was a 50 percent chance it was COVID-19, but the results weren’t going to have an impact on her except for the fact she needed to notify her family. And, by the time she got the results, she said most of her family would have been in isolation for 14 days.
Truitt said that while in the hospital, she probably slept 18 to 20 hours a day.
One of the parts of Truitt’s story that scares her the most was that she doesn’t know when she would have been sick enough to take herself to the doctor if it wasn’t for hitting her eye.
“I just don’t know if I would have taken myself to the doctor,” she said.
Going home
Truitt was sent home from the hospital on March 19 without knowing her test results. She had implicit instructions to stay at home for 14 days, regardless of the test results.
By March 19, there more than 15,000 confirmed cases in the U.S., 287 cases in Georgia with 10 deaths, and two confirmed cases in Troup County.
Truitt said she was one of the first patients released from the hospital wing dedicated to PIUs at WellStar. When she went home, she continued to sleep most of the time.
While home, she said the exhaustion of the illness continued to be the worst part. She said she couldn’t go to the restroom or get a drink of water out of the kitchen without being completely worn out.
“I can’t describe how overwhelming the exhaustion was,” she said. “That is what has taken me the longest to get over, which in some ways is good because I needed to rest.”
Guilt-ridden
Truitt got her test results on Saturday, March 21, confirming she had COVID-19.
By that Saturday, she would have been the fourth confirmed case in Troup County.
She said the primary reaction to the news was thinking about all the people she interacted with before going to the doctor, and ultimately, into isolation.
“I was very guilt-ridden,” Truitt said.
She said her three-month-old and 18-month-old grandchildren were with her for a whole weekend. She went to her son’s talent show at school. She went to church, saw her sister and mother-in-law. She went to dinner with her best friend, who has Parkinson’s disease.
All those interactions went flooding into her head, especially her mother-in-law, who is older, and has heart problems and asthma. Luckily, Truitt said she isn’t experiencing any symptoms.
“I cried for like six hours that night,” Truitt said. “I was so emotionally exhausted. Because the news didn’t impact me, I was actually healing, but I felt like I had just gone out and contaminated all these people.”
Little victories
Since she’s been home, Truitt said the recovery has been a rollercoaster, similar to how she felt when she was first sick. She said this past Tuesday, she woke up with a fever and feared the virus was back, and she would re-experience everything she thought she had just been through.
“I was up most of that night running a low-grade fever and had the chills,” Truitt said. “I’m not going to lie, I was scared and had a little bit of a panic attack because I was like I can’t go back to feeling like that again.”
However, she has had other days where she has gotten up to make breakfast, which felt like a win. Even though, afterward, she is worn out. She said unloading the dishwasher sometimes requires breaks, but it can still be done.
Truitt now sets goals for herself, like walking around her home several times until she gets tired. Earlier this week, she went for a drive for the first time in two weeks. She didn’t go very far, and never got out of the car, but said it was an adventure for her.
Following her doctor’s advice, she’s in isolation until Thursday, April 2.
Once isolation is over, she’s looking forward to seeing her family again, including her church and school family.
“I usually have my granddaughter and grandson every weekend,” Truitt said. “When this is over, I will have gone an entire month without seeing them. I have never gone that long in their lives without seeing them.”
Truitt lives on her own, which has self-admittedly made this situation harder, but she has talked to family members every day through video chat on the computer or through phone calls and text messages.
“Even my grumpy teenage son has talked to me on the phone,” Truitt joked.
She also appreciates the care she received through WellStar.
“All the nurses were phenomenal,” Truitt said. “If I needed something, they were there as soon as they could be.”
She said the nurses had a running joke that as long as Truitt had orange juice, she would be happy.
Truitt praised the care she received from Dr. Melhim Bou Alwan, medical director of the WellStar Hospitalist Program, who was one the only doctors she talked to face to face. Bou Alwan also called her to check up on her wellbeing since her release.
Truitt has also interacted with Dr. Kenneth Horlander, pulmonology physician with Emory, over the phone.
“They have all been stellar,” she said. “I can’t say enough good things about them.”
‘Just stay home’
Truitt’s biggest takeaway from this ordeal is that people just don’t know enough about this virus to make their own determination. She said the symptoms reported in the media are changing seemingly day-by-day.
“I had no clue how I got this,” she said. “I realize people need to have necessities, but if you don’t need to leave your house, please just stay home.”
Truitt said this was one of her worst experiences, and it’s not worth taking the chance to spread the virus.
“I’ve had the flu, I’ve given birth to children, but this is worse than anything I have encountered in my life,” Truitt said. “I wish I could find a way to put into words that level of inability to care that you’re hungry, and it just doesn’t really matter because you’re not going to do a thing about it because that would mean getting up.”
As of Monday, there were more than 140,000 COVID-19 cases in the U.S., with 2,405 deaths. More than 5,000 people have recovered. In Georgia, the department of public health has reported 2,809 confirmed cases with 87 deaths. In Troup County, there are 11 reported cases and one death, a 61-year-old woman with an underlying health concern. |
---
abstract: 'For the general obstacle problem, we prove by direct methods an epiperimetric inequality at regular and singular points, thus answering a question of Weiss (Invent. Math., 138 (1999), 23–50). In particular at singular points we introduce a new tool, which we call logarithmic epiperimetric inequality, which yields an explicit logarithmic modulus of continuity on the $C^1$ regularity of the singular set, thus improving previous results of Caffarelli and Monneau [@Caff3; @Caff_rev; @Monneau].'
address:
- 'Maria Colombo: Institute for Theoretical Studies, ETH Zürich, Clausiusstrasse 47, CH-8092 Zürich, Switzerland '
- 'Luca Spolaor: Massachusetts Institute of Technology (MIT), 77 Massachusetts Avenue, Cambridge MA 02139, USA'
- 'Bozhidar Velichkov: Laboratoire Jean Kuntzmann (LJK), Université Grenoble Alpes Bâtiment IMAG, 700 Avenue Centrale, 38401 Saint-Martin-d’Hères'
author:
- 'Maria Colombo, Luca Spolaor, Bozhidar Velichkov'
bibliography:
- 'references-Cal.bib'
---
**Keywords:** epiperimetric inequality, monotonicity formula, obstacle problem, free boundary, singular points
Introduction
============
In this paper we study the regularity of the free-boundary of nonnegative local minimizers $u$ of the functional $$\mathcal E(u):=\int |\nabla u|^2\,dx+\int \max\{u(x),0\}\,dx\,.$$ Our main result is a logarithmic epiperimetric inequality, which is a new tool for the study of the singular set of minimizers of variational energies. It is also an alternative approach to the regularity of the singular free boundary as proposed by Caffarelli [@Caff3; @Caff_rev]. Before we state it we recall that, given $u\in H^1(B_1)$, the *Weiss’ boundary adjusted energy of $u$* is defined by $$W(u)=\int_{B_1}|\nabla u|^2\,dx-2\int_{\partial B_1}u^2\,d\HH^{d-1}+\int_{B_1}\max\{u(x),0\}\,dx\,.$$ The class $\KK$ of admissible blow-ups of $u$ at singular points is defined by $$\label{defn:K}
\KK:=\{Q_A \colon \R^d \to \R \,:\, Q_A(x) = x \cdot Ax,\,\text{ $A$ symmetric non-negative with }{\rm{tr}} A = \sfrac14\}\,.$$ [The energy $W$ is constant on $\KK$, precisely we have $ W(Q_A)=\frac{\omega_d}{8\, d (d+2)}$, for every $Q_A\in \KK$. We refer to this constant as to the *energy density at the singular points* and denote it by $\Theta$.]{}
\[t:epi:B\] There are dimensional constants $\delta>0$ and $\eps>0$ such that the following claim holds. For every non-negative function $c\in H^1(\partial B_1)$, with $2$-homogeneous extension $z$ on $B_1$, satisfying $$\text{dist}_{L^2(\partial B_1)}\left(c,\KK\right)\le \delta\qquad\text{and}\qquad 0\le W(z)-\Theta\le 1,$$ [there is a non-negative function $h\in H^1(B_1)$ with $h=c$ on $\partial B_1$ satisfying the inequality ]{} $$\label{e:epi_flat_point_sing}
W(h)\le W(z)-\eps\big(W(z)-\Theta\big)^{1+\gamma}\,,\qquad \mbox{where}\quad
\begin{cases}
\gamma=0 & \mbox{if }d=2\\
\gamma=\frac{d-1}{d+3} & \mbox{if }d\geq3
\end{cases}.$$
At flat points we recover the Weiss’ epiperimetric inequality with a direct proof. To state it, recall that the collection $\KK_+$ of possible blow-ups at flat points is defined by $$\label{defn:K+}
\KK_+:=\left\{q_\nu\colon \R^d\to \R\,:\,q_\nu(x)=(\max\{x\cdot\nu,0\})^2\mbox{ for some } \nu\in\R^d\text{ such that } |\nu|=\frac12\right\}.$$ [The energy $W$ is constant on $\KK_+$, precisely we have $ W(q_\nu)=\frac{\omega_d}{16\, d (d+2)}$, for every $q_\nu\in \KK_+$. We will refer to this constant as the *energy density at the flat points* and denote it by $\Theta_+$.]{}
\[t:epi:A\] There are dimensional constants $\delta_0>0$, $\delta>0$ and $\eps>0$ such that the following claim holds. For every non-negative function $c\in H^1(\partial B_1)$ satisfying $$\{x_d<-\delta_0\}\subset\{c=0\} \quad \mbox{and}\quad \|c-q_{e_d}\|_{L^2(\partial B_1)}\le \delta\,,$$ there exists a non-negative function $h\in H^1(B_1)$ such that $h=c$ on $\partial B_1$ and $$\label{e:epi_flat_point}
W(h)-\Theta_{+}\le (1-\eps)\big(W(z)-\Theta_{+}\big)\,,$$ where $z$ is the $2$-homogeneous extension of $c$ to $B_1$.
Theorem \[t:epi:A\] was already proved by Weiss in [@Weiss2] using a very elegant and innovative contradiction argument, later exploited also by Garofalo-Petrosyan-Garcia and Focardi-Spadaro in the context of the thin obstacle problem (see [@GaPeVe; @FoSp]). [ However, the same proof works only at singular points of maximal and minimal dimension under some special assumptions on the projection of the trace on $\KK$, which can be verified only in dimension $d=2$. Notice that the dimension of a singular point is the maximal $\dim(\ker A)$ among all $Q_A\in \KK$ blow-ups of $u$ at the singular point. Hence, no epiperimetric inequality was known in the literature for the whole singular set, as it happens in Theorem \[t:epi:B\]]{} and Weiss himself suggests that “...it should however be possible to give a direct proof of the epiperimetric inequality which would then also cover singular sets of intermediate dimension” (see [@Weiss2]). Theorems \[t:epi:B\] and \[t:epi:A\] answer affirmatively to this question, and in particular Theorem \[t:epi:B\] is the first instance in the literature of an epiperimetric inequality of logarithmic type and the first instance in which the epiperimetric inequality for singular points has a direct proof. The methods developed to prove the epiperimetric inequality at singular points of any stratum have a quite general nature and will be applied to provide similar results in other problems, for instance in the case of the thin obstacle problem [@CSVthin].
The proof of these theorems is direct (i.e. we produce explicit competitors) and it is remarkable in our opinion how the failure of Weiss’ contradiction argument translates into a weakening of the epiperimetric inequality, that is the necessity of introducing the exponent $\gamma$ in . To explain this better, notice that, in analogy with Reifenberg and White’s pioneering work (see [@Reif2; @Wh]) and similarly to previous work of the last two authors (see [@SpVe]), the key ingredients are
- a Fourier decomposition of the trace $c-q_\nu$ (resp. $c-Q_A$) onto the eigenfunctions of $\mathbb{S}^{d-1}$;
- an energy improvement with respect to $z$ obtained by taking the harmonic extension of the modes with homogeneity larger than two;
- a choice of $\nu$ (resp. $A$) to control the projection of $c-q_\nu$ (resp. $c-Q_A$) onto the eigenfunctions of homogeneity one and two, with the projection on the higher modes.
At flat points and at every point in dimension $d=2$, the estimate of the third bullet is linear, however in general dimension at singular points we can only prove a control of the form $$\|P (c-Q_A)\|_{H^1({\partial}B_1)}\le C\|(Id-P)(c-Q_A)\|_{H^1(\partial B_1)}^{1-\gamma}\qquad \gamma\in(0,1)\,,$$ where $P$ denotes the projection on the modes relative to homogeneity two (see ). The reason for this different behavior is essentially the following: [at the flat points we are able to eliminate the lower modes (the modes corresponding to homogeneity smaller than two) on a spherical cap by means of the choice of the vector $\nu$; this is possible since the space of admissible functions $q_\nu$ is an open manifold of the same dimension as the eigenspace corresponding to the lower modes, so we can apply an implicit function argument (see Lemma \[l:inversa\]).]{} At general singular points, we would like to eliminate the modes of homogeneity two, that is the modes corresponding to the eigenvalue $2d$ on the sphere and whose eigenspace can be identified with the space of $d\times d$ real symmetric matrices $S_d(\R)$. However, the positivity constraint on the competitor forces the choice of the matrix $A$ to be in the space of nonnegative symmetric matrices $S_d^+(\R)$. Now these two spaces have the same dimension, but, due to the non-negativity assumption, the set $S_d^+(\R)\subset S_d(\R)$ is not open, so we cannot apply the implicit function theorem here. Indeed, if we are in its interior, which corresponds to the singular points studied by Weiss, then the argument works and we can eliminate the second modes; but at the boundary of $S_d^+(\R)$ an implicit function argument only provides us with a matrix in the larger space $S_d(\R)$. This leaves us to estimate the difference between the element of $S_d(\R)$, corresponding to the second modes of the trace $c$, and its projection on $S_d^+(\R)$. We can do this by means of the additional condition that $c$ is positive, which suggests that this difference should be comparable to the higher modes of the trace, but because of capacitary reasons the bound comes with an exponent $\gamma\neq 0$. Roughly speaking, if the negative part produced by the second modes is very small, concentrated on a set of small capacity, then it can be compensated by a function with very small energy, much smaller than the distance to $S_d^+(\R)$ in the space of symmetric matrices. In particular, it seems that this obstruction is of the same nature as the one that appears in [@Weiss2], where the strong convergence of the traces cannot *see* the nodal sets of small capacity. A similar phenomenon can be found in the theory of minimal surfaces. Indeed if we think about the collection of singular points of lower dimension as a minimal surface in codimension higher than one, then it is known the existence of non-integrable cones, that is cones with non-integrable Jacobi fields. In this case the best possible rate of convergence to the blow-up is indeed logarithmic, as shown in [@AdSi].
We should remark that an estimate of the form is essentially the best one can get by using only the positivity of the trace $c$ (see Example \[esempio\]). It follows that Theorem \[t:epi:B\] is essentially optimal, as it concerns positive traces on the sphere. However it is conceivable that for solutions of the obstacle problem a better inequality could be obtained, by using more properties of the minimizers. It is well known that Theorem \[t:epi:A\] leads to the uniqueness of the blow-up at every flat point and also to the $C^{1,\alpha}$ regularity of the regular part of the free-boundary (see [@Weiss2]). We show that Theorem \[t:epi:B\] yields the uniqueness of the blow-up and the $C^{1}$ regularity of the singular set, with an explicit logarithmic modulus of continuity. This is an improvement on the results of Caffarelli and Monneau, where such a modulus arises by contradiction arguments and is therefore not explicit (see [@Caff3; @Monneau]). The method of the present paper is flexible enough to cover more general and nonlinear functionals, such as the area. The stratification of the singular set for the area functional, even in the context of Riemannian manifolds, and the $C^1$ regularity of the strata were recently obtained in [@FoGeSp; @FoGelliSp]. Before giving the precise statements, we need some additional definitions. We split the free-boundary of a minimizer $u$ in *regular* and *singular* part, defined as $$\begin{gathered}
{\rm Reg}(u):= \{ x\in \partial \{ u>0\} \cap \Omega: \mbox{ any blow up at $x$ is of the form } q_\nu\in \KK_+ \} \notag\\
{\rm Sing}(u):=\{ x\in \partial \{ u>0\} \cap \Omega: \mbox{ at least one blow up at $x$ is {\bf{not}} of the form } q_\nu\in \KK_+ \}\notag\end{gathered}$$ Their regularity is the content of the following results.
\[t:uniq\] Let $ \gamma= \frac{d-1}{d+3}$, $\Omega\subset\R^d$ be an open set and $u\in H^1(\Omega)$ a minimizer of $\mathcal E$. Then the blow up of $u$ at each point of the free boundary $\partial \{ u>0\} \cap \Omega$ is unique. Moreover, the following convergence holds.
1. For every $x_0\in {{\rm Reg}}(u) \cap \Omega$ there exist $r:= r(x_0)$, $C:= C(x_0)$ and $\nu({x_0}) \in \R^d$, with $|\nu(x_0)|=\sfrac12$, such that $$\int_{\partial B_1} \left| u_{x_1,r} - q_{\nu(x_1)} \right| \, d\HH^{n-1} \leq C r^{\frac{(n+2) \eps}{2(1-\eps)}}\,, \quad \mbox{for every}\quad r \leq r_0 \mbox{ and } x_1\in {{\rm Reg}}(u) \cap B_r(x_0).$$
2. For every $x_0 \in {{\rm Sing}}(u)$, there exist $r:= r(x_0)$, $C:= C(x_0)$ and $Q_{x_0} \in \KK$ such that $$\label{eqn:log-uniq}
\int_{\partial B_1} \left| u_{x_0,r} - Q_{x_0}\right| \, d\HH^{n-1} \leq C (\log r )^{-\frac{1-\gamma}{2\gamma}} \,,\quad \mbox{for every}\quad r \leq r_0.$$
The next regularity result recovers all the previously known results and improves the regularity of the singular set to $C^{1,\log}$. Before stating it we need to make precise what we mean by singular points of intermediate dimension. Given $k=0,\dots,d-1$, we define the *singular set of dimension $k$* (also called $k$-th stratum) $S_k(u)$ as $$\begin{aligned}
S_k(u)
&:=\{x\in {{\rm Sing}}(u)\,:\,\dim(\ker(A))\leq k\,\mbox{ for every blow-up }\,Q_A\in \KK\,\mbox{ of $u$ at $x$}\}\\
&=\bigcup_{l=1}^k\{x\in {{\rm Sing}}(u)\,:\,\dim(\ker(A))= l\,\mbox{ for \emph{the unique} blow-up }\,Q_A\in \KK\,\mbox{ of $u$ at $x$}\}\,,\end{aligned}$$ where the equivalence of the two definitions is guaranteed by Theorem \[t:uniq\]. In the case of the stratum $S_0(u)$ the inequality can be improved to $C^{1,\beta}$ convergence.
\[t:reg\] Let $\eps>0$ be the constant from Theorem \[t:epi:A\], $\beta =\frac{(d+2) \eps}{2(1-\eps)} \big( 1+ \frac{(d+2) \eps}{2(1-\eps)}\big)^{-1}$, $\Omega\subset\R^d$ be an open set and $u\in H^1(\Omega)$ a minimizer of $\mathcal E$. Then
1. ${{\rm Reg}}(u)$ is locally the graph of a $C^{1,\beta}$ function; namely, for every $x_0\in {{\rm Reg}}(u) \cap \Omega$ there exists $r:= r(x_0)$ such that ${{\rm Reg}}(u) \cap B_{r}(x_0)$ is a $C^{1,\beta}$- submanifold of dimension $(d-1)$;
2. For every $k=0,..., d-1$, $S_k(u)$ is contained in the union of countably many submanifolds of dimension $k$ and class $C^{1, log}$; namely for every $x_0\in {{\rm Sing}}(u) \cap \Omega$ there exists $r_0:= r_0(x_0)$ and $C:= C(x_0)$ such that a logarithmic estimate holds $$\label{eqn:log-cont-fb_intro}
|Q(x_1) - Q(x_2)| \leq C (\log |x_1-x_2|)^{-\frac{1-\gamma}{2\gamma}} \qquad \mbox{for any } x_1,x_2 \in S_k \cap B_r(x_0).$$
3. If the dimension $d=2$, then we have the estimate $$\label{eqn:log-cont-fb_intro_d2}
|Q(x_1) - Q(x_2)| \leq C |x_1-x_2|^\beta \qquad \mbox{for any } x_1,x_2 \in S_k \cap B_r(x_0)\,,$$ for $k=1,2$, where $\beta$ is the same as in (1). In particular $S_0$ consists of isolated points and $S_1$ is contained in the union of at most countably many curves of class $C^{1, \beta}$.
Thanks to a result of Caffarelli and Riviére (see [@CaRe]) it is possible to improve (3) to the following result: the boundary of a connected component of the interior of the free-boundary is analytic except at finitely many singular points.
Theorems \[t:uniq\] and \[t:reg\] remain true if we consider a Hölder continuous weight function $q:\Omega\to\R^+$ and more general functionals, for instance $$\mathcal{E}_q(u):=\int_\Omega \left[|\nabla u|^2+q(x) |u| \right]\,dx, \qquad \mathcal{A}_q(u):=\int_\Omega \left[\sqrt{|\nabla u|^2+1} +q(x) |u| \right]\,dx.$$ In this case, the regular and singular parts at a given point $x$ are defined as for $\mathcal E$, up to a constant which depends on $q(x)$. Given $u\in H^1(B_1)$ positive minimizer of $\mathcal E$, we define $$\begin{split}
{\rm Reg}_q(u)&:= \Big\{ x\in \partial \{ u>0\} \cap \Omega: \mbox{ any blow up at $x$ is of the form } q_\nu \mbox{ for } |\nu|=\frac{q(x)}2\Big\} ,
\end{split}$$ $$\begin{split}
{\rm Sing}_q(u)&:= \Big\{ x\in \partial \{ u>0\} \cap \Omega: \mbox{ at least one blow up at $x$ is {\bf{not}} of the form } q_\nu, \mbox{ for } |\nu|=\frac{q(x)}2 \Big\} ,
\end{split}$$ $$S_{q,k}(u)
:=\{x\in {{\rm Sing}}_q(u)\,:\,\dim(\ker(A))\leq k\,\mbox{ for every blow-up }\,Q_A\in \KK\,\mbox{ of $u$ at $x$}\}.$$
\[c:Q\_funct\] Let $\alpha>0$, $\Omega\subset\R^d$ be an open set and $q\in C^{0,\alpha}(\Omega;\R^+)$ be an Hölder continuous function such that $q\ge c_q>0$, where $c_q$ is a given constant. Let $u\in H^1(\Omega)$ be a minimizer of $\mathcal E_q$ or $\mathcal A_q$. Then the blow up of $u$ at each point of the free boundary $\partial \{ u>0\} \cap \Omega$ is unique and
1. there exists $\beta>0$ such that ${{\rm Reg}}_q(u)$ is locally the graph of a $C^{1,\beta}$ function;
2. For every $k=0,..., d-1$, $S_{q,k}(u)$ is contained in the union of countably many submanifolds of dimension $k$ and class $C^{1, log}$; namely for every $x_0\in {{\rm Sing}}_q(u) \cap \Omega$ there exists $r_0:= r_0(x_0)$ and $C:= C(x_0)$ such that a logarithmic estimate holds $$\label{eqn:log-cont-fb}
|Q(x_1) - Q(x_2)| \leq C (\log |x_1-x_2|)^{-\frac{1-\gamma}{2\gamma}} \qquad \mbox{for any } x_1,x_2 \in {{\rm Sing}}_q(u) \cap B_r(x_0).$$
Compared to a similar result obtained from the epiperimetric inequality with indirect proof, here we have quantitative estimates as and, for the regular set, an explicit Hölder regularity in terms of the dimension and the Hölder exponent of $q$.
Organization of the paper {#organization-of-the-paper .unnumbered}
-------------------------
The paper is divided in four short sections. In Section \[s:preliminari\] we fix notations and easy preliminary computations. In Section \[s:flat\] we prove the Weiss epiperimetric inequality Theorem \[t:epi:A\], while Section \[s:sing\] is dedicated to Theorem \[t:epi:B\]. Finally, in Section \[s:regularity\] we apply these two theorems to deduce the various regularity results.
Preliminaries {#s:preliminari}
=============
In this section we fix some notations and we recall some known facts about the solutions of the obstacle problem, their blow-up limits, the decomposition of the free boundary in a regular and singular part and its realtion with the Weiss boundary adjusted functional. The final subsection is dedicated to the Fourier analysis on the unit sphere in $\R^d$, which will be useful for both Theorems \[t:epi:B\] and \[t:epi:A\].
Notations
---------
We will use the following notations. $B_1$ is the $d$-dimensional unit ball centered in zero and $\omega_d=|B_1|$ is the Lebesgue measure of $B_1$. We denote by $\mathbb{S}^{d-1}$ or $\partial B_1$ the unit $(d-1)$-dimensional sphere in $\R^d$ equipped with the $(d-1)$-dimensional Hausdorff measure $\HH^{d-1}$. $\theta$ will denote the variable on the sphere $\partial B_1$. For an open set $\Omega$ in $\R^d$ or on the sphere $\mathbb{S}^{d-1}$ we will denote by $H^1(\Omega)\subset L^2(\Omega)$ the Sobolev space of weakly differentiable functions on $\Omega$ with gradients in $L^2(\Omega;\R^d)$ and by $H^1_0(\Omega)$ the space of functions $H^1(\Omega)$ which are zero on $\partial\Omega$.
For a function $f:\R^d\to\R$ we denote by $f_+$ its positive part, $f_+(x)=\max\{f(x),0\}$. For instance, given a vector $\nu\in\R^d$ we will often use the notations $$(x\cdot\nu)_+=\max\{x\cdot\nu,0\}\qquad\text{and}\qquad (x\cdot\nu)_+^2=\big(\max\{x\cdot\nu,0\}\big)^2,$$ where $x\cdot\nu$ is the scalar product of the vectors $x$ and $\nu$ in $\R^d$.
Weiss boundary adjusted energy
------------------------------
For a function $u\in H^1(\Omega)$, with $\Omega\subset \R^d$, we denote by $W$, $W_0$ and $\W$ the functionals $$\begin{gathered}
W_0(u,x_0,r):= \frac1{r^{d+2}} \int_{B_r(x_0)}|\nabla u|^2\,dx-\frac2{r^{d+3}}\int_{\partial B_r(x_0)}u^2\,d\HH^{d-1} \,,\notag\\
\W(u,x_0,r):=W_0(u,x_0,r)+\frac1{r^{d+2}}\int_{B_r(x_0)}u(x)\,dx,\notag\\
W(u,x_0,r):=W_0(u,x_0,r)+\frac1{r^{d+2}}\int_{B_r(x_0)}\max\{u(x),0\}\,dx,\notag\end{gathered}$$ where $x_0\in {\partial}\{u>0\}$ and $0<r<{{\rm {dist}}}(x_0,{\partial}\Omega)$, and we notice that for non-negative functions $u\in H^1(B_1)$ we have $\W(u,x_0,r)=W(u,x_0,r)$. In particular, we set $$W(u,0,r)=W(u,r)\qquad\text{and}\qquad W(u,1)=W(u),$$ and we recall the scaling property $$W(u,x_0,r)=W(u_{r,x_0})\,,\quad\text{where}\quad u_{r,x_0}(x)=\frac{u(rx+x_0)}{r^2}.$$
For any $u\in H^1(\Omega)$ the following identity holds for $x_0\in {\partial}\{u>0\}$ and $0<r<{{\rm {dist}}}(x_0,{\partial}\Omega)$ $$\label{e:Weiss_monotonicity}
\frac{d}{dr}W(u,x_0, r)=\frac{d+2}{r} \big[W(z_{r,x_0},1)-W(u_{r,x_0},1)\big]+\frac{1}{r}\int_{\partial B_1}|x\cdot \nabla u_{r,x_0}-2u_{r,x_0}|^2\,d\HH^{d-1}\,,$$ where $ z_{r,x_0}(x):=|x|^2\,u_{r,x_0}\big(\frac{x}{|x|}\big)$ (see for instance [@Weiss2]).
Global homogeneous solutions of the obstacle problem {#sub:Theta}
----------------------------------------------------
Wa say that the function $u_0:\R^d\to\R$ is a blow-up limit of $u$ in the point $x_0$, if $$u_0=\lim_{n\to\infty}u_{r_n,x_0}\qquad\text{for some sequence $(r_n)_n$ with} \, \lim_{n\to\infty}r_n=0,$$ where the converegnce is locally uniform and strong in $H^1_{loc}(\R^d)$. Thanks to work of Caffarelli (see [@Caff_rev]), it is well known that $u_0$ is a global homogeneous solution of the obstacle problem. Precisely, $u_0\in \KK\cup\KK_+$ (introduced in and ). Moreover, we claim that $$\label{e:WThetaK}
W(Q)=\frac{\omega_d}{8\, d (d+2)}=:\Theta\ \text{for every}\ Q\in\KK\,,\quad\text{and}\quad W(q)=\frac{\omega_d}{16\, d (d+2)}=:\Theta_+\ \text{for every}\ q\in\KK_+.$$ Indeed, for every $Q_A\in \KK$ we have $\Delta Q_A=2\,\text{tr} A=\frac12$ and so an integration by parts gives $$W_0(Q_A)=\int_{B_1}|\nabla Q_A|^2-2\int_{\partial B_1}Q_A^2=-\int_{B_1}Q_A\Delta Q_A=-\frac12\int_{B_1}Q_A.$$ Since $Q_A$ is positive and denoting $(a_{ij})_{ij}$ the coefficients of the matrix $A$, we get $$W(Q_A)=\W(Q_A)=W_0(Q_A)+\int_{B_1}Q_A=\frac12\int_{B_1}Q_A=\frac12\int_{B_1}\sum_{i=1}^d a_{ii} x_i^2\,dx =\frac{\text{tr}A}2\int_{B_1}x_d^2\,dx =\Theta.$$ Analogously, for any $q_\nu\in \KK_+$ we have $\Delta q_\nu=2\,|\nu|^2=\frac12$ on the set $\{x\cdot\nu>0\}$, so that $$W(q_\nu)=\W(q_\nu)=W_0(q_\nu)+\int_{B_1}q_\nu=\frac12\int_{B_1}q_\nu
=\frac{|\nu|^2}2\int_{B_1\cap\{x_d>0\}}x_d^2\,dx =\frac{\omega_d}{16\, d (d+2)}=\Theta_+.$$
Regular and singular free boundaries
------------------------------------
We recall that, as observed by Weiss [@Weiss1], a consequence of is that if $u\in H^1(\Omega)$ is a nonnegative minimizer of $\mathcal{E}$ in the open set $\Omega\subset\R^d$ and $x_0\in\Omega$, then the function $r \mapsto W(u,x_0,r)$ is nondecreasing (in its domain of definition $0<r<\text{dist}(x_0,\partial\Omega)$) and there exists the limit $$\label{e:Theta_u}
\Theta_u(x_0):=\lim_{r\to 0}W(u,x_0,r)=\inf_{r>0}W(u,x_0,r)=\lim_{r\to 0}W(u_{r,x_0})\,.$$ Moreover, if $q$ is a blow-up limit of the minimizer $u$ in $x_0$, then $$W(q)=\lim_{n\to\infty}W(u_{r_n,x_0})=\Theta_u(x_0).$$ Since we have that $q\in\KK\cup\KK_+$, there are only two possible values for the energy density $\Theta_u(x_0)$: $$\Theta_u(x_0)=\Theta_+\qquad\text{or}\qquad \Theta_u(x_0)=\Theta.$$ Hence we can redefine the regular and the singular part of the free boundary $\partial\{u>0\}\cap\Omega$ as $$\begin{split}
{\rm Reg}(u)= \{ x\in \partial \{ u>0\} \cap \Omega: \Theta_u(x) = \Theta_+\},
\end{split}$$ $$\begin{split}
{\rm Sing}(u)=\{ x\in \partial \{ u>0\} \cap \Omega: \Theta_u(x) =\Theta\}.
\end{split}$$ By definition the free boundary $\partial \{ u>0\} \cap \Omega$ is a disjoint union of ${\rm Reg}(u)$ and ${\rm Sing}(u)$. Moreover, by the definition of the density and the fact that $x_0\mapsto W(u,x_0,r)$ is continuous, the function $x_0\mapsto \Theta_u(x_0)$ is upper semicontinuous. This, together with and the fact that all the blow-up limits are in $\KK\cup\KK_+$, finally gives the following characterization of ${\rm Reg}(u)$ and ${\rm Sing}(u)$:
- the set ${\rm Reg}(u)$ is a relatively open subset of the free boundary $\partial \{ u>0\}$, and every blow-up limit at a point of ${\rm Reg}(u)$ is of the form $q_\nu$, for some $q_\nu\in\KK_+$;
- the set ${\rm Sing}(u)$ is closed, and every blow-up limit at a point of ${\rm Sing}(u)$ is of the form $Q_A$, for some $Q_A\in\KK$.
Eigenvalues and eigenfunctions on subdomains of the sphere {#sub:spectrum}
----------------------------------------------------------
Let $S\subseteq \mathbb{S}^{d-1}$ be an open set. Let $0<\lambda_1\le \lambda_2\le \dots\le\lambda_j\le \dots$ be the eigenvalues (counted with multiplicity) of the spherical Laplace-Beltrami operator with Dirichlet conditions on $\partial S$ and $\{\phi_j\}_{j\ge1}$ be the corresponding eigenfunctions, that is the solutions of the problem $$\label{defn:eigenval-in-s}
-\Delta_{\mathbb S^{d-1}} \phi_j=\lambda_j\phi_j\quad\text{in}\quad S,\qquad \phi_j=0\quad\text{on}\quad \partial S,\qquad \int_S\phi_j^2(\theta)\,d\HH^{d-1}(\theta)=1.$$ Any function $\psi \in H_0^1(S)$ can be decomposed as $ \psi(\theta)=\sum_{j=1}^{\infty}c_j\phi_j(\theta)$. The following lemma compares the energies of $2$-homogeneous and $\alpha$-homogeneous functions by means of the Fourier decomposition of their common values on $\partial B_1$.
\[l:fourier\] Let $\psi\in H_0^1(S)$ and consider the $2$-homogeneous extension $\varphi (r,\theta)=r^2\psi(\theta)$ and the $\alpha$-homogeneous extension $\tilde \varphi (r,\theta)=r^\alpha\psi(\theta)$ respectively of $\psi$ to $B_1$, for some $\alpha>2$. Set $$\label{eps_choice}
\eps_\alpha:=\frac{\alpha-2}{d+\alpha}\qquad\text{and}\qquad \lambda_\alpha:=\alpha(\alpha+d-2)\,.$$ Then the following inequality holds $$\label{e:W_0}
W_0(\tilde\varphi)-(1-\eps_\alpha)W_0(\varphi)= \frac{\eps_\alpha}{d+2\alpha-2}\sum_{j=1}^\infty (-\lambda_j+\lambda_\alpha) c_j^2\,.$$
Since $\| \varphi_j\|_{L^2(\partial B_1)} =1$ and $\|\nabla_{\theta} \varphi_j\|_{L^2(\partial B_1)} =\lambda_j$ for every $j \in \{0\} \cup \N$, the energy of the $\alpha$-homogeneous function $\tilde\varphi(r,\theta)=r^\alpha \psi(\theta)$ can be written as $$\begin{aligned}
W_0(\tilde \varphi)&= \sum_{j=1}^\infty c_j^2\left(\int_0^1 r^{d-1}\,dr\int_S\,d\HH^{d-1} \left[\alpha^2r^{2\alpha-2}\phi_j^2+r^{2\alpha-2}|\nabla_\theta\phi_j|^2\right]-2\int_S \phi_j^2\,d\HH^{d-1}\right)\\
&= \sum_{j=1}^\infty c_j^2\left(\frac{\alpha^2+\lambda_j}{d+2\alpha-2}-2\right).
\end{aligned}$$ When $\alpha=2$ and $\varphi(r,\theta)=r^2 \psi(\theta)$, we get $$W_0(\varphi)=\sum_{j=1}^\infty c_j^2\left(\frac{4+\lambda_j}{d+2}-2\right).$$ We now notice that for every $\lambda$ we have $$\Big(\frac{\alpha^2+\lambda}{d+2\alpha-2}-2\Big)-(1-\eps_\alpha)\Big(\frac{4+\lambda}{d+2}-2\Big)=\frac{\lambda(2-\alpha)}{(d+\alpha)(d+2\alpha-2)}+\frac{(\alpha-2)\alpha (\alpha+d-2)}{(d+\alpha)(d+2\alpha-2)},$$ which concludes the proof of Lemma \[l:fourier\].
The above lemma, in particular, shows that if the decomosition of $\psi$ involves only eigenfunctions corresponding to eigenvalues $\lambda_j\ge\lambda_\alpha$, then the $\alpha$-homogeneous extension $\tilde\varphi$ has a strictly lower energy than the two-homogeneous extension $\varphi$. In order to choose appropriately $\alpha$ we will need some additional information on the spectrum of the Laplacian on $S$. We recall that the function $\phi_j:S\to\R$ is a solution of the first equation in if and only if its $\alpha_j$-homogeneous extension $\varphi_j(r,\theta)=r^{\alpha_j}\phi_j(\theta)$ is harmonic in the cone $\{(r,\theta)\in \R^+\times\partial B_1\ :\ \theta\in S\},$ where the homogeneity $\alpha_j$ is uniquely determined by the identity $\lambda_j=\alpha_j(\alpha_j+d-2).$
[**The spectrum on the sphere $\mathbb{S}^{d-1}$.**]{} By the fact that the homogeneous harmonic functions in $\R^d$ are necessarily polynomials, we have that:
- $\lambda_1=0$ and the corresponding eigenfunction is the constant $\phi_1=|\partial B_1|^{-1/2}= (d\omega_d)^{-1/2}$.
- $\lambda_2=\dots=\lambda_{d+1}=d-1$, the corresponding homogeneity constants are $\alpha_2=\dots=\alpha_{d+1}=1$ and the corresponding eigenspace coincides with the space of linear functions in $\R^d$.
- $\lambda_{d+2}=\dots=\lambda_{d(d+3)/2}=2d$, the corresponding homogeneity constants are $\alpha_{d+2}=\dots=\alpha_{d(d+3)/2}=2$. The corresponding eigenspace has dimension $d(d-1)/2$ and is generated by the (restrictions to $\mathbb{S}^{d-1}$ of the) two-homogeneous harmonic polynomials: $$E_{2d}=\{Q_A \colon \R^d \to \R \,:\, Q_A(x) = x \cdot Ax,\,\text{ $A$ symmetric with }{\rm{tr}} A = 0\}.$$
- If $j> d(d+3)/2$ (that is $\lambda_j>2d$), then $\lambda_j\ge 3(3+d-2)=3(d+1)$.
[**The spectrum on the half-sphere $\partial B_1^+=\{x_d>0\}\cap \partial B_1$.**]{} We notice that the odd extension (with respect to the plane $\{x_d=0\}$) of any eigenfunction $\phi_j$ on the half-sphere $\partial B_1^+$ is an eigenfunction on the entire sphere $\partial B_1$, which is zero on the equator $\{x_d=0\}\cap \partial B_1$. Thus, one can easily deduce that:
- $\lambda_1=d-1$ and the corresponding eigenfunction is $\phi_1(x)=\frac{x_d}{\sqrt\omega_d}.$
- $\lambda_2=\dots=\lambda_{d}=2d$, the corresponding homogeneity constants are $\alpha_2=\dots=\alpha_{d}=2$ and the corresponding eigenspace $E_{2d}$ has dimension ($d-1$) and is generated by the polynomials $$Q_j(x)=x_d x_{j-1},\qquad\text{for every}\qquad j=2,\dots,d.$$
- If $j> d$ (that is $\lambda_j>2d$), then $\lambda_j\ge 3(3+d-2)=3(d+1)$.
[**The spectrum on the spherical cap $S_{\delta}=\partial B_1\cap\{x_d>-\delta\}$.**]{} We first notice that the spectrum $\{\lambda_j(\delta)\}_{j\ge 1}$ of the spherical cap $S_\delta$ varies continuously with respect to $\delta$. Thus, for $\delta>0$ small enough (smaller than some dimensional constant), we have
- $\lambda_1(\delta)$ is simple (isolated) eigenvalue and $\lambda_1(\delta)\le d-1$;
- $d-1< \lambda_j(\delta)<2d$, for every $j=2,\dots,d$;
- $\lambda_j(\delta)\ge 3d$, for every $j> d$.
Moreover, a standard separation of variables argument gives that:
- the first eigenfunction $\phi_1$ on $S_{\delta}$ is positive and depends only on the first variable $x_d$, that is $\phi_1(x)=\phi_1(x_d).$
- the eigenfunctions $\phi_2,\dots,\phi_d$ correspond to the same eigenvalue $\lambda_2(\delta)=\dots=\lambda_d(\delta)$ and there is a function $\phi=\phi(x_d)$ such that $$\phi_j(x)=x_{j-1} \phi(x_d)\quad \text{for every}\quad j=2,\dots,d.$$
The epiperimetric inequality at flat points: proof of Theorem \[t:epi:A\] {#s:flat}
=========================================================================
In order to prove Theorem \[t:epi:A\] we decompose the function $z$ as $$z=q_\nu+\varphi,$$ where $q_\nu(x)=(x\cdot\nu)_+^2$ and $\nu\in\R^d$ to be chosen later. We then replace the $2$-homogeneous function $\varphi (r,\theta)=r^2\phi(\theta)$ by an $\alpha$-homogeneous function $\tilde\varphi(r,\theta)=r^\alpha\phi(\theta)$, for some $\alpha>2$. The final competitor will be of the form $$h=q_\nu+\tilde\varphi,$$ and $\eps=\eps_\alpha$ will be given by $$\label{e:eps}
\eps_\alpha:=\frac{\alpha-2}{d+\alpha}.$$ We notice that the competitor $h$ is non-negative in $B_1$, thus we only need to prove the inequality $$\label{e:tildepi}
\W(h)-\Theta_+-(1-\eps)\left(\W(z)-\Theta_+\right) \le 0.$$ We divide the proof into three steps.
[*Step 1*.]{} Using the properties of $q_\nu$, we first reduce the inequality to a comparison of the energy of $\tilde\varphi$ to the one of $\varphi$. Precisely, in Subsection \[sub:decomposition\], we prove the inequality $$\label{e:mainest0}
\W(h)-\Theta_+-(1-\eps)\Big(\W(z)-\Theta_+\Big) \le W_0(\tilde \varphi)-(1-\eps)W_0(\varphi).$$
[*Step 2*.]{} In Subsection \[sub:choice\] we prove that we can choose $q_\nu$ in such a way that the function $\phi:=c-q_\nu$ does not contain modes of the first $d$ eigenvalues on the spherical cap $S_{\delta_0}$. Precisely, we prove the following claim. For every $\delta_0>0$ there exists $\delta>0$ such that $$\label{e:claim}
\begin{array}{ll}
\ds\quad\text{for every}\ c\in H^1_0(S_{\delta_0})\ \text{satisfying}\ \|c-q_{e_d/2}\|_{L^2(\partial B_1)} \le \delta\ \text{there exists}\ \nu\in\R^d\ \text{such that}\\
\ds\quad u_\lambda\in H^1_0(S_{\delta_0})\ \text{and}\ \int_{S_{\delta_0}}c(\theta)\phi_j(\theta)\,d\HH^{d-1}(\theta)=\int_{S_{\delta_0}}q_\nu(\theta)\phi_j(\theta)\,d\HH^{d-1}(\theta),\ \text{for every}\ j=1,\dots,d,
\end{array}$$ where $\phi_1,\dots,\phi_d$ are the first $d$, orthonormal in $L^2(\partial B_1)$, eigenfunctions of the Laplace-Beltrami operator on $S_{\delta_0}$ with Dirichlet boundary conditions on $\partial S_{\delta_0}$.
[*Step 3*.]{} In Subsection \[sub:fourier\] we use Lemma \[l:fourier\] and the choice of $\nu$ from Step 2 to prove the inequality $$\label{e:mainest2}
\ds W_0(\tilde \varphi)-(1-\eps)W_0(\varphi)\le 0,$$ which together with gives .
Decomposition of the energy {#sub:decomposition}
---------------------------
We prove in the following lemma:
\[l:decomposition\] Let $\alpha>2$, $\eps_\alpha$ as in , $\nu=(\nu_1,\dots,\nu_d)\in\R^d$ and $q_\nu(x)=(x\cdot\nu)_+^2$. Suppose that $\phi\in H^1(\partial B_1)$, $\varphi (r,\theta)=r^2\phi(\theta)$ and $\tilde\varphi(r,\theta)=r^\alpha\phi(\theta)$. Then $$\label{e:mainest}
\ds \Big(\W(q_\nu+\tilde\varphi)-\Theta_+\Big)-(1-\eps_\alpha)\Big(\W(q_\nu+\varphi)-\Theta_+\Big)\le W_0(\tilde \varphi)-(1-\eps_\alpha)W_0(\varphi).$$
Suppose, without loss of generality that, $\ds q_\nu(x)=c_0q(x)$, where for the sake of simplicity we set $q:=q_{e_d/2}\in\KK_+$. Notice that for every $\psi\in H^1(B_1)$ we have $$\begin{aligned}
\W(c_0q+\psi)-&\Theta_+=c_0^2\int_{B_1}|\nabla q|^2-2c_0^2\int_{\partial B_1}q^2+c_0\int_{B_1}q-\frac12\int_{B_1}q\\
&\qquad\qquad+2c_0\left(\int_{B_1}\nabla q\cdot\nabla\psi-2\int_{\partial B_1}q\psi\right)
+\int_{B_1}|\nabla \psi|^2-2\int_{\partial B_1}\psi^2+\int_{B_1}\psi\\
&=-\frac{(c_0-1)^2}2\int_{B_1}q+2c_0\left(-\int_{B_1}\Delta q\,\psi+\int_{\partial B_1} \partial_r q\,\psi-2\int_{\partial B_1}q\psi\right)+W_0(\psi)+\int_{B_1}\psi\\
&=-(c_0-1)^2\Theta_++W_0(\psi)+\int_{B_1}\psi-c_0\int_{B_1^+}\psi\,,
$$ where we used that $
\Theta_+=\frac12 \int_{B_1}q$, $\Delta q=\frac12\,\chi_{B_1^+}$ and ${\partial}_r q=2\,q$. If $\psi=\tilde\varphi=r^2\,\phi$, then we have $$\int_{B_1}\tilde\varphi-c_0\int_{B_1^+}\tilde\varphi=\frac1{d+\alpha}\left(\int_{\partial B_1}\phi-c_0\int_{\partial B_1^+}\phi\right)=:\frac1{d+\alpha}\beta(\phi),$$ and we can write the energy of $c_0q+\tilde\varphi$ in the form $$\begin{aligned}
\W(c_0q+\tilde\varphi)-\Theta_+=-(c_0-1)^2\Theta_++W_0(\tilde\varphi)+\frac{1}{d+\alpha}\beta(\phi).\end{aligned}$$ Applying the above estimate to $\varphi$ and $\tilde\varphi$ and thanks to the definition of $\eps_\alpha$, we get $$\begin{aligned}
\W(c_0q+\tilde \varphi)&-\Theta_+-(1-\eps_\alpha)\big(\W(c_0q+ \varphi)-\Theta_+\big)\\
&=-\eps_\alpha (c_0-1)^2\Theta_++W_0(\tilde \varphi)-(1-\eps_\alpha)W_0(\varphi)+\left(\frac1{d+\alpha}-\frac{1-\eps_\alpha}{d+2}\right)\beta(\phi)\\
&=-\eps_\alpha (c_0-1)^2\Theta_++W_0(\tilde \varphi)-(1-\eps_\alpha)W_0(\varphi),\end{aligned}$$ which concludes the proof of Lemma \[l:decomposition\].
Choice of $\nu$ {#sub:choice}
---------------
In this section we prove the claim , which is a straightforward consequence of the following lemma.
\[l:inversa\] Given $\delta_0>0$, we denote by $S_{\delta_0}$ the set $\{x_d>-\delta_0\}\cap\partial B_1$ and by $\phi_1,\dots,\phi_d$ the first $d$ eigenfunctions on the set $S_{\delta_0}$. Then the function $$F:\R^d\to\R^d,\qquad F(\nu) = \left(\int_{S_{\delta_0}}q_\nu\phi_1,\dots,\int_{S_{\delta_0}}q_\nu\phi_d \right),$$ is a $C^1$ diffeomorphism in a neighbourhood $U\subset\R^d$ of $\ds\frac{e_d}2$.
We first notice that $F$ is a $C^1$ function in a neighborhood of $e_d/2$, because the function $\R^d\times\R^d\ni (x,y)\mapsto (x\cdot y)_+^2$ is $C^1$. We now calculate the partial derivatives of $F=(F_1,\dots,F_d)$ in $e_d/2$. Using the fact that the first eigenfunction depends only on one varibale, $\phi_1=\phi_1(x_d)$, and that the higher eigenfunctions can be written in the form $\phi_j(x)=x_{j-1}\phi(x_d)$, for every $j=2,\dots,d$ (see Subsection \[sub:spectrum\]), we get that $$F_1(\nu)=\int_{\partial B_1}q_\nu(x)\,\phi_1(x_d)\,dx\qquad\text{and}\qquad F_j(\nu)=\int_{\partial B_1}q_\nu(x)\,x_{j-1}\phi(x_d)\,dx,\quad\forall j=2,\dots,d.$$ Setting $\partial B_1^+=\{x_d>0\}\cap\partial B_1$ we have $$\frac{\partial F_1}{\partial \nu_d}(e_d/2)=\int_{\partial B_1^+}x_d^2\phi_1(x_d)\,dx>0,$$ $$\frac{\partial F_1}{\partial \nu_j}(e_d/2)=\int_{\partial B_1^+}x_d x_j\phi_1(x_d)\,dx=0,\ \forall j=1,\dots,d-1.$$ where the positivity of the first term follows from the positivity of $\phi_1$, while the second term is zero since $x_j$ is odd. Moreover, for every $j=2,\dots,d$ and $i=1,\dots,d$, we have $$\begin{aligned}
\frac{\partial F_j}{\partial \nu_i}(e_d/2)&=\int_{\partial B_1^+}\!\!\!x_i x_d x_{j-1}\phi(x_d)\,dx=\delta_{i(j-1)}\int_{\partial B_1^+} \!\!\!x_i^2 x_d \phi(x_d)\,dx=\frac{\delta_{i(j-1)}}{d-1}\int_{\partial B_1^+} \!\!\!(1-x_d^2) x_d\phi(x_d)\,dx\,,\end{aligned}$$ where we used the fact that $x_i$ and $x_j$ are odd for the first equality, and $\int x_j^2=\frac{1}{d-1}\sum_{j=1}^{d-1}\int x_j^2=\frac1{d-1}\int(1-x_d^2)$. By the positivity of $\phi$ and the fact that $\lim_{\delta_0\to0}\|\phi-c_2x_d^+\|_{L^2(\partial B_1)}=0$, for dimensional constants $c_1$ and $c_2$ (which is due to the fact that on the half-sphere $\partial B_1^+$ the eigenfunctions are of the form $\phi_j(x)=c_2x_dx_{j-1}$ for $j=2,\dots,d$) we get that for $\delta_0$ small enough $DF(e_d/2)$ is an invertible matrix and so, by the inverse function theorem there is a neighborhood of $e_d/2$ on which $F$ is a $C^1$ diffeomorphism.
Homogeneity improvement of $\varphi$ {#sub:fourier}
------------------------------------
We prove . Indeed, by the fact that the Fourier expansion of $\phi(\theta):=c(\theta)-q_\nu(\theta)$ does not contain the first $d$ modes $\phi_1,\dots,\phi_d$ on the spherical cap $S_{\delta_0}$ (claim ), we obtain that the function $\phi$ can be expanded in Fourier series as $$\phi(\theta)=\sum_{j=d+1}^{\infty}c_j\phi_j(\theta)\quad\text{on the spherical cap}\quad S_{\delta_0}=\partial B_1\cap \{x_d>-\delta_0\}.$$ Thus, by Lemma \[l:fourier\] we get $$\begin{aligned}
W_0(\tilde\varphi)-(1-\eps_\alpha)W_0(\varphi)&=\frac{\eps_\alpha}{d+2\alpha-2}\sum_{j=d+1}^\infty (-\lambda_j+\lambda_\alpha) c_j^2,\end{aligned}$$ where $\lambda_j$ are the eigenvalue of the Dirichlet Laplacian on $S_{\delta_0}$ and $\lambda_\alpha=\alpha(\alpha+d-2)$. On the other hand, for $\delta_0>0$ small enough, we have that $\lambda_j\ge 3d$, for $j\ge d+1$ (see Subsection \[sub:spectrum\]), so that $-\lambda_j+\lambda_\alpha\leq 0$ whenever $\alpha>2$ and $\alpha (\alpha+d-2)\le 3d$. . Thus, choosing for instance $$\alpha=\frac52\qquad\text{and}\qquad \eps=\frac{\alpha-2}{d+\alpha}=\frac{1}{2d+5},$$ we conclude the proof of and Theorem \[t:epi:A\].
The epiperimetric inequality for singular points: proof of Theorem \[t:epi:B\] {#s:sing}
==============================================================================
We first notice that given any two-homogeneous function $z(r,\theta)=r^2\,c(\theta)$, we can decompose it in Fourier series on the sphere $\partial B_1$ as $$\begin{aligned}
c(\theta)=\sum_{j=1}^\infty c_j \phi_j(\theta)=\; c_1\phi_1(\theta)\quad+\sum_{\{j\,:\,\lambda_j=d-1\}} c_j\,\phi_j(\theta)\quad+\sum_{\{j\,:\,\lambda_j=2d\}} c_j\,\phi_j(\theta)\quad+\sum_{\{j\,:\, \lambda_j>2d\}} c_j \phi_j(\theta)\,.
$$ Therefore $z$ can be decomposed in a unique way as $$z=q_\nu+Q_A+\varphi,$$ where
(i) $\nu\in\R^d$ is such that $q_\nu(x)=(x\cdot\nu)_+^2$ contains in its Forurier expansion precisely the sum $$\ds\sum_{\{j\,:\,\lambda_j=d-1\}} c_j\,\phi_j(\theta) \ ;$$
(ii) $A$ is a symmetric matrix depending on the coefficients $c_j$, corresponding to the eigenvalues $\lambda_j=0,d-1,2d$, and $Q_A(x)=x\cdot Ax$;
(iii) $\varphi$ is a two-homogeneous function, in polar coordinates $\varphi(r,\theta)=r^2\phi(\theta)$, containing only higher modes on $\partial B_1$, that is the trace $\phi$ can be written in the form $$\label{e:fourier_phi}
\phi(\theta)=\sum_{\{j\,:\, \lambda_j>2d\}} c_j \phi_j(\theta),$$ where $\{\phi_j\}_{j\in\N}$ are the eigenfunctions of the spherical laplacian as in with $S= \partial B_1$.
Notice that, in the above representation $A$ might not be positive definite. Let $B$ be a symmetric positive definite matrix and $Q_B(x)=x\cdot Bx$. Then, $z$ can be rewritten as $$z=q_\nu+ Q_B+ (Q_A-Q_B)+\varphi\,.$$ We then replace the $2$-homogeneous function $\psi:=(Q_A-Q_B)+\varphi$ by an $\alpha$-homogeneous function $\tilde\psi$ with the same boundary values as $\psi$. We will choose $\alpha>2$ such that $$\label{e:choice_of_alpha}
\eps_\alpha:=\frac{\alpha-2}{d+\alpha}=\ds\eps \left(C_4\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2}\right)^\gamma,$$ where $C_4$ is the dimensional constant from the inequality and $\gamma$ is the constant from . Subsequently we will choose $\eps$ to be small enough, but yet depending only on the dimension.
Finally, the competitor $h$ is given by $$h=q_\nu+Q_B+ \tilde\psi.$$ Since $\inf\{\psi,0\}\le \inf\{\tilde\psi,0\}$ and $q_\nu+Q_B\ge 0$, by the choice of $B$, $h$ is non-negative in $B_1$ and so we only need to prove the inequality $$W(h)\le W(z)-\eps\big(W(z)-\Theta\big)^{1+\gamma}\,.$$ The proof of Theorem \[t:epi:B\] will be carried out in four steps.\
[*Step 1.*]{} In Subsection \[sub:sing:decomposition\] we set $ c_0=4\sum_{j=1}^d\nu_j\ $ and $\ \ds b=4\,\text{tr}B$ and we prove the identity $$\begin{aligned}
W(h)&-\Theta-(1-\eps_\alpha)\left(W(z)-\Theta\right)\label{e:sing:energy}\\
&=-\frac{\eps_\alpha}2\left((1-b-c_0)^2+(1-b)^2\right)\Theta+W_0(\tilde\psi)-(1-\eps_\alpha)W_0(\psi).\nonumber\end{aligned}$$
[*Step 2.*]{} We now choose $Q_B$. If $A$ is positive definite ($Q_A\ge 0$), then we choose $B=A$. If $Q_A$ changes sign, then up to a change of coordinates we can assume that there exist $ a_j\ge 0$ for every $j=1,\dots,d $ such that $$Q_A(x)=-\sum_{j=1}^k a_jx_j^2+\sum_{j=k+1}^da_j x_j^2, \qquad \quad
a_d\ge \frac1{4d}> \sum_{j=1}^k a_j,$$ where the last inequality being due to the fact that $Q_A$ is $L^2(\partial B_1)$-close to the set of admissible blow-ups $\KK$. We set $$\label{e:Q_B}
Q_B(x):=\sum_{j=k+1}^d a_jx_j^2-\Big(\sum_{j=1}^k a_j\Big)x_d^2\geq 0\,$$ where the last inequality, that is the positive definiteness of $B$, depends on $a_d\ge \frac1{4d}> \sum_{j=1}^k a_j$. In Subsection \[sub:sing:main\] we then prove that there exists a dimensional constant $C_2>0$ such that $$\label{e:sing:main}
W_0(\tilde\psi)-(1-\eps_\alpha)W_0(\psi)\le \eps_\alpha^2 C_2\sum_{j=1}^k a_j^2-\frac{\eps_\alpha}{2} \|\nabla_\theta \phi\|_{L^2(\partial B_1)}^2.$$
[*Step 3.*]{} In Subsection \[sub:sing:pre-final\] we prove that there are dimensional constants $C_3>0$ and $\gamma\in[0,1)$ such that $$\label{e:sing:pre-final}
\sum_{j=1}^k a_j^2\le C_3\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2(1-\gamma)}.$$ In the supplementary Subsection \[sub:sing:complementary\] we show that this estimate can be improved in several ways:
1. in dimension two holds with $\gamma=0$;
2. the dimensional constants $\gamma$ can be replaced by a (smaller) constant $\gamma_k$, this time depending on $d$ and $k$. In the two extremal cases $k=0$ and $k=d-1$ the constant is zero.\
[*Step 4.*]{} In Subsection \[sub:sing:final\] we prove that there is a dimensional constant $C_4$, such that $$\label{e:sing:final}
W(z)-\Theta\le C_4\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^2.$$
[*Conclusion of the proof.*]{} The proof of Theorem \[t:epi:B\] now follows directly by , , and . Indeed, by and we get that $$\begin{aligned}
W_0(\tilde\psi)-(1-\eps_\alpha)W_0(\psi)&\le \eps_\alpha^2 C_2\sum_{j=1}^k a_j^2-\frac{\eps_\alpha}2\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^2\\
&\le \eps_\alpha^2 C_2C_3\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2(1-\gamma)}-\frac{\eps_\alpha}2\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^2.\end{aligned}$$ By the definition of $\eps_\alpha$ and we get $$\begin{aligned}
W_0(\tilde\psi)-(1-\eps_\alpha)W_0(\psi)&\le \eps^2C_4^{2\gamma}\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{4\gamma} C_2C_3\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2(1-\gamma)}-\frac{\eps}2 C_4^{\gamma}\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2\gamma} \|\nabla_\theta \phi\|_{L^2(\partial B_1)}^2\\
&= \eps C_4^{\gamma}\left(\eps C_2C_3 C_4^{\gamma}-\frac12\right) \|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2+2\gamma},\end{aligned}$$ which is negative for $\eps$ small enough (but yet, $\eps$ depends only on the dimension). Finally, by , the definition of $\eps_\alpha$ and we obtain $$\begin{aligned}
W(h)-\Theta&\le \left(1-\eps_\alpha\right)\big(W(z)-\Theta\big)
= \left(1-\eps\, C_4^\gamma\, \|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{2\gamma}\right)\big(W(z)-\Theta\big)\\
& \le \Big(1-\eps\,\big(W(z)-\Theta\big)^\gamma\Big)\big(W(z)-\Theta\big),\end{aligned}$$ which is precisely . We now proceed with the proof of , , and .
Decomposition of the energy {#sub:sing:decomposition}
---------------------------
We prove the following lemma, which implies easily .
\[l:sing:decomposition\] Let $\alpha>2$ and $\eps_\alpha=\frac{\alpha-2}{d+\alpha}$; let $0\neq \nu=(\nu_1,\dots,\nu_d)\in\R^d$, $q_\nu(x)=(x\cdot\nu)_+^2$, $c_0=4\sum_{j=1}^d\nu_j^2$; let $B$ be a symmetric matrix with and $b=4\,\text{tr}B\neq0$ and $Q_B(x)=x\cdot Bx$. Suppose that $\phi\in H^1(\partial B_1)$, $\varphi (r,\theta)=r^2\phi(\theta)$ and $\tilde\varphi(r,\theta)=r^\alpha\phi(\theta)$. Then $$\begin{aligned}
\ds \W(q_\nu+Q_B+\tilde\varphi)&-\Theta-(1-\eps_\alpha)\Big(\W(q_\nu+Q_B+\varphi)-\Theta\Big)\\
&= -\frac{\eps_\alpha}2\left((1-b-c_0)^2+(1-b)^2\right)\Theta+W_0(\tilde \varphi)-(1-\eps_\alpha)W_0(\varphi).\end{aligned}$$
We $Q=\frac1b Q_B$. Thus, we have $Q\in\KK$. In particular, $\Delta Q=1/2$ in $B_1$ and $W(Q)=\Theta$. We notice that for every function $\eta\in H^1(B_1)$, we have $$\begin{aligned}
\W(bQ+\eta)-\Theta&=b^2W_0(Q)+W_0(\eta)+2b\left(\int_{B_1}\nabla Q\cdot\nabla\eta-2\int_{\partial B_1}Q\eta\right)+b\int_{B_1}Q+\int_{B_1}\eta-\Theta\\
&=b^2W_0(Q)+W_0(\eta)-2b\int_{B_1}\eta\Delta Q+b\int_{B_1}Q+\int_{B_1}\eta-\Theta,\end{aligned}$$ which gives $$\label{e:saluta_andonio}
\W(bQ+\eta)-\Theta=-(1-b)^2\Theta+W_0(\eta)+(1-b)\int_{B_1}\eta.$$ We set $q=\frac1{c_0}q_\nu$. Thus $q\in\KK_+$ and $W(q)=\Theta_+=\frac12\int_{B_1} q$. Setting $\eta=c_0q+\psi$ in we obtain $$\begin{aligned}
\W(bQ+c_0q+\psi)&-\Theta=-(1-b)^2\Theta+W_0(c_0q+\psi)+(1-b)\int_{B_1}(c_0q+\psi)\nonumber\\
&=-(1-b)^2\Theta+c_0^2W_0(q)+W_0(\psi)\nonumber\\
&\quad +2c_0\left(\int_{B_1}\nabla q\cdot\nabla\psi-2\int_{\partial B_1}q\psi\right)+(1-b)\int_{B_1}(c_0q+\psi)\nonumber\\
&=-(1-b)^2\Theta-c_0^2\frac{\Theta}2+W_0(\psi) -2c_0\int_{B_1}\psi\Delta q+(1-b)c_0\Theta+(1-b)\int_{B_1}\psi\nonumber\\
&=-\frac{(1-b-c_0)^2+(1-b)^2}2\Theta+W_0(\psi)+\beta(\psi),\label{e:sing:decomposition}\end{aligned}$$ where in the last line we set $$\beta(\psi):=(1-b)\int_{B_1}\psi-c_0\int_{B_1^+}\psi.$$ Taking $\tilde \psi$ to be the $\alpha$-homogeneous extension of $\psi$, we get that $\beta(\tilde\psi)-(1-\eps_\alpha)\beta(\psi)=0$, which concludes the proof of the lemma.
Homogeneity improvement of $\psi$ {#sub:sing:main}
---------------------------------
In this subsection we prove the inequality .
We first notice that if $Q_A$ is non-negative, then we can choose $Q_B=Q_A$ and $\sum_{j=1}^k a_j^2=0$. Thus, follows directly by Lemma \[l:fourier\] and the fact that for the eigenvalues on the sphere $\lambda_j>2d$ implies $\lambda_j\ge 3(d+1)$.
In the rest of this subsection, we assume that $Q_A$ changes sign and $Q_B$ is given by . In particular, $Q_A-Q_B$ is a homogeneous polynomial of second degree with $\Delta Q_A-Q_B =0$, so it is an element of the eigenspace $E_{2d}$, corresponding to the eigenvalue $2d$. We choose $\phi_2\in E_{2d}$ and $c_2\in\R$ such that $$Q_A-Q_B=c_2\phi_2\,,\quad\text{where}\quad\int_{\partial B_1}\phi_2^2(\theta)\,d\HH^{d-1}(\theta)=1.$$ Thus, on $\partial B_1$ we can write $\psi$ as $$\psi(\theta)=c_2\phi_2(\theta)+\phi(\theta)=c_2\phi_2(\theta)+\sum_{\{j\,:\, \lambda_j>2d\}} c_j \phi_j(\theta).$$ Applying Lemma \[l:fourier\] we have $$\begin{aligned}
W_0(\tilde\psi)-(1-\eps_\alpha)W_0(\psi)
&= \frac{\eps_\alpha}{d+2\alpha-2}\Big((\alpha-2)(d+\alpha)c_2^2+\sum_{\{j\,:\, \lambda_j>2d\}} (-\lambda_j+\lambda_\alpha) c_j^2\Big)\nonumber\\
&= \frac{\eps_\alpha^2(d+\alpha)^2}{(d+2\alpha-2)}c_2^2+\frac{\eps_\alpha}{d+2}\sum_{\{j\,:\, \lambda_j>2d\}} (-\lambda_j+\lambda_\alpha) c_j^2\nonumber
$$ Choosing the constant $\eps$ small enough, the equation implies that $\ds 2<\alpha\le \frac52$; by the fact that $\lambda_j>2d\Rightarrow \lambda_j\ge3(d+1)$ (see Subsection \[sub:spectrum\]) we have $$\lambda_j-\lambda_\alpha\ge 3(d+1)-\frac52\Big(d+\frac12\Big)> \frac{d+2}{2}\,,\quad\text{whenever}\quad \lambda_j>2d.$$ Hence, the right-hand side in the previous equality can be estimated by $$\begin{aligned}
W_0(\tilde\psi)-(1-\eps_\alpha)W_0(\psi)
&\le \frac{\eps_\alpha^2(d+3)^2}{(d+2)}c_2^2-\frac{\eps_\alpha}2\sum_{\{j\,:\, \lambda_j>2d\}} c_j^2\nonumber\\
&= \frac{\eps_\alpha^2(d+3)^2}{(d+2)}\int_{\partial B_1}(Q_A-Q_B)^2-\frac{\eps_\alpha}2\int_{\partial B_1}\phi^2.\label{e:sing:main:part1}\end{aligned}$$ It order to estimate the first term in the right-hand side, we notice that $Q_A-Q_B = \big(\sum_{j=1}^k a_j \big)x_d^2 - \sum_{j=1}^k a_jx_j^2$ , hence its $L^2$-norm is a degree $2$ homogeneous polynomial in $(a_1,..., a_k)$ (with coefficients depending only on $d$). Hence there exists a dimensional constant $C_d$ such that $$\int_{\partial B_1}(Q_A-Q_B)^2 \le C_d\sum_{j=1}^k a_j^2.$$ Together with , this gives .
The higher modes control $\sum_{j=1}^k a_j^2$ {#sub:sing:pre-final}
---------------------------------------------
In this section we prove the inequality from Step 3. Since the trace $c(\theta)$ is positive on $\partial B_1$ and can be written as $$c(\theta)=\Big(-\sum_{j=1}^k a_j\theta_j^2+\sum_{j=k+1}^d a_j\theta_j^2\Big)+q_\nu(\theta)+\phi(\theta)\ge 0,$$ we get that $$\phi(\theta)\ge \Big(\sum_{j=1}^k a_j\theta_j^2-\sum_{j=k+1}^d a_j\theta_j^2\Big)_+\ge \Big(a_1\theta_1^2-\sum_{j=2}^d \theta_j^2\Big)_+ ,$$ on the half-sphere $\partial B_1\cap\{q_\nu=0\}$. Thus, we get $$\phi(\theta)\ge \frac{a_1}4\theta_1^2\quad\text{on the set}\quad U_{a_1}\cap\{q_\nu=0\},\quad\text{where}\quad U_{a_1}=\Big\{\theta\in\partial B_1\ :\ a_1\theta_1^2>2\sum_{j=2}^d \theta_j^2\Big\}.$$ Notice that that for $a_1$ small enough we have $$\frac12(d-1)\omega_{d-1}\sqrt{a_1}^{d-1}\le \HH^{d-1}(U_{a_1})\le 2(d-1)\omega_{d-1}\sqrt{a_1}^{d-1}.$$ Thus, we obtain $$\int_{\partial B_1}\phi^2\ge C_d a_1^2 \sqrt{a_1}^{d-1}=C_d a_1^{(d+3)/2},$$ for a dimensional constant $C_d>0$. Without loss of generality we can suppose that $$a_1^2\ge \frac{1}{k}\sum_{j=1}^k a_j^2\ge \frac{1}{d}\sum_{j=1}^k a_j^2,$$ and so, we get $$\int_{\partial B_1}|\nabla_\theta \phi|^2\ge 2d\int_{\partial B_1}\phi^2\ge 2d\,C_d\, a_1^{(d+3)/2}\ge C_d\,\Big(\sum_{j=1}^k a_j^2\Big)^{(d+3)/4},$$ which gives with $\ds\gamma=\frac{d-1}{d+3}$ and a dimensional constant $C_3$.
The higher modes control $W(z)-\Theta$ {#sub:sing:final}
--------------------------------------
In this section we prove the inequality from the final Step 4. Using the decomposition $z=q_\nu+Q_A+\psi$ and the identity we get, with $\psi=r^2\,\phi$ and using $\int_{{\partial}B_1} \phi=0$ since it contains only high modes, $$\begin{aligned}
W(z)-\Theta
&=-\frac{(1-b-c_0)^2+(1-b)^2}2\Theta+\frac{1}{d+2}\int_{\partial B_1}\left(|\nabla_\theta \phi|^2-2d\phi^2\right)-\frac{c_0}{d+2}\int_{\partial B_1^+}\phi\\
&\le -\frac{c_0^2}4\Theta+\frac{1}{d+2}\int_{\partial B_1}\left(|\nabla_\theta \phi|^2-2d\phi^2\right)-\frac{c_0}{d+2}\int_{\partial B_1^+}\phi,\end{aligned}$$ where the last inequality follows by the fact that $$(1-b-c_0)^2+(1-b)^2\ge \frac{c_0^2}2\,,\quad\text{for every}\quad b,c_0\in\R.$$ By the Cauchy-Schwarz inequality, we have $$\begin{aligned}
-\frac{c_0}{d+2}\int_{\partial B_1^+}\phi&\le \frac{c_0^2}{4}\Theta+\Big(\frac{1}{(d+2)\Theta}\int_{\partial B_1^+}\phi\Big)^2\\
&\le \frac{c_0^2}{4}\Theta+\frac{|\partial B_1|}{(d+2)\Theta}\int_{\partial B_1}\phi^2= \frac{c_0^2}{4}\Theta+8d^2\int_{\partial B_1}\phi^2.\end{aligned}$$
Thus, we get $$\begin{aligned}
W(z)-\Theta
&\le \frac{1}{d+2}\int_{\partial B_1}\left(|\nabla_\theta \phi|^2-2d\phi^2\right)+8d^2\int_{\partial B_1}\phi^2\\
&\le \frac{1}{d+2}\int_{\partial B_1}|\nabla_\theta \phi|^2+8d^2\int_{\partial B_1}\phi^2\le \left(\frac{1}{d+2}+4d\right)\int_{\partial B_1}|\nabla_\theta \phi|^2,\end{aligned}$$ where the last inequality is due to the fact that $\phi$ contains only modes $\phi_j$ corresponding to eigenvalues $\lambda_j>2d$. This gives where the constant $C_4$ can be choosen as $\ds C_4=1+4d$.
Improvement of the decay rate {#sub:sing:complementary}
-----------------------------
This subsection is dedicated to the improvement of the inequality . The main result, contained in the following lemma, is more general and holds in any dimension.
\[l:improvement\] Suppose that $0\le k<d$ and $$Q_A(x)=-\sum_{j=1}^k a_jx_j^2+\sum_{j=k+1}^d a_j x_j^2\ ,\quad\text{where}\quad \begin{cases} 0<a_j\quad \text{for every}\quad j=1,\dots,k,\\
0\le a_j\le1\quad \text{for every}\quad j=k+1,\dots,d.
\end{cases}$$ Let $\phi\in H^1(\partial B_1)$ be of zero mean, that is $\ds\int_{\partial B_1}\phi(\theta)\,d\HH^{d-1}(\theta)=0$, and such that $$\phi\ge Q_A\quad\text{on the half-sphere}\quad \{\xi\in \partial B_1\ :\ \xi\cdot \nu >0\},$$ determined by some unit vector $\nu\in\partial B_1$.
Then, there are dimensional constants $C>0$ and $\delta>0$ such that if $\ds \sum_{j=1}^k a_j^2\le \delta$, then $$\sum_{j=1}^k a_j^2\le C_d\|\nabla_\theta\varphi\|_{L^2(\partial B_1)}^{2(1-\gamma_k)},$$ where $$\gamma_k=\begin{cases} 0\,,\quad \text{if}\quad k=0,\\
\ds\frac{d-k}{d-k+4}\,,\quad \text{for every}\quad k=1,\dots,d-2,\\
0\,,\quad \text{if}\quad k=d-1.
\end{cases}$$
The above lemma is to be applied to the traces $c$ of the solutions $u$ of an obstacle problem, which can be written in the form $c(\theta)=Q_A(\theta)+q_\nu(\theta)+\phi(\theta)$. We notice that, although one might think that $k$ corresponds precisely to point of the $k$-th stratum, we do not know a way to deduce the precise form of $Q_A$ just from looking at the blow-up limits of $u$. This means that even if the blow up $Q_B$ is such that $\dim(\ker B)=k$, we still cannot infer anything on the structure of $B$. It follows that this result cannot be applied to improve the regularity of the singular sets of $\partial \{u>0\}$, except in dimension two, where $\gamma_0=\gamma_1=0$. This corresponds to the assumption of Weiss on the projection of $c$ on the set of admissible blow-ups $\KK$, which again finds application only in dimension two.
If $k=0$, then the inequality is trivial and so, we can suppose that $k\ge 1$.
[*Suppose that $1\le k< d-1$.* ]{} Without loss of generality we can suppose $\ds a_1^2\ge \frac1k\sum_{i=1}^k a_i^2$.\
Setting $X'=(x_1,\dots,x_k)$, $X''=(x_{k+1},\dots,x_d)$ and $\|\cdot\|=\|\cdot\|_{L^2(\partial B_1)}$, we have $$\begin{aligned}
\Big\|\Big(\sum_{i=1}^k a_ix_i^2-\sum_{i=k+1}^da_ix_i^2\Big)_+\Big\|&\ge \Big\|\Big(a_1x_1^2-\sum_{i=k+1}^da_ix_i^2\Big)_+\Big\|\ge \left\|\left(a_1x_1^2-|X''|^2\right)_+\right\|\\
&=\frac1k\sum_{j=1}^k\left\|\left(a_1x_j^2-|X''|^2\right)_+\right\|\ge \frac1d\left\|\left(a_1|X'|^2-|X''|^2\right)_+\right\|.\end{aligned}$$ We now notice that $$a_1|X'|^2-|X''|^2\ge \frac{a_1}2|X'|^2\quad\text{on the set}\quad U_{a_1}=\Big\{X=(X',X'')\in\partial B_1\ :\ \frac{a_1}2|X'|^2\ge |X''|^2\Big\},$$ and for $a_1$ small enough we get $$\frac12k\omega_k\sqrt{a_1}^{d-k}\le \HH^{d-1}(U_{a_1})\le 2k\omega_{k}\sqrt{a_1}^{d-k}.$$ In particular, $$\|\inf\{Q_A,0\}\|_{L^2(\partial B_1)}^2\ge \left\|\left(a_1|X'|^2-|X''|^2\right)_+\right\|_{L^2(\partial B_1)}^2\ge C_da_1^{\frac{d-k+4}2}\ge C_d \Big(\sum_{i=1}^k a_i^2\Big)^{\frac{d-k+4}4}.$$ Now, since $Q_A$ is even and $\|\phi\|_{L^2(\partial B_1)}^2\le \frac{1}{d-1}\|\nabla_\theta\phi\|_{L^2(\partial B_1)}^2$, we obtain the claimed inequality $$\sum_{i=1}^k a_i^2\le C_d\|\nabla_\theta\phi\|_{L^2(\partial B_1)}^{\frac8{d-k+4}}.$$
[*Suppose that $k=d-1$.* ]{} We argue by contradiction. Suppose that there are a sequence of functions $\phi_n:\partial B_1\to\R$ of zero mean and vectors $\nu_n\in\partial B_1$ and $(a_n^1,\dots,a_n^k)$ such that $$\phi_n(\theta)\ge a_n^1\theta_1^2\quad\text{on the set}\quad \{\theta\in\partial B_1\ : \theta_d=0\,,\ \theta\cdot \nu_n>0\},$$ $$\ds a_n^1\ge \Big(\frac1k\sum_{j=1}^k|a_n^j|^2\Big)^{1/2}\qquad\text{and}\qquad \sum_{j=1}^k|a_n^j|^2\ge n\|\nabla\phi_n\|_{L^2(\partial B_1)}^2.$$ Thus, the sequence of functions $\psi_n:=\phi_n/ a_n^1$ is such that $\ds\lim_{n\to\infty }\|\nabla\psi_n\|_{L^2(\partial B_1)}^2=0$ and $$\psi_n(\theta)\ge \theta_1^2\quad\text{on the set}\quad \{\theta\in\partial B_1\ : \theta_d=0\,,\ \theta\cdot \nu_n>0\},$$ which is in contradiction with the trace inequality $$\int_{\{\theta_d=0\}\cap \partial B_1}\psi_n^2\,d\HH^{d-2}\le C\int_{\partial B_1}\big(|\nabla\psi_n|^2+\psi_n^2\big)\,d\HH^{d-1}.$$
On the sharpness of the non-homogeneous estimate in Theorem \[t:epi:B\]
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We conclude this section with an example, which shows that in dimension higher than three one cannot estimate the distance to the cone $\mathcal K$ by just using the energy of the higher modes $\phi$ to the power one. Indeed, such an estimate would be in contradiction with inequality below. In particular, Example \[esempio\] shows that for general traces in higher dimension our method cannot be improved.
\[esempio\] Consider the non-negative trace $c:\partial B_1\to\R^+$ given by $$c(\theta)=\left(\frac1{4(d-1)}\sum_{j=1}^{d-1}\theta_j^2 - \eps\theta_d^2\right)_+.$$ Notice that, since $c$ is even its Fourier expansion on the sphere $\partial B_1$ does not contain linear terms. As in the proof of Theorem \[t:epi:B\], the trace $c$ can be uniquely decomposed as $c(\theta)=Q(\theta)+\phi(\theta),$ where $Q$ is a homogeneous polynomial of second degree and $\phi$ contains only higher modes, that is $$\ds \phi(\theta)=\sum_{\{j\,:\,\lambda_j>2d\}}c_j\phi_j(\theta).$$ We claim that $$\label{e:esempio}
\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{\frac4{d+1}}\lesssim \text{dist}_{L^2(\partial B_1)}(Q,\mathcal K).$$ In order to prove we set $$P(\theta)= \frac1{4(d-1)}\sum_{j=1}^{d-1}\theta_j^2- \eps\theta_d^2\qquad\text{and}\qquad R(\theta)=\left(\eps\theta_d^2-\frac1{4(d-1)}\sum_{j=1}^{d-1}\theta_j^2\right)_+,$$ and we notice that $c(\theta)=P(\theta)-R(\theta).$ It is easy to check that the term $R$ has the following asymptotic behavior when the parameter $\eps$ is small: $$\|R\|_{L^\infty(\partial B_1)}=\eps\ ,\qquad \HH^{d-1}(\{R>0\})\sim {\eps}^{\frac{d-1}2}\ , \qquad\|\nabla_\theta R\|_{L^\infty(\partial B_1)}\sim\sqrt\eps\ ,$$ $$\|R\|_{L^2(\partial B_1)}\sim {\eps}^{\frac{d+3}4}\qquad\text{and}\qquad \|\nabla_\theta R\|_{L^2(\partial B_1)}\sim {\eps}^{\frac{d+1}4}.$$ The function $R$ can be decomposed as $$R(\theta)=\frac{c_0}{\sqrt{\HH^{d-1}(\partial B_1)}}+c_2\phi_2(\theta)-\phi(\theta),$$ where
- $c_0\in\R$ corresponds to the first (constant) mode of the Fourier expansion of $R$ on $\partial B_1$ and can be estimated in terms of $\eps$ as $$\ds c_0=\frac{1}{\sqrt{\HH^{d-1}(\partial B_1)}}\int_{\partial B_1}R\,d\HH^{d-1}\le \|R\|_{L^2(\partial B_1)}\lesssim {\eps}^{\frac{d+3}4};$$
- $\phi_2(\theta)$ is an eigenfunction of the Laplacian on the sphere corresponding to the eigenvalue $2d$ and $\|\phi_2\|_{L^2(\partial B_1)}=1$ and the constant $c_2\in\R$ can be estimated as $$\ds |c_2|\le \left|\int_{\partial B_1}R\phi_2\right|\le \|R\|_{L^2(\partial B_1)}\lesssim {\eps}^{\frac{d+3}4};$$
- the function $\phi$ is precisely the one from the decomposition of $c$, contains only higher modes and satisfies the following estimate: $$\ds \|\nabla_\theta \phi\|_{L^2(\partial B_1)}\le \|\nabla_\theta R\|_{L^2(\partial B_1)}+|c_2|\|\nabla_\theta \phi_2\|_{L^2(\partial B_1)}\lesssim {\eps}^{\frac{d+1}4}+{\eps}^{\frac{d+3}4}2d\lesssim {\eps}^{\frac{d+1}4}.$$
On the other hand, the $L^2(\partial B_1)$ distance from $Q=P-c_0-c_2\phi_2$ to the cone $\mathcal K$ of nonnegative homogeneous polynomials of second degree has the behavior $$\text{dist}_{L^2(\partial B_1)}\Big(P-c_0-c_2\phi_2,\mathcal K\Big)\sim \text{dist}_{L^2(\partial B_1)}\big(P,\mathcal K\big)\sim \eps.$$ Thus, we finally get the claimed inequality $$\|\nabla_\theta \phi\|_{L^2(\partial B_1)}^{\frac4{d+1}}\lesssim \eps\sim \text{dist}_{L^2(\partial B_1)}\Big(P-c_0-c_2\phi_2,\mathcal K\Big).$$
Uniqueness of blow-up and regularity of free boundary {#s:regularity}
=====================================================
In this Section we prove Theorems \[t:uniq\] and \[t:reg\], focusing on the statement 2 of each result. We show in detail how the logarithmic estimates follow from the “modified” epiperimetric inequality of Theorem \[t:epi:B\] and we prefer to skip the analogous estimates on the Hölder continuity at regular points, since this is the main improvement of the present paper and since the proof of the latter is a simpler version of the estimates below and it is already contained in [@Weiss2 Theorem 4 and 5].
\[p:decay\] Let $\Omega\subset\R^d$ be an open set and $u\in H^1(\Omega)$ a minimizer of $\mathcal E$. Then for every compact set $K\Subset\Omega$, there is a constant $C:=C(d, K, \Omega)>0$ such that for every free boundary point $x_0\in {\rm Sing }(u)\cap K$, the following decay holds $$\label{e:L^2decay}
\| u_{x_0,t}-u_{x_0,s} \|_{L^1(\partial B_1)} \leq C\, (-\log(t))^{-\frac{1-\gamma}{2\gamma}} \qquad \mbox{for all}\quad 0< s<t < {{\rm {dist}}}(K,{\partial}\Omega)\,.$$
[*Step 1 (closeness of the blow ups for a given point $x_0$).*]{} Let $x_0 \in K$ and let $r_0\in (0, {{\rm {dist}}}(K,{\partial}\Omega)]$ be such that the epiperimetric inequality of Theorem \[t:epi:B\] can be applied to the rescaling $u_{x_0,r}$ for every $r \leq r_0$. We claim that $$\| u_{x_0,t}-u_{x_0,s} \|_{L^1(\partial B_1)} \leq C\, (-\log(t/r_0))^{-\frac{1-\gamma}{2\gamma}} \qquad \mbox{for all}\quad 0< s<t < r_0\,.$$
We assume $x_0=0$ without loss of generality and $$e(r) = W(u,r)-\Theta_u(0).$$ By the monotonicity formula and the epiperimetric inequality of Theorem \[t:epi:B\], there exists a radius $r_0>0$ such that for every $r \leq r_0$ $$\label{eqn:epi-applied}
\frac{d}{dr}e(r) \geq \frac{d+2}{r} \big( W(c_r)-\Theta_u(0)-e(r) \big) +f(r)\geq \frac{c}{r} e(r)^{1+\gamma} +2f(r)$$ where $\gamma \in (0,1)$ is a dimensional constant and $$f(r):=\frac{1}{r}\int_{\partial B_1}|x\cdot \nabla u_r-2u_r|^2\,d\HH^{1}.$$ We obtain that $$\label{e:mon_rem}\frac{d}{dr}\Big(\frac{-1}{\gamma e(r)^\gamma} - c \log r\Big) =\frac{1}{ e(r)^{1+\gamma}}\frac{d}{dr}e(r)- \frac{c}{r} \geq \frac{1}{ e(r)^{1+\gamma}} f(r) \geq 0$$ and this in turn implies that $-{e(r)^{-\gamma}} - c\gamma \log r$ is an increasing function of $r$, namely that $e(r)$ decays as $$\label{eqn:e-logar}
e(r) \leq ({e(r_0)^{-\gamma}+c \gamma \log r_0-c \gamma \log r})^{\frac {-1}{\gamma}} \leq (-c \gamma \log (r/r_0))^{\frac {-1}{\gamma}}.$$ For any $0<s<t<r_0$ we estimate the $L^1$ distance between the blow ups at scale $s$ and $t$ through the Cauchy-Schwarz inequality and the monotonicity formula $$\begin{aligned}
\label{e:imp_1}
\int_{{\partial}B_1}\left| u_t-u_s \right| \,d\,\HH^{n-1}
&\leq \int_{{\partial}B_1}\int_s^t\frac{1}{r}\left| x\cdot \nabla u_r-2u_r \right| \,dr\,d\HH^{n-1} \notag\\
&\leq \big({n \omega_n}\big)^{1/2} \int_s^t \frac 1 r \left(\frac 1 r \int_{{\partial}B_1} \left| x\cdot \nabla u_r-2u_r \right|^2 \,d\HH^{n-1} \right)^{1/2}\,dr \notag\\
&\leq \Big({ \frac{n \omega_n}{2}} \Big)^{1/2} \int_s^t \frac 1 r (e'(r))^{1/2}\, dr \notag\\
& \leq \Big({ \frac{n \omega_n}{2}} \Big)^{1/2} (\log(t)-\log(s))^{1/2} (e(t)-e(s))^{1/2}
\,.\end{aligned}$$ Let $0<s^2<t^2<r_0$ such that $s/r_0\in [2^{-2^{i+1}}, 2^{-2^i})$, $t/r_0\in [2^{-2^{j+1}}, 2^{-2^j})$ for some $j\leq i$ and applying the previous estimate to the exponentially dyadic decomposition, we obtain $$\begin{aligned}
\label{e:imp_2}
\int_{{\partial}B_1}\left| u_t-u_s \right| \,d\,\HH^{n-1}&\leq \int_{{\partial}B_1}\left| u_t- u_{2^{-2^{j+1}}r_0} \right| \,d\,\HH^{n-1} \notag
\\&+ \int_{{\partial}B_1}\left| u_{2^{-2^{i}}r_0}-u_s \right| \,d\,\HH^{n-1} + \sum_{k=j+1}^{i-1} \int_{{\partial}B_1}\left| u_{2^{-2^{k+1}}r_0}-u_{2^{-2^{k}}r_0} \right| \,d\,\HH^{n-1} \notag
\\
&\leq C \sum_{k=j}^{i} \left(\log\big(2^{-2^{k}}\big)- \log\big(2^{-2^{k+1}}\big)\right)^{1/2}\left(e\big(2^{-2^{k}}\big)- e\big(2^{-2^{k+1}}\big) \right)^{1/2}\notag
\\
&\leq C \sum_{k=j}^{i} 2^{k/2}e\big(2^{-2^{k}}\big)^{1/2}
\leq C \sum_{k=j}^{i} 2^{(1-1/\gamma)k/2}
\\&\leq C 2^{(1-1/\gamma)j/2} \leq C (-\log(t/r_0))^{\frac{\gamma-1}{2\gamma}}\notag
\,,\end{aligned}$$ where $C$ is a dimensional constant that may vary from line to line.
We claim that for every $\eps>0$ there exists $r_0>0$ such that $$e(u_{x,r}) \leq \eps \qquad \mbox{for every }x\in {\rm Sing }(u)\cap K,\; r\leq r_0.$$
Assume by contradiction that there exists a sequence $x_k \to x_0$ and $r_k \to 0$ such that $\eps <e(u_{x_k,r_k})$ for any $k\in \N$. By the monotonicity of $W$, for any $\rho>0$ and $k$ large enough $$\eps <W(u,{x_k,r_k})- \Theta_u(0) \leq W(u,{x_k,\rho})- W(u,{x_0,\rho})+W(u,{x_0,\rho})- \Theta_u(0).$$ In turn, the right-hand side can be made arbitrarily small by choosing first $\rho$ sufficiently small (to make the difference of the last two terms small) and then $k$ sufficiently large.
We claim that for every $\eps>0$ there exists $r_0>0$ such that $${{\rm {dist}}}_{L^2}(u_{x,r}, K ) \leq \eps \qquad\mbox{for every }x\in {\rm Sing }(u)\cap K,\; r\leq r_0.
\qquad$$ (notice that this statement holds also if in place of the $L^2$-distance we consider the $H^1$-distance).
Assume by contradiction that there exists $\eps>0$ a sequence $x_k \to x_0$ and $r_k \to 0$ such that $$\label{eqn:faraway}
\eps < {{\rm {dist}}}_{L^2}(u_{x_k,r_k}, K ) \qquad \mbox{for any }k\in \N.$$
Since the sequence $\{u_{x_k,r_k}\}_{k\in \N}$ is uniformly bounded in $H^{2,\infty}$, it converges strongly in $H^1$ up to a (not relabelled) subsequence to $u_0$. Moreover, thanks to Step 2, the limit $u_0$ must satisfy $W(u_0, x_0, 1)= \Theta_u(0)$, so that it belongs to $K$. This contradicts .
We can now conclude the proof of the Proposition.
We observe that for every $r_0>0$ and $t \leq r_0^2$, we have $\log(t/r_0) \leq 2 \log t$. From Step 1 and 3, we deduce that there exists $r_0>0$ such that for all $0< s<t < r_0^2$, $x_0\in {\rm Sing }(u)\cap K$ $$\| u_{x_0,t}-u_{x_0,s} \|_{L^1(\partial B_1)} \leq C\, (-\log(t))^{-\frac{1-\gamma}{2\gamma}}.$$ From we have $$\| u_{x_0,t}-u_{x_0,r_0^2} \|_{L^1(\partial B_1)} \leq C (-\log(r_0))^{1/2} e({{\rm {dist}}}(K,{\partial}\Omega))^{1/2}$$ and the right hand side is estimated by $C (-\log(r_0))^{-\frac{1-\gamma}{2\gamma}}$ for a constant $C$ depending only on $d, r_0$, $ e({{\rm {dist}}}(K,{\partial}\Omega))$, ${{\rm {dist}}}(K,{\partial}\Omega)$.
As a consequence of the previous proposition we can prove the uniqueness of the blow up Theorem \[t:uniq\], with a logarithmic rate of convergence of the blow up sequence at each point of the singular set (and uniform in any compact set inside the domain).
We notice that $$|Q_{x_1} - Q_{x_2}| \leq c(n) \int_{\partial B_1} | Q_{x_1}(x) - Q_{x_2}(x)| \, d\HH^{n-1}(x)$$ By the triangular inequality $$\| Q_{x_1} - Q_{x_2}\|_{L^1(\partial B_1)} \leq \| u_{x_1, r} - Q_{x_1}\|_{L^1(\partial B_1)} + \| u_{x_1, r}-u_{x_2, r}\|_{L^1(\partial B_1)} + \| u_{x_2, r} - Q_{x_2}\|_{L^1(\partial B_1)}$$
Recalling that $u \in C^{1,1}$ and that $\nabla u(x_1)= 0$, we estimate the term in the middle with $$\begin{split}
\| u_{x_1, r}-u_{x_2, r}\|_{L^1(\partial B_1)} &\leq \int_{\partial B_1} \int_0^1 \frac{ |\nabla u (x_1+rx+ t(x_2-x_1))| |x_2-x_1|}{r^2} \, dt \, d\HH(x)
\\
&\leq
C\| u \|_{C^{1,1}(B_r(x_0))} \frac{(r+|x_2-x_1|)\, |x_2-x_1|}{r^2}
\end{split}$$
We choose $r= |x_1-x_2| (-\log |x_1-x_2|)^{-\frac{1-\gamma}{2\gamma}}$ and we assume that $r_0$ satisfies the inequality $ |r_0| (-\log |r_0|)^{-\frac{1-\gamma}{2\gamma}} \leq {{\rm {dist}}}(K , \partial \Omega)$. By Theorem \[t:uniq\] we see that $$\begin{split}
\| u_{x_1, r} - Q_{x_1}\|_{L^1(\partial B_1)} + \| u_{x_2, r} - Q_{x_2}\|_{L^1(\partial B_1)}
& \leq C (-\log(r ))^{-\frac{1-\gamma}{2\gamma}}
\\&= C (-\log |x_1-x_2| - \frac{1-\gamma}{2\gamma} \log( \log |x_1-x_2|))^{-\frac{1-\gamma}{2\gamma}}
\end{split}$$ Noticing that the inequality $a- \frac{1-\gamma}{2\gamma} \log a \geq a/2$ holds for $a$ greater than a given $a_0 >0$ (depending only on $\gamma$ and therefore on $d$), we apply this inequality to $a= -\log |x_1-x_2|$ to get $$\| u_{x_1, r} - Q_{x_1}\|_{L^1(\partial B_1)} + \| u_{x_2, r} - Q_{x_2}\|_{L^1(\partial B_1)}
\leq C (-\log|x_1-x_2| )^{-\frac{1-\gamma}{2\gamma}}.$$
Putting together the previous inequalities, we find .
Proof of Theorem \[c:Q\_funct\]
-------------------------------
We notice that if $u\in H^1(\Omega)$ is a minimizer of $\mathcal E_q$ or $\mathcal A_q$, then it is locally $W^{2,\infty}$ by the results of [@Gerh] and moreover it is an almost-minimizer of the functional $\mathcal E$ with a constant $C$ depending only on $\|q\|_{C^{0,\gamma}(\Omega)},c_q$ and $\| u\|_{W^{2,\infty}_{loc}}$.
We say that $u\in H^1(\Omega)$ is an almost minimizer of $\mathcal E$ if there exists a constant $C>0$ such that for every ball $B_{r}(x_0)\subset \Omega$ and for every $v \in H^1(B_r(x_0))$ which agrees with $u$ on $\partial B_r(x_0)$ $$\label{e:alm_mon}
\int_{B_r(x_0)}\left[|\nabla u|^2+q(x_0)\max\{u, 0\} \right]\,dx\leq (1+ Cr^\gamma)\int_{B_r(x_0)}\left[|\nabla v|^2+q(x_0)\max\{v, 0\}\right]\,dx\,.$$
In the following we show that the statement of Theorem \[c:Q\_funct\], in particular the logarithmic estimate, holds true also if we drop the assumption that $u \in W^{2,\infty}_{loc}(\Omega)$ is a minimizer of $\mathcal E_q$ or $\mathcal A_q$ and we only assume the almost minimality.
The main modifications with respect to the arguments of Section \[s:regularity\] appear in Proposition \[p:decay\] and we outline them below.
Up to a rescaling, we may assume that $q(x_0)=1$. Applying the epiperimetric inequality of Theorem \[t:epi:B\] to $u_{r,x_0}$, we find that has to be modified for almost monotonicity to get $$\frac{d}{dr}e(r) \geq \frac{n+2}{r} \big( W(c_r)-\Theta_u(0)-e(r) \big) +f(r)\geq \frac{c_0}{r} e(r)^{1+\gamma} - \frac{c_1}{r^{1-\alpha}} +2f(r)$$ (where $e(r):=W(u_r,1)-\Theta_u(0)$ and the notation is the same as in Section \[s:regularity\]) for some constants $c_0,c_1>0$.
We define now $\tilde e(r)= e(r)+2 \alpha^{-1} c_1 r^\alpha$ and we notice that from the previous inequality and since $a^{1+\gamma}+b^{1+\gamma} \geq 2^{-\gamma} (a+b)^{1+\gamma}$ for any $a,b \geq 0$ $$\tilde e'(r) \geq \frac{c_0}{r} e(r)^{1+\gamma} + \frac{c_1}{r^{1-\alpha}} +2f(r)
\geq \frac{c_0}{r} [e(r) + {c_1}{r^{\frac{\alpha}{1+\gamma}}} ]^{1+\gamma}+2f(r)$$ For $r$ sufficiently small, the previous inequality implies that $$\tilde e'(r) \geq \frac{c_0}{r} \tilde e(r)^{1+\gamma}+2f(r)$$ From the previous inequality, we see that $\tilde e(r)$ satisfies the same inequality that $e(r)$ solved in . Hence, with the same argument as in , we see that $\tilde e$ satisfies the same estimate as $e$ in $$e(r)+2 \alpha^{-1} c_1 r^\alpha = \tilde e(r) \leq (-c \gamma \log (r/r_0))^{\frac {-1}{\gamma}}.$$ This inequality implies that, up to a constant, also $e(r)$ satisfies a logarithmic estimate and we can carry out the rest of the proof of Proposition \[p:decay\] and of Theorems \[t:uniq\] and \[t:reg\].
|
ed to five dps?
0.0001
Suppose 31*z + 41943600 = 58*z - 36*z. What is z rounded to the nearest one million?
-5000000
Let h = -296833 + 296832.99999863929. What is h rounded to seven dps?
-0.0000014
Let d = 88813.0000075441 - 88813. Round d to 7 dps.
0.0000075
Let q = -0.058 - 593.942. Let l = q - -594.000431. Round l to four decimal places.
0.0004
Let z = -1.53 - -27.33. Let l = -25.79999632 + z. What is l rounded to 6 dps?
0.000004
Let l be (-3132611845)/(-186) + 1/(-12)*-10. What is l rounded to the nearest 100000?
16800000
Let v = -422.46932 + -0.32068. What is v rounded to the nearest integer?
-423
Let z(d) = -332*d - 66. Let h be z(-24). Suppose -12578 = -16*a + h. Round a to the nearest one hundred.
1300
Let i(t) = -28241*t - 143. Let l be i(-3). What is l rounded to the nearest ten thousand?
80000
Let g = 753227972 - 753227820.9999905. Let p = g - 151. What is p rounded to six dps?
0.00001
Let x = 34936589 - 34936494.000612. Let s = -153 + 248. Let h = s - x. What is h rounded to four dps?
0.0006
Let j = 141.03 - 134. What is j rounded to the nearest 10?
10
Let r(q) = 349119*q**2 + 19*q + 120. Let t be r(-5). Round t to the nearest one hundred thousand.
8700000
Let f be 2*(-3)/6*32/(-8). Suppose -116 = 4*d - 5*k + 157, 130 = -2*d - f*k. Round d to the nearest 10.
-70
Let t = 95.2 + -263.1. Let c = t + 174.77. Round c to the nearest integer.
7
Suppose -72*o = -299*o - 12994161. Round o to the nearest one hundred.
-57200
Let r = -9869987.71986 - -9870130. Let k = r - 422.28145. Let c = -280 - k. What is c rounded to four dps?
0.0013
Let b = -1924.94744 - 0.15256. What is b rounded to the nearest 10?
-1930
Suppose -1836 + 90402 = 2*j. Suppose -10*i + 13*i = j. Let g = 8461 - i. What is g rounded to the nearest one thousand?
-6000
Suppose -165*m + 399287133 + 11415579 = -416046288. What is m rounded to the nearest 100000?
5000000
Let y = -18 - -17.9932. Let c = y + -0.0279. Let i = c + 0.054. Round i to three dps.
0.019
Let x = -2.122 + -0.018. Let t = x + 29.04. What is t rounded to the nearest ten?
30
Let d = 113.9 + -113.8999985791. Round d to seven decimal places.
0.0000014
Let d = 19134996 + -34933996. What is d rounded to the nearest one million?
-16000000
Let w = 2.11 + -2.376. Let g = w - 607.734. Let j = -608.0271 - g. What is j rounded to three dps?
-0.027
Let d = -71.8 + 90. Let h = -6.07 + d. Let x = 0.37 + h. Round x to the nearest integer.
13
Let k = 0.085 + -213.085. Let v = 45220513764.00000099 + -45220513977. Let d = k - v. Round d to seven dps.
-0.000001
Let z = -80.9 + 388.5. Let d = z + -280. Round d to zero dps.
28
Let k = -50.7 - -40.1. Let z = k - -56.2. What is z rounded to 0 decimal places?
46
Let q = -156 + 156.0346. Let v = q - 0.0635. Round v to 3 dps.
-0.029
Let c = 31.6 - 723.6. Let i = 704.32 + c. What is i rounded to 0 dps?
12
Let f be 11 + (1 + -3)*2. Suppose -f*w - 5301 = 3015. Round w to the nearest 100.
-1200
Suppose 173 = 5*v + 1538. Let z = v - -253. What is z rounded to the nearest 10?
-20
Suppose 8*p + 4*s - 3778142 = 6*p, 0 = -p + 5*s + 1889050. Let m(d) = -230313*d - 4. Let y be m(-3). Suppose 3*o = y + p. Round o to the nearest 100000.
900000
Let m = -17491 + 17490.985249. Round m to four dps.
-0.0148
Let f = 76 - 78. Let v(y) = y**2 + y + 2. Let r be v(f). Suppose -r*g = -3*p + 8760003, -4*p + 2*p - 10949998 = 5*g. Round g to the nearest 100000.
-2200000
Let j = 1 - 1.11. Let y = j - -29.11. Let i = y - 29.17. Round i to 2 dps.
-0.17
Let u = 266697.999840347 + -266698. What is u rounded to six dps?
-0.00016
Let v = -13225 + 13152.87. What is v rounded to zero decimal places?
-72
Suppose 0 = 163*l + 272054354 + 26235646. What is l rounded to the nearest 10000?
-1830000
Let w = 576.9 - 574. Let r = w - 2.9007336. What is r rounded to 5 dps?
-0.00073
Let w = -0.01858 - -0.01866624. What is w rounded to 5 dps?
0.00009
Let v = 0.48967 + -0.647575. Let t = v - 38.803595. Let r = t - -39. What is r rounded to three dps?
0.039
Let c = 14.46 - 14.4620341. What is c rounded to 4 decimal places?
-0.002
Let f = -16930971 - -10158971. Round f to the nearest 100000.
-6800000
Let v = 14848.644 + -14896. Round v to the nearest ten.
-50
Let w = -1.4696 + -323.9604. Let j = w + 328. What is j rounded to one dp?
2.6
Suppose 5*i = -z + 144149997, 2*i + i - 2*z = 86490006. Suppose -4*v = -v + i. What is v rounded to the nearest one million?
-10000000
Let u = 4795410 - 4795409.921701984. Let w = 0.0783 - u. Round w to 7 decimal places.
0.000002
Let j = 4163 - 4162.3. Let m = 6.56 + -6. Let x = m + j. Round x to 1 dp.
1.3
Let n(p) = -5185*p**3 - 2*p + 1. Let u be 2/(-6) + (-52)/(-12) + -1. Let j be n(u). What is j rounded to the nearest 10000?
-140000
Let q = 30.056 - 30.05597185. What is q rounded to seven dps?
0.0000282
Let m = 366 - 365.8579. Let l = 35.6179 + m. Let r = 40.9 - l. What is r rounded to 0 dps?
5
Let s(n) = -n**3 + 2*n**2 - n + 4. Let a be s(2). Suppose h - 11*g - 3390000 = -9*g, -a*h + 6780000 = -3*g. Round h to the nearest one hundred thousand.
3400000
Let t = 1.055 - 1.04727. Round t to three decimal places.
0.008
Let n = 472.91 + -475. Let q = -2.003 - n. Let j = -0.123 + q. What is j rounded to 1 decimal place?
0
Suppose -73*m - 771430000 = -18*m. What is m rounded to the nearest one hundred thousand?
-14000000
Suppose -69*c + 2*x - 174 = -73*c, -2*c = -3*x - 67. Let p be 37 + 0 + 2 + -2. Suppose c*y = p*y + 388. Round y to the nearest ten.
100
Let q = -650.9549 - -651. Let h = 0.02 + q. Round h to three decimal places.
0.065
Let k = 34265.67 + -34565. Round k to 0 dps.
-299
Let r = 467055.00005 + -467075. Let l = 24 + -44. Let y = r - l. Round y to five dps.
0.00005
Let k = -0.221 - 0.079. Let v = 0.2999185 + k. What is v rounded to six dps?
-0.000082
Let m = -365413 + 365328.9905. Let u = m - -84. What is u rounded to 2 dps?
-0.01
Let h = -303.737589283 + -265.262409983. Let k = h - -569. What is k rounded to 7 dps?
0.0000007
Let x = 2233.99994633 + -2234. What is x rounded to 5 decimal places?
-0.00005
Suppose -5*d - 201*d + 1833400 = 0. Round d to the nearest 1000.
9000
Let g = 15.8 - 162.8. Let l = g - -146.9834. Round l to two dps.
-0.02
Suppose 3*h - 2*x = 5, -3*x + 0 = 3*h - 30. Let d(t) = -77173*t**3 - 2*t**2 + 2*t - 10. Let q be d(h). Let l = 11453325 - q. Round l to the nearest one million.
21000000
Let d = 0.852 - 0.85202431. What is d rounded to five decimal places?
-0.00002
Let u = 2.37046 + 89.63468. Let f = -92 + u. Round f to three dps.
0.005
Let j = 480094659.75459837 + -480094662. Let f = 0.05460537 - j. Let o = f - 2.3. What is o rounded to 6 dps?
0.000007
Suppose 102*a = 83*a + 16340000. Let r be 4/6*(2 + 4). Suppose t + a = 2*s, -3440000 = r*t - 2*s + 3*s. Round t to the nearest 100000.
-900000
Suppose 2793 = d + 2*f + 874, 0 = 2*d - 5*f - 3847. Let w = -1008 + d. Round w to the nearest ten.
910
Let u = 848429.4 + -848436.6136709. Let v = 0.0146109 + u. Let o = 7.2 + v. Round o to four decimal places.
0.0009
Let h = 821.21 - 827.7599. What is h rounded to 0 decimal places?
-7
Let r = 96607189649.99997881 + -96607188466. Let s = r - 1184. What is s rounded to six decimal places?
-0.000021
Let c = 1892814.210004825703 + -0.210024825703. Let w = -1892787 + c. Let x = -27 + w. What is x rounded to 4 decimal places?
0
Let x = 392.3 - 45.3. Let b = -346.99999144 + x. What is b rounded to six dps?
0.000009
Let i = -12 + -16. Let b = -42228 - -42199.9608. Let j = b - i. Round j to 3 decimal places.
-0.039
Let b(c) = 55853*c**3 + 17*c**2 - c + 35. Let t be b(-15). What is t rounded to the nearest one million?
-189000000
Let n = 7 + -6.9. Let m = n - 0.06. Let k = m + 1.5. Round k to 1 decimal place.
1.5
Let n = 135210.0000164727 - 135210. Round n to 7 decimal places.
0.0000165
Let z = 6.563 + -1326.763. What is z rounded to the nearest ten?
-1320
Let a = -47885.893 + 47953. Let o = a + -66.7. Round o to 2 dps.
0.41
Let h = 336 - 336.4532. Let g = h - -0.542. What is g rounded to three decimal places?
0.089
Let k(b) = -b**3 + 6*b**2 + 8*b - 9. Let z be k(7). Let d be 14 - -16789 - (-3)/2*z. What is d rounded to the nearest one thousand?
17000
Suppose -2*w = 8, 2*f - 52 = 3*w + 2*w. Let o be 16*(-8)/f + 275008. What is o rounded to the nearest ten thousand?
280000
Let j = -311 + 310 |
/*
Copyright 2016 The Kubernetes Authors.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
package v1
import (
api "k8s.io/kubernetes/pkg/api"
v1 "k8s.io/kubernetes/pkg/api/v1"
watch "k8s.io/kubernetes/pkg/watch"
)
// ComponentStatusesGetter has a method to return a ComponentStatusInterface.
// A group's client should implement this interface.
type ComponentStatusesGetter interface {
ComponentStatuses() ComponentStatusInterface
}
// ComponentStatusInterface has methods to work with ComponentStatus resources.
type ComponentStatusInterface interface {
Create(*v1.ComponentStatus) (*v1.ComponentStatus, error)
Update(*v1.ComponentStatus) (*v1.ComponentStatus, error)
Delete(name string, options *api.DeleteOptions) error
DeleteCollection(options *api.DeleteOptions, listOptions api.ListOptions) error
Get(name string) (*v1.ComponentStatus, error)
List(opts api.ListOptions) (*v1.ComponentStatusList, error)
Watch(opts api.ListOptions) (watch.Interface, error)
ComponentStatusExpansion
}
// componentStatuses implements ComponentStatusInterface
type componentStatuses struct {
client *CoreClient
}
// newComponentStatuses returns a ComponentStatuses
func newComponentStatuses(c *CoreClient) *componentStatuses {
return &componentStatuses{
client: c,
}
}
// Create takes the representation of a componentStatus and creates it. Returns the server's representation of the componentStatus, and an error, if there is any.
func (c *componentStatuses) Create(componentStatus *v1.ComponentStatus) (result *v1.ComponentStatus, err error) {
result = &v1.ComponentStatus{}
err = c.client.Post().
Resource("componentstatuses").
Body(componentStatus).
Do().
Into(result)
return
}
// Update takes the representation of a componentStatus and updates it. Returns the server's representation of the componentStatus, and an error, if there is any.
func (c *componentStatuses) Update(componentStatus *v1.ComponentStatus) (result *v1.ComponentStatus, err error) {
result = &v1.ComponentStatus{}
err = c.client.Put().
Resource("componentstatuses").
Name(componentStatus.Name).
Body(componentStatus).
Do().
Into(result)
return
}
// Delete takes name of the componentStatus and deletes it. Returns an error if one occurs.
func (c *componentStatuses) Delete(name string, options *api.DeleteOptions) error {
return c.client.Delete().
Resource("componentstatuses").
Name(name).
Body(options).
Do().
Error()
}
// DeleteCollection deletes a collection of objects.
func (c *componentStatuses) DeleteCollection(options *api.DeleteOptions, listOptions api.ListOptions) error {
return c.client.Delete().
Resource("componentstatuses").
VersionedParams(&listOptions, api.ParameterCodec).
Body(options).
Do().
Error()
}
// Get takes name of the componentStatus, and returns the corresponding componentStatus object, and an error if there is any.
func (c *componentStatuses) Get(name string) (result *v1.ComponentStatus, err error) {
result = &v1.ComponentStatus{}
err = c.client.Get().
Resource("componentstatuses").
Name(name).
Do().
Into(result)
return
}
// List takes label and field selectors, and returns the list of ComponentStatuses that match those selectors.
func (c *componentStatuses) List(opts api.ListOptions) (result *v1.ComponentStatusList, err error) {
result = &v1.ComponentStatusList{}
err = c.client.Get().
Resource("componentstatuses").
VersionedParams(&opts, api.ParameterCodec).
Do().
Into(result)
return
}
// Watch returns a watch.Interface that watches the requested componentStatuses.
func (c *componentStatuses) Watch(opts api.ListOptions) (watch.Interface, error) {
return c.client.Get().
Prefix("watch").
Resource("componentstatuses").
VersionedParams(&opts, api.ParameterCodec).
Watch()
}
|
package openradar
import (
"appengine"
"appengine/datastore"
"time"
)
func getRadar(context appengine.Context, radarNumber int64) (radar *Radar, err error) {
key := datastore.NewKey(context, "Radar", "", radarNumber, nil)
radar = &Radar{}
err = datastore.Get(context, key, radar)
radar.Key = key
return radar, err
}
func createRadar(context appengine.Context, radarNumber int64, username string) (radar *Radar, err error) {
key := datastore.NewKey(context, "Radar", "", radarNumber, nil)
radar = &Radar{}
radar.Number = radarNumber
radar.UserName = username
radar.Published = false
now := time.Now()
radar.Originated = now
radar.Created = now
radar.Modified = now
_, err = datastore.Put(context, key, radar)
radar.Key = key
return radar, err
}
func deleteRadar(context appengine.Context, radarNumber int64) (err error) {
key := datastore.NewKey(context, "Radar", "", radarNumber, nil)
return datastore.Delete(context, key)
}
func updateRadar(context appengine.Context, radar *Radar) (err error) {
key := radar.Key
_, err = datastore.Put(context, key, radar)
return err
}
func getCommentsForRadar(context appengine.Context, username string, radar *Radar) (err error) {
q2 := datastore.NewQuery("Comment").Filter("RadarNumber =", radar.Number).Order("Created")
var comments []Comment
keys, err := q2.GetAll(context, &comments)
// build a map of comments by number
commentsByNumber := make(map[int64]*Comment)
for i, _ := range comments {
comment := &comments[i]
comment.Replies = make([]*Comment, 0)
comment.Key = keys[i]
comment.Number = comment.Key.IntID()
if comment.UserName == username {
comment.IsEditable = true
}
if username != "" {
comment.AllowReplies = true
}
commentsByNumber[comment.Number] = comment
}
// resolve threading and build a map holding the comments that were threaded
commentsThatWereThreaded := make(map[int64]*Comment)
for i, _ := range comments {
comment := &comments[i]
isReplyTo := comment.IsReplyTo
if isReplyTo != 0 {
parent, found := commentsByNumber[isReplyTo]
if found {
parent.Replies = append(parent.Replies, comment)
commentsThatWereThreaded[comment.Number] = comment
}
}
}
// attach top-level comments to the radar
radar.Comments = make([]*Comment, 0)
for i, _ := range comments {
comment := &comments[i]
_, found := commentsThatWereThreaded[comment.Number]
if !found {
radar.Comments = append(radar.Comments, comment)
}
}
return err
}
func getComment(context appengine.Context, username string, commentNumber int64) (comment *Comment, err error) {
key := datastore.NewKey(context, "Comment", "", commentNumber, nil)
comment = &Comment{}
err = datastore.Get(context, key, comment)
comment.Number = key.IntID()
comment.Key = key
comment.IsSaved = true
if comment.UserName == username {
comment.IsEditable = true
}
if username != "" {
comment.AllowReplies = true
}
return comment, err
}
func saveComment(context appengine.Context, comment *Comment) (err error) {
key := datastore.NewKey(context, "Comment", "", comment.Number, nil)
now := time.Now()
comment.Modified = now
context.Infof("Saving comment %+v", comment)
key, err = datastore.Put(context, key, comment)
comment.Number = key.IntID()
comment.Key = key
return err
}
func deleteComment(context appengine.Context, comment *Comment) (err error) {
return datastore.Delete(context, comment.Key)
}
|
<?xml version="1.0" encoding="utf-8"?>
<selector xmlns:android="http://schemas.android.com/apk/res/android">
<item android:state_selected="true" android:color="@color/dcn_ucenter_navi_text_color_pressed"/>
<item android:state_pressed="true" android:color="@color/dcn_ucenter_navi_text_color_pressed"/>
<item android:color="@color/dcn_ucenter_navi_text_color_normal"/>
</selector> |
Q:
Linked List Recursive removeAll method
I'm trying to define a recursive method that removes all instances in the singly-linked list that are equal to the target value. I defined a remove method and an accompanying removeAux method. How can I change this so that if the head needs to be removed, the head is reassigned as well? Here is what I have so far:
public class LinkedList<T extends Comparable<T>> {
private class Node {
private T data;
private Node next;
private Node(T data) {
this.data = data;
next = null;
}
}
private Node head;
public LinkedList() {
head = null;
}
public void remove(T target) {
if (head == null) {
return;
}
while (target.compareTo(head.data) == 0) {
head = head.next;
}
removeAux(target, head, null);
}
public void removeAux(T target, Node current, Node previous) {
if (target.compareTo(current.data) == 0) {
if (previous == null) {
head = current.next;
} else {
previous.next = current.next;
}
current = current.next;
removeAux(target, current, previous); // previous doesn't change
} else {
removeAux(target, current.next, current);
}
}
A:
I prefer to pass a reference to the previous when you remove to switch previous to the next something like this
public void remove(T target){
removeAux(target,head, null);
}
public void removeAux(T target, Node current, Node previous) {
//case base
if(current == null)
return;
if (target.compareTo(current.data) == 0) {
if (previous == null) {
// is the head
head = current.next;
} else {
//is not the head
previous.next = current.next;
}
current = current.next;
removeAux(target, current, previous); // previous doesn't change
} else {
removeAux(target, current.next, current);
}
}
Check this answer graphically linked list may help you to think how to implement it.
If this for training is good but you can do in iterative way.
|
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<title>CodeMirror: Compression Helper</title>
<link rel="stylesheet" type="text/css" href="http://fonts.googleapis.com/css?family=Droid+Sans|Droid+Sans:bold"/>
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<?php
namespace DeliciousBrains\WP_Offload_Media\Aws3\Aws\Crypto;
abstract class MaterialsProvider implements \DeliciousBrains\WP_Offload_Media\Aws3\Aws\Crypto\MaterialsProviderInterface
{
private static $supportedKeySizes = [128 => true, 192 => true, 256 => true];
/**
* Returns if the requested size is supported by AES.
*
* @param int $keySize Size of the requested key in bits.
*
* @return bool
*/
public static function isSupportedKeySize($keySize)
{
return isset(self::$supportedKeySizes[$keySize]);
}
/**
* Performs further initialization of the MaterialsProvider based on the
* data inside the MetadataEnvelope.
*
* @param MetadataEnvelope $envelope A storage envelope for encryption
* metadata to be read from.
*
* @return MaterialsProvider
*
* @throws \RuntimeException Thrown when there is an empty or improperly
* formed materials description in the envelope.
*
* @internal
*/
public abstract function fromDecryptionEnvelope(\DeliciousBrains\WP_Offload_Media\Aws3\Aws\Crypto\MetadataEnvelope $envelope);
/**
* Returns the material description for this Provider so it can be verified
* by encryption mechanisms.
*
* @return string
*/
public abstract function getMaterialsDescription();
/**
* Returns the wrap algorithm name for this Provider.
*
* @return string
*/
public abstract function getWrapAlgorithmName();
/**
* Takes a content encryption key (CEK) and description to return an
* encrypted key according to the Provider's specifications.
*
* @param string $unencryptedCek Key for use in encrypting other data
* that itself needs to be encrypted by the
* Provider.
* @param string $materialDescription Material Description for use in
* encrypting the $cek.
*
* @return string
*/
public abstract function encryptCek($unencryptedCek, $materialDescription);
/**
* Takes an encrypted content encryption key (CEK) and material description
* for use decrypting the key according to the Provider's specifications.
*
* @param string $encryptedCek Encrypted key to be decrypted by the Provider
* for use decrypting other data.
* @param string $materialDescription Material Description for use in
* encrypting the $cek.
*
* @return string
*/
public abstract function decryptCek($encryptedCek, $materialDescription);
/**
* @param string $keySize Length of a cipher key in bits for generating a
* random content encryption key (CEK).
*
* @return string
*/
public function generateCek($keySize)
{
return openssl_random_pseudo_bytes($keySize / 8);
}
/**
* @param string $openSslName Cipher OpenSSL name to use for generating
* an initialization vector.
*
* @return string
*/
public function generateIv($openSslName)
{
return openssl_random_pseudo_bytes(openssl_cipher_iv_length($openSslName));
}
}
|
/*
This file is part of solidity.
solidity is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
solidity is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with solidity. If not, see <http://www.gnu.org/licenses/>.
*/
// SPDX-License-Identifier: GPL-3.0
/**
* @author Christian <c@ethdev.com>
* @date 2015
* Versioning.
*/
#pragma once
#include <libsolutil/Common.h>
#include <string>
namespace solidity::frontend
{
extern char const* VersionNumber;
extern std::string const VersionString;
extern std::string const VersionStringStrict;
extern bytes const VersionCompactBytes;
extern bool const VersionIsRelease;
}
|
Q:
PHP for loop within for loop. Trying to sum multiple array columns to get combinations
i am trying to loop through a two-dimensional array and take a sum of the combinations of the columns automatically.
Suppose i have an array called $a with 4 columns:0,1,2,3,
$a=array();
$a[0][0]=1;
$a[0][1]=3;
$a[0][2]=5;
$a[1][0]=10;
$a[1][1]=2;
$a[1][2]=5;
$a[1][3]=7;
$a[2][0]=9;
$a[2][1]=8;
$a[2][2]=9;
$a[2][3]=8;
$a[3][0]=9;
$a[3][1]=8;
$a[3][2]=9;
$a[3][3]=8;
$a[3][4]=1;
And i am trying to sum over all of the combinations of the columns like sum(0,0;1,0;2;0,3;0) etc using this code
for($i=0;$i<count($a[0]);$i++){
for($l=0;$l<count($a[1]);$l++){
for($s=0;$s<count($a[2]);$s++){
for($m=0;$m<count($a[3]);$m++){
echo $sum[]= $a[0][$i]+$a[1][$l]+$a[2][$s]+$a[3][$m];
echo $sum;
echo "<br>";
}
}
}
}
?>
And the code works, the problem is that i am doing these for loops manually, there must be some way in which i can simplify this by somehow inserting the count of the number of columns?
I tried something like
$numberofcolumns=4;
for($n=0;$n<$numberofcolumns;$n++){
for($i=0;$i<count($a[$n]);$i++){
for($m=0;$m<count($a[$n+1]);$m++){
echo $sums[]= $a[$n][$i]+$a[$n+1][$m];
}
}
}
but that doesn't work, there must be some way to simplify the for loops so that i don't have to manually type in the for loops each column
anybody have a clue?
A:
You can use recursion, or just straight nested loops for this, but when working with combinations or permutations, the total number of possibilities can explode and become a huge number, consuming lots of memory to the point where you just cant run the code. Using an iterator is a nice way to trade cpu efficiency for memory efficiency. Here's an iterator I wrote.
class CartesianProductIterator implements Iterator {
protected $iterators;
function __construct(array $iters) {
$this->iterators = $iters;
}
function rewind() {
foreach ($this->iterators as $it) {
$it->rewind();
}
}
function current() {
$values = array();
foreach ($this->iterators as $it) {
$values[] = $it->current();
}
return $values;
}
function key() {
return null;
}
function next() {
/*
loop them in reverse, but exclude first
why? example, odometer: 55199
you always check the rightmost digit first to see if incrementing it would roll it over and need to be "rewound" to 0,
which causes the digit to the left to increase as well, which may also cause it to roll over as well, and so on...
looping in reverse operates from right column to the left.
we dont rewind the first column because if the leftmost column is on its last element and needs to roll over
then this iterator has reached its end, and so rewind() needs to be explicitly called
*/
for ($i = count($this->iterators) - 1; $i > 0; --$i) {
$it = $this->iterators[$i];
$it->next();
if ($it->valid()) {
// were done advancing because we found a column that didnt roll over
return;
} else {
$it->rewind();
}
}
//if execution reached here, then all of the columns have rolled over, so we must attempt to roll over the left most column
$this->iterators[0]->next();
}
function valid() {
return $this->iterators[0]->valid();
}
}
Then use it as
$iterators = array();
foreach ($a as $columnNumber => $values) {
$iterators[] = new ArrayIterator($values);
}
foreach (new CartesianProductIterator($iterators) as $combo) {
// combo has 1 value from each of the ArrayIterators we instantiated
printf("summing %s = %d\n", join('+', $combo), array_sum($combo));
}
heres a demo http://codepad.org/UasdgvWf
|
[Results of immunotherapy in 244 children with asthma or allergic rhinitis (author's transl)].
The results of immunotherapy in 244 children with asthma or allergic rhinitis have been evaluated by means of a questionaire directed at the parents. 86,9% of the children showed improvement. Additional information has been obtained about the side-effects of therapy--2,9% regularily showed dyspnoea--, the severity of symptoms before treatment and the influence of age on the above mentioned parameters. The results are discussed, compared with similar studies in adults and possible consequences for future diagnostic measures and therapy are proposed. |
Seven Obama alumni won their primary contests Tuesday, out of the 16 candidates with ties to the former president who competed in what was the biggest night of voting so far this year.
That brings the number of candidates connected to former President Barack Obama who are advancing to November's general election to at least 17, according to an NBC News tally on Wednesday. According to the Obama Alumni Association, which is tracking the bids of former staffers, more than 66 veterans from his political campaigns, two administrations and Senate office are running in federal, state or local elections this year, and more may add their names as the primary season continues.
A couple of the June 5 races, which occurred in California, Montana, New Jersey, New Mexico and four other states, saw alums pitted against each other. And in some cases, their success Tuesday has them poised for historic firsts.
Deb Haaland, 57, who according to The Associated Press won the Democratic primary in New Mexico's 1st Congressional District, would be the country's first Native American congresswoman if she wins again in November. She was a full-time Obama volunteer in 2008 and the New Mexico Native American vote director for his re-election campaign in 2012, and credits him with helping her find the courage to run. Many of her volunteers date back to those campaigns, and her office is still decorated with old Obama signs, she told NBC News last month.
“I feel like if I hadn't worked for the president, I would never have had the courage or the wherewithal to run,” she said at the time. "I think about him every single day."
Deidre DeJear, 32, won the Democratic primary for secretary of state in Iowa, where she'll challenge the Republican incumbent, Paul D. Pate, according to The Associated Press. DeJear was the state's director of African-American outreach on Obama’s 2012 campaign, and a volunteer on his 2008 campaign. She is the first black person to be nominated by a major party to statewide office in Iowa, and if she wins in November, she would be the first to be elected to statewide office in Iowa, too, according to WQAD.
DeJear defeated Jim Mowrer, who worked at the Pentagon during the Obama administration and on Obama's 2008 campaign, according to his LinkedIn page.
Ammar Campa-Najjar, 29, came in second in California's 50th Congressional District top-two primary, where he'll take on incumbent Rep. Duncan Hunter, a Republican, according to The A.P. (The Associated Press has confirmed winners that NBC News has not yet called because the margins of the races are small enough to not yet meet NBC News' statistical standards.)
Campa-Najjar was a deputy regional field director for Southern California on Obama's 2012 campaign before moving to Washington for stints at the White House and Department of Labor.
Tom Malinowski, 52, who served as an assistant secretary of state for democracy, human rights and labor in the Obama administration, won in New Jersey’s 7th Congressional District, according to The A.P., where he'll challenge the vulnerable Republican incumbent, Rep. Leonard Lance.
Also in New Jersey, Andy Kim ran uncontested in the Democratic primary in the state's 3rd Congressional District. He spent six years in the Obama administration, most recently serving as the director for Iraq on the White House National Security Council.
On previous primary election nights, Rich Cordray, former head of the Consumer Financial Protection Bureau, and Betty Sutton, an Obama appointee at the U.S. Saint Lawrence Seaway Development Corporation, advanced their joint-ticket bid to be governor and lieutenant governor in Ohio, while Colin Allred won in Texas' 32nd C.D. |
Today was sunny. Most predictions were for at least 5 gigawatts of solar PV arriving into the UK electricity system. This number hasn’t been reached for almost six months. (My website at Solar Forecast was a little more conservative and I think the algorithm was too pessimistic).
The electricity market didn’t predict the abundance of sun. As a result, it was hugely oversupplied in the middle of the day. If you’d been buying, you could have bought electricity for less than £10 a megawatt hour (1p a kilowatt hour) in the early afternoon. In fact, for the entire day so far the system price has been less than £30, a strikingly unusual state of affairs.
Phil Harper wrote to me a few minutes ago pointing out that today was the first obvious sighting of the California Duck in the UK this year. Electricity demand in the middle of the day was seriously dented by the superabundance of PV-generated electricity, an increasingly important feature of the Californian power market from March to September. Last Monday, the UK need for electricity was flat from noon to late afternoon at around 40 gigawatts. Today, it dipped sharply as the sun burnt off the haze. At 14.30, demand for other sources of power was around 35 gigawatts over 5 gigawatts less than a week ago. (I do not know why demand remains somewhat lower even now at around 10pm).
The chart below shows the dent in demand. The pattern will get even clearer over the next six months. Some sources suggest that UK PV installations will top 10 gigawatts by mid year, meaning that early afternoon power needs will dip by at least 8 gigawatts below usual levels on very sunny days.
As usual, DECC is either disguising these numbers in its monthly releases or is still unable to cope with the rate of installation. Despite being warned by National Statistics for fiddling with its estimates, it continues to make huge ad hoc changes in its statistics from month to month without acknowledging its problems in keeping up with solar volumes.
Solar is making a significant difference to the operation of the UK electricity market. |
//AD <- These first 4 characters need to be the first 4 characters to identify the ECMAScript file to Avidemux
print("Testing factory RoTexy");
admTestFacRoText();
print("Testing factory RoText");
/* End of test
*/
|
The United Arab Emirates received a unanimous vote of approval from the International Board on Books for Young People (IBBY), in response to a membership application submitted by Sheikha Budoor bint Sultan Al Qasimi, Chairperson of the Emirates Publishers Association and the Founder and Director of Kalimat. The UAE’s acceptance into the group paved the way for the launch of UAE National Chapter of the IBBY, which was officially announced in October 2009.
The UAE Chapter of IBBY aims to promote understanding and to facilitate the exchange of information through children’s books, to encourage and develop a wide array of literary and artistic works for children. It also organizes competitions, seminars and workshops for those involved in the field of children’s literature, encourages the publication and distribution of quality children’s books, especially in developing areas. Furthermore, the IBBY encourages the nationwide establishment of public libraries and strives to stimulate the translation of high quality children’s books both from and into Arabic and helps to raise the standard of children’s literature in the UAE to the highest international levels.
The UAE Pioneers Award Honours UAEBBY
The very prestigious UAE Pioneers Award was launched in 2014 to identify the UAE’s pioneers in different areas and honour them. This year the pioneers and supporters in the field of culture and reading in the UAE were honoured. The 2016 Awards were presented by His Highness Sheikh Mohammed bin Rashid Al Maktoum, Vice President and Prime Minister of the UAE and Ruler of Dubai. UAEBBY won the “Best NGO to Support Reading Among Young People” and Etisalat Telecom was awarded “Best Private Sector Initiative to Encourage Reading Among Children” in honour of the Etisalat Award for Arabic Children’s Literature that is organized and administered by UAEBBY.
Sharjah IBBY Children in Crisis Fund
IBBY is very pleased to announce the launch of the Sharjah IBBY Children in Crisis Fund to support a reading culture for children in the region of Central Asia, the Middle East and North Africa. This wonderful opportunity is the result of negotiations between the IBBY Foundation, lead by Patricia Aldana and the IBBY section in the United Arab Emirates – UAEBBY, lead by HE Sheikha Bodour Bint Sultan Al Qasimi.The first projects in the region will be announced later this year. |
1. Field of the Invention
The present invention relates to a Code Division Multiple Access (CDMA) system. More particularly, the present invention relates to a method and an apparatus for acquiring initial synchronization in a CDMA system.
2. Description of the Related Art
A Time Division Duplex (TDD) scheme is applied to a CDMA system, and the CDMA system based on the TDD scheme can use the same frequency band shared by both a downlink and an uplink and freely control and operate data capacities thereof by changing allocation of Time Slots (hereinafter, referred to as “TSs”) depending on a condition. Among such types of systems, a Time Division Synchronous Code Division Multiple Access (TD-SCDMA) system has been commercialized and is currently used in China.
FIG. 1 illustrates a structure of a sub-frame used in TD-SCDMA according to the related art.
Referring to FIG. 1, one sub-frames includes seven TSs having the same length for data transmission and a Special Time Slot (STS). The STS is used to distinguish between the downlink and the uplink, and includes a Downlink Pilot Time Slot (DwPTS), a Guard Period (GP), and an Uplink Pilot Time Slot (UpPTS). The DwPTS and the UpPTS include information for physical transmission synchronization. That is, a sequence for synchronization of forward link transmission is transmitted in a DwPTS field and a sequence for synchronization of reverse link transmission is transmitted in an UpPTS field. The TS in which data transmission is performed includes a data symbol interval and a mid-amble, and user data is included in the data symbol interval and includes pilot signal information for a mid-amble channel estimation. In general, TS0 is mainly used for data transmission for a broadcasting channel within a cell, TS1 is always used for uplink data transmission, and TS2 to TS6 are used for uplink or downlink data transmission according to higher allocation. Basically, TS1 and TS2 are allocated to the uplink, and TS3 to TS6 are allocated to the downlink. D and U within each TS block refer to the downlink and the uplink, respectively.
FIG. 2 illustrates a detailed structure of the DwPTS used for initial synchronization acquisition in the downlink according to the related art.
Referring to FIG. 2, the DwPTS includes GP and downlink synchronization (SYNC-DL) codes. The SYNC-DL code is transmitted with constant power and is not spread. Power of a SYNC-DL sequence is determined by higher layer signaling.
When the CDMA system based on the TDD scheme is initially driven, initial synchronization acquisition is necessary. The initial synchronization acquisition generally includes three steps described below and may be embodied in various types according to the implementation.
1. First Step: Search of the DwPTS and Identification of the SYNC-DL Sequence
A SYNC-DL sequence index is determined by performing slot synchronization by using the SYNC-DL sequence in the DwPTS in a second TS (STS) of one sub-frame. This is determined through comparison between a threshold and a maximum value from 32×6400 hypotheses acquired by performing a correlation through a matched filter. At this time, it may be required to acquire a plurality of hypotheses in consideration of several cells and the number of effective multi-path for each cell.
2. Second Step: Identification of Scrambling and Basic Mid-amble Codes
A corresponding mid-amble code group can be known from the SYNC-DL sequence acquired in the first step, i.e., Search of the DwPTS and identification of the SYNC-DL sequence, and a corresponding mid-amble code is identified among four basic mid-amble codes included in the group. The identified mid-amble code is equally used during one sub-frame. Further, since a relation between the mid-amble code and the scrambling code corresponds to a one-to-one correspondence mapping relation, when the mid-amble code is determined, the scrambling code is automatically determined. A correlation between the mid-amble code and the scrambling code is shown in Table 1 below.
TABLE 1Associated CodesCodeSYNC-DLSYNC-ULScramblingBasic Mid-ambleGroupIDIDCode IDCode IDGroup00 . . . 7001112233Group18 . . . 15442556677...Group31248 . . . 255124124321251251261261271273. Third Step: Control Multi-frame Synchronization
A phase of a channel value through a mid-amble of a Primary-Common Control Physical CHannel (P-CCPCH) is reflected to the SYNC-DL, and a position of a control multi-frame is determined by using information on a phase of the DwPTS.
4. Forth Step: Broadcasting CHannel (BCH) Decoding
Only when a CRC becomes “Good” through demodulation of the BCH are all the steps successfully completed and general communication starts. Such a step may not be included in an initial synchronization process.
Meanwhile, in the DCMA system based on the TDD scheme, channels related to initial synchronization having the structure shown in FIG. 1 are periodically received. Particularly, since the SYNC-DL including 64 chips is received every 5 ms interval in the TD-SCDMA system, the TD-SCDMA system has relatively low detection capabilities in comparison with Wide-band Code Division Multiple Access (W-DDCMA)/Frequency Division Duplex (FDD) systems in which initial synchronization is acquired using successively received pilot channels.
Accordingly, the TDD system acquires initial timing synchronization through the following two methods.
A first method finds an approximate position by using a power ratio between a SYNC-DL signal which exists in one sub-frame and a GAP adjacent to the SYNC-DL signal and then re-searches the vicinity of the position through a Maximum Likelihood (ML) scheme. Through the method, an approximate position is found by calculating a power ratio ((GP_left+GP_right)power/SYNC-DL power) between the SYNC-DL signal and GPs adjacent to a left side and a right side of the SYNC-DL in every sub-frame. At this time, the power ratio can be set and calculated as a chip interval or a multiple of the chip interval. However, since the method using the power ratio has low accuracy, a region having a minimum value should be found through the observation during significantly many sub-frames, and afterward energy is accumulated for every half chip by using the ML scheme for a predetermined interval in order to find accurate timing information in the unit of half chips in the decreased search interval. Thereafter, a position which is reported to have the highest energy is determined as a final timing position. Since the method requires only the calculation of the power ratio, a receiver structure is relatively simple. Further, since a first synchronization acquisition search interval is limited to the vicinity of the approximately found position, complexity can be reduced and a small size memory can be used. However, the method takes two or three times as long in comparison with a second method to find the accurate position, so that large degradation of the capability of this method should be expected.
The second method is a method of detecting a signal of one sub-frame by using the ML scheme, acquiring initial timing, and acquiring a code ID used as a corresponding pilot. For example, in TD-SCDMA, the method searches and compares energy amounts accumulated in all positions of entire sub-frame intervals (that is, 6400 chips) by using the ML scheme, and then calculates a SYNC-DL code having a largest energy value and a position determined in the unit of half chips. Although the method also calculates a final position through the observation for a plurality of sub-frame intervals, it takes less than half the time to acquire initial timing in comparison with the first method. However, since the method can determine the final position only when having energy values of all positions, memory size needs to be large. Accordingly, the method has a benefit in an aspect of the capability, but has a problem in an aspect of the complexity and memory size. Further, the second method can achieve the originally intended capability when there is only the downlink, but significant capability degradation is generated when an uplink signal transmitted from another terminal is located in the same frequency band.
In addition, in the first and second steps of the initial synchronization acquisition, when detection of the signal timing and acquisition of the SYNC-DL/Mid-amble ID is successfully declared, the subsequent step is performed. Mean Cell Search Time (MCST) may increase due to a false alarm which may be generated at this time. Particularly, when an error is generated due to the false alarm in the second step, a back side estimates a wrong residual frequency offset, and frame synchronization acquisition in the third step fails. Accordingly, the second step should be performed again, but this requires a lot of time. Therefore, it is required to minimize generation of the false alarm. However, it is difficult to acquire the desired capability just by simply controlling a threshold value. Further, when an initial synchronization acquiring process is performed in a place where a signal does not exist, the false alarm may be generated and thus an unnecessary cell searching process may be additionally performed. Accordingly, an additional reliability check algorithm is needed to reduce capability degradation due to the false alarm.
The above information is presented as background information only to assist with an understanding of the present disclosure. No determination has been made, and no assertion is made, as to whether any of the above might be applicable as prior art with regard to the present invention. |
A Rose with no thorns?!
So sailing along in 2016,
celebrating victories,
overcoming every storm,
dealing with every challenge and unpleasant news,
in the best way I possibly could:
publish a book, an instagram post,
art, radio show, write a song.
Colour my hair! Even knitted a scarf!!
Well it looks like a scarf!
And then came May, and “Brexit” happened!! Knocked the sail out of my wind or vice versa and I kinda grew to a halt.
So inadvertently, went on my first activist match, gay pride parade n carnival troupe in a costume that gave me enhanced bazongas!
Escaped into the musical world of a group of amazingly talented musicians, Sun Ra meets The Sylvers meets city council boys international aka meanwood boys!!
Enrolled at the College of Music, hurrah for the circle of 5ths. Sang and played guitar at amazing jams and soul nights.
My first kiss, yes, you heard me you know like the movie, “Never Been Kissed” (ok, take away your jealous judgmental faces and comments, ye “brethren y eglise”. I don’t need to go to confession, I’m not going to be condemned to hell! Lighten up!!)
Strange charcoal symbols, and got obsessed with building pyramids on my art course! Wrote and wrote and wrote at my Writers group.
Joined the Labour party and escaped being appointed BME or Women’s officer!
Keeping busy still, excessive volunteering with a BME hub and BHM! Not forgetting the demo to save the NHS dressed in my lab coat!!
Disillusioned by the health service,
the conspiracy theories, I finally watched the “Hypernormalisation” documentary everyone was banging on about!!
And used up all my internet data!
Still don’t know who or what to believe, Kemet, Christianity or Yoruba deities.
Phew, no wonder I took myself off to Alicante last week,
to get some perspective back,
help me back on my feet.
Much needed sun and sangria was a plenty! 😎
Fed up of awkwardly latching onto other peoples families (or OPFs), I decided to experiment and investigate the myth that, it’s not good to be by yourself on Xmas day”
Eh, still here,
didn’t get kidnapped by Santa’s elves
or the tooth fairy!!
Haha!!
Took a call from a well wisher at 11.30 pm, who became sad I’d been home alone (like the movie, 🎬 right) on Xmas day and insisted on picking me up to come hang out with their family, aw bless.
I couldn’t resist the sweet potato/yam African food offer!
So before the year runs out completely, I’m gonna try to steer back to reality. |
Phil Smith
Lynden Gooch is relieved to back in the first team fold at Sunderland after admitting he rushed his return from injury last season.
Gooch was a suprise starter at the beginning of David Moyes’ tenure last season, before a dip in form saw him taken out of the side. It was in the U23 set-up that he suffered a serious ankle injury, from which his season never really recovered.
A superb display at Brunton Park in the Carabao Cup means he is now firmly in contention for a spot in the starting XI and he says he has been invigorated as a result.
“It was a frustrating time,” he said. “I was doing really well and it stopped my momentum. It was really hard getting back.
“I probably came back earlier than I should have, trying to push myself and help the team. It took me a while and I probably wasn’t back to normal, back to my best, until the end of the season.
“I just wanted to make sure that this season with the new manager I was ready to go.
“I had a little setback towards the end of pre-season, which halted me a bit, but it’s all come together now.
“Last season was up and down. It started so well for me then everything crashed down around December time and the club going down was a huge disappointment. I definitely needed the summer to recharge the batteries and get back focused on helping the team as much as I could.”
Simon Grayson has vowed to give Sunderland’s younger players a chance this season, with George Honeyman starting in every league game so far.
The Black Cats boss also has big hopes for Duncan Watmore and Paddy McNair, who are nearing returns from cruciate ligament injuries.
Gooch says Grayson has been a great source of encouragement for the club’s youngsters.
He said: “From day one the manager said we would all get the chance and on Tuesday I got mine. Carlisle was my first start for a long time after my injury and everything so it was a relief. For the last six or so months it’s been tough but it’s worked out in the end.
“He just demands hard work, togetherness. I think everyone can see that, that all the boys are pulling together. The gaffer said from day one we’re a family now and we stick together no matter what. I think you can see that.
“We’re picking up points and doing well and I think we’re on the right track.” |
import React, {useRef, useEffect, useState} from 'react'
import {Flex, Text, Heading} from '../src'
const useAddRuleForPseudoClass = (ref, pseudoClass) => {
const [modifiedClassName, setModifiedClassName] = useState('')
useEffect(() => {
if (!ref.current) {
return
}
for (const className of ref.current.classList) {
const fullSelector = `.${className}${pseudoClass}`
const classNameWithSelector = fullSelector.replace(':', '-')
for (const ss of document.styleSheets) {
let newRule = ''
for (const rule of ss.cssRules) {
if (fullSelector === rule.selectorText) {
newRule = `${classNameWithSelector} { ${rule.style.cssText}}`
setModifiedClassName(classNameWithSelector.substring(1))
}
}
if (newRule) {
ss.insertRule(newRule, ss.cssRules.length)
break
}
}
}
}, [ref, pseudoClass])
return [modifiedClassName]
}
// Finds a CSS rule for the provided pseudo-class, adds a new
// class with the same css text to the stylesheet, and forwards
// that new class onto the child component.
export const WithPseudoClass = props => {
const ref = useRef()
const [modifiedClassName] = useAddRuleForPseudoClass(ref, props.pseudoClass)
return React.cloneElement(props.children, {
ref,
className: modifiedClassName
})
}
export const StickerSheet = ({children, title}) => {
return (
<Flex p={[3, 4]} flexDirection="column">
<Heading>{title}</Heading>
{children}
</Flex>
)
}
export const ComponentStickerSheet = ({props = [], pseudoClasses = [], title, children}) => {
const rows = [{}]
for (const prop of props) {
for (const value of prop.values) {
const modifiedProps = {}
modifiedProps[prop.prop] = value
rows.push(modifiedProps)
}
}
const propsModifiedChildren = rows.map(modifiedProps => {
const keys = Object.keys(modifiedProps)
const label = keys.length === 0 ? 'normal' : keys.map(key => `${key}: ${modifiedProps[key]}`).join(', ')
return (
<StickerSheetRow
label={label}
key={label}
childWrapper={child => React.cloneElement(child, {mr: 2, ...child.props, ...modifiedProps})}
>
{children}
</StickerSheetRow>
)
})
const pseudoClassChildren = pseudoClasses.map(pseudoClass => {
return (
<StickerSheetRow
label={pseudoClass}
key={pseudoClass}
childWrapper={child => (
<WithPseudoClass pseudoClass={pseudoClass}>
{React.cloneElement(child, {mr: 2, ...child.props})}
</WithPseudoClass>
)}
>
{children}
</StickerSheetRow>
)
})
return (
<Flex flexDirection="column" mb={2}>
<Text fontSize={3} fontWeight="bold">
{title}
</Text>
{propsModifiedChildren[0]}
{pseudoClassChildren}
{propsModifiedChildren.slice(1)}
</Flex>
)
}
const StickerSheetRow = ({children, label, childWrapper}) => {
return (
<Flex flexDirection="column">
<Text mr={2}>{label}</Text>
<Flex mb={2}>{React.Children.map(children, child => childWrapper(child))}</Flex>
</Flex>
)
}
|
Martin Järveoja
Martin Järveoja (; born 18 August 1987) is an Estonian rally co-driver. He is currently teamed with Ott Tänak and is competing for Hyundai in the World Rally Championship.
Rally career
He is the son of Estonian politician Toomas Järveoja, and originally a Judo competitor (he was five-time champion in Estonia). Järveoja began his rally career in 2006, co-driving for several drivers, including his cousin Ken Järveoja and uncle Tarmo Järveoja, competing in the regional and national championships.
In 2010, Järveoja made his debut in the World Rally Championship, co-driving for Karl Kruuda in Jordan. The pair finished fifth in the 2014 World Rally Championship-2 after wins in Finland and Sweden.
In December 2016, Järveoja signed a contract with M-Sport World Rally Team and formed a partnership with Ott Tänak. He and Tänak claimed their first World Rally Championship victory in the 2017 Rally Italia Sardegna.
From 2018, Järveoja and Tänak compete for Toyota Gazoo Racing WRT. In 2019, they won in Sweden, Chile, Portugal, Finland, Germany and Wales. They were crowned the world champions in Catalunya, with one race to spare.
Victories
WRC victories
Results
WRC results
* Season still in progress.
WRC-2 results
JWRC results
SWRC results
References
External links
Martin Järveoja on Instagram
Profile on WRC.com
Profile on eWRC-results.com
Category:1987 births
Category:Living people
Category:Estonian rally co-drivers
Category:World Rally Championship co-drivers
Category:Estonian male judoka
Category:People from Elva |
Latin America’s share of the voluntary carbon pie has grow dramatically over the last two years, but the Dominican Republic has focused almost exclusivly on offsets recognized under the Kyoto Protocol. Policymakers aim to fix that, and we dropped in for a look at the progress they’re making — and the challenges they’re likely to face.
Latin America’s share of the voluntary carbon pie has grow dramatically over the last two years, but the Dominican Republic has focused almost exclusivly on offsets recognized under the Kyoto Protocol. Policymakers aim to fix that, and we dropped in for a look at the progress they’re making — and the challenges they’re likely to face.
20 October 2010| If demand for voluntary carbon credits is flat lining in the US and failed REDD+ talks are casting a shadow over forest carbon markets, one would never guess it from the vitality of the Latin American Carbon Forum held last week in the Dominican Republic.
Latin America has good reason to be interested in voluntary carbon markets – credits from Latin American projects saw a dramatic increase in market share in 2009 and are reportedly still going strong. In the current year, Brazil, Colombia and other nations continue to develop market mechanisms that are unique to the region and the world.
But the Dominican Republic hardly rivals its southern neighbors as it struggles to find its place in the UN’s Clean Development Mechanism (CDM) and has no projects actively generating voluntary carbon credits (VERs). Addressing conference delegates, the DR’s Vice President Rafael Albuquerque recognized these market barriers – both in his nation and the developing world.
“Climate change is a serious and growing danger for our people, and climate change is science, not fiction,” he remarked. “The reality of climate change cannot be argued but our capacity to take collective measures is challenged.”
Regarding upcoming climate negotiations in Cancun, Albuquerque advocated for an international regime that synthesizes adaptation, mitigation, transparency and finance as “a clear formula that respects the principle of collective solutions.”
How is the Vice President’s high minded call to “act fairly, bravely and looking to the future” realized domestically? To date, the DR has registered hardly a handful of CDM projects. Further, its classification as a “frontier” (i.e. risky) investment location – coupled with the threat of political turnover in the 2012 presidential election – stymies greater private sector engagement.
Yet despite the island nation’s investment risks, some project developers and investors see the DR’s forests for their trees. And they’re moving in, armed with lessons learned and some sizable personal capital commitments.
Eyes on the sky, feet on the ground
While attending the LACF, Ecosystem Marketplace caught up with Anthony Simmons, chief operating officer for Citivest International, who is drumming up business and support for the island nation’s first large-scale forest carbon VER project – not to mention throwing some of his own financial weight behind the project.
If all goes as planned, Simmons claims that Phase I of the project will feature an afforestation/reforestation project on 104,000 hectares that directly engages 9,500 local cacao farmers in the region stretching between San Francisco de Macoris and Hato Mayor.
Rather than aggregate and manage thousands of landowners through a grouped project approach – also a topic of intense interest among conference-goers – Citivest partnered with Conacado, the National Confederation of Dominican Cacao Producers under which many local landowners operate.
Through the partnership, Citivest gains access not only to Conacado’s thousands of cocoa-producing members but also historical data on the project area – the kind of agricultural data Simmons says is not readily available through the Dominican Republic’s CDM-focused Designated National Authority (DNA).
Speaking to the current dearth of historical land use data, Simmons says that this data isn’t as hard to obtain as officials suspect. “What the DNA hasn’t figured out yet is that you can get data from agriculture agencies like co-ops because they’ve been around for years.”
Through agriculture cooperatives, Citivest is collecting land area crop data and title, deed and ownership information. The Conocado partnership also enables Citivest to manage 9,500+ stakeholders at a collective rather than individual level.
“This country is really an agriculture powerhouse and the agricultural co-ops are at the front lines,” he describes. “The co-ops have good records of working with and tracking their membership, so it’s easy to get data, records of names or land titles right through them instead of individuals – or the DNA.”
By the end of 2010, Citivest aims to offer upwards of eight million ex ante vintage 2011 credits from the project that Simmons says imparts “all the sustainable development bells and whistles” – i.e. not your run-of-the-mill community benefits.
Project co-benefits in this case might include a climate event warning system, local “hip” cultural events and amenities to stymie the brain drain from rural to urban areas and multiple revenue streams from carbon credits and cacao futures.
Lots of eggs, lots of baskets
Citivest boldly goes where no VER project has gone before thanks in part to Simmons’ personal cash outlay, which he says gives him the necessary autonomy to circumvent bureaucratic project hassles. But what about those project stakeholders and developers without the material goods to grease the grid?
If the goal is to attract and marry some of the markets’ emerging capital solutions to an early-stage emissions reduction project, MGM Innova Capital president and CEO Marco Monroy offers this advice: smart projects in this market are those with multiple revenue streams.
“It helps to have a second source of funds because depending exclusively on carbon makes the investment riskier,” says Monroy. “The way to protect your company from carbon market uncertainty is to have a dual income and be happy with other market returns in case carbon doesn’t happen.”
Monroy says of these project types, “If we invest in forestry and energy efficiency, we’re doing the most we can do to reduce emissions in the medium and long term.” Monroy further notes that the MCDF will invest in projects that have both low-carbon and social components “to take the benefits of carbon markets to individuals and companies that have not yet had the benefit of carbon.”
Other conference attendees were also bullish on market prospects for multi-purpose project types like energy efficiency, landfill and agricultural methane – and their growing appeal to venture capitalists. The financial crisis itself might have lent surviving offset providers some new-found credibility in the eyes of investors.
“Post-crisis, we have grounded expectations of what’s available in the markets and what we can deliver,” notes John Paul Moscarella, Senior Managing Director at Emerging Energy and Environment. “There’s also a real trend toward clean energy and clean tech and we seem to be in the early days of this ‘next phase.'”
“Those kinds of megatrends will take billions if not trillions of dollars to bring to market. Investors like that, the potential for getting in on the ground with those Google-like stories.”
Molly Peters-Stanley is the Voluntary Carbon Associate in the Ecosystem Marketplace’s Carbon Program. She can be reached at mpeters-stanley@ecosystemmarketplace.com. Please see our Reprint Guidelines for details on republishing our articles. |
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abstract: 'The next challenge of game AI lies in Real Time Strategy (RTS) games. RTS games provide partially observable gaming environments, where agents interact with one another in an action space much larger than that of GO. Mastering RTS games requires both strong macro strategies and delicate micro level execution. Recently, great progress has been made in micro level execution, while complete solutions for macro strategies are still lacking. In this paper, we propose a novel learning-based Hierarchical Macro Strategy model for mastering MOBA games, a sub-genre of RTS games. Trained by the Hierarchical Macro Strategy model, agents explicitly make macro strategy decisions and further guide their micro level execution. Moreover, each of the agents makes independent strategy decisions, while simultaneously communicating with the allies through leveraging a novel imitated cross-agent communication mechanism. We perform comprehensive evaluations on a popular 5v5 Multiplayer Online Battle Arena (MOBA) game. Our 5-AI team achieves a 48% winning rate against human player teams which are ranked top 1% in the player ranking system.'
author:
- |
$^{1}$Bin Wu, $^{1}$Qiang Fu, $^{1}$Jing Liang, $^{1}$Peng Qu, $^{1}$Xiaoqian Li, $^{1}$Liang Wang, $^{2}$Wei Liu, $^{1}$Wei Yang, $^{1}$Yongsheng Liu\
$^{1,2}$Tencent AI Lab\
$^{1}${benbinwu, leonfu, masonliang, pengqu, xiaoqianli, enginewang, willyang, kakarliu}@tencent.com\
$^{2}$wliu@ee.columbia.edu\
bibliography:
- 'aaai19.bib'
title: |
Hierarchical Macro Strategy Model for\
MOBA Game AI
---
Introduction
============
Light has been shed on artificial general intelligence after AlphaGo defeated world GO champion Lee Seedol [@silver2016mastering]. Since then, game AI has drawn unprecedented attention from not only researchers but also the public. Game AI aims much more than robots playing games. Rather, games provide ideal environments that simulate the real world. AI researchers can conduct experiments in games, and transfer successful AI ability to the real world. Although AlphaGo is a milestone to the goal of general AI, the class of problems it represents is still simple compared to the real world. Therefore, recently researchers have put much attention to real time strategy (RTS) games such as Defense of the Ancients (Dota) [@dota] and StarCraft [@vinyals2017starcraft; @tian2017elf], which represents a class of problems with next level complexity. Dota is a famous set of science fiction 5v5 Multiplayer Online Battle Arena (MOBA) games. Each player controls one unit and cooperate with four allies to defend allies’ turrets, attack enemies’ turrets, collect resources by killing creeps, etc. The goal is to destroy enemies’ base.
There are four major aspects that make RTS games much more difficult compared to GO: 1) **Computational complexity**. The computational complexity in terms of action space or state space of RTS games can be up to $10^{20,000}$, while the complexity of GO is about $10^{250}$ [@openaifive0]. 2) **Multi-agent**. Playing RTS games usually involves multiple agents. It is crucial for multiple agents to coordinate and cooporate. 3) **Imperfect information**. Different to GO, many RTS games make use of fog of war [@vinyals2017starcraft] to increase game uncertainty. When the game map is not fully observable, it is essential to consider gaming among one another. 4) **Sparse and delayed rewards**. Learning upon game rewards in GO is challenging because the rewards are usually sparse and delayed. RTS game length could often be larger than 20,000 frames, while each GO game is usually no more than 361 steps.
To master RTS games, players need to have strong skills in both macro strategy operation and micro level execution. In recent study, much attention and attempts have been put to micro level execution [@vinyals2017starcraft; @tian2017elf; @synnaeve2011bayesian; @wender2012applying]. So far, Dota2 AI developed by OpenAI using reinforcement learning, i.e., OpenAI Five, has made the most advanced progress [@dota]. OpenAI Five was trained directly on micro level action space using proximal policy optimization algorithms along with team rewards [@schulman2017proximal]. OpenAI Five has shown strong teamfights skills and coordination comparable to top professional Dota2 teams during a demonstration match held in The International 2018 [@ti8]. OpenAI’s approach did not explicitly model macro strategy and tried to learn the entire game using micro level play. However, OpenAI Five was not able to defeat professional teams due to weakness in macro strategy management [@openaifive; @openaifive2]. Related work has also been done in explicit macro strategy operation, mostly focused on navigation. Navigation aims to provide reasonable destination spots and efficient routes for agents. Most related work in navigation used influence maps or potential fields [@deloura2001game; @hagelback2008rise; @do2015development]. Influence maps quantify units using handcrafted equations. Then, multiple influence maps are fused using rules to provide a single-value output to navigate agents. Providing destination is the most important purpose of navigation in terms of macro strategy operation. The ability to get to the right spots at right time makes essential difference between high level players and the others. Planning has also been used in macro strategy operation. Ontanon *et al*. proposed Adversarial Hierarchical-Task Network (AHTN) Planning [@ontanon2015adversarial] to search hierarchical tasks in RTS game playing. Although AHTN shows promising results in a mini-RTS game, it suffers from efficiency issue which makes it difficult to apply to full MOBA games directly.
Despite of the rich and promising literature, previous work in macro strategy failed to provide complete solution:
First, reasoning macro strategy implicitly by learning upon micro level action space may be too difficult. OpenAI Five’s ability gap between micro level execution and macro strategy operation was obvious. It might be over-optimistic to leave models to figure out high level strategies by simply looking at micro level actions and rewards. We consider explicit macro strategy level modeling to be necessary.
Second, previous work on explicit macro strategy heavily relied on handcrafted equations for influence maps/potential fields computation and fusion. In practice, there are usually thousands of numerical parameters to manually decide, which makes it nearly impossible to achieve good performance. Planning methods on the other hand cannot meet efficiency requirement of full MOBA games.
Third, one of the most challenging problems in RTS game macro strategy operation is coordination among multiple agents. Nevertheless, to the best of our knowledge, previous work did not consider it in an explicit way. OpenAI Five considers multi-agent coordination using team rewards on micro level modeling. However, each agent of OpenAI Five makes decision without being aware of allies’ macro strategy decisions, making it difficult to develop top coordination ability in macro strategy level.
Finally, we have found that modeling strategic phase is crucial for MOBA game AI performance. However, to the best of our knowledge, previous work did not consider this. Teaching agents to learn macro strategy operation, however, is challenging. Mathematically defining macro strategy, e.g., besiege and split push, is difficult in the first place. Also, incorporating macro strategy on top of OpenAI Five’s reinforcement learning framework [@dota] requires corresponding execution to gain rewards, while macro strategy execution is a complex ability to learn by itself. Therefore, we consider supervised learning to be a better scheme because high quality game replays can be fully leveraged to learn macro strategy along with corresponding execution samples. Note that macro strategy and execution learned using supervised learning can further act as an initial policy for reinforcement learning.
In this paper, we propose Hierarchical Macro Strategy (HMS) model - a general supervised learning framework for MOBA games such as Dota. HMS directly tackles with **computational complexity** and **multi-agent** challenges of MOBA games. More specifically, HMS is a hierarchical model which conducts macro strategy operation by predicting attention on the game map under guidance of game phase modeling. Thereby, HMS reduces computational complexity by incorporating game knowledge. Moreover, each HMS agent conducts learning with a novel mechanism of communication with teammates agents to cope with multi-agent challenge. Finally, we have conducted extensive experiments in a popular MOBA game to evaluate our AI ability. We matched with hundreds of human player teams that ranked above 99% of players in the ranked system and achieved 48% winning rate.
The rest of this paper is organized as follows: First, we briefly introduce Multiplayer Online Battle Arena (MOBA) games and compare the computational complexity with GO. Second, we illustrate our proposed Hierarchical Macro Strategy model. Then, we present experimental results in the fourth section. Finally, we conclude and discuss future work.
Multiplayer Online Battle Arena (MOBA) Games
============================================
Game Description
----------------
MOBA is currently the most popular sub-genre of the RTS games. MOBA games are responsible for more than 30% of the online gameplay all over the world, with titles such as Dota, League of Legends, and Honour of Kings [@moba_hot]. According to a worldwide digital games market report in February 2018, MOBA games ranked first in grossing in both PC and mobile games [@hok].
In MOBA, the standard game mode requires two 5-player teams play against each other. Each player controls one unit, i.e., hero. There are numerous of heroes in MOBA, e.g., more than 80 in Honour of Kings. Each hero is uniquely designed with special characteristics and skills. Players control movement and skill releasing of heroes via the game interface.
As shown in Figure. \[ui\], Honour of Kings players use left bottom steer button to control movements, while right bottom set of buttons to control skills. Surroundings are observable via the main screen. Players can also learn full map situation via the left top corner mini-map, where observable turrets, creeps, and heroes are displayed as thumbnails. Units are only observable either if they are allies’ units or if they are within a certain distance to allies’ units.
There are three lanes of turrets for each team to defend, three turrets in each lane. There are also four jungle areas on the map, where creep resources can be collected to increase gold and experience. Each hero starts with minimum gold and level 1. Each team tries to leverage resources to obtain as much gold and experience as possible to purchase items and upgrade levels. The final goal is to destroy enemy’s base. A conceptual map of MOBA is shown in Figure. \[map\].
To master MOBA games, players need to have both excellent macro strategy operation and proficient micro level execution. Common macro strategies consist of opening, laning, ganking, ambushing, etc. Proficient micro level execution requires high accuracy of control and deep understanding of damage and effects of skills. Both macro strategy operation and micro level execution require mastery of timing to excel, which makes it extremely challenging and interesting. More discussion of MOBA can be found in [@silva2017moba].
Next, we will quantify the computational complexity of MOBA using Honour of Kings as an example.
Computational Complexity
------------------------
The normal game length of Honour of Kings is about 20 minutes, i.e., approximately 20,000 frames in terms of gamecore. At each frame, players make decision with tens of options, including movement button with 24 directions, and a few skill buttons with corresponding releasing position/directions. Even with significant discretization and simplification, as well as reaction time increased to 200ms, the action space is at magnitude of $10^{1,500}$.
As for state space, the resolution of Honour of Kings map is 130,000 by 130,000 pixels, and the diameter of each unit is 1,000. At each frame, each unit may have different status such as hit points, levels, gold. Again, the state space is at magnitude of $10^{20,000}$ with significant simplification.
Comparison of action space and state space between MOBA and GO is listed in Table. \[tab:comparison\].
[|L[1.5cm]{}|L[3cm]{}|L[3cm]{}|]{} & GO & MOBA\
Action Space & $250^{150} \approx 10^{360}$ (250 pos available, 150 decisions per game in average) & $10^{1500}$ (10 options, 1500 actions per game)\
State Space & $3^{360} \approx 10^{170}$ (361 pos, 3 states each) & $10^{20000}$ (10 heroes, 2000+pos \* 10+states)\
\[tab:comparison\]
MOBA AI Macro Strategy Architecture
-----------------------------------
Our motivation of designing MOBA AI macro strategy model was inspired from how human players make strategic decisions. During MOBA games, experienced human players are fully aware of game phases, e.g., opening phase, laning phase, mid game phase, and late game phase [@silva2017moba]. During each phase, players pay attention to the game map and make corresponding decision on where to dispatch the heroes. For example, during the laning phase players tend to focus more on their own lanes rather than backing up allies, while during mid to late phases, players pay more attention to teamfight spots and pushing enemies’ base.
To sum up, we formulate the macro strategy operation process as “phase recognition -> attention prediction -> execution”. To model this process, we propose a two-layer macro strategy architecture, i.e., phase and attention:
- **Phase** layer aims to recognize current game phase so that attention layer can have better sense about where to pay attention to.\
- **Attention** layer aims to predict the best region on game maps to dispatch heroes.\
**Phase** and **Attention** layers act as high level guidance for micro level execution. We will describe details of modeling in the next section. The network structure of micro level model is almost identical to the one used in OpenAI Five[^1] [@dota], but in a supervised learning manner. We did minor modification to adapt it to Honour of Kings, such as deleting Teleport.
Hierarchical Macro Strategy Model
=================================
We propose a Hierarchical Macro Strategy (HMS) model to consider both phase and attention layers in a unified neural network. We will first present the unified network architecture. Then, we illustrate how we construct each of the phase and attention layers.
Model Overview
--------------
We propose a Hierarchical Macro Strategy model (HMS) to model both attention and phase layers as a multi-task model. It takes game features as input. The output consists of two tasks, i.e., attention layer as the main task and phase layer as an auxiliary task. The output of attention layer directly conveys macro strategy embedding to micro level models, while resource layer acts as an axillary task which help refine the shared layers between attention and phase tasks. The illustrating network structure of HMS is listed in Figure. \[hms\_network\]. HMS takes both image and vector features as input, carrying visual features and global features respectively. In image part, we use convolutional layers. In vector part, we use fully connected layers. The image and vector parts merge in two separate tasks, i.e., attention and phase. Ultimately, attention and phase tasks take input from shared layers through their own layers and output to compute loss.
{width="1.7\columnwidth"}
Attention Layer
---------------
Similar to how players make decisions according to the game map, attention layer predicts the best region for agents to move to. However, it is tricky to tell from data that where is a player’s destination. We observe that regions where attack takes place can be indicator of players’ destination, because otherwise players would not have spent time on such spots. According to this observation, we define ground-truth regions as the regions where players conduct their next attack. An illustrating example is shown in Figure. \[transfer\_label\].
![Illustrating example for label extraction in attention layer.[]{data-label="transfer_label"}](transfer_label.png){width="1\columnwidth"}
Let $s$ to be one session in a game which contains several frames, and $s-1$ indicates the session right before $s$. In Figure. \[transfer\_label\], $s-1$ is the first session in the game. Let $t_s$ to be the starting frame of $s$. Note that a session ends along with attack behavior, therefore there exists a region $y_s$ in $t_s$ where the hero conducts attack. As shown in Figure. \[transfer\_label\], label for $s-1$ is $y_s$, while label for $s$ is $y_{s+1}$. Intuitively, by setting up labels in this way, we expect agents to learn to move to $y_s$ at the beginning of game. Similarly, agents are supposed to move to appropriate regions given game situation.
Phase layer
-----------
Phase layer aims to recognize the current phase. Extracting game phases ground-truth is difficult because phase definition used by human players is abstract. Although roughly correlated to time, phases such as opening, laning, and late game depend on complicated judgment based on current game situation, which makes it difficult to extract ground-truth of game phases from replays. Fortunately, we observe clear correlation between game phases with major resources. For example, during the opening phase players usually aim at taking outer turrets and baron, while for late game, players operate to destroy enemies’ base.
Therefore, we propose to model phases with respect to major resources. More specifically, major resources indicate turrets, baron, dragon, and base. We marked the major resources on the map in Figure. \[strategy\_layer\]. Label definition of phase layer is similar to attention layer. The only difference is that $y_s$ in phase layer indicates attack behavior on turrets, baron, dragon, and base instead of in regions. Intuitively, phase layer modeling splits the entire game into several phases via modeling which macro resource to take in current phase.
We do not consider other resources such as lane creeps, heroes, and neutral creeps as major objectives because usually these resources are for bigger goal, such as destroying turrets or base with higher chance. Figure. \[strategy\_series\] shows a series of attack behavior during the bottom outer turret strategy. The player killed two neutral creeps in the nearby jungle and several lane creeps in the bottom lane before attacking the bottom outer turret.
We expect the model to learn when and what major resources to take given game situation, and in the meanwhile learn attention distribution that serve each of the major resources.
Imitated Cross-agents Communication
-----------------------------------
Cross-agents communication is essential for a team of agents to cooperate. There is rich literature of cross-agent communication on multi-agent reinforcement learning research [@sukhbaatar2016learning; @foerster2016learning]. However, it is challenging to learn communication using training data in supervised learning because the actual communication is unknown.
To enable agents to communicate in supervised learning setting, we have designed a novel cross-agents communication mechanism. During training phase, we put attention labels of allies as features for training. During testing phase, we put attention prediction of allies as features and make decision correspondingly. In this way, our agents can “communicate” with one another and learn to cooperate upon allies’ decisions. We name this mechanism as Imitated Cross-agents Communication due to its supervised nature.
Experiments
===========
In this section, we evaluate our model performance. We first describe the experimental setup, including data preparation and model setup. Then, we present qualitative results such as attention distribution under different phase. Finally, we list the statistics of matches with human player teams and evaluate improvement brought by our proposed model.
Experimental Setup
------------------
### Data Preparation
To train a model, we collect around 300 thousand game replays made of King Professional League competition and training records. Finally, 250 million instances were used for training. We consider both visual and attributes features. On visual side, we extract 85 features such as position and hit points of all units and then blur the visual features into 12\*12 resolution. On attributes side, we extract 181 features such as roles of heroes, time period of game, hero ID, heroes’ gold and level status and Kill-Death-Assistance statistics.
### Model Setup
We use a mixture of convolutional and fully-connected layers to take inputs from visual and attributes features respectively. On convolutional side, we set five shared convolutional layers, each with 512 channels, $padding=1$, and one RELU. Each of the tasks has two convolutional layers with exactly the same configuration with shared layers. On fully-connected layers side, we set two shared fully-connected layers with 512 nodes. Each of the tasks has two fully-connected layers with exactly the same configuration with shared layers. Then, we use one concatenation layer and two fully-connected layers to fuse results of convolutional layers and fully-connected layers. We use ADAM as the optimizer with base learning rate at 10e-6. Batch size was set at 128. The loss weights of both phase and attention tasks are set at 1. We used CAFFE [@jia2014caffe] with eight GPU cards. The duration to train an HMS model was about 12 hours.
Finally, the output for attention layer corresponds to 144 regions of the map, resolution of which is exactly the same as the visual inputs. The output of the phase task corresponds to 14 major resources circled in Figure. \[strategy\_layer\].
Experimental Results
--------------------
### Opening Attention
Opening is one of the most important strategies in MOBA. We show one opening attention of different heroes learned by our model in Figure. \[opening\]. In Figure. \[opening\], each subfigure consists of two square images. The left-hand-side square image indicates the attention distribution of the right-hand-side MOBA mini-map. The hottest region is highlighted with red circle. We list attention prediction of four heroes, i.e., Diaochan, Hanxin, Arthur, and Houyi. The four heroes belong to master, assasin, warrior, and archer respectively. According to the attention prediction, Diaochan is dispatched to middle lane, Hanxin will move to left jungle area, and Authur and Houyi will guard the bottom jungle area. The fifth hero Miyamoto Musashi, which was not plotted, will guard the top outer turret. This opening is considered safe and efficient, and widely used in Honour of Kings games.
{width="2\columnwidth"}
### Attention Distribution Affected by Phase Layer
We visualize attention distribution of different phases in Figure. \[upper\_outer\] and \[base\]. We can see that attention distributes around the major resource of each phase. For example, for upper outer turret phase in Figure. \[upper\_outer\], the attention distributes around upper outer region, as well as nearby jungle area. Also, as shown in Figure. \[base\], attention distributes mainly in the middle lane, especially area in front of the base. These examples show that our phase layer modeling affects attention distribution in practice. To further examine how phase layer correlates with game phases, we conduct t-Distributed Stochastic Neighbor Embedding (t-SNE) on phase layer output. As shown in Figure. \[tsne\], samples are coloured with respect to different time stages. We can observe that samples are clearly separable with respect to time stages. For example, blue, orange and green (0-10 minuets) samples place close to one another, while red and purple samples (more than 10 minuets) form another group.
{width="1.5\columnwidth"}
### Macro Strategy Embedding
We evaluate how important is the macro strategy modeling. We removed the macro strategy embedding and trained the model using micro level actions from the replays. The micro level model design is similar to OpenAI Five [@dota]. Detail description of the micro level modeling is out of the scope of this paper.
The result is listed in Table. \[match\_stats\], column AI Without Macro Strategy. As the result shows, HMS outperformed AI Without Macro Strategy with 75% winning rates. HMS performed much better than AI Without Macro Strategy in terms of number of kills, turrets destruction, and gold. The most obvious performance change is that AI Without Macro Strategy mainly focused on nearby targets. Agents did not care much about backing up teammates and pushing lane creeps in relatively large distance. They spent most of the time on killing neutral creeps and nearby lane creeps. The performance change can be observed from the comparison of engagement rate and number of turrets in Table. \[match\_stats\]. This phenomenon may reflect how important macro strategy modeling is to highlight important spots.
[|L[2.5cm]{}|L[3.5cm]{}|L[2.5cm]{}|L[3.5cm]{}|L[3.5cm]{}|]{} Opponents & AI Without Macro Strategy & Human Teams & AI Without Communication & AI Without Phase Layer\
Winning rate & **75%** - 25% & 48.3% - **51.7%** & **62.5%** - 37.5% & **65%** - 35%\
Kill & **26.0** - 21.1 & 22.6 - **26.3** & **19.9** - 19.4 & **25.6** - 22.8\
Game Length & 16.1 min & 16.1 min & 18.2 min & 18.2 min\
Gold/Min & **2399** - 2287 & 2603 - **2616** & **2633** - 2554 & **2500** - 2333\
Engagement Rate & **49%** - 42% & 48% - 48% & **49%** - 47% & **50%** - 49%\
Turrets & **6.1** - 3.2 & 6.1 - **6.2** & **6.21** - 5.26 & **6.73** - 5.42\
Dragons & **1.22** - 0.2 & 0.55 - 0.55 & **0.65** - 0.49 & **1** - 0.41\
Barons & **0.62** - 0.31 & **0.64** - 0.61 & **0.45** - 0.41 & **0.71** - 0.2\
Dark Barons & **0.41** - 0.22 & 0.36 - **0.38** & 0.35 - 0.32 & **0.49** - 0.04\
\[match\_stats\]
### Match against Human Players
To evaluate our AI performance more accurately, we conduct matches between our AI and human players. We invited 250 human player teams whose average ranking is King in Honour of Kings rank system (above 1% of human players). Following the standard procedure of ranked match in Honour of Kings, we obey ban-pick rules to pick and ban heroes before each match. The ban-pick module was implemented using simple rules. Note that gamecores of Honour of Kings limit commands frequency to a level similar with human.
The overall statistics are listed in Table. \[match\_stats\], column Human Teams. Our AI achieved 48% winning rate in the 250 games. The statistics show that our AI team did not have advantage on teamfight over human teams. The number of kills made by AI is about 15% less than human teams. Other items such as turrets destruction, engagement rate, and gold per minute were similar between AI and human. We have further observed that our AI destroyed 2.5 more turrets than human on average in the first 10 minutes. After 10 minutes, turrets difference shrank due to weaker teamfight ability compared to human teams. Arguably, our AI’s macro strategy operation ability is close to or above our human opponents.
### Imitated Cross-agents Communication
To evaluate how important the cross-agents communication mechanism is to the AI ability, we conduct matches between HMS and HMS trained without cross-agents communication. The result is listed in Table. \[match\_stats\], column AI Without Communication. HMS achieved a 62.5% winning rate over the version without communication. We have observed obvious cross-agents cooperation learned when cross-agents communication was introduced. For example, rate of reasonable opening increased from 22% to 83% according to experts’ evaluation.
### Phase layer
We evaluate how phase layer affects the performance of HMS. We removed the phase layer and compared it with the full version of HMS. The result is listed in Table. \[match\_stats\], column AI Without phase layer. The result shows that phase layer modeling improved HMS significantly with 65% winning rate. We have also observed obvious AI ability downgrade when phase layer was removed. For example, agents were no longer accurate about timing when baron first appears, while the full version HMS agents got ready at 2:00 to gain baron as soon as possible.
Conclusion and Future Work
==========================
In this paper, we proposed a novel Hierarchical Macro Strategy model which models macro strategy operation for MOBA games. HMS explicitly models agents’ attention on game maps and considers game phase modeling. We also proposed a novel imitated cross-agent communication mechanism which enables agents to cooperate.
We used Honour of Kings as an example of MOBA games to implement and evaluate HMS. We conducted matches between our AI and top 1% human player teams. Our AI achieves a 48% winning rate. To the best of our knowledge, our proposed HMS model is the first learning based model that explicitly models macro strategy for MOBA games. HMS used supervised learning to learn macro strategy operation and corresponding micro level execution from high quality replays. A trained HMS model can be further used as an initial policy for reinforcement learning framework.
Our proposed HMS model exhibits a strong potential in MOBA games. It may be generalized to more RTS games with appropriate adaptations. For example, the attention layer modeling may be applicable to StarCraft, where the definition of attention can be extended to more meaningful behaviors such as building operation. Also, Imitated Cross-agents Communication can be used to learn to cooperate. Phase layer modeling is more game-specific. The resource collection procedure in StarCraft is different from that of MOBA, where gold is mined near the base. Therefore, phase layer modeling may require game-specific design for different games. However, the underlying idea to capture game phases can be generalized to Starcraft as well.
HMS may also inspire macro strategy modeling in domains where multiple agents cooperate on a map and historical data is available. For example, in robot soccer, attention layer modeling and Imitated Cross-agents Communication may help robots position and cooperate given parsed soccer recordings.
In the future, we will incorporate planning based on HMS. Planning by MCTS roll-outs in Go has been proven essential to outperform top human players [@silver2016mastering]. We expect planning can be essential for RTS games as well, because it may not only be useful for imperfect information gaming but also be crucial to bringing in expected rewards which supervised learning fails to consider.
[^1]: <https://d4mucfpksywv.cloudfront.net/research-covers/openai-five/network-architecture.pdf>
|
Grouper social club
Grouper was an online, invite-only social club that uses data gathered from Facebook profiles to organize group outings (called Groupers). Matches for the outings were gathered and analyzed first by a computer and then by a human to ensure strong matches. The excursions were planned in venues throughout 25 cities for six people. Groupers consisted of two groups of three friends and can consist of three males and three females, six males, six females, or any other possible combination.
Michael Waxman founded the New York-based startup in 2011. The company was run by a staff of 25 people. In 2013, Time Inc. listed Grouper in its 10 NYC Startups to Watch for 2013. Three years later, in October 2016, the company shut down.
How a Grouper works
Grouper is an invite-only service that matches two individuals according to data found – with the permission of the user – on the user's Facebook profile, including age, career, education, etc. The company determines a match between two individuals using both algorithms and its member experience team. A time is then set for the "Grouper". The two parties are asked to each bring two friends. No names, photos, or information are disclosed before the actual meet. Upon arrival at the determined location, the group receives a complimentary first round of drinks, including tax and tip, at a reserved table (the cost is included in Grouper's service fee).
The company offers arrangements for both opposite- and same-sex Groupers.
Communication with users
Grouper features real-time customer relationship management (CRM). The service also grants users direct contact with the director of membership experience, who engages users with personalized reminder texts and bits of advice for success on Groupers.
The member experience team communicates with users throughout the Grouper. Users receive a customized message from the member experience team on the morning after their grouper inquiring as to the how the night out went. This feedback is analyzed and stored for future matching.
Active cities and expansion
For more than a year after its initial launch, Grouper was only available in New York City. By June 2012, the service had grown to San Francisco and Washington D.C.
By September 2012, Grouper had expanded its services to 10 additional cities, Atlanta, Austin, Brooklyn, Boston, Chicago, Los Angeles, Seattle, Miami, Philadelphia, and Dallas. That December the service became available to users in Toronto.
The company reported its services are officially available in 25 cities in the US and Toronto, including 2013 additions Nashville, Denver, and others. Additionally, Grouper London is launching in November 2013.
Technological developments
In April 2013, the meet-up service released its Grouper iPhone app. The company has reported that the app, which features push notifications and alerts, allows users to set up a Grouper in as little as an hour, avoiding the long questionnaires other services require their users to fill out.
Partnerships and acquisitions
Y Combinator, a company that funds startups, is the primary backing for Grouper.
In October 2012, Grouper announced its Hackaton program. The concept involved flying select designers and software developers to New York City for a week-long, expenses-paid trip. The company invited the designers into their headquarters to work on new Grouper product development and brainstorm with the team.
Grouper arranged the trip after establishing partnerships with Airbnb and Hipmunk.
Grouper announced a partnership with Uber in January 2013. The alliance was made to encourage users to utilize Uber for transportation on Grouper dates.
References
Category:Companies established in 2011
Category:Dating
Category:Defunct social networking services
Category:Social planning websites |
Use and outcomes of peritoneal dialysis among Aboriginal people in Canada.
There has been a dramatic increase in the incidence of ESRD among Aboriginal people in North America. Although peritoneal dialysis (PD) seems to be the dialysis modality of choice for this often rural-dwelling population, few data exist to confirm this. This study was conducted to evaluate rates of PD use, technique failure, and mortality among incident Aboriginal dialysis patients. Adults of white or Aboriginal race who initiated dialysis in three Canadian provinces between January 1, 1990, and December 31, 2000, were included and followed until December 31, 2001. Logistic regression and Cox proportional hazards models were used to examine adjusted associations between Aboriginal race and PD use, technique failure, and mortality. Among the 3823 patients of white (n = 3138; 82.1%) or Aboriginal (n = 685; 17.9%) race, 835 (21.8%) initiated dialysis on PD. After adjustment for age and comorbidity and comparison with white patients, Aboriginal patients were significantly less likely to initiate therapy on PD compared with white patients (odds ratio, 0.51; 95% confidence interval, 0.40 to 0.65), with a nonsignificant trend toward a higher risk for technique failure (hazards ratio, 1.46; 95% confidence interval, 0.95 to 2.23). Adjusted survival among Aboriginal PD patients seemed similar to both white PD patients and Aboriginal patients who were treated with hemodialysis. In summary, among people who were treated with dialysis in Canada, PD was used less frequently in Aboriginal patients than in those of white race. Although Aboriginal patients who initiate dialysis on PD seemed more likely to experience technique failure, their adjusted risk for death was similar to that of white patients. Future studies should address barriers to the initiation and maintenance of PD in the Aboriginal population, especially those who reside in rural locations. |
For more What in the World watch Sundays at 10 a.m. & 1 p.m. ET on CNN
By Global Public Square staff
Some startling images caught our eye this week. A shopping free-for-all at a major electronics chain, the equivalent of America's Best Buy. People making off with flat-screen TVs…refrigerators…and more…all at bargain basement prices. No, it’s not the holidays yet. This is what happened when the government of Venezuela decided to play Robin Hood: the army took over the privately owned chain and slashed prices.
The incident got us thinking. We often talk about best practices for economies. Perhaps there should also be a list of things to avoid – a checklist titled ‘How to ruin your economy.’ Well, it so happens this isn't just a theoretical list, because Venezuela is actually ticking each of those boxes in practice.
So let's go to rule #1. Attack big business. That's exactly what we saw Venezuela do this week with "Daka" – the electronics chain. President Nicolas Maduro says that his opposition is in cahoots with Washington to bring down his economy. Apparently that's why TVs were so expensive. As we saw this week, there's an easy fix: Have the army take over. Sounds like a lasting solution.
That brings me to rule #2. Create hyperinflation. It turns out those TV salesmen in Venezuela aren't the only robbers. The truth is the overall price of goods has risen 54 percent in Venezuela this year. So, if your household groceries cost $100 a week in January, they'll now cost you $154. The ripple effect is clear. Prices go up, so salaries have to go up, and so anything you produce costs more. Mission accomplished, your economy is now less competitive.
Rule #3. Induce a currency crisis. The easiest way to curb inflation is to increase the value of your currency. Basically, print less money. But it turns out Caracas actually has a cash crunch, so it actually needs to do the opposite. Meanwhile, the black market for American dollars is thriving. The official exchange rate is 6.3 Bolivars for every greenback. In reality, the black market rate is 7 to 10 times that amount. For a country which imports 70 percent of its basic goods, this is a big problem. You may remember recently that Venezuela ran out of toilet paper. Why? Well, it's running out of a different kind of paper – the money to pay for it.
Which brings me to rule #4. Subsidize, subsidize, subsidize. If Caracas is running out of money, thegovernment doesn't seem to know. Just last month, President Maduro raised public sector salaries by 10 percent across the board. This comes after two recent elections, where the government lavished subsidies to win votes. Gas is essentially free in Venezuela. In fact it's also nearly free in neighboring Cuba, which Venezuela has been subsidizing for years.
I could go on and on, but I'll point out just one more rule. Number #5, which is…Become a dictatorship. President Nicholas Maduro won a vote this week to get what is known as “decree powers” – the ability to pass laws without consulting Congress. He says he needs these powers to fix the economy and tackle corruption. After all, Venezuela is ranked 181st of 189 countries for doing business. It is ranked 9th for corruption. It took years for Hugo Chavez to take Venezuela to this point…and now Maduro wants to double down on the very same policies.
So, on points 1 through 5, Venezuela is on a fast-track to total ruin. The world saw this coming under Chavez. We hoped for change, but in his dying days Chavez handpicked a “mini-me” to stay the course. The sad truth is that Venezuela is wasting the world's largest oil reserves. It could have been as wealthy as Saudi Arabia or Qatar. It could have outstripped Mexico or Brazil. Instead, it is beginning to resemble North Korea, simply by following the most ruinous set of policies in the world.
I am not so sure I understand your psycho-babble. It is largely the hope of mankind we learn from our past mistakes (both obvious and not so obvious) and move on with increased vigor and wisdom. You may not consider the laws of macro-economics as sacred physics but they are. I believe this is what the author in suggesting.
Talk about Sico Babbbble.Macro economics has never been a science.It IS one fad after the other that keeps the 1% in charge
November 19, 2013 at 8:44 pm |
Cynthia Avishegnath
1st, you have never read about agile and adaptive in dynamic systems and engineering management.
2nd, you have no idea about having used dynamics being used in modeling economics.
3rd, you are not familiar with the Bible, from whence I derived the sarcasm.
November 19, 2013 at 9:57 pm |
Sternberg
Well, we are working diligently on #1. And Mr. Obama has figured out a way to subsidize about 2/3 of us to varying degrees with his ACA. Then there was his "cash for clunkers" that no one wants to bring up in polite company anymore. Looks like we are well on our way.
Give me a break PLEASE I'm so sick and tired of hearing everything in it present happen under President Obama watch, have we forgotten George Bush and the hole he put this Country into before left office. Dear sir please come back to the real world not the screw up world of the fairs and balances Fox News Network.
GIVE VENEZUELANS A BREAK. Stop comparing Venezuela to the U.S. It is very, irreconcilably different. Our country is totally screwed, yours isn't.
November 19, 2013 at 11:02 pm |
Jackie
Jesusportillo – people need to start looking and understanding what is going around them. If they don't take note on what is happening in Venezuela since 1999, not only in US but in any other country that can happen.
Americans need to understand that Obama is now, the present, therefore going back and blaming Bush and previous presidents won't do anything. Obama hasn't show the minimum to his country to show he cares and that he really wanted to "fix" economy here. No actions, no actions, no actions...blah blah blah "I'm the victim" "Poor me"
Just wait for our next surprise (what ALL socialists, dictators do-) New upcoming law -> You can run for president indefinitely, and have control of all those ignorants who support you.
Sadly Venezuela was in pretty bad shape way before 1999 and Chavez. Mostly because the government was controlled from Washington, Chavez tried the oppositte and that did not work out either. Very sad situation.
January 31, 2014 at 11:34 am |
FLAWIDA JACK
2 more sure fire ways to ruin an economy:
1. Elect a person to the highest office in the land, despite the fact he has no real world experience, or knowledge.
2. Repeat rune #1.
Since they couldn't completely destroy the ecnomy with Gee dubya, they thought they could finish us off with Robme. Since that fell apart, they fell to plan "C", obstruct everything and caus as much trouble for the president as possible.
Just look over Africa (French speaking + Cameroon) and you will see just that. And I wonder how long will the current growth will last. So we shouldn't forget that the so said growth is being fueled by the reinvestment of debt relieve proceeds. What about the political elites of Africa working hard to destroy their own economies?
Seth before you start doing stupid comments, i recommend you look out the window... For us that are living here in venezuela, seeing the wreck that our country is, and where is going, is not stupid propaganda.
Daka is out of stock, not because of the militarism getting in the way, because when the president said open those doors, the people when there and kick the door open, and sacked 50% or more of the store, and the president applaud that, since they are hitting the capitalism where it hurts. The next days every major and minor store in the country got flooded with people due to the goverment demanding a 50% or more offer on every single article in the store, because it's the capitalism monster that is ruining venezuela
This week they past from electronic stores that are basicly in bankrupcy to clothing and hardware stores, one of the biggest hardware store in the country is being forced to do an 80% offer on every articles, and people are flooding to buy everything from the store. The only thing that is doing is people buying tons of things for half the price or more so they can reselled them at the price they were originaly are in the blackmarket, and most if not all the minor companies going broke and closing, and most of the major countries going broke or firing tons of people
Venezuela is going through a really dark time, due to this "socialism" the ignorant president and his combo are pulling on us, when half the population are ignorant sheep that will follow him for anything he throws at him, while the rest of us have to consider migrate to other countries and leave our home behind or stay in a dieing country, that could have been one of the richest, which is now in debt with several countries.
So go cry me a river, and this satiric news, is actually really accurate on the sad state of vzla
Venezuela is like that because of the venezuelans. Chavez was consequence and people voted for him. Venezuela is a society that failed. I mean, it has been 15 years, the only thing you can read from it is... the government fits the culture. Because if it was a mistake it would have been only for 4 years, but no... the opposition is very mediocre as well, that is why is a cultural problem and that is what the Venezuelans do not want to realized "I AM THE MISTAKE" FOR BEING LAZY, FOR BLAMING OTHERS, FROM EXPECTING FROM OTHER TO DO THE THINGS FOR ME. The Venezuelan situation will last for many years, you will see.
What a joke this article is... as with those who speak as if Venezuela had been a powerful economy BEFORE Chavez arrived !! Oh please... it must have been the most corrupt stereotyipical banana republic in South America... and some of these people would like to blame Chavez for the crap that has ALWAYS gone on in a country run by a little oligarchy who sucked on every oil pipe there ever was in the vicinity. With the crap going on in the US... it is somewhat comical to be hearing "lessons" from some people. Oh well... the world is full of morons, who watch moronic news channels.
Exactly dude! Listen I don't know what you though about Chavez. We didn't like it so we left. But when I heard this piece by Zakaria I almost passed out in laughter. He is either an idiot or (more likely) gets paid very well to say crap like this.
Venezuela is indeed in serious trouble, but this are the wrong reasons. 1)Since when big bussines= all business, if your government can't stand up against private interests you might as well have no government. 2) subsidize? Are you kidding me? Farms, oil, areonautics, weapons, teachnology, banks! Everything that is important in America is or was heavily subsidize. 3) dictatorship?!! Half of America don't vote, our two parties do the same thing in economics, and lobyists! All around congress and the senate make sure your vote doesn't count anyways. Listen Venezuelas sucks I agree, But maybe is time for us to buy a big fat mirror...
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The Global Public Square is where you can make sense of the world every day with insights and explanations from CNN's Fareed Zakaria, leading journalists at CNN, and other international thinkers. Join GPS editor Jason Miks and get informed about global issues, exposed to unique stories, and engaged with diverse and original perspectives. |
/** @license MIT License (c) copyright 2013 original author or authors */
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* function.js
*
* Collection of helper functions for wrapping and executing 'traditional'
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* @author brian@hovercraftstudios.com
* @contributor renato.riccieri@gmail.com
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compose: compose
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Orlando Magic Fall Short in Milwaukee
The Orlando Magic fell to the Milwaukee Bucks 104-100 Tuesday night in what turned out to be a surprisingly entertaining game between two of the Eastern Conference’s worst teams. The game was close throughout, neither team gaining much of an advantage. Missed free throws and missed opportunities at the rim would prove too costly for the Magic, as the Bucks slipped away with the win.
The Magic were led in scoring by Arron Afflalo with 21 points. Nik Vucevic contributed 19 points and 9 rebounds just missing a Vucci double. E’twan Moore was huge off the bench throwing in 17 points as the bench’s lone contributor.
The Bucks were led in scoring by Caron Butler with 21 points. Orlando had a tough time staying in front of Milwaukee’s guards tonight. Brandon Knight chipped in 18, and South Dakota State Jackrabbit Nate Wolters added 15. This kind of performance by Wolters surely will cause a rush at the Empire Mall in Sioux Falls, with kids clamoring to buy Nate’s jersey.
As I mentioned earlier, the game was close throughout, a lot of sloppy play by both teams, as you might expect coming off the All Star break. Orlando squandered 15 turnovers tonight, and were out rebounded by 6. This was a tough game to figure out exactly what went wrong, and why the Magic couldn’t get over the hump against a team they clearly should beat, even on the road, just by watching it. The stat sheet tells a different tale.
Orlando shot 9-16 at the charity stripe tonight. Milwaukee shot 22-30. There’s your ballgame. The Magic also missed what seemed to be a handful of point blank looks at the rim tonight on putbacks and layups. A few more made free throws, any contribution from the bench, and a little better defense against the Bucks penetration and this recap would have a much different feel.
The Magic play the second night of a back to back tomorrow night against the Cavaliers. Tip is at 7:10
Matt Jensen is new to the MBO team and a proud contributing writer. He operates as MBO’s Sr. Sioux Falls Correspondent. Follow him on Twitter here |
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On January 23, 2009, the Chinese Communist Party’s official People’s Daily newspaper published its coveted list of “national civilized villages,” selected on a three-year basis by the Central Commission for Guiding Cultural and Ethical Progress. These were villages that had, according to the commission, shown strong leadership, done “solid and effective work,” “maintained social order and stability,” and provided quality social services. From the thousands of villages in China’s southern province of Guangdong, just 25 were chosen for this exceptionally rare honour. Among them was Wukan, an unknown fishing village on the outskirts of Lufeng, a small but growing city on the province’s central coast.
The “Documents” section of the January 23, 2009, edition of the People’s Daily includes a list of “national civilised cities” and “national civilised villages.”
Three years later, as the selection process for the next raft of “national civilized villages” was no doubt kicking into high gear, protests erupted in civilised Wukan, exposing local anger over dirty land deals that had long festered beneath the surface. The uprising, stemming from the death in police custody of a popular village leader, quickly became global news as villagers erected barricades against armed police equipped with tear gas and water cannons. Wukan became a village under siege.
In fact, isolated protests over corrupt land deals had already begun in Wukan in 2009, the year it was honoured as a “national civilized village.” What, one must ask, was this “solid and effective work” being done by Wukan’s Communist Party leaders, who had fled the village in the early hours of the 2011 protest movement?
Was civilized Wukan nothing more than a cynical deception?
Months later, after the protests gave way to negotiations with provincial officials on the principles of “fairness and openness,” and after democratic elections were held for a new village committee, there emerged another myth of civilized Wukan.
Wukan was a model this time not of “sound and effective work” or solid social services, but of conflict resolution in a China plagued by social tensions at the grass roots, particularly over the thorny issue of land reclamation and appropriation.
“The Wukan incident has again confirmed that democracy and supervision are effective weapons in controlling and preventing corruption,” said an editorial in the People’s Daily almost three years to the day from its hailing of civilized Wukan.
The chief cause of the corruption occurring in Wukan was the lack of democracy and supervision. The lesson from this is that we must fully preserve as the core the exercise of democratic and supervisory rights by villagers, solidly advancing democratic management and democratic politics in the countryside.
Wukan seemed to be an illustration, moreover, of the responsiveness of the Party leadership. But few asked the tougher questions about this supposed new paradigm of civilised governance at the village level — not least how such a civilized village could resolve its thorny land issues as an uncivilised and hostile Communist Party bureaucracy loomed overhead.
The news cycle moved on. Villagers returned to their fishing boats. Wukan was forgotten.
But Wukan’s troubles, it seems, never ceased. Earlier this year, as the village’s democratically elected leader, Lin Zulian, called for renewed meetings over still unresolved land disputes, he was detained and charged with abuse of power and accepting bribes. Protests broke out afresh, with villagers professing Lin’s innocence even as his alleged confession was aired on national television.
“We villagers don’t believe it,” one woman told National Public Radio, “because in our hearts, we think of Lin Zulian as a good party secretary.”
In grainy footage aired on state television in June 2016, Wukan village leader Lin Zulian confesses to bribery and abuse of power.
Lin Zulian’s awkward and halting confession, of a piece with other apparently forced public confessions by lawyers and human rights activists in recent years, raised serious questions about the motives behind his arrest. This looked suspiciously like yet another attempt to reign in political activism under a hardline Chinese president who blacklisted such topics as “civil society” and “constitutional democracy” in 2013, during the first year of his administration.
Was this the proverbial “settling of accounts after the autumn harvest” (秋后算账)? Were these the ripened yet bitter fruits of Wukan’s democratic revolution?
In recent days, a true settling of accounts has come to the village of Wukan. Tensions have spilled into open conflict, with video circulating online of villagers hurling bricks at tight rows of armed police. Thousands of police have reportedly pushed into the village, placing it under lockdown and arresting scores of villagers.
A new myth of Wukan is emerging. In fact, says the Global Times newspaper, while “a majority of Wukan villagers have calmed down,” a troublemaking minority, urged on by “foreign media,” are “unscrupulously inciting, planning, and directing chaos.” This is a familiar theme, in which calls for democracy, transparency or even basic fairness, are a great deception perpetrated by “foreign forces” hoping to uncivilize China and drag it down into darkness.
For Xi Jinping, the Wukan model is a dangerous precedent that must be not just crushed but discredited. This time, it is Wukan’s failed experiment in engagement and democracy that will be mythologised, and Lin Zulian’s shame that will be paraded before the public.
Only China’s Party leadership has a rightful claim to the civilized. This much was clear in the official news release last week on Lin Zulian’s conviction and sentencing to three years in prison: |
Partial brachiocephalic perfusion in aortic arch replacement.
Eleven patients who underwent replacement of the aortic arch or adjacent areas for aneurysmal disease between 1989 and 1991, using hypothermic cardiopulmonary bypass at 20 degrees to 23 degrees C with partial brachiocephalic perfusion, were studied. Selective perfusion of the innominate artery was performed in all 11 patients through the right axillary artery, while partial brachiocephalic perfusion was carried out using a separate arterial roller pump with a perfusion flow rate of 10 ml/kg per min. Direct cannulation to the left common carotid and left subclavian artery was not performed in this method. There were 4 men and 7 women who ranged in age from 26 to 78 years, with a mean age of 56 years. The etiology of aneurysmal disease was aortic dissection in 10 patients, and aortitis syndrome in 1. The cardiopulmonary bypass time was 214.3 +/- 39.3 min, aortic cross-clamp time 131.5 +/- 33.4 min, and partial brachiocephalic perfusion time 57.6 +/- 15.1 min. There were three operative deaths (27.3%), the causes being multiple organ failure, acute peritonitis, and infection of the composite graft in the ascending aorta, in one patient each, respectively. However, there were no deaths related to the technique of partial brachiocephalic perfusion and no neurological complications were seen in this series. Thus, we believe that partial brachiocephalic perfusion under hypothermic cardiopulmonary bypass is safe and effective in surgery for aortic aneurysms involving the aortic arch. |
KYODO NEWS - Jan 30, 2019 - 12:46 | All, Japan
Police on Wednesday raided the Tokyo office of a yakuza gangster group associated with a man wanted for alleged murder and violation of the fire arms control law.
Masaru Abe, 56, a member of a group under the Sumiyoshikai crime syndicate, is wanted in connection with a fatal shooting in the capital's Kabukicho entertainment district earlier this month.
The victim, Lee Hung Jong, 65, who was found collapsed inside a karaoke establishment with three gunshot wounds on Jan. 21, was a member of a separate group under Sumiyoshikai more than 20 years ago, and is believed to be acquainted with Abe, according to the police.
Abe is alleged to have fled from the scene on a motorcycle before getting in a van and being driven to southern Saitama Prefecture, which neighbors Tokyo.
Abe is suspected of shooting Lee from close range inside a room on the fifth floor of the karaoke establishment in Kabukicho around 6:30 p.m. on Jan. 21, police said.
The area is known for hosting a number of yakuza gangsters and is also a popular commercial area among foreign visitors.
Ex-yakuza gangster shot dead in Tokyo's Kabukicho, suspect at large
(Kabukicho) |
Here is an amazing video I’ve found on you tube of a Pit Bull giving birth. If you guys plan to breed pit bull’s at least make sure that the mother is the larger of them carrying the pups. The smaller breeds of pit bull’s that get pregnant by a larger breed are at risk since the puppies may be too large to carry. |
Q:
Getting filtered results with subquery
I have a table with something like the following:
ID Name Color
------------
1 Bob Blue
2 John Yellow
1 Bob Green
3 Sara Red
3 Sara Green
What I would like to do is return a filtered list of results whereby the following data is returned:
ID Name Color
------------
1 Bob Blue
2 John Yellow
3 Sara Red
i.e. I would like to return 1 row per user. (I do not mind which row is returned for the particular user - I just need that the [ID] is unique.) I have something already that works but is really slow where I create a temp table adding all the ID's and then using a "OUTER APPLY" selecting the top 1 from the same table, i.e.
CREATE TABLE #tb
(
[ID] [int]
)
INSERT INTO #tb
select distinct [ID] from MyTable
select
T1.[ID],
T2.[Name],
T2.Color
from
#tb T1
OUTER APPLY
(
SELECT TOP 1 * FROM MyTable T2 WHERE T2.[ID] = T1.[ID]
) AS V2
DROP TABLE #tb
Can somebody suggest how I may improve it?
Thanks
A:
Try:
WITH CTE AS
(
SELECT ROW_NUMBER() OVER (PARTITION BY ID ORDER BY ID) AS 'RowNo',
ID, Name, Color
FROM table
)
SELECT ID,Name,color
FROM CTE
WHERE RowNo = 1
or
select
*
from
(
Select
ID, Name, Color,
rank() over (partition by Id order by sum(Name) desc) as Rank
from
table
group by
ID
)
HRRanks
where
rank = 1
|
Q:
How to create a caption for a pure CSS/HTML Slider with thumbnails, no java/jquery
I'm trying to create a slider that has image thumbnails that you use to navigate with. I also want to create a caption for each slide, to appear and disappear with their specific slides.
This is what I have at the moment, http://jsfiddle.net/yb02jzbq/
(Sourced from http://thecodeplayer.com/walkthrough/css3-image-slider-with-stylized-thumbnails)
As you can see it's just missing the captions, if you remove the id="d-slide1" in one of the first divs, you will see what I'm trying to achieve. I'd prefer if the captions also followed the main images effects (if easier than scaling, could you make it slide in from right to left?)
A:
Sorry for the late response. I think I solved your problem. First I changed your titles to class='d-slide' in order to remove dependency on id's and counters(for unique IDs). Also instead of a gazillion lines for each ID, you use:
.d-slide{visibility:hidden; display:inline-block;}
After that's it's easy. This line does the trick for me:
.slider input[name='slide_switch']:checked+label+img+.d-slide {
visibility: visible;
}
Here is the fiddle.
|
Treatment strategies and outcome of surgery for synchronous colorectal liver metastases.
To report survival following different operative strategies and perioperative chemotherapy in patients with synchronous colorectal liver metastases in a tertiary academic referral centre. We performed a retrospective analysis, based on a prospective database, of patients who presented with synchronous colorectal liver metastases. Follow-up data were obtained from medical records, letters or telephone contacts. The main endpoint was overall survival. An additional event of interest was postoperative mortality according to treatment strategy. Predefined variables were analysed to identify associated risk factors. Overall, 109 patients undergoing liver resection for synchronous colorectal liver metastases between 2000 and 2010 were identified. The majority of patients had resection of the primary tumour first (n = 82), the classic approach; notably fewer were treated according to a combined (n = 20) or a reverse "liver first" strategy (n = 7). Most patients (92%) received preoperative, interval and/or postoperative chemotherapy. Median overall survival of the entire population was 33.6 months (interquartile range [IQR] 11-92.7 months). Patients undergoing classic surgery had a median overall survival of 40.3 months (IQR 14.9-96.6 months). The 3-year survival rates of the three patient groups were 53% in the classic, 47% in the combined and 58% in the reverse group. The lowest rate of 180-day mortality (9%) was after the classic surgical approach. On a multivariate Cox proportional hazards regression analysis, patient age >60 years (hazard ratio [HR] 2.1, 95% confidence interval [CI] 1.1-3.9; p = 0.018), R2-status (HR 2.08, 95% CI 1.03-4.2; p = 0.040), and >4 liver metastases (HR 2.4, 95% CI 1.2-4.6; p = 0.011) were associated significantly with worse overall survival. In patients undergoing surgical resection for synchronous colorectal liver metastases, promising survival rates could be achieved, irrespective of the chosen surgical strategy. The presence of five or more liver metastases, patient age over 60 years and R2-status were found to be adverse risk factors. |
The present invention relates to a Brillouin/Erbium laser arrangement and in particular, to a bidirectional single elliptical polarization high efficiency and output power all fibre laser arrangement and its application to current sensing.
Brillouin fibre lasers (BFL) are particularly useful in fibre sensors due to extremely narrow linewidths and they have been the subject of considerable research at a number of different wavelengths [S. P. Smith, F. Zarinetchi, and S. Ezekiel, Opt. Lett., vol. 16, p. 393,1991]. They have found applications such as gyroscopes [S. Huang, K. Toyama, B. Y. Kim, and H. J. Shaw, Opt, Lett., vol. 18, pp. 555-557, 1993] and current sensors [A. Kxc3xcng, P. -A. Nicati, and P. A. Robert, IEEE Photon. Technol, Lett., Vol. 8, p. 1680, 1996]. Such devices are realized by using two counter-propagating Brillouin lasers sharing the same fibre ring resonator and experiencing different apparent cavity lengths due to nonreciprocal phaseshifts induced by either Sagnac or Faraday effects. These two counter-propagating Brillouin lasers will therefore oscillate at slightly different optical frequencies and the optical beat frequency will be linearly proportional to either the rotation rate or the electric current. These types of sensors have much simpler signal processing than more conventional devices [I. G. Clarke, Opt. Lett., vol. 18, pp. 158-160, 1993] based on Sagnac loop. To achieve maximum sensitivity of the current sensor to the Faraday effect it is necessary to keep the laser polarization states circular although some degree of ellipticity is acceptable.
The conventional technique to produce a BFL is to construct a critically coupled fibre resonator, required because of the small magnitude of the Brillouin gain [G. P. Agrawal, in Nonlinear Fibre Optics, Academic Press, San Diego, Calif., 1989]. Principal disadvantages of critically coupled BFLs include the small output power that can be achieved, the requirement of cavity matching to the pump signal, and the difficulty in incorporating intra-cavity elements because of their associated loss.
Brillouin/erbium fibre lasers (BEFL) [G. J. Cowle and D. Yu. Stepanov, J. Lightwave Technol., VOL. 15, PP. 1198-1204, 1997] combine Brillouin gain as used in BFLs with gain from erbium-doped fibre (EDF) to yield laser sources with unique properties. Narrow bandwidth nonlinear gain from stimulated Brillouin scattering in Single Mode Optical Fibre (SMOF) precisely determines the wavelength of operation, and gain in erbium-doped fibre (EDF) allows efficient operation and large power extraction. BEFLs do not require cavity matching to the Brillouin pump frequency since the BEFL resonator is not critically coupled. The Brillouin pump can be removed from the laser cavity to avoid spurious injection locking. In [G. J. Cowle and D. Yu. Stepanov, Opt. Lett., vol. 21, pp. 1250-1252, 1996] the laser cavity was made non-resonant in the direction of the Brillouin pump injection using a pigtailed bulk isolator. However, such an approach is undesirable for the sensing applications which require bidirectional operation.
It is an object of at least preferred embodiments of the present invention to provide an improved laser arrangement which overcomes the disadvantages of the aforementioned laser arrangements and is further preferably capable of being applied to electric current measurements.
In accordance with a first aspect of the present invention there is provided a laser arrangement comprising a ring cavity, at least two gain portions in said ring cavity, an input-output coupling connected to said ring cavity, a discriminator means connected in said ring cavity adapted to discriminate between a pumping signal and an output signal, and pumping means for providing said pumping signal and connected to said gain portions of said ring cavity such that, upon activation of said pumping means, said laser arrangement operates as a bidirectional laser producing a laser output at said input-output coupling.
In one embodiment, the laser arrangement comprises a ring cavity with Brillouin gain portions, a bidirectional optical amplifier and an elliptical polarizer interposed in predetermined portions of the ring cavity, input-output couplings connected to the ring cavity, and pumping means connected to the Brillouin gain portions of the ring cavity, such that, upon activation of the pumping means, the laser arrangement operates as a bidirectional laser and produces an output at said input-output couplings.
Preferably the laser arrangement acts as a Brillouin laser for obtaining a bidirectional single polarization high power output at the frequencies shifted down from the frequencies of the pumping means by an amount determined by the Brillouin shift in the glass fibre.
In accordance with the second aspect of the present invention the aforementioned laser arrangement is applied to the measurement of an electric current by measuring the optical beat frequency between counterpropagating waves in the ring cavity. The optical beat frequency being linearly proportional to the current value.
Preferably, the optical amplifier is formed from the one piece of rare earth doped optical fibre with a separate pumping means connected to the rare earth doped optical fibre.
Preferably, the elliptical polarizer is formed from the one piece of spun highly birefringent polarizing fibre (PSHBF) polarizing in the wavelength range of the laser operation [I. G. Clarke, Opt. Lett., vol. 18, pp 158-160, 1993].
The Brillouin pump should be removed from the ring cavity to enable the laser to be operated in the BEFL mode. This can be achieved using a number of different techniques with the preferred embodiment utilising a polarizing spun highly birefringent fibre. Alternatively, a blazed grating or other discriminators, could be utilized, provided that the discriminator does not inhibit the bidirectional operation of the laser arrangement.
In broad terms, the preferred embodiment of the present invention provides a Brillouin laser, comprising Brillouin gain portions and a rare-earth doped optical amplifier inserted into a ring cavity.
More specifically, the preferred embodiment of the present invention provides a bidirectional single polarization high output power laser arrangement at the frequencies shifted down from the frequencies of the pumping means by an amount determined by the Brillouin shift in the glass fibre, comprising Brillouin gain portions for obtaining gain in opposite directions at shifted frequencies, input/output couplers to provide input/output coupling and feedback through the ring cavity, an optical amplifier to compensate for the ring cavity losses, and a polarizing spun highly birefringent fibre (PSHBF) to prevent injection of the Brillouin pumping means into the optical amplifier.
The concept of the laser arrangement is as follows: First increase the gain of the optical amplifier to a level just below that required for the arrangement to operate as a laser. Elliptically polarized light from an external narrow linewidth laser is then injected into the predetermined portions of the ring cavity to stimulate Brillouin scattering in both clockwise and counterclockwise directions. In scalar-type backward stimulated Brillouin scattering, circularly or elliptically polarized Brillouin pump is reflected into the Stokes wave as if from a conventional mirror [B. Ya. Zeldovich, N. E. Pilipetsky, and V. V. Shkunov, in Principles of Phase Conjugation, Springer-Verlag, Berlin, 1985], ie. with the reversal of rotation sense and preservation of the orientation of the ellipse. With sufficient intensity of the injected Brillouin pump an elliptically polarized Brillouin signal is generated in the opposite direction and with the opposite rotation sense supported by the PSHBF at a frequency separated from the injected signal by the Stokes shift and it will eventually have sufficient gain to reach a lasing threshold by virtue of the combination of the Brillouin gain and the gain in the optical amplifier.
Preferable key features of the laser are that it does not need a low loss resonator, instead using an optical amplifier to equalise the resonator losses, which allows it to obtain high power output, and it does not require an optical isolator, instead using a PSHBF to isolate the Brillouin pump, thus allowing for the bidirectional operation. The PSHBF prevents both depletion of the optical amplifier gain by an injection locking to the Brillouin pumping means and provides feedback for the Brillouin signal.
In a preferred embodiment, the Brillouin gain portions are lengths of single mode optical fibre and the optical amplifier comprises a section of erbium doped fibre which is optically pumped through a wavelength division multiplexing (WDM) coupler. With sufficient pump power applied, the ring laser would operate as a normal erbium doped fibre ring laser. However, in this embodiment, laser action is originated from signals shifted down in frequency by an amount determined by the Brillouin shift in the glass fibre, generated from an external narrow linewidth laser source. The Brillouin pump signals injected in opposite directions are non-resonant in the laser cavity as they are blocked by the PSHBF in the ring and hence do not enter the EDF section of the ring. However the Brillouin signals generated in the opposite directions with respect to the corresponding Brillouin pumps are amplified by the amplifying section of the ring. The polarizing spun highly birefringent fibre prevents the ring from operating as an injection locked laser and sets the internal polarization state of the laser.
Such an arrangement has advantages in producing bidirectional high output power narrow linewidth laser sources for fibre sensors. The laser has only one elliptically polarized eigenstate in both clockwise and counter-clockwise directions. This makes the laser very attractive for current sensing using the Faraday effect. Additionally, the laser also has application in the gyroscope area. Elliptical polarization of the counter propagating laser eigenstates also ensures that spatial hole burning in the amplifying section of the laser is reduced as the standing wave pattern is close to a helicoidal shape and thus the light field intensity approaches uniformity along the doped fibre.
To measure nonreciprocal phaseshifts induced by the Faraday effect when an electric current is applied to a conducting coil wound around the PSHBF section of the laser, the frequency of the optical beat produced by the counter-propagating lasing modes can be analysed using a radio-frequency spectrum analyser (RFSA). For experimental convenience and to prevent possible lock-in of the counter-propagating lasing modes at low currents, the optical beat frequency in this embodiment is preferably biased using a frequency shifter by shifting the frequency of one of the Brillouin pumps, thus shifting the corresponding Brillouin gain maximum. Given the sweep time xcfx84 of the RFSA is much longer than the electric current waveform period T and the ratio xcfx84/T is known, the waveform can be reconstructed from the RFSA spectrum and the current can be measured. |
/*
* GUSEMU32 - mixing engine (similar to Interwave GF1 compatibility)
*
* Copyright (C) 2000-2007 Tibor "TS" Schütz
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
* THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include "gusemu.h"
#include "gustate.h"
#define GUSregb(position) (* (gusptr+(position)))
#define GUSregw(position) (*(GUSword *) (gusptr+(position)))
#define GUSregd(position) (*(GUSdword *)(gusptr+(position)))
#define GUSvoice(position) (*(GUSword *)(voiceptr+(position)))
/* samples are always 16bit stereo (4 bytes each, first right then left interleaved) */
void gus_mixvoices(GUSEmuState * state, unsigned int playback_freq, unsigned int numsamples,
GUSsample *bufferpos)
{
/* note that byte registers are stored in the upper half of each voice register! */
GUSbyte *gusptr;
int Voice;
GUSword *voiceptr;
unsigned int count;
for (count = 0; count < numsamples * 2; count++)
*(bufferpos + count) = 0; /* clear */
gusptr = state->gusdatapos;
voiceptr = (GUSword *) gusptr;
if (!(GUSregb(GUS4cReset) & 0x01)) /* reset flag active? */
return;
for (Voice = 0; Voice <= (GUSregb(NumVoices) & 31); Voice++)
{
if (GUSvoice(wVSRControl) & 0x200)
GUSvoice(wVSRControl) |= 0x100; /* voice stop request */
if (GUSvoice(wVSRVolRampControl) & 0x200)
GUSvoice(wVSRVolRampControl) |= 0x100; /* Volume ramp stop request */
if (!(GUSvoice(wVSRControl) & GUSvoice(wVSRVolRampControl) & 0x100)) /* neither voice nor volume calculation active - save some time here ;) */
{
unsigned int sample;
unsigned int LoopStart = (GUSvoice(wVSRLoopStartHi) << 16) | GUSvoice(wVSRLoopStartLo); /* 23.9 format */
unsigned int LoopEnd = (GUSvoice(wVSRLoopEndHi) << 16) | GUSvoice(wVSRLoopEndLo); /* 23.9 format */
unsigned int CurrPos = (GUSvoice(wVSRCurrPosHi) << 16) | GUSvoice(wVSRCurrPosLo); /* 23.9 format */
int VoiceIncrement = ((((unsigned long) GUSvoice(wVSRFreq) * 44100) / playback_freq) * (14 >> 1)) /
((GUSregb(NumVoices) & 31) + 1); /* 6.10 increment/frame to 23.9 increment/sample */
int PanningPos = (GUSvoice(wVSRPanning) >> 8) & 0xf;
unsigned int Volume32 = 32 * GUSvoice(wVSRCurrVol); /* 32 times larger than original gus for maintaining precision while ramping */
unsigned int StartVol32 = (GUSvoice(wVSRVolRampStartVol) & 0xff00) * 32;
unsigned int EndVol32 = (GUSvoice(wVSRVolRampEndVol) & 0xff00) * 32;
int VolumeIncrement32 = (32 * 16 * (GUSvoice(wVSRVolRampRate) & 0x3f00) >> 8) >> ((((GUSvoice(wVSRVolRampRate) & 0xc000) >> 8) >> 6) * 3); /* including 1/8/64/512 volume speed divisor */
VolumeIncrement32 = (((VolumeIncrement32 * 44100 / 2) / playback_freq) * 14) / ((GUSregb(NumVoices) & 31) + 1); /* adjust ramping speed to playback speed */
if (GUSvoice(wVSRControl) & 0x4000)
VoiceIncrement = -VoiceIncrement; /* reverse playback */
if (GUSvoice(wVSRVolRampControl) & 0x4000)
VolumeIncrement32 = -VolumeIncrement32; /* reverse ramping */
for (sample = 0; sample < numsamples; sample++)
{
int sample1, sample2, Volume;
if (GUSvoice(wVSRControl) & 0x400) /* 16bit */
{
int offset = ((CurrPos >> 9) & 0xc0000) + (((CurrPos >> 9) & 0x1ffff) << 1);
GUSchar *adr;
adr = (GUSchar *) state->himemaddr + offset;
sample1 = (*adr & 0xff) + (*(adr + 1) * 256);
sample2 = (*(adr + 2) & 0xff) + (*(adr + 2 + 1) * 256);
}
else /* 8bit */
{
int offset = (CurrPos >> 9) & 0xfffff;
GUSchar *adr;
adr = (GUSchar *) state->himemaddr + offset;
sample1 = (*adr) * 256;
sample2 = (*(adr + 1)) * 256;
}
Volume = ((((Volume32 >> (4 + 5)) & 0xff) + 256) << (Volume32 >> ((4 + 8) + 5))) / 512; /* semi-logarithmic volume, +5 due to additional precision */
sample1 = (((sample1 * Volume) >> 16) * (512 - (CurrPos % 512))) / 512;
sample2 = (((sample2 * Volume) >> 16) * (CurrPos % 512)) / 512;
sample1 += sample2;
if (!(GUSvoice(wVSRVolRampControl) & 0x100))
{
Volume32 += VolumeIncrement32;
if ((GUSvoice(wVSRVolRampControl) & 0x4000) ? (Volume32 <= StartVol32) : (Volume32 >= EndVol32)) /* ramp up boundary cross */
{
if (GUSvoice(wVSRVolRampControl) & 0x2000)
GUSvoice(wVSRVolRampControl) |= 0x8000; /* volramp IRQ enabled? -> IRQ wait flag */
if (GUSvoice(wVSRVolRampControl) & 0x800) /* loop enabled */
{
if (GUSvoice(wVSRVolRampControl) & 0x1000) /* bidir. loop */
{
GUSvoice(wVSRVolRampControl) ^= 0x4000; /* toggle dir */
VolumeIncrement32 = -VolumeIncrement32;
}
else
Volume32 = (GUSvoice(wVSRVolRampControl) & 0x4000) ? EndVol32 : StartVol32; /* unidir. loop ramp */
}
else
{
GUSvoice(wVSRVolRampControl) |= 0x100;
Volume32 =
(GUSvoice(wVSRVolRampControl) & 0x4000) ? StartVol32 : EndVol32;
}
}
}
if ((GUSvoice(wVSRVolRampControl) & 0xa000) == 0xa000) /* volramp IRQ set and enabled? */
{
GUSregd(voicevolrampirq) |= 1 << Voice; /* set irq slot */
}
else
{
GUSregd(voicevolrampirq) &= (~(1 << Voice)); /* clear irq slot */
GUSvoice(wVSRVolRampControl) &= 0x7f00;
}
if (!(GUSvoice(wVSRControl) & 0x100))
{
CurrPos += VoiceIncrement;
if ((GUSvoice(wVSRControl) & 0x4000) ? (CurrPos <= LoopStart) : (CurrPos >= LoopEnd)) /* playback boundary cross */
{
if (GUSvoice(wVSRControl) & 0x2000)
GUSvoice(wVSRControl) |= 0x8000; /* voice IRQ enabled -> IRQ wait flag */
if (GUSvoice(wVSRControl) & 0x800) /* loop enabled */
{
if (GUSvoice(wVSRControl) & 0x1000) /* pingpong loop */
{
GUSvoice(wVSRControl) ^= 0x4000; /* toggle dir */
VoiceIncrement = -VoiceIncrement;
}
else
CurrPos = (GUSvoice(wVSRControl) & 0x4000) ? LoopEnd : LoopStart; /* unidir. loop */
}
else if (!(GUSvoice(wVSRVolRampControl) & 0x400))
GUSvoice(wVSRControl) |= 0x100; /* loop disabled, rollover check */
}
}
if ((GUSvoice(wVSRControl) & 0xa000) == 0xa000) /* wavetable IRQ set and enabled? */
{
GUSregd(voicewavetableirq) |= 1 << Voice; /* set irq slot */
}
else
{
GUSregd(voicewavetableirq) &= (~(1 << Voice)); /* clear irq slot */
GUSvoice(wVSRControl) &= 0x7f00;
}
/* mix samples into buffer */
*(bufferpos + 2 * sample) += (GUSsample) ((sample1 * PanningPos) >> 4); /* right */
*(bufferpos + 2 * sample + 1) += (GUSsample) ((sample1 * (15 - PanningPos)) >> 4); /* left */
}
/* write back voice and volume */
GUSvoice(wVSRCurrVol) = Volume32 / 32;
GUSvoice(wVSRCurrPosHi) = CurrPos >> 16;
GUSvoice(wVSRCurrPosLo) = CurrPos & 0xffff;
}
voiceptr += 16; /* next voice */
}
}
void gus_irqgen(GUSEmuState * state, unsigned int elapsed_time)
/* time given in microseconds */
{
int requestedIRQs = 0;
GUSbyte *gusptr;
gusptr = state->gusdatapos;
if (GUSregb(TimerDataReg2x9) & 1) /* start timer 1 (80us decrement rate) */
{
unsigned int timer1fraction = state->timer1fraction;
int newtimerirqs;
newtimerirqs = (elapsed_time + timer1fraction) / (80 * (256 - GUSregb(GUS46Counter1)));
state->timer1fraction = (elapsed_time + timer1fraction) % (80 * (256 - GUSregb(GUS46Counter1)));
if (newtimerirqs)
{
if (!(GUSregb(TimerDataReg2x9) & 0x40))
GUSregb(TimerStatus2x8) |= 0xc0; /* maskable bits */
if (GUSregb(GUS45TimerCtrl) & 4) /* timer1 irq enable */
{
GUSregb(TimerStatus2x8) |= 4; /* nonmaskable bit */
GUSregb(IRQStatReg2x6) |= 4; /* timer 1 irq pending */
GUSregw(TimerIRQs) += newtimerirqs;
requestedIRQs += newtimerirqs;
}
}
}
if (GUSregb(TimerDataReg2x9) & 2) /* start timer 2 (320us decrement rate) */
{
unsigned int timer2fraction = state->timer2fraction;
int newtimerirqs;
newtimerirqs = (elapsed_time + timer2fraction) / (320 * (256 - GUSregb(GUS47Counter2)));
state->timer2fraction = (elapsed_time + timer2fraction) % (320 * (256 - GUSregb(GUS47Counter2)));
if (newtimerirqs)
{
if (!(GUSregb(TimerDataReg2x9) & 0x20))
GUSregb(TimerStatus2x8) |= 0xa0; /* maskable bits */
if (GUSregb(GUS45TimerCtrl) & 8) /* timer2 irq enable */
{
GUSregb(TimerStatus2x8) |= 2; /* nonmaskable bit */
GUSregb(IRQStatReg2x6) |= 8; /* timer 2 irq pending */
GUSregw(TimerIRQs) += newtimerirqs;
requestedIRQs += newtimerirqs;
}
}
}
if (GUSregb(GUS4cReset) & 0x4) /* synth IRQ enable */
{
if (GUSregd(voicewavetableirq))
GUSregb(IRQStatReg2x6) |= 0x20;
if (GUSregd(voicevolrampirq))
GUSregb(IRQStatReg2x6) |= 0x40;
}
if ((!requestedIRQs) && GUSregb(IRQStatReg2x6))
requestedIRQs++;
if (GUSregb(IRQStatReg2x6))
GUSregw(BusyTimerIRQs) = GUS_irqrequest(state, state->gusirq, requestedIRQs);
}
|
Simultaneous detection of folic acid and methotrexate by an optical sensor based on molecularly imprinted polymers on dual-color CdTe quantum dots.
In this work, molecularly imprinted polymers (MIPs) were used on the surface of cadmium telluride quantum dots (CdTe QDs) for the simultaneous determination of folic acid (FA) and methotrexate (MTX). For this purpose, two different sizes of CdTe QDs with emission peaks in the yellow (QDY) and orange (QDO) spectral regions were initially synthesized and capped with MIPs. FA and MTX were used as templates for the synthesis of the two composites and designated as QDY-MIPs and QDO-MIPs, respectively. Fourier transform infrared spectroscopy, transmission electron microscopy, and fluorescence spectroscopy were employed to characterize the composites. QDY-MIPs and QDO-MIPs were then mixed (to form QDs-MIPs) and excited at identical excitation wavelengths; they emitted two different emission wavelengths without any spectral overlap. The fluorescence signals of QDY-MIPs and QDO-MIPs diminished in intensity with increasing concentration of the corresponding template molecules. Under optimal conditions, the dynamic range was 0.5-20 μmol L-1 for FA and MTX, and the detection limits for FA and MTX were 32.0 nmol L-1 and 34.0 nmol L-1, respectively. The reproducibility of the method was checked for 12.5 μmol L-1 of FA and MTX to find RSD values of 4.2% and 6.3%, respectively. Finally, the applicability of the method was checked using human blood plasma samples. Results indicated the successful application of the method as a fluorescent probe for the rapid and simultaneous detection of FA and MTX in real samples. |
Update, Jan. 4: Sign-ups are underway now. PlayStation 4 players will need to supply their PSN ID, name and an email address, and agree to a private beta agreement. Sony said that signing up does not guarantee participation.
Dreams, Media Molecule’s make-anything-including-a-game-Media-Molecule-made-10-years-ago sandbox creator for PlayStation 4, is getting ready to open up a public beta as planned beginning next week. The studio is kicking things off with a livestream showcase tomorrow, which will be followed by the beginning of the sign-up period.
The Dreams Creator Beta started as a semi-closed test at the end of December, and originally exclusive to those who subscribed to the Media Molecule online mailing list. Back in December, Media Molecule said the plan was to open the Dreams beta to a wider audience beginning Jan. 8.
The livestream is at noon ET on Friday, Jan. 4, and will be available through Media Molecule’s Twitch and Facebook channels, as well as PlayStation Events.
The beta includes Dreams’ creators mode demo, which focuses solely on the creation aspects of the game. In a preview over the summer, Polygon also saw the Dream Surfing mode, which delivers users an endless stream of levels made by others from the community.
Media Molecule has been spooling out news about Dreams here and there since the ambitious toolkit was first announced in 2013. It’s due to launch sometime this year. For those who loved the LittleBigPlanet series the British studio created for PlayStation 3, Dreams is striving to give would-be games designers an even more detailed tableau to work with and more power and control over it. In fact, Media Molecule itself showed off a virtuoso recreation of LittleBigPlanet’s opening level within Dreams at the beginning of November. |
After six years as one of Dallas most beloved restaurants, chef Matt McCallister’s FT33 will close its doors this summer.
McCallister announced the restaurant’s closure on his Facebook page, saying that the restaurant will serve its final artfully-arranged plates in June. “While part of me feels a sense of relief to finally get to this moment, it is still bittersweet and full of emotion,” he wrote. Scope out an excerpt from the statement below:
While part of me feels a sense of relief to finally get to this moment, it is still bittersweet and full of emotion.In 2012, I opened FT33 with big dreams of turning Dallas upside down by focusing on creative food without the pretension (the real irony is that statement, in and of itself, is pretentious). My ego (insecurity) was huge and my knowledge of running a great restaurant was negligible. In the beginning, I set aside most things in my life to go after my dream of running an ambitious restaurant and had no clue what I was doing…I had no real defined set of standards or even a philosophy of my own personal cooking style.
Since its debut, FT33 has been the Dallas restaurant most likely to be in the national spotlight and a stalwart of the Eater 38. The restaurant earned McCallister tons of acclaim, including multiple James Beard Award nominations, a coveted Food & Wine Best New Chef nod, and a five-star review from former Dallas Morning News critic Leslie Brenner. “I feel that the food we are cooking now is what FT always aspired to be but it took a while to find its true voice,” McCallister continued. “I’ve also grown up a bit…maybe I’ve grown beyond what FT once fulfilled for me. That isn’t a bad thing…it just is.”
McCallister hints at a new project that’s coming soon in the post, but doesn’t give any new details on what that restaurant will be. He’s most recently been involved with developing the menu at Malibu Poke, a quick-service restaurant from TJ’s Seafood owner Jon Alexis that just announced plans to expand in both Dallas and Austin. The closure of FT33 comes nine months after McCallister closed the doors to Filament, his Southern restaurant in Deep Ellum.
FT33 will close its doors on June 23. Stay tuned for more details on McCallister’s next move, and see below for his full statement.
It is with mixed emotions that I announce the last day of service at FT33 will be June 23rd, 2018. This is also the 2... Posted by Matthew McCallister on Tuesday, May 8, 2018 |
Eugene TELFAIR, Plaintiff-Appellant,
v.
FIRST UNION MORTGAGE CORPORATION, Defendant-Appellee.
No. 99-10846.
United States Court of Appeals,
Eleventh Circuit.
July 7, 2000.
Appeal from the United States District Court for the Southern District of Georgia.(no. 98-00193-CV-1),
William T. Moore, Jr., Judge.
Before TJOFLAT, MARCUS and KRAVITCH, Circuit Judges.
KRAVITCH, Circuit Judge:
In this review of the bankruptcy court's grant of Appellee's motion for summary judgment we
consider the propriety of an attorney's fees award to an oversecured creditor in a Chapter 13 bankruptcy
proceeding and determine whether Georgia law imposes fiduciary duties on a mortgagee's administration of
a mortgagor's escrow fund. Finally, we review the bankruptcy court's consideration of an affidavit
purportedly inconsistent with the affiant's prior testimony as well as the bankruptcy court's denial of
Appellant's motion for class certification. We affirm the district court's decision affirming the bankruptcy
court on all grounds.
I. BACKGROUND AND PROCEDURAL HISTORY
Appellant Eugene Telfair and his wife obtained a Veteran's Administration (VA) guaranteed loan in
1984 from Appellee First Union Mortgage Corporation's ("First Union") predecessor-in-interest. Pursuant
to a VA form Security Deed ("the Deed"), the Telfairs secured the loan with their home and agreed to make
single monthly payments towards the principal and interest as well as to pay a pro rata share of the annual
tax and insurance obligations to be placed in an escrow account.1 First Union would make payments from
1
See Security Deed ¶ 2, in BR, Part A, Tab 1, Ex. B.
this fund as they came due; any excess funds either would be refunded to the Telfairs or applied to future
payments at First Union's discretion and the Telfairs would be responsible for any shortfall.2 The Deed also
provided that the Telfairs would be charged for any expenses and attorney's fees incurred by First Union in
protecting the secured property, whether from default, foreclosure proceedings, or litigation.3 Finally, the
Deed obligated the Telfairs to maintain hazard insurance on their home continuously, the provider of which
had to be approved by First Union. If the Telfairs failed to provide proof of such continuous coverage, the
Deed authorized First Union to "force place" hazard insurance to protect its collateral.4 First Union exercised
this prerogative in 1988 when the Telfairs failed to provide proof of coverage.
On December 7, 1992, Mr. Telfair filed a Chapter 13 bankruptcy petition in which he proposed a
series of payments to satisfy the existing arrearage on the First Union mortgage; the plan was confirmed on
May 3, 1993. Outside of the plan, the Telfairs remained responsible for making their usual monthly mortgage
payments to First Union, a responsibility that was not always met. After confirmation, First Union filed three
separate motions to lift the automatic stay imposed by 11 U.S.C. § 362(a) to recover its costs incurred in
attempting to recoup the defaulted payments. First Union assessed attorney's fees incurred with these motions
against the Telfairs' account, which created a delinquency following the Chapter 13 payments and discharge.5
First Union then notified the Telfairs of its intent to foreclose on the property based upon this default.
The Telfairs responded by filing a two-count complaint against First Union in the bankruptcy court
asserting various violations by First Union in its assessment of attorney's fees and its forced placement of the
2
See id. ¶ 3.
3
See id. ¶ 6.
4
See id. ¶ 8.
5
Mr. Telfair and First Union dispute the nature of the funds First Union diverted to pay the attorney's fees.
The bankruptcy court found that First Union had applied unspecified "post-petition payments" to pay the
attorney's fees and we see no reason to delve deeper because it does not affect our disposition of this appeal.
2
hazard insurance. The Telfairs also sought certification of their claims for class action under Federal Rule
of Civil Procedure 23. After First Union moved for summary judgment on both counts, the bankruptcy court
held a class certification hearing during which it also entertained argument on the summary judgment motion.
The bankruptcy court first concluded that Mrs. Telfair was not an appropriate class representative and
dismissed her claim. The court then granted summary judgment to First Union on both substantive counts,
rendering Mr. Telfair's request for class certification moot. The bankruptcy court also denied Mr. Telfair's
motion to strike an affidavit submitted by First Union in support of its summary judgment motion. The
district court affirmed the bankruptcy court on all grounds, and Mr. Telfair ("Telfair") timely appealed.
II. DISCUSSION
In his appeal, Telfair challenges the bankruptcy and district courts' conclusions that First Union's
appropriation of attorney's fees from the Telfairs' account did not implicate 11 U.S.C. § 506(b) or 11 U.S.C.
§ 362(a) and did not violate any fiduciary duties of First Union. We review the bankruptcy court's findings
of facts for clear error and the legal conclusions of the bankruptcy and district courts de novo. See In re
Southeast Bank Corp., 97 F.3d 476, 478 (11th Cir.1996). Telfair also appeals the bankruptcy court's denial
of his motion to strike an affidavit, which we will uphold unless it was an abuse of discretion. See Goulah
v. Ford Motor Co., 118 F.3d 1478, 1483 (11th Cir.1997).6
A. Attorney's Fees
During the pendency of the Chapter 13 plan, the Telfairs defaulted on several regular loan payments.
In order to recoup the costs incurred in attempting to cure these defaults, First Union filed three separate
requests for attorney's fees. First Union voluntarily withdrew the first two requests in order to verify receipt
of payments allegedly sent by the Telfairs. After the third filing, two money order payments could not be
6
Telfair raised an assortment of other arguments before the district court and in his briefs submitted to
this court, relying on such diverse provisions as Bankruptcy Rule 2016, REPSA, 12 U.S.C. § 2609, 24 C.F.R.
3500.17(b), and Ga.Code Ann. § 13-1-11. These arguments were not timely raised before the bankruptcy
court, and we decline to hear them for the first time on this appeal. See In re Daikin Miami Overseas, Inc.,
868 F.2d 1201, 1206 (11th Cir.1989).
3
verified, and the bankruptcy court granted the Telfairs ninety days to trace the missing payments. The
Telfairs declined to either trace or resubmit the payments. After the plan was discharged, First Union applied
post-petition mortgage payments to the outstanding attorney's fees, an action which Telfair contends violated
two provisions of the bankruptcy code: 11 U.S.C. § 506(b), governing costs and fees for oversecured claims,7
and 11 U.S.C. § 362(a), the automatic stay provision.8 Neither of these claims has merit.
1. Section 506
Under his Chapter 13 plan, Telfair agreed to pay supplemental payments towards the arrearage owed
to First Union. After this plan was confirmed on May 3, 1993, the Telfairs made all of the required plan
payments and the plan was eventually discharged on April 23, 1997. During that time, however, the Telfairs
had defaulted on several of their regular loan payments due after confirmation. The attorney's fees assessed
by First Union were expended in curing these defaults and thus were allowed under the terms of the Deed.
Telfair does not dispute that the Deed provided for the fees taken by First Union, but asserts that First Union
should have requested them as part of an amendment to the plan under section 506(b), which provides:
To the extent that an allowed secured claim is secured by property the value of which, after any
recovery under subsection (c) of this section, is greater than the amount of such claim, there shall be
allowed to the holder of such claim, interest on such claim, and any reasonable fees, costs, or charges
provided for under the agreement under which such claim arose.
7
An oversecured claim is one for which the collateral exceeds the debt. See In re Delta Resources, Inc.,
54 F.3d 722, 724 n. 1 (11th Cir.1995).
8
Before the bankruptcy and district courts, Telfair also argued that assessment of the attorney's fees
violated the discharge provisions of 11 U.S.C. §§ 1328 and § 524. Section 1328 provides that upon
completion of plan payments, the bankruptcy court shall discharge any debts under the plan or disallowed
under section 502 except for any debt provided for under section 1322(b)(5), which allows a homeowner to
cure a default through a plan up until the time of foreclosure. See 11 U.S.C. § 1328 (1999). Section 524
clarifies that a discharge voids any conflicting judgments on discharged debt and bars any future claim for
discharged debt. See 11 U.S.C. § 524 (1999). The bankruptcy and district courts found these provisions
inapplicable to the post-confirmation attorney's fees sought by First Union because (1) they were not provided
for under the plan; (2) they were not disallowed under section 502; and (3) they would be excludable in any
event under section 1322(b)(5). Telfair does not appear to challenge this aspect of the courts' conclusion on
appeal as he mentions it only in passing in his initial brief. Even if he had raised this issue however, we
would affirm the bankruptcy and district courts.
4
11 U.S.C. § 506(b) (1999). Holders of these oversecured claims are entitled, under this section, to any
interest, fees, or costs provided for in the underlying debt instrument. Because First Union failed to secure
an amendment to the plan before paying itself attorney's fees, Telfair contends that it removed assets from
the estate in violation of the automatic stay.
The district court affirmed the bankruptcy court's conclusion that section 506(b) only governs fee
petitions until the time of confirmation. Because the attorney's fees incurred by First Union arose from its
attempts to cure post-confirmation defaults, the bankruptcy and district courts determined that the terms of
the Deed, without reference to section 506(b), governed the award of fees. The Deed expressly provided for
the attorney's fees assessed by First Union against Telfair.
In considering an oversecured creditor's claim for interest, the Supreme Court has stated that interest
accrues under section 506(b) "as part of the allowed claim from the petition date until the confirmation or
effective date of the plan." Rake v. Wade, 508 U.S. 464, 471, 113 S.Ct. 2187, 2191, 124 L.Ed.2d 424 (1993).9
The fact that the parties in Rake agreed that section 506(b) only applied in the post-petition, pre-confirmation
period does not undermine the imperative effect of the Court's decision, and this court has recognized as such.
See In re Delta Resources, Inc., 54 F.3d 722, 727 (11th Cir.1995); see also 4 Collier on Bankruptcy ¶
506.04[2] (Lawrence P. King et al. eds., 15th ed. 2000) ("Section 506(b) ... has no application to a secured
creditor's entitlement to post-confirmation interest....").
Telfair relies on a pre-Rake decision for the proposition that a mortgagee should not divert
maintenance payments to pay for attorney's fees without court approval. See In re Rathe, 114 B.R. 253
(Bankr.D.Idaho 1990). The creditor in Rathe, however, sought to include attorney's fees as part of its secured
claim, and could only do so under section 506(b). See id. at 256. To the extent that the reasoning of In re
Rathe is inconsistent with the intervening Rake decision, it has been overruled.
9
Rake was overruled by statute on other grounds, but the new legislation did not affect agreements entered
into before October 22, 1994 and so would not affect our disposition of this case in any event. See In re
Smith, 85 F.3d 1555, 1558 n. 3 (11th Cir.1996).
5
Telfair next seeks to distinguish Rake on the ground that it involved interest accruing on claims prior
to confirmation and only in dictum suggested that its holding would apply to attorney's fees. This court,
however, can find no basis to distinguish Rake 's statement that section 506(b) "applies only from the date
of filing through the confirmation date," 508 U.S. at 468, 113 S.Ct. at 2190, on the ground that it dealt with
interest rather than attorney's fees. Cf. In re Harko, 211 B.R. 116, 119 (2d Cir.BAP 1997) ("There is nothing
in the language of § 506(b) to suggest that interest, as opposed to fees, costs and charges, should be treated
any differently and the majority of courts have so held."). Indeed, a contrary result would be inconsistent
with the purpose of section 506(b), which allows oversecured creditors to include post-petition interest and
certain fees as part of the secured claim they will receive upon confirmation of the plan. See In re Delta
Resources, 54 F.3d at 729. In this case, the attorney's fees that First Union sought were not part of its secured
claim; they arose apart from the plan and after confirmation.
Telfair's final argument is that the mutable nature of a Chapter 13 proceeding even after confirmation
counsels in favor of bankruptcy courts using section 506(b) to maintain their control over post-confirmation
awards of attorney's fees. Telfair suggests that without this instrument, "secured creditors in Chapter 13 cases
are going to run amok" following confirmation.10 We appreciate Telfair's concern, but are satisfied that the
terms of debt instruments agreed to by debtors and creditors provide adequate protection for Chapter 13
debtors.11
2. Section 362(a)
Pursuant to section 362(a), the filing of a bankruptcy petition acts as an automatic stay against
actions or claims against the property of the bankruptcy estate. See 11 U.S.C. § 362(a) (1999).12 Telfair
10
Appellant's Br. at 32.
11
Section 1322, which also governs post-confirmation awards of interest or fees, provides further
protection to homeowners and homestead lenders. See 11 U.S.C. § 1322 (1999).
12
The relevant portion of section 362(a) reads:
6
contends that First Union's diversion of payments to recover attorney's fees ran afoul of the stay provision
because the funds were property of his bankruptcy estate. Central to our consideration of this contention is
a determination of what constitutes property of the estate following confirmation of a bankruptcy plan.
According to section 1306:
(a) Property of the estate includes, in addition to the property specified in section 541 of this title—
. . .
(2) earnings from services performed by the debtor after the commencement of the case but
before the case is closed, dismissed, or converted to a case under chapter 7, 11, or 12 of this
title, whichever occurs first.
(b) Except as provided in a confirmed plan or order confirming a plan, the debtor shall remain in
possession of all property of the estate.
11 U.S.C. § 1306 (1999). A later section of the code provides that "[e]xcept as otherwise provided in the plan
or order confirming the plan, the confirmation of the plan vests all of the property of the estate in the debtor."
11 U.S.C. § 1327(b) (1999). Read together, these two provisions create a tension to the extent they govern
the debtor's post-confirmation earnings: section 362 appears to protect those earnings while section 1327(b)
would vest those same earnings in the debtor, thereby divesting them of the protection of section 362(a).
In resolving this conflict, courts have adopted one of three models: the estate termination approach,
the estate preservation approach, and the estate transformation approach. Under the estate termination
[A] petition filed under section 301, 302, or 303 of this title ... operates as a stay, applicable
to all entities, of—
. . .
(3) any act to obtain possession of property of the estate or of property from the
estate or to exercise control over property of the estate;
(4) any act to create, prefect, or enforce any lien against property of the estate;
. . . .
11 U.S.C. § 362(a) (1999).
7
approach, all property of the estate becomes property of the debtor upon confirmation and ceases to be
property of the estate. See In re Petruccelli, 113 B.R. 5, 15 (Bankr.S.D.Cal.1990). According to the estate
preservation approach, all property of the estate remains property of the estate after confirmation until
discharge, dismissal, or conversion. See In re Kolenda, 212 B.R. 851, 853 (W.D.Mich.1997). A compromise
between these two extremes is struck by the estate transformation approach, which regards only that property
necessary for the execution of the plan as remaining property of the estate after confirmation. See In re
Heath, 115 F.3d 521, 524 (7th Cir.1997); In re McKnight, 136 B.R. 891, 894 (Bankr.S.D.Ga.1992).
Urging this court to adopt the estate preservation approach, Telfair raises the specter of unscrupulous
debtors "free to do whatever they please with their property when it is revested in them."13 Telfair presents
a fair challenge to the estate termination approach, which does not protect the post-confirmation obligations
of the bankruptcy plan. The estate transformation approach, however, protects the interests of both the debtor
and the creditors.
Consideration of the case law and the general concerns of the bankruptcy code assures us that the
estate transformation approach, adopted by the bankruptcy courts in the Southern District of Georgia, should
be the law of this circuit. We therefore echo the conclusion of the Seventh Circuit and "read the two sections,
1306(a)(2) and 1327(b), to mean simply that while the filing of the petition for bankruptcy places all the
property of the debtor in the control of the bankruptcy court, the plan upon confirmation returns so much of
that property to the debtor's control as is not necessary to the fulfillment of the plan." In re Heath, 115 F.3d
at 524. In this case, after confirmation, only the amount required for the plan payments remained property
of the estate. Telfair's regular loan payments, made outside of the plan, were therefore no longer property
13
Appellant's Br. at 36.
8
of the estate and First Union's application of a portion of those payments to attorney's fees pursuant to the
Deed did not violate section 362(a).14
B. Forced Insurance
Under the terms of the Deed, the Telfairs were required to maintain hazard insurance on their home,
with a provision allowing First Union to "force place" hazard insurance if the Telfairs let their coverage lapse.
In 1988, the Telfairs failed to provide proof of coverage and First Union exercised its prerogative to "force
place" insurance on the secured property. Rather than obtaining a policy with the Telfair's previous insurance
company, First Union arranged for coverage by Transamerica Premier Insurance Company and then, a year
later, by Balboa Insurance Company ("Balboa"), both which charged substantially higher premiums and paid
considerable commissions to First Union.15 First Union paid for these premiums with funds from the Telfairs'
escrow account. Telfair contends that this arrangement violated First Union's fiduciary duties arising from
either its administration of the Telfairs' escrow account as a trust or its role as the Telfairs' agent.
As evidence that the escrow account was an enforceable trust or obligated First Union as their agent,
Telfair cites the Deed's requirement that he and his wife "pay to [First Union] as trustee (under the terms of
this trust as hereinafter stated)"16 tax and insurance payments that First Union would pay as they came due.
Unpersuaded by this semantic argument, the bankruptcy court concluded, and the district court agreed, that,
under Georgia law, a mortgagee's administration of an escrow account gives rise to neither a trust nor an
agency relationship.
14
Even if First Union technically applied plan payments to attorney's fees and then applied a regular loan
payment towards the plan payments, our conclusion would not be different because, ultimately, all the plan
payments were properly applied, as evidenced by the bankruptcy court's discharge of Telfair's plan.
15
Telfair attributes a nefarious purpose to First Union's arrangement with Balboa; the change in coverage,
however, was prompted by the Telfairs' own lapse and, according to First Union, discontinuation of coverage
in Georgia by the Telfairs' previous carrier. In addition, although First Union alerted the Telfairs to the higher
rates, the Telfairs did not secure replacement insurance until 1998, ten years after the initial lapse.
16
Security Deed, ¶ 2, in BR, Part A, Tab 1, Ex. B.
9
A trust born under Georgia law may be either express or implied. An express trust must be in writing
and "shall have each of the following elements, ascertainable with reasonable certainty: (1) An intention by
the settler to create a trust; (2) Trust property; (3) A beneficiary; (4) A trustee; and (5) Active duties
imposed on the trustee, which duties may be specified in writing or implied by law." Ga.Code Ann. § 53-12-
20 (1997). An implied constructive trust, as claimed by the Telfairs, is found "whenever the circumstances
are such that the person holding legal title to property, either from fraud or otherwise, cannot enjoy the
beneficial interest in the property without violating some established principle of equity." Id. § 53-12-93(a).
As correctly found by the bankruptcy and district courts, there is no evidence that either type of trust
was formed because there is no indication that the Telfairs and First Union intended the escrow funds to
comprise a trust corpus. Rather, First Union's retention of future tax and insurance payments inured to the
benefit of both parties in protecting the secured property.17 See Moore v. Bank of Fitzgerald, 225 Ga.App.
122, 483 S.E.2d 135, 139 (1997) ("[A]bsent special circumstances ... there is ... no confidential relationship
between lender and borrower or mortgagee and mortgagor for they are creditor and debtor with clearly
opposite interests.") (internal quotation marks and citation omitted). Although the Deed used the word
"trust," the Georgia Court of Appeals has noted that
[t]he majority rule appears to be that funds paid by a mortgagor to an escrow account to be used by
the mortgagee to meet tax and insurance obligations ... do not constitute trust properties such as
would render the mortgagee accountable to the mortgagor for any earnings or profits from the funds.
Knight v. First Fed. Sav. & Loan Ass'n, 151 Ga.App. 447, 260 S.E.2d 511, 515 (1979). This observation is
in accord with the case law. See Ferdinand S. Tinio, Annotation, Rights in funds representing "escrow"
payments made by mortgagor in advance to cover taxes or insurance, 50 A.L.R.3d 697 § 3 (1973); see also
17
Telfair's citation to First Union employee's deposition testimony that the funds in the escrow accounts
belong to the customers, see BR, Part J, Tab 111 at 20 (Pam Swallow Dep.), is unavailing. Although this
testimony may have enlightened the bankruptcy court's consideration of whether, as a matter of Georgia law,
the escrow funds comprised an enforceable trust, the bankruptcy court was not bound by it in reaching its
ultimate conclusion.
10
Judd v. First Fed. Sav. & Loan Ass'n, 710 F.2d 1237, 1241 (7th Cir.1983) (mere use of trust terminology in
a VA form security deed does not create a fiduciary duty).
Liberty National Life Insurance Co. v. United States, 463 F.2d 1027 (5th Cir.1972), relied on by
Telfair, is not to the contrary.18 In Liberty National, the former Fifth Circuit concluded that a mortgagor's
escrow funds created a trust asset of the mortgagee bank for federal income tax purposes. See 463 F.2d at
1029-30. Not only was this opinion decided on federal rather than state law, but the narrowness of its holding
was recognized by this court five years later when it concluded that, for other tax purposes, mortgage escrow
funds created "a contractual obligation and nothing more." Southwestern Life Ins. Co. v. United States, 560
F.2d 627, 634 (5th Cir.1977).
The same reasoning compels the conclusion that First Union's administration of the Telfairs' escrow
account did not thrust on them the role of agent. Under Georgia law, agency results from the manifestation
of mutual consent that one person will act on the other's behalf and subject to the other's control. See Smith
v. Merck, 206 Ga. 361, 57 S.E.2d 326, 332 (1950). In the case of escrow funds held by a mortgagee for
payment of tax and insurance payments on behalf of a mortgagor pursuant to a security agreement, the
mortgagee does not act as agent because the mortgagee acts neither for the sole benefit of the mortgagor nor
under the mortgagor's control. See Georgia Farm Bureau Mut. Ins. Co. v. First Fed. Sav. & Loan Ass'n, 152
Ga.App. 16, 262 S.E.2d 147, 150 (1979) (a mortgagee does not act as the agent of its mortgagor when it
sought insurance for the secured property). Here, for example, although the terms of the Deed constrain First
Union's use of the escrow funds, any insurance obtained with those funds had to meet First Union's approval,
and the Telfairs lacked the authority to either direct the use of the escrowed funds or to terminate First Union's
control thereof. We therefore affirm the conclusion of the bankruptcy and district courts that administration
18
In Bonner v. City of Prichard, 661 F.2d 1206, 1209 (11th Cir.1981) (en banc), this court adopted as
binding precedent all decisions of the former Fifth Circuit handed down prior to October 1, 1981.
11
of escrow funds such as the one here, without more, does not create an agency relationship under Georgia
law.
C. The De Gorter Affidavit
Telfair contends error in the bankruptcy court's consideration of an affidavit submitted by First
Union. The affidavit of David de Gorter, Balboa's former Assistant Vice President for Marketing, describes
Balboa's insurance product. Because de Gorter had professed ignorance of many specifics of the product
during his previous deposition, Telfair maintains that the subsequent inconsistent affidavit should have been
stricken as a "sham." See Van T. Junkins & Assocs. v. U.S. Indus., 736 F.2d 656, 656 (11th Cir.1984) ("[A]
district court may find an affidavit which contradicts testimony on deposition a sham when the party merely
contradicts its prior testimony without giving any valid explanation."). The bankruptcy court, however,
accepted First Union's explanation of the disparity: that de Gorter had informed himself of the insurance
policy's terms in the interval between his deposition and affidavit. This is a valid explanation, and we cannot
say that its acceptance by the bankruptcy and district courts was an abuse of discretion. In any event, de
Gorter's familiarity was based only on other materials in the record, so it is difficult to see whence any
prejudice would have come.
D. Class Certification
After determining that none of Telfair's underlying claims had merit, the bankruptcy court came to
the ineluctable conclusion that there were no claims to certify as a class action lawsuit.19 It was within the
court's discretion to consider the merits of the claims before their amenability to class certification. See
Cowen v. Bank United of Texas, 70 F.3d 937, 941 (7th Cir.1995); Wright v. Schock, 742 F.2d 541, 543-44
(9th Cir.1984); Katz v. Carte Blanche Corp., 496 F.2d 747, 758 (3d Cir.1974) (en banc). With no
meritorious claims, certification of those claims as a class action is moot. Because we agree with the
19
The bankruptcy court also denied Mrs. Telfair's motion for class certification on the ground that her
claims were not sufficiently representative, but she does not appeal this decision.
12
bankruptcy and district courts' disposition of the merits of Telfair's claims, we also affirm the denial of the
motion for class certification.
III. CONCLUSION
For the foregoing reasons, we AFFIRM the district court's decision affirming the bankruptcy court
in all respects.
13
|
Jerome Gelb
2015-11-21 03:44:28 -0500
The QUR’AN commands to kill infidels:
1. Allah is an enemy to unbelievers. – Sura 2:98
2. On unbelievers is the curse of Allah. – Sura 2:161
3. Slay them wherever ye find them and drive them out of the places whence they drove you out, for persecution is worse than slaughter. – 2:191
4. Fight against them until idolatry is no more and Allah’s religion reigns supreme. (different translation: ) Fight them until there is no persecution and the religion is God’s entirely. – Sura 2:193 and 8:39
5. Fighting is obligatory for you, much as you dislike it. – 2:216
(different translation: ) Prescribed for you is fighting, though it is hateful to you.
….. martyrs…. Enter heaven – Surah 3:140-43
6. If you should die or be killed in the cause of Allah, His mercy and forgiveness would surely be better than all they riches they amass. If you should die or be killed, before Him you shall all be gathered. – 3:157-8
7. You must not think that those who were slain in the cause of Allah are dead. They are alive, and well-provided for by their Lord. – Surah 3:169- 71
8. Let those fight in the cause of God who sell the life of this world for the hereafter. To him who fights in the cause of God, whether he is slain or victorious, soon we shall give him a great reward. – Surah 4:74
9. Those who believe fight in the cause of God, and those who reject faith fight in the cause of evil. – 4:76
10. But if they turn renegades, seize them and slay them wherever you find them. – 4:89
11. Therefore, we stirred among them enmity and hatred, which shall endure till the Day of Resurrection, when Allah will declare to them all that theyhave done. – 5:14
12. O believers, take not Jews and Christians as friends; they are friends of each other. Those of you who make them his friends is one of them. God does not guide an unjust people. – 5:54
13. Make war on them until idolatry is no more and Allah’s religion reigns supreme – 8:39
14. O Prophet! Exhort the believers to fight. If there are 20 steadfast men among you, they shall vanquish 200; and if there are a hundred, they shall rout a thousand unbelievers, for they are devoid of understanding. – 8:65
15. It is not for any Prophet to have captives until he has made slaughter in the land. – 8:67
16. Allah will humble the unbelievers. Allah and His apostle are free from obligations to idol-worshipers. Proclaim a woeful punishment to the unbelievers. – 9:2-3
17. When the sacred months are over, slay the idolaters wherever you find them. Arrest them, besiege them, and lie in ambush everywhere for them. – 9:5
18. Believers! Know that idolators are unclean. – 9:28
19. Fight those who believe neither in God nor the Last Day, nor what has been forbidden by God and his messenger, nor acknowledge the religion of Truth, even if they are People of the Book, until they pay the tribute and have been humbled. – 9:29 (another source: ) The unbelievers are impure and their abode is hell. (another source: ) Humiliate the non- Muslims to such an extent that they surrender and pay tribute.
20. Whether unarmed or well-equipped, march on and fight for the cause of Allah, with your wealth and your persons. – 9:41
21. O Prophet! Make war on the unbelievers and the hypocrites. Be harsh with them. Their ultimate abode is hell, a hapless journey’s end. – 9:73
22. Allah has purchased of their faithful lives and worldly goods, and in return has promised them the Garden. They will fight for His cause, kill and be killed. – 9:111
23. Fight unbelievers who are near to you. 9:123 (different translation: Believers! Make war on the infidels who dwell around you. Let them find harshness in you. (another source: ) Ye who believe! Murder those of the disbelievers….
24. As for those who are slain in the cause of Allah, He will not allow their works to perish. He will vouchsafe them guidance and ennoble their state; He will admit them to the Paradise He has made known to them. – 10:4-15
25. Allah has cursed the unbelievers and proposed for them a blazing hell. – 33:60
26. Unbelievers are enemies of Allah and they will roast in hell. – 41:14
27. When you meet the unbelievers, smite their necks, then when you have made wide slaughter among them, tie fast the bonds, then set them free, either by grace or ransom, until the war lays down its burdens. – 47:4 (different translation: ) When you meet the unbelievers in the battlefield, strike off their heads, and when you have laid them low, bind your captives firmly.
28. Those who are slain in the way of Allah – he will never let their deeds be lost. Soon will he guide them and improve their condition, and admit them to the Garden, which he has announced for them. – 47:5
29. Muslims are harsh against the unbelievers, merciful to one another. – 48:25
30. Muhammad is Allah’s apostle. Those who follow him are ruthless to the unbelievers but merciful to one another. Through them, Allah seeks to enrage the unbelievers. – 48:29
31. Prophet! Make war on the unbelievers and the hypocrites and deal sternly with them. Hell shall be their home, evil their fate. – 66:9
32. The unbelievers among the People of the Book and the pagans shall burn forever in the fire of hell. They are the vilest of all creatures. – 98:51
33. Fight them so that Allah may punish them at your hands, and put them to shame.
commented |
An 18 point haul from captain Sergio Aguero and a further 12 from Graziano Pelle, along with 7 a piece from Alexis Sanchez and Dele Alli, meant that our recommended XV brought home a respectable 59 points for Gameweek 33. With the largest double gameweek of the season now upon us, read on as we analyse the defensive and attacking odds for Gameweek 34, where we have taken into account both games for those players and teams that play twice in our implied chance percentages. In a slight break from tradition, we have chosen to save money by filling our bench with cheap players who are likely to start, allowing us to put out the strongest possible starting XI as we aim to maximise our points potential.
Defensive odds
Team Clean Sheet Odds Implied chance Man Utd 1.53 & 2 83% Arsenal 2 & 1.91 76% Liverpool 2.88 & 2.55 60% Man City 3.75 & 2.45 56% West Ham 4.6 & 2.62 52% Newcastle 2.8 & 6.5 46% Watford 3.3 & 4.75 45% Everton 3 & 5.75 44% West Brom 2.62 & 10 44% Tottenham 2.45 41% Leicester 2.7 37% Norwich 2.88 35% Sunderland 3.4 29% Chelsea 3.6 28% Swansea 3.6 28% Southampton 3.8 26% Crystal Palace 9 & 6 26% Bournemouth 4 25% Stoke 4.75 21% Aston Villa 10 10%
With an extremely favourable double gameweek that includes home clashes against Aston Villa and Crystal Palace, Manchester United top the bookies defensive rankings with an 83% chance of keeping at least 1 clean sheet. The Championship-bound Villains have only scored once in their last 5 away games, whilst Alan Pardew’s men have been lean in front of goal lately, scoring just 3 goals in their last 4 outings, blanking in 2 of those. As a result, the Red Devils will be confident of adding to the 10 clean sheets already accrued at Old Trafford in the league this term. David de Gea represents a solid option between the sticks, whilst Timothy Fosu-Mensah has seemingly usurped Matteo Darmian at right back following some impressive performances of late.
Arsenal’s (76%) favourable double header sees them welcome both Palace and West Brom to The Emirates. With 2 clean sheets in their last 3 games, the Gunners back line will be looking forward to facing the aforementioned Eagles and Tony Pulis’ men, who are the 3rd lowest scorers away from home in the division, having mustered just 12 goals in 16 games. Hector Bellerin’s attacking threat sees him make our squad following a goal and 3 assists in his last 4, whilst Gabriel represents a cheap route into Arsene Wenger’s defensive unit.
Liverpool (60%), Manchester City (56%) and West Ham (52%) all enjoy a pair of fixtures too and make up the top 5 defensive prospects for the gameweek. However, with our keeper and 3 starting defenders covered by our double-ups on United and Arsenal, we choose to avoid the rotation risks at Liverpool and City, who are both still involved in European competitions (at the time of writing), and choose cheap double gameweek players in order to hoard finances for our front 7. We draft in Angelo Ogbonna for coverage of the Hammers’ defence, whilst Everton’s Joel Robles satisfies our goalkeeping requirements off the back of a 14 point haul in Gameweek 33, and Newcastle’s Jerome Lascelles occupies the final place on our bench in light of his double, albeit we do not expect him to feature for our squad.
Before moving onto our analysis of the bookmakers attacking odds, a quick look at the bottom rungs of the clean sheet ladder tells us that defensive assets from Bournemouth (25% – home to Liverpool), Stoke (21% – home to Tottenham) and Aston Villa (10% – away to Man United) should be avoided this weekend.
Attacking odds
Player Goalscorer Odds Implied chance Sergio Aguero 2.5 & 1.73 75% Marcus Rashford 2.2 & 2.2 70% Daniel Sturridge 2.5 & 2.1 69% Alexis Sanchez 2.75 & 2.05 67% Danny Welbeck 2.75 & 2.05 67% Romelu Lukaku 2.4 & 2.63 64% Roberto Firmino 3.25 & 2.63 57% Andy Carroll 3.75 & 2.4 57% Odion Ighalo 3.3 & 2.88 55% Kevin de Bruyne 4.1 & 2.75 52% Aleksandar Mitrovic 3 & 3.75 51% Jesse Lingard 3.2 & 3.4 51% Dimitri Payet 4 & 2.88 51% Saido Berahino 3.2 & 4 48% Harry Kane 2.2 45% Jamie Vardy 2.25 44% Ross Barkley 4.1 & 4.5 41% Diego Costa 2.55 39% Georginio Wijnaldum 4.5 & 4.75 39% Connor Wickham 6 & 4.75 34% Graziano Pelle 3.2 31% Stephane Sessegnon 5.5 & 6.5 31% Dieumerci Mbokani 3.25 31% Jermain Defoe 3.25 31% Riyad Mahrez 3.25 31% Nordin Amrabat 6.75 & 6 29% Alberto Paloschi 3.6 28% Callum Wilson 3.75 27% Dele Alli 3.75 27% Gylfi Sigurdsson 3.8 26% Sadio Mane 4 25% Yannick Bolasie 8.5 & 6.5 25% Josh King 4.25 24% Wahbi Khazri 4.35 23% Pedro 4.35 23% Bojan 4.5 22% Xerdan Shaqiri 6 17% Robbie Brady 7 14% Jordan Ayew 7 14% Jack Grealish 11 9%
Despite missing a penalty in the Champions League midweek, Sergio Aguero retains the faith of the bookies and our captain’s armband for the 3rd week in a row, with a 75% chance of netting over the course of the double. The Argentine will travel to London to face Chelsea before heading to the North East to tackle Newcastle. In their last 6 games each, the Blues and the Toon have managed just 1 clean sheet between them, highlighting their lack of defensive resolve and Aguero’s resulting potential. Having netted in both of his last 2 league outings, further profits could be just around the corner for Sergio.
Marcus Rashford (70%) joins Aguero upfront courtesy of a couple of tasty fixtures against the porous defences of Aston Villa and Crystal Palace: the pair have conceded 106 goals between them this term. United’s latest prodigy has burst onto the scene over the past few months, bagging 6 goals in 11 appearances in all competitions, and at a price of just £4.5m looks a handy enabler for Gameweek 34 squads. Romelu Lukaku (64%) completes our front 3. Despite no goal in 4, the Belgian powerhouse has still managed 18 this season and represents the Toffees’ chief threat ahead of a home game with Southampton (no clean sheet in 7) and a trip across the Mersey for a derby date with fierce rivals Liverpool. Further appeasing our faith is the fact that Big Rom bagged in both of the reverse fixtures earlier this campaign (2 vs Southampton, 1 vs Liverpool).
With 3 goals and 3 assists in his last 5 games, Alexis Sanchez (67%) is our 1st midfield pick. A tasty pair of home ties against Crystal Palace and West Brom, both who have relatively little to play for, bodes well for the Chilean as Arsenal look to cement a top 3 finish. Kevin de Bruyne (52%) is another premium-priced midfielder who makes our XI having returned from a spell on the sidelines with aplomb, striking 3 times in 4 appearances domestically and in Europe. Facing the same leaky defences as teammate Sergio Aguero, a double up on City’s main attacking outlets is called for.
Roberto Firmino (57%) and Dimitri Payet (51%) complete our midfield quartet this time round.
A double against Bournemouth and Everton, who have 2 clean sheets between them in their last 10 games, brings Liverpool’s Brazilian attacker onto our radars following a sparkling run of form that has seen him card 7 goals and 4 assists in the league since the turn of the year. Meanwhile, the mercurial Payet has also been in strong form this calendar year, notching 4 goals and 5 assists for the Hammers in the top flight. A visit to The King Power won’t be easy, seeing as Leicester have kept 5 clean sheets in their last 6 home games, but a home clash with Watford on Wednesday could prove profitable, given that the Hornets haven’t registered an away shutout in their last 7 attempts. With only £4.5m of our budget remaining, Danny Drinkwater, who has chalked up 2 goals and 6 assists this term, makes our bench and completes our squad.
Other viable options for our front 8 include Daniel Sturridge (69%), who has 2 goals and an assist in 3 league outings, Danny Welbeck (67%), who looks to have cemented to forward role at the tip of Arsenal’s potent attack, and Manchester United winger Jesse Lingard (51%), but the trio miss out on our recommended XV due to squad selection and/or budget restraints.
The Gameweek Squad
YOU’VE DONE YOUR RESEARCH. WHY NOT SET UP YOUR FREE DAILY FANTASY TEAM HERE TO COMPETE FOR £50
Daniel Victory is a Fantasy football and anytime goalscorer betting enthusiast. Enjoys SSS – statistics, strategising and spreadsheets. Follow his great tips on Twitter. |
07-0404 Exxon Mobil Corp. v. Dan Gill
IN THE SUPREME COURT OF TEXAS
════════════
No. 07-0404
════════════
Exxon Mobil Corp.,
Petitioner,
v.
Dan Gill, et al.,
Respondents
════════════════════════════════════════════════════
On Petition for Review from the
Court of Appeals for the Thirteenth District of
Texas
════════════════════════════════════════════════════
PER CURIAM
Justice O’Neill and Justice Guzman did not participate in
the decision.
For several years, Exxon Mobil Corp. offered service station dealers
individual rebates based upon a dealer’s sales volume and hours of operation.
Three Texas dealers, Dan Gill, Howard Granby, and Patrick Morrow (“the
Dealers”), sued Exxon in the county court at law of Nueces County on behalf of
all Exxon dealers in the nation, complaining that unbeknownst to them, Exxon
added the cost of the rebate programs back into the wholesale price Exxon
charged them for gasoline. The Dealers initially moved to certify a nationwide
class, but after this Court’s decision in Compaq Computer Corp. v. Lapray, 135 S.W.3d 657 (Tex. 2004), they sought
certification of only a statewide class, and plaintiffs’ counsel refiled the claims for all other Exxon dealers in the United
States in federal court. The federal court rendered summary judgment for Exxon.
Flagler Auto., Inc. v. Exxon Mobil Corp., 582 F. Supp.
2d 367 (E.D.N.Y. 2008). Meanwhile, the Texas trial court certified a
class of all Texas dealers, and the court of appeals affirmed. 221 S.W.3d 841 (Tex. App.–Corpus Christi-Edinburg 2007). Because the lower courts did not
correctly construe and apply our decision in Shell Oil Co. v. HRN, Inc.,
144 S.W.3d 429, 434-436 (Tex. 2004), we reverse and remand the case to the trial
court.
“Courts must perform a rigorous analysis before ruling on class
certification to determine whether all prerequisites to certification have been
met.” Sw. Ref. Co. v. Bernal, 22 S.W.3d 425, 435 (Tex. 2000)
(citation and internal quotation marks omitted). In so doing, courts “may
look beyond the pleadings.” Intratex Gas Co. v.
Beeson, 22 S.W.3d 398, 404 (Tex. 2000). “Because class determinations
generally involve considerations that are enmeshed in the factual and legal
issues comprising the plaintiff’s cause of action, the trial court must be able
to make a reasoned determination of the certification issues.” Id. (citation and internal quotation marks omitted).
And while “[d]eciding the merits of the suit in order
to determine . . . its maintainability as a
class action is not appropriate,” Beeson, 22 S.W.3d at 404 (citations
omitted), “the substantive law . . . must be taken into consideration
in determining whether the purported class can meet the certification
prerequisites under [Texas Rule of Civil Procedure] 42,” Union Pac. Res.
Group, Inc. v. Hankins, 111 S.W.3d 69, 72-73 (Tex. 2003).
The parties do not dispute that each dealer’s sales agreement with Exxon
contained essentially the same open-price provision, obligating the dealer to
pay Exxon its “established” price or price “in effect” at the time of the
loading of the delivery vehicle (referred to as the DTW or DTT price, short for
dealer tank wagon or dealer tank truck). Such provisions are permitted by
section 2.305 of the Uniform Commercial Code, in Texas, Tex. Bus. & Com. Code § 2.305,
which states in pertinent part:
(a) The parties if they so intend can conclude a contract for
sale even though the price is not settled. In such a case the price is a
reasonable price at the time for delivery
. . . .
(b) A price to be fixed by the seller or by the buyer means a
price for him to fix in good faith.
Comment 3
creates a safe harbor within (b), advising that “in the normal case a ‘posted
price’ or a future seller’s or buyer’s ‘given price,’ ‘price in effect,’ ‘market
price,’ or the like satisfies the good faith requirement.” Tex. Bus. & Com.
Code § 2.305 cmt. 3. See Romo v. Austin
Nat’l Bank, 615 S.W.2d 168, 171 n.2 (Tex. 1981) (“Although the official
comments to the Code were not enacted by the Legislature, they serve as a
valuable aid in construing the statutory language.” (citations omitted)).
The Dealers do not contend that they were charged anything other than the
DTW or DTT price, or that the prices charged were commercially unreasonable in
amount or discriminatory. Rather, they complain that Exxon promised that the
rebate programs would provide dealers real economic benefits but recouped the
rebates by factoring them back into prices without disclosing what it was doing.
Exxon admits that it took rebate costs into account in setting prices but
disputes whether the costs were fully recouped and how much dealers knew.
The trial court certified a class asserting three claims: (1) breach of
the sales agreements; (2) breach of section 2.305’s duty of good faith; and (3)
breach of rebate promises. See 221 S.W.3d 841,
848. The court of appeals viewed the first two as “the same” — for breach
of the open-price provisions, id. at 851 — but
saw the third claim as separate — “for breach of the promise to provide economic
benefits under the rebate programs,” id. at 852.
The court of appeals construed all three as claims for breach of contract and
rejected Exxon’s argument that the Dealers really alleged fraud. Id. at
849 (“The claims are . . . contract claims,
not tort claims, as Exxon suggests.”); id. (“plaintiffs have not asserted a cause of action for fraud”);
id. at 853 (“this is a contract case”). The
Dealers also tell us in their brief that “Exxon is simply wrong when it argues
that this breach-of-contract case . . . is a
fraud case.”
The Dealers have a compelling reason to confine their claim to breach of
contract: generally speaking, to recover for fraud or other misrepresentation,
plaintiffs must offer evidence that they relied on the defendant’s misconduct.
See Henry Schein, Inc. v.
Stromboe, 102 S.W.3d 675, 686 (Tex. 2002).
Such evidence is often different for each individual, depending on how and what
each was told, what each knew of the matter, and how each reacted, thus
precluding the predominance of common issues required to maintain a class action
under Rule 42(b)(3). See id. at 693-694.
To recover for breach of contract, proof of reliance is not required.
Accepting the Dealers’ assertion that theirs is a contract action only,
we see no distinction in their claims. They do not allege that Exxon’s promises
regarding the rebates were a separate contract or modified the sales agreements.
They do not assert an independent breach-of-contract action based on any
promises made by Exxon. Their complaint that they never received the rebate
benefits Exxon promised is simply the basis for their claim that Exxon did not
act in good faith and therefore breached the open-price provisions. Thus, we
have before us a single claim for breach of the open-price provisions, and the
issue is whether the trial court acted properly in certifying it as a class
action.
As noted above, comment 3 to section 2.305 provides that a seller who
charges a “price in effect” or the like, as Exxon did, acts in good faith “in
the normal case.” Tex. Bus. & Com. Code § 2.305 cmt. 3. In Shell Oil Co. v. HRN,
Inc., 144 S.W.3d 429 (Tex. 2004), we explained that “the normal case” is
generally one that does not involve discriminatory pricing and that:
Beyond prohibiting discriminatory pricing, the [UCC] drafters
wished to minimize judicial intrusion into the setting of prices under
open-price-term contracts. They understood that requiring sellers in open-price
industries, such as the oil and gas industry, to justify the reasonableness [of]
their prices in order to satisfy section 2.305 would mean that in every case the
seller is going to be in a lawsuit and that every sales contract would become a
public utility rate case. The drafters reasonably foresaw that almost any price
could be attacked unless it benefitted from a strong
presumption. Thus, they adopted a safe harbor, Comment 3’s posted price
presumption, to preserve the practice of using sellers’ standard prices while
seeking to avoid discriminatory prices.
Id. at 435 (citation and internal quotation marks
omitted). To avoid having “a jury
. . . determine in every section 2.305(b) case whether there
was any improper motive animating the price-setter, even if the prices
ultimately charged were undisputedly within the range of those charged
throughout the industry,” we concluded that the required good faith must be
measured objectively, with reference to commercial realities, rather than
subjectively, based on the person’s motives or alleged dishonesty. Id. at 435-436 (citation and internal quotation marks
omitted).
HRN involved allegations by service station dealers that Shell Oil
Co. had violated its open-price contracts, like those involved in the present
case, by dishonestly setting prices so high that dealers could not remain
competitive in the market, thereby forcing them out of business to be replaced
by company-owned stations more profitable to Shell. Id.
at 432. But the dealers did not claim that the prices charged were
commercially unreasonable or discriminatory. Their struggles to compete
effectively did not make the case “abnormal” for purposes of comment 3’s safe
harbor. Id. at 437-438.
The trial court in the present case acknowledged that under HRN,
“a party merely challenging the commercial reasonableness of an open-price
without other factors must show price discrimination,” but it distinguished
HRN because of the Dealers’ “specific claims of dishonesty in fact based
on Exxon’s promise of a rebate and acts allegedly taken to remove the benefit
promised.” We do not see the distinction. The dealers’ claims of dishonesty in
HRN — that Shell was setting prices to drive them out of business — were
just as specific, and certainly as reprehensible, as those asserted by the
Dealers in the present case. Here, as in HRN, there is no claim that the
open prices charged were commercially unreasonable in amount or discriminatory.
The Dealers here point to nothing in the contracts that prohibited Exxon from
taking rebate costs into account in setting prices.
The court of appeals distinguished HRN because this case involves
“specific promises of economic remuneration for keeping stores open specified
hours and selling specified volumes of gasoline.” 221 S.W.3d at 852. But as we have already noted, the Dealers
do not assert a cause of action for breach of such promises. They disavow any
claim of fraud, and they do not assert that any promises Exxon made to them
constituted a contract or modified their sales agreements. The Dealers’ only
claim is for breach of the open-price provisions, and the question is whether
Exxon’s alleged failure to disclose that it was setting prices to recoup rebate
costs may violate section 2.305’s good faith requirement when Shell’s alleged
practice of setting prices to drive dealers out of business did not. The answer
is no.
Thus, it appears that the Dealers’ claim lacks merit. As noted at the
outset, a federal district court has already reached this very conclusion in an
identical case on behalf of all Exxon dealers in the United States outside
Texas. Flagler Auto., Inc. v. Exxon Mobil Corp., 582 F.
Supp. 2d 367 (E.D.N.Y. 2008). The federal Eleventh Circuit has held the
same in a similar case involving a different oil company and rebate, Autry
Petroleum Co. v. BP Prods. N. Am., Inc., 2009 U.S. App. LEXIS 13978, 2009 WL 1833864 (11th
Cir. 2009) (per curiam). In
Autry, as here, dealers complained that the oil company had factored the
cost of a rebate program back into the prices charged. Citing HRN, the
court in Autry concluded: “The good-faith safe harbor provided in UCC
[§ 2-305(2)] would be undermined — and the certainty a safe harbor provides
would be frustrated — if, without more, an allegation of subjective bad faith
trumped the normal case presumption of good faith.” Id.
at *6.
The Dealers point to an earlier Eleventh Circuit case, Allapattah Services, Inc. v. Exxon Corp., 333
F.3d 1248 (11th Cir. 2003), yet another case involving claims by service station
dealers that an oil company breached “open price” provisions. In that case, the
company promised to discount its pricing to offset credit transaction charges
but later withdrew the offset without notice. The court approved class action
treatment. But Allapattah was different, the
court later explained in Autry, because there, “Exxon made specific,
express promises about the way it would adjust its prices,” agreeing that rebate
costs would not be added back in. Autry, at *5-6. The Dealers in this
case make no such allegation. To the contrary, they allege that Exxon factored
rebate costs into prices “secretly,” without disclosing what it was doing.
The trial court and court of appeals misconstrued our decision in
HRN and misapplied it to this case. When a class has been certified based
on a significant misunderstanding of the law, we have concluded that “remand to
the trial court is appropriate so that it may determine the effect . . . on the requirements for class
certification.” BMG Direct Mktg., Inc. v. Peake, 178 S.W.3d 763, 778 (Tex. 2005).
Accordingly, the trial court’s class certification order is vacated and the case
is remanded to that court for further proceedings.
Opinion
delivered: November 20, 2009 |
### Start
### 4MRecover-22.0.iso
set extract_path=""
set timeout=0
menuentry "4MRecover" --hotkey=1 {
linux ${extract_path}/boot/bzImage root=/dev/ram0 vga=normal
initrd ${extract_path}/boot/initrd.gz
}
### End |
This node is used to specify additional parameters on a Maya field.
Currently, the only additional parameter is the “Is Normal” flag.
This makes it possible for the user to model external forces to the tissue or cloth, using Maya fields.
Attribute
Meaning
field
The message attribute of a Maya field node
isNormal
Whether the field should be applied only in the surface normal direction
outField
This is connected to the “fields” attribute of the zTissue or zCloth nodes
that this field should influence |
Q:
Probability of non-uniform draw without repeats.
I'm programming a machine that places one of eleven balls in sequence. The probabilities of the machine picking ball $i$ is given by $p_i$, and not necessarily does $p_i=p_j$ (this is what I mean by non-uniform).
The machine first picks a ball $i$, and notes its number. If $i$ is then picked again, it redraws until $j$ is picked.
Given ball $i$ is drawn first, what is the probability of ball $j$ being drawn second? (And then of ball $k\neq i,j$ being drawn third.)
My conjecture is that given ball $i$ is first, I can simply multiply all $p_{j\neq i}$ with a scalar $\alpha$ so that $\sum \alpha p_{j\neq i}=1$. I think I can prove this works with $p_i=p_j$, but I don't know if it generalizes.
A:
Here is how I am interpreting the question: You are trying to draw three distinct balls from the collection. Each time you draw a ball you note its number and replace it. Should you draw that number again, you put it back and repeat the draw.
Under this scenario, the probabilities just rescale by a constant factor, as imagined in the original post. To see that, let's suppose you first draw ball $1$. Let $\hat {p_2}$ be the probability that the next draw is ball $2$. Indeed, three things can happen on the next draw: you get ball $2$, you get one of $3,\cdots, 11$, you get ball $1$ again. Thus $$\hat {p_2}=p_2\times 1+ (p_3+\cdots +p_{11})\times 0 + p_1\times \hat {p_2}=p_2+p_1\times \hat {p_2}\implies \hat {p_2}=\frac {p_2}{1-p_1}$$
Nothing special about ball $2$ of course, all the probabilities just scale by $\frac 1{1-p_1}$ and we are done.
|
Banks race to issue bonds for capital hike
Many banks have issued a large amount of bonds to raise capital in a move to meet high demand during year-end’s peak lending season and prepare to meet the State Bank of Vietnam (SBV)’s regulations on tightening the use of short-term funds for long-term loans from early next year.
In October alone, State-owned Vietcombank made three issues of nearly 3.3 million bonds at par value of 100,000 VND (4.27 USD), raising a total of 329.3 billion VND. The interest rate on the six-year bonds is fixed at 7.475 percent per year, much higher than the current rate of 6.6 percent per year applied for the bank’s 5-year saving deposits.
The month also saw two other State-owned banks – BIDV and VietinBank – issue two-year bonds worth a total of 3.45 trillion VND and 450 billion VND, respectively. Before this issue, BIDV made four bond issues in 2018 totalling 1.01 trillion VND while the figure for VietinBank was up to 18.6 trillion VND.
Photo: enternews.vn
Military Bank also successfully raised nearly 1.39 trillion VND through the issue of six-year and 10-year bonds. The interest rate on the bonds is floating and determined by the bank’s reference interest rate on the 12-month saving deposit rate plus 1-1.5 percent per year for five-year bonds and 1.8 percent for 10-year bonds.
VIB in October raised 2.2 trillion VND from three-year bonds at a fixed interest rate of 6.3 percent per year.
According to the banks, the proceeds will be used to supplement capital and improve their financial capacity.
Statistics from 28 banks showed that the total mobilised capital through the issue of valuable papers, including bonds, at the banks in the first nine months of this year reached nearly 346.63 trillion VND, up more than 11 percent over the beginning of the year.
The rise of the total mobilised capital through valuable papers was much higher than the 9.75 percent growth rate of banks’ saving deposits.
Besides the issue in the domestic market, some banks such as HDBank and VIB also planned to issue international bonds. HDBank, for example, expects to issue 3,000 convertible bonds worth 300 million USD through private placement in 2018 or 2019.
According to experts, banks prefer to issue bonds to meet rising capital demand at year-end and prepare long-term capital to satisfy the SBV’s regulation on reducing short-term funds for long-term loans from 45 percent to 40 percent, effective from January 1, next year.
For State-owned banks like Vietcombank, VietinBank and BIDV, increasing capital is one of their most urgent tasks at the moment, because if they cannot do so before 2020, their capital adequacy ratio (CAR) will fall below the minimum level stipulated by the SBV and under Basel II norms – a set of banking laws and regulations issued by the Basel Committee on banking supervision to enhance competition and transparency in the banking system and make banks more resistant to market changes.
However, raising capital has not been easy as the banks are struggling to find foreign investors while they are not allowed to hold on to dividends to increase capital, so the banks have decided to issue bonds. |
Reporting to the Senior Director of Culture and Employee Engagement, the People Development Program Manager is responsible for assisting in the planning, development and implementation of career development and training services for SAG-AFTRA. The position routinely collaborates with the People & Culture business partners and recruitment teams, Knowledge Management and members of management to communicate and execute program objectives. As a member of the People & Culture team, you will be tasked with the following areas of responsibility:
Career Development:
• Provide staff with guidance and recommendations for training and career development in collaboration with the manager and business partner.
• Conduct skills, personality and career assessments to assist employees in developing internal career pathing plans.
• Assess skill gaps between high potential talent for succession planning. Collaborate with business partners and managers to develop succession plans
• Oversee the recruitment job skills assessment process. Provide guidance to the recruitment team responsible for administering assessments. Collaborate with the business partners, managers and recruitment to implement changes as needed.
• Maintain ongoing communication with employees to determine progress of internal career search and/or development plan
• Attend weekly recruitment team meetings to review open requisitions and discuss internal candidates’ readiness for consideration.
Training:
• Collaborate with Knowledge Management to conduct training needs assessments.
• Assist the Senior Director in designing, planning and implementing identified training programs across SAG-AFTRA.
• Assist with the ongoing development of the new hire orientation and onboarding program.
• Monitor and evaluate training program compliance and effectiveness.
Perform other duties as assigned or as the situation dictates.
Qualifications
What You’ll Need
We want to make sure you’re successful. To be considered, you must have:
• Strong knowledge of Learning & Professional Development best practices; able to develop and implement creative programs that comply with all federal, state, and local laws and regulations.
• Strong interpersonal skills: high degree of patience and tact, and must be able to cultivate relationships with people from diverse backgrounds, both internally and externally.
• Strong communication skills in English, both oral and written.
• Strong consultative skills to collaboratively design impactful solutions and manage stakeholder expectations.
• Able to use sound judgment, discretion and maintain confidentiality on development matters.
• Highly developed customer service skills.
Minimum Qualifications
• Bachelor’s Degree and five years of experience in related field.
• A minimum of four years of program/project management, preferably in the fields of learning and professional development.
• Minimum of 3 years of management experience required.
Preference will be given to candidates that possess:
• SPHR or PHR/SHRM certification or equivalent human resources management credential is a plus.
• Experience working in a union environment is highly desirable.
• Working knowledge of learning applications preferred.
What You’ll Get
We are a great place to work because we offer:
• Colleagues that are passionate about what we do and how they contribute to our mission
• Balance between work and home life responsibilities
• Affordable and comprehensive medical and dental plans
• Generous pension plan
• Employee discounts and perksThis job is no longer available. Click here to view current job listings.
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Dietary fructose causes liver damage in animal model
Date:
June 19, 2013
Source:
Wake Forest Baptist Medical Center
Summary:
The role of dietary fructose in the development of obesity and fatty liver diseases remains controversial, with previous studies indicating that the problems resulted from fructose and a diet too high in calories. However, a new study conducted in an animal model showed that fructose rapidly caused liver damage even without weight gain. The researchers found that over the six-week study period liver damage more than doubled in the animals fed a high-fructose diet as compared to those in the control group.
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FULL STORY
Soft drinks. Fructose is the most commonly added sugar in the American diet.
The role of dietary fructose in the development of obesity and fatty liver diseases remains controversial, with previous studies indicating that the problems resulted from fructose and a diet too high in calories.
However, a new study conducted in an animal model at Wake Forest Baptist Medical Center showed that fructose rapidly caused liver damage even without weight gain. The researchers found that over the six-week study period liver damage more than doubled in the animals fed a high-fructose diet as compared to those in the control group.
The study is published in the June 19 online edition of the American Journal of Clinical Nutrition.
"Is a calorie a calorie? Are they all created equal? Based on this study, we would say not," said Kylie Kavanagh, D.V.M., assistant professor of pathology-comparative medicine at Wake Forest Baptist and lead author of the study.
In a previous trial which is referenced in the current journal article, Kavanagh's team studied monkeys who were allowed to eat as much as they wanted of low-fat food with added fructose for seven years, as compared to a control group fed a low-fructose, low-fat diet for the same time period. Not surprisingly, the animals allowed to eat as much as they wanted of the high-fructose diet gained 50 percent more weight than the control group. They developed diabetes at three times the rate of the control group and also developed hepatic steatosis, or non-alcoholic fatty liver disease.
The big question for the researchers was what caused the liver damage. Was it because the animals got fat from eating too much, or was it something else?
To answer that question, this study was designed to prevent weight gain. Ten middle-aged, normal weight monkeys who had never eaten fructose were divided into two groups based on comparable body shapes and waist circumference. Over six weeks, one group was fed a calorie-controlled diet consisting of 24 percent fructose, while the control group was fed a calorie-controlled diet with only a negligible amount of fructose, approximately 0.5 percent.
Both diets had the same amount of fat, carbohydrate and protein, but the sources were different, Kavanagh said. The high-fructose group's diet was made from flour, butter, pork fat, eggs and fructose (the main ingredient in corn syrup), similar to what many people eat, while the control group's diet was made from healthy complex carbohydrates and soy protein.
Every week the research team weighed both groups and measured their waist circumference, then adjusted the amount of food provided to prevent weight gain. At the end of the study, the researchers measured biomarkers of liver damage through blood samples and examined what type of bacteria was in the intestine through fecal samples and intestinal biopsies.
"What surprised us the most was how quickly the liver was affected and how extensive the damage was, especially without weight gain as a factor," Kavanagh said. "Six weeks in monkeys is roughly equivalent to three months in humans."
In the high-fructose group, the researchers found that the type of intestinal bacteria hadn't changed, but that they were migrating to the liver more rapidly and causing damage there. It appears that something about the high fructose levels was causing the intestines to be less protective than normal, and consequently allowing the bacteria to leak out at a 30 percent higher rate, Kavanagh said.
One of the limitations of the study was that it only tested for fructose and not dextrose. Fructose and dextrose are simple sugars found naturally in plants.
"We studied fructose because it is the most commonly added sugar in the American diet, but based on our study findings, we can't say conclusively that fructose caused the liver damage," Kavanagh said. "What we can say is that high added sugars caused bacteria to exit the intestines, go into the blood stream and damage the liver.
"The liver damage began even in the absence of weight gain. This could have clinical implications because most doctors and scientists have thought that it was the fat in and around tissues in the body that caused the health problems."
The Wake Forest Baptist team plans to begin a new study using the same controls but testing for both fructose and dextrose over a longer time frame.
The study was supported by Wake Forest School of Medicine and grants RR019963, OD010965 and AG033641 from the National Institutes of Health.
Co-authors are Ashley Wylie and Kelly Tucker, B.S., of Wake Forest Baptist; John Culler, D.V.M., Ph.D., of North Carolina State University; Timothy Hamp, B.S., Anthony Fodor, Ph.D., and Raad Gharaibeh, Ph.D., of the University of North Carolina at Charlotte.
July 31, 2015 School is just around the corner, which means backpacks and packed lunches await your children. One expert offers tips for parents to promote healthy dental habits while away from ... read more
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July 29, 2015 Viewing aquarium displays led to noticeable reductions in blood pressure and heart rate, a research team found in the first study of its kind. They also noted that higher numbers of fish helped to ... read more
June 27, 2014 A high-fructose, high-fat diet can cause harmful effects to the livers of adult rats, according to new research, providing new insight into the effects of adding fructose to a Western diet high in ... read more
Feb. 26, 2014 A meta-analysis of all available human trials says fructose in and of itself is not to blame for the increase in non-alcoholic fatty liver disease. Since the disease is closely linked to obesity and ... read more
Feb. 21, 2012 Is fructose being unfairly blamed for the obesity epidemic? Or do we just eat and drink too many calories? Researchers reviewed more than 40 published studies on whether the fructose molecule itself ... read more |
Rhythm & Hues Sued by Fired Employees
A fired Rhythm & Hues employee is suing the bankrupt visual-effects company for unpaid wages and benefits on behalf of the more than 250 people in California who were laid off this week.
The suit was filed in California bankruptcy court by Anthony Barcelo, who worked as a compositing technical director at the company's El Segundo, Calif. office.
He alleges that Rhythm & Hues is in violation of California and federal labor laws because it failed to provide pink-slipped workers with 60 days written notice of their impending lay-off.
"The employees were given no notice that this was coming, which would have allowed them to make a soft landing," said René S. Roupinian, an attorney for the plaintiff. "Mr. Barcelo asked for and received notices at several points that his job was secure, so he feels particularly betrayed. He is in dire financial straits, and he has a family to support."
Roupinian said that Barcelo and others did not receive their last paycheck. She claims that he is owed more than $10,000 in pay and benefits.
A spokesman for Rhythm & Hues did not respond to request from TheWrap for comment.
Until last week, Rhythm & Hues employed roughly 700 people in California and a total of 1,400 people when taking into account its branches in places like Canada and Malaysia.
The company filed for Chapter 11 protection this week after it could not find a buyer. Prime Focus, an Indian-based effects company, considered acquiring the company, but according to an individual with knowledge of the negotiations, it could not secure financing in time.
Rhythm & Hues has been one of the leading visual-effects companies for more than two decades and is currently nominated for two Oscars for its work on "Life of Pi" and "Snow White and the Huntsman."
The company is asking a bankruptcy court judge in California to approve a $17 million loan from Universal Pictures and Twentieth Century Fox. It plans to use that money to complete work on Universal's "R.I.P.D." and Fox's "Percy Jackson: Sea of Monsters.”
Roupinian said Barcelo's attorneys will next ask the court to declare the case a class action suit.
Her firm, Outten & Golden, is representing terminated employees from another high-profile effects shop the succumbed to financial problems recently, Digital Domain. After filing for bankruptcy, Digital Domain was acquired by Galloping Horse America and Reliance Mediaworks for $30.2 million last September. |
Q:
Align text to right in C
I am little struggling how to make my output to show like this:
a
aa
aaa
My current output shows this instead:
a
aa
aaa
Below are my code:
void displayA(int a){
for(int i = 0; i < a; i++)
printf("a");
}
int main(void){
displayA(1);
printf("\n");
displayA(2);
printf("\n");
displayA(3);
printf("\n");
return 0;
}
Any suggestion? Thanks.
Thanks for the answer. I realized that my coding logic was wrong. Using the suggestion below helped me figure it out. Thanks!
A:
You can use printf("%*s", <width>, "a"); to print any text right aligned by variable no. of spaces.
Check here live.
|
The Archaeological Institute of America promotes a vivid and informed public interest in the cultures and civilizations of the past, supports archaeological research, fosters the sound professional practice of archaeology, advocates the preservation of the world's archaeological heritage, and represents the discipline in the wider world.
The Cincinnati Local Society of the Archaeological Institute of America (AIA) supports the AIA's central mission and is hosted by the Dept. of Classics at the University of Cincinnati. Founded in 1905, it is one of the oldest of the more than 100 local societies of the AIA in the U.S., Canada, Athens, and Iberia. AIA local societies are run by and for their own AIA members, giving individual members the satisfaction of being involved in the AIA on both the national and local level.
AIA headquarters sponsors national lectures annually for each society. But the heart of every AIA Society is its locally planned programs -- field trips, local tours, symposia, film festivals, and study groups -- as well as additional lectures organized by each society. Members of local societies enjoy a full program of activities throughout the year that serves to foster and enhance their interest in archaeology. |
---
abstract: 'Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. Cai, Miyake, Dür, and Briegel recently constructed a ground state of a two-dimensional quantum magnet by combining multiple Affleck-Kennedy-Lieb-Tasaki quasichains of mixed spin-3/2 and spin-1/2 entities and by mapping pairs of neighboring spin-1/2 particles to individual spin-3/2 particles \[Phys. Rev. A [**82**]{}, 052309 (2010)\]. They showed that this state enables universal quantum computation by single-spin measurements. Here, we give an alternative understanding of how this state gives rise to universal measurement-based quantum computation: by local operations, each quasichain can be converted to a 1D cluster state and entangling gates between two neighboring logical qubits can be implemented by single-spin measurements. We further argue that a 2D cluster state can be distilled from the Cai-Miyake-Dür-Briegel state.'
author:
- 'Tzu-Chieh Wei'
- Robert Raussendorf
- Leong Chuan Kwek
title: 'Quantum computational universality of the Cai-Miyake-Dür-Briegel 2D quantum state from Affleck-Kennedy-Lieb-Tasaki quasichains'
---
Introduction
=============
Measurement-based quantum computation (MBQC) provides a framework where quantum computation [@NielsenChuang00] is achieved by single-spin measurements on a highly entangled resource state [@Oneway; @Oneway2]. The first known resource state is the so-called cluster state on a square lattice [@Cluster]. Graph states [@Hein] on other two-dimensional regular lattices were also shown to be universal resources [@Universal]. It turns out that universal resource states are shown to be rare, of zero measure [@Gross1]. However, resource states beyond graph states have been constructed [@Gross], mostly due to the understanding of MBQC from the perspective of matrix-product-states (MPS) and projected-entangled-pair-states (PEPS) [@Verstraete; @correlation]. In fact, there exist universal resource states that are unique ground states of two-body interacting Hamiltonians [@BartlettRudolph; @Chen; @Cai10; @Honeycomb; @Honeycomb2], even though cluster states are not [@Nielsen].
Among the small class of known universal states is the construction by Cai, Miyake, Dür, and Briegel (CMDB) [@Cai10]. It is based on chains of Affleck-Kennedy-Lieb-Tasaki (AKLT) states [@AKLT], originally constructed in the setting of condensed matter physics. It was shown earlier that one-dimensional spin-1 AKLT states can serve as resources for restricted quantum computations [@Gross; @Brennen], and universal computation can be achieved by [*active*]{} coupling of many such 1D chains [@Brennen]. The merit of the CMDB construction [@Cai10] is to avoid such active coupling by mapping two connecting spin-1/2 entities into one spin-3/2 entity, and patching many 1D AKLT quasichains into a two-dimensional structure. Moreover, the gap above the ground state of the constructed 2D model was shown to be finite [@Cai10]. Here, we show that by local operations, the ground state of an AKLT quasichain of mixed spin-3/2 and spin-1/2 entities can be converted to a 1D cluster state. Furthermore, entangling gates between two logical qubits on neighboring quasichains can be implemented by measuring the spin-3/2 particle connecting them. This provides an alternative understanding of the quantum-computational universality using the CMDB state. Moreover, we argue that from this state a 2D cluster state can be distilled by local operations.
The structure of the remaining of the paper is as follows. In Sec. \[sec:1Dquasichain\] we review the 1D AKLT quasichain. In Sec. \[sec:2D\] we review the 2D Cai-Miyake-Dür-Briegel model. In Sec. \[sec:1Dcluster\] we show how the 1D quasichain AKLT state can be locally converted to a 1D cluster state. In Sec. \[sec:2Dcluster\] we show how to understand the quantum computational universality of the CMDB state and how it can be locally converted to a 2D cluster state. In Sec. \[sec:conclusion\] we make some concluding remarks.
1D AKLT quasichain {#sec:1Dquasichain}
==================
 1D AKLT quasichain. (a) The larger circles represent spin-3/2 particles and are connected by thick solid lines. They form the backbone of the quasichain. The smaller circles represent spin-1/2 particles, which are connected via dashed lines to corresponding spin-3/2 particles. (b) The schematic of the ground state of the 1D AKLT quasichain. Each spin-3/2 can be regarded as three virtual spin-1/2 particles, each forming a singlet with the neighbor virtual qubit. The three qubits at $A$ site is then projected into their symmetric subspace, with the projection indicated by a transparent circle. ](fig1Da.png){width="8cm"}
In [@Cai10] the 1D AKLT model defined on a quasichain is considered, which consists of spin-3/2 particles (labeled by $A_i$’s) located at the backbone and spin-1/2 particles (labeled by $b_i$’s) connected to $A$’s, as shown in Fig. \[fig:fig1D\]a. The Hamiltonian of the quasichain is [@Cai10] $$\label{eqn:H1D}
H=\sum_{i=1}^{N-1} P^{S=3}_{A_i,A_{i+1}}
+\sum_{i=1}^N P^{S=2}_{A_i,b_i}
+P^{S=2}_{A_1,b_0}+P^{S=2}_{A_N,b_{N+1}},$$ where $P^{S}_{u,v}$ represents the projector onto the spin-$S$ subspace of the joint $u$ and $v$ spins, which can be expressed as a polynomial of $\vec{S}_u\cdot\vec{S}_v$. The original AKLT chain is defined on a chain of spin-1 particles, with the ends terminated by spin-1/2 particles [@AKLT]. The quasichain, similar to the original AKLT chain, can be shown to possess a unique ground state with a finite spectral gap [@Cai10]. As illustrated in Fig. \[fig:fig1D\]b, the ground state is a valence-bond-solid state of the AKLT type, in which every $A$ is composed of three virtual spin-1/2 particles, each forming a singlet pair with its neighboring spin-1/2 particle, followed by a projection $\Pi_S$ (defined below) of the three virtual qubits to their symmetric subspace. To be more precise, the ground state is the following valence-bond state, $$\label{eqn:vbs}
|\psi_{\rm AKLT}\rangle\sim\mathop{\otimes}_{A}
\Pi_{S,A} \mathop{\otimes}_{{\rm edge}\, e} |\phi\rangle_e,$$ where $|\phi\rangle_e=(|01\rangle-|10\rangle)/\sqrt{2}$ is a singlet state for the pair of qubits residing on the (dashed) edge $e$; see Fig. \[fig:fig1D\]b.
The correspondence of the states of the three virtual particles to those of a spin-3/2 particle is given as follows,
\[eqn:relabel\] $$\begin{aligned}
\!\!\!\!\!\!\!\!\!\!\!\!&&\ket{000}\leftrightarrow \Big\vert\frac{3}{2},\frac{3}{2}\Big\rangle,\\
\!\!\!\!\!\!\!\!\!\!\!\!&&\ket{111}\leftrightarrow \Big\vert\frac{3}{2},-\frac{3}{2}\Big\rangle,\\
\!\!\!\!\!\!\!\!\!\!\!\!&&\ket{W}\equiv\frac{1}{\sqrt{3}}(\ket{001}+\ket{010}+\ket{100})\leftrightarrow
\Big\vert\frac{3}{2},\frac{1}{2}\Big\rangle,\\
\!\!\!\!\!\!\!\!\!\!\!\!&&\ket{\overline{W}}\equiv\frac{1}{\sqrt{3}}(\ket{110}+\ket{101}+\ket{011})\leftrightarrow
\Big\vert\frac{3}{2},-\frac{1}{2}\Big\rangle,\end{aligned}$$
where the qubit states $|0/1\rangle$ are the eigenstates of spin-1/2 angular momentum operators $\hat{S}^2$ and $\hat{S}_z$, i.e., $|0\rangle\equiv |1/2,1/2\rangle$ and $|1\rangle\equiv
|1/2,-1/2\rangle$. The projector onto the symmetric subspace can be simply written as $\Pi_S\equiv |000\rangle\langle 000|+ |W\rangle
\langle W| +|\overline{W}\rangle \langle \overline{W}| + |111
\rangle\langle 111|$. The quasichain AKLT state in Eq. (\[eqn:vbs\]) is written in terms of the virtual-qubit representation for the central spin-3/2 particles; the relabeling in Eq. (\[eqn:relabel\]) provides a translation to the spin-3/2 representation. We note that the quantization-axis label on the states is implicitly assumed to be along the $z$-axis. In the following, when necessary, we will explicitly write out the quantization axis.
2D Cai-Miyake-Dür-Briegel model {#sec:2D}
===============================
 The 2D Cai-Miyake-Dür-Brigel model. The model consists of many AKLT quasichains and merge the two neighboring spin-1/2 particles, e.g., $b_1$ and $b_2$, to a single spin-3/2 particle $B$ via $U$ in Eq. (\[eqn:U\]).](fig2D-CMDB.png){width="8cm"}
To build up a 2D model with a finite gap above the ground state, Cai et al. stack up 1D quasichains and their mirror images in a staggered way, as shown in Fig. \[fig:fig2D-CMDB\]. The two neighboring spin-1/2 particles, e.g., $b_1$ and $b_2$, possess in total four levels and can be formally mapped to a spin-3/2 particle $B$ by a unitary transformation $U$, $$\label{eqn:U}
U=\sum_{m_1,m_2=\pm 1/2} \Big\vert \frac{3}{2},m_1+2m_2\Big\rangle_{B}\Big\langle
\frac{1}{2},m_1\Big\vert_{b_1}\Big\langle\frac{1}{2},m_2\Big\vert_{b_2}.$$ The Hamiltonian of the resulting 2D system is obtained from the sum of Hamiltonians of many 1D quasichains (\[eqn:H1D\]), followed by the unitary transformations $U$’s merging all pairs of neighboring $b$’s to single spin-3/2 $B$’s. For example, a term $f(\vec{S}_A\cdot \vec{s}_{b_1})$ in the Hamiltonian (\[eqn:H1D\]) is transformed to $f(\vec{S}_A\cdot U\vec{s}_{b_1}U^\dagger)$, with $U\vec{s}_{b_1} U^\dagger$ and similarly $U\vec{s}_{b_2} U^\dagger$ being observables of the spin-3/2 $B$. For the explicit form of the resulting 2D Hamiltonian, we refer the readers to the paper by Cai et al. [@Cai10]. Because of the spectral gap in the quasichains, the whole system by patching them together using the unitary $U$’s has a gap as well. We note that in the following discussions of quantum computational universality it is actually convenient to treat $B$ in terms of the two virtual spin-1/2 $b$ particles before the unitary $U$. Any unitary transformation on the composite $b_1$ and $b_1$ is a local unitary transformation on $B$. Moreover, joint measurements on $b_1$ and $b_2$ is a local measurement on $B$. We also remark that with open boundary conditions the CMDB model contains boundary spin-1/2 particles. To remove these and make the model consist solely of spin-3/2 particles, one can use periodic boundary conditions by merging two associated opposite-end spin-1/2’s to one spin-3/2.
From the ground state of the AKLT quasichain to a 1D cluster state {#sec:1Dcluster}
==================================================================
In this section we consider the ground state of the AKLT quasichain and shall show that it can be locally converted to a 1D cluster state. The local conversion is achieved by a generalized measurement, also called positive-operator-value measure (POVM) [@NielsenChuang00] at each site, as was used previously in the 2D AKLT state on the honeycomb lattice [@Honeycomb]. The idea is to “project” the four levels of a spin-3/2 particle down to two levels, forming an effective qubit. To bring out the “hidden” cluster state from the quasichain AKLT state, we generalize the projection and introduce the following POVM at each $A$ site, which consists of three rank-two elements [@Honeycomb]
\[POVM1\] $$\begin{aligned}
\!\!\!\!\!\!\!\!\!\!{F}_{A,z}&=&\sqrt{\frac{2}{3}}(\ketbra{+3/2}_z+\ketbra{-3/2}_z), \\
\!\!\!\!\!\!\!\!\!\!{F}_{A,x}&=&\sqrt{\frac{2}{3}}(\ketbra{+3/2}_x+\ketbra{-3/2}_x),\\
\!\!\!\!\!\!\!\!\!\!{F}_{A,y}&=&\sqrt{\frac{2}{3}}(\ketbra{+3/2}_y+\ketbra{-3/2}_y),\end{aligned}$$
where the subscripts $x$, $y$ and $z$ indicating the measurement outcome in fact represent the effective quantization axes and we have omitted the total spin magnitude $S=3/2$ in the Dirac brackets. In contrast to the usual orthogonal or von Neumann measurement, the POVM elements need not be orthogonal, as $F_{A,x}F_{A,z}\ne 0$. But similar to von Neumann measurement, given the outcome $a$ of the POVM $a=x$, $y$ or $z$, the state $|\psi\rangle$ undergoing the measurement becomes $|\psi\rangle \rightarrow
F_{A,a}|\psi\rangle$ [@NielsenChuang00]. It can be verified that these POVM elements satisfy the conservation of probability, i.e., $\sum_{\nu \in \{x,y,z\}}F^\dagger_{A,\nu} F_{A,\nu} = I_{S=3/2}$, where $I_{S=3/2}$ is the identity operator for the spin-3/2 Hilbert space. Physically, $F_{A,\nu}=({S}_{A,\nu}^2-1/4)/\sqrt{6}$ is proportional to a projector onto the two-dimensional subspace spanned by the two eigenstates of the $\nu$-component spin operator with eigenvalues $S_\nu=\pm 3/2$. From the viewpoint of three virtual qubits, the POVM elements can be written as
\[POVM2\] $$\begin{aligned}
\!\!\!\!\!\!\!\!\!\!\tilde{F}_{A,z}&=&\sqrt{\frac{2}{3}}(\ketbra{000}+\ketbra{111}), \\
\!\!\!\!\!\!\!\!\!\!\tilde{F}_{A,x}&=&\sqrt{\frac{2}{3}}(\ketbra{+++}+\ketbra{---}),\\
\!\!\!\!\!\!\!\!\!\!\tilde{F}_{A,y}&=&\sqrt{\frac{2}{3}}(\ketbra{i,i,i}+\ketbra{-\!i,-\!i,-\!i}),\end{aligned}$$
where $|0/1\rangle$, $\ket{\pm}\equiv(\ket{0}\pm\ket{1})/\sqrt{2}$ and $\ket{\pm i}\equiv (\ket{0}\pm i\ket{1})/\sqrt{2}$ are eigenstates of Pauli operators $\sigma_z$, $\sigma_x$ and $\sigma_y$, respectively. Note for convenience we shall also use $\ket{0/1}_a$ (with $a=x$, $y$, or $z$) to denote eigenstates of $\sigma_a$, i.e., $\sigma_a\ket{0/1}_a=\pm\ket{0/1}_a$. We note that in this notation, $\tilde{F}$’s can be conveniently written as $$\label{POVM3}
\tilde{F}_{A,a}=\sqrt{\frac{2}{3}}(\ket{000}_a\bra{000}+\ket{111}_a\bra{111}).$$ One advantage of using the virtual-qubit representation is that the stabilizer formalism [@Stabilizer] can be employed and insight about the post-POVM state can thus be gained. The above POVM elements in the second form obey the relation $\sum_{\nu \in
\{x,y,z\}}\tilde{F}^\dagger_{A,\nu} \tilde{F}_{A,\nu} = \Pi_{S,A}$, i.e., project onto the symmetric subspace, as required. The outcome of the POVM at any site $A$ is random, which can be $x$, $y$ or $z$, and it can be correlated with the outcomes at other sites due to the entanglement in the AKLT state [@AKLT].
One important consequence after the POVM on a spin-3/2 $A$ is that, even though it has four levels, its state after the POVM is restricted to the two-dimensional Hilbert subspace, spanned by $|+3/2\rangle$ and $|-3/2\rangle$, or in terms of the three virtual qubits by $|000\rangle$ and $|111\rangle$ with the quantization axis given by the POVM outcome. Thus, after the POVM, one can treat each $A$ site as the carrier of one qubit.
Strategy
--------
Given the outcomes $\{a_v\}$ of POVMs at all center sites $\{v\}$, we know the post-POVM state is given by
$$\begin{aligned}
|\psi'\rangle &\sim& \mathop{\otimes}_{v} \tilde{F}_{v,a_v}
|\psi_{\rm AKLT}\rangle\\
&\sim& \mathop{\otimes}_{v} \tilde{F}_{v,a_v} \mathop{\otimes}_{{\rm
edge}\, e} |\phi\rangle_e,\end{aligned}$$
where we have used the virtual-qubit version of $F$’s and in going from the first line to the second, we have used the fact that $\tilde{F}$’s projects into the symmetric subspace of three qubits as well and thus there is no need to keep the projectors $\Pi_{S,v}$’s. To understand what the post-POVM state is, we then employ the stabilizer formalism [@Stabilizer] and try to find its stabilizer operators. For a singlet state $|\phi\rangle_{12}=(|01\rangle-|10\rangle)/\sqrt{2}$ of two qubits $1$ and $2$, it is easy to see that there are stabilizer operators [@stabilizer2] $-\sigma_a^{[1]}\otimes\sigma_a^{[2]}$ with $a=x$, $y$, or $z$, namely, $$-\sigma_x\otimes\sigma_x|\phi\rangle=-\sigma_y\otimes\sigma_y|\phi\rangle=-\sigma_z\otimes\sigma_z|\phi\rangle
=|\phi\rangle.$$ The key ingredient of the stabilizer formalism applied to this example is that given two of the above commuting and independent operators, e.g., $-\sigma_x\otimes\sigma_x$ and $-\sigma_z\otimes\sigma_z$, the state $|\phi\rangle$ is uniquely determined. If operators such as the above commute with all $\tilde{F}$’s, they will remain the stabilizer operators for the post-POVM state.
Another type of stabilizer operators arises from the POVMs. For example, using the form given in Eq. (\[POVM3\]), we see that there are operators (two of them being independent) that satisfy $$\label{eqn:stabilizerF} \sigma_a^{[1]}\otimes \sigma_a^{[2]}
\tilde{F}_{A,a} =\sigma_a^{[1]}\otimes \sigma_a^{[3]}
\tilde{F}_{A,a} =\sigma_a^{[2]}\otimes \sigma_a^{[3]}
\tilde{F}_{A,a}= \tilde{F}_{A,a}.$$ Hence, these are stabilizer operators of the post-POVM state.
A third type of stabilizer operators that we shall identify below give rise to the graph-state stabilizer operators. These emerge from POVMs across a few sites. Once we identify all stabilizer operators, the state is uniquely determined if the number of independent stabilizer operators equals that of spins.
Encoding {#sec:encoding}
--------
 Encoding of a qubit. (a) The encoding of a qubit state for two particles: center spin-3/2 $u$ and the connected spin-1/2 $2'$ after a POVM on $u$ giving the outcome $a_u$. (b) This illustrates the case where the spin-3/2 particle is located at either end, and thus it has two neighboring qubits: $0$ and $2'$. (c) When the POVM’s on two consecutive sites of center spin-3/2 particles give the same outcome, i.e., $a_u=a_v$, the qubit is encoded by the two blocks, consisting two spin-3/2’s and two spin-1/2’s.](figEncoding.png){width="8cm"}
Suppose the POVM on one of the center spin-3/2 $u$ results in $a_u\in\{x,y,z\}$; see Fig. \[fig:figEncoding\]a. As seen from Eq. (\[POVM3\]) or the stabilizer operators in Eq. (\[eqn:stabilizerF\]), the three virtual qubits at $u$ are projected to the subspace spanned by $|000\rangle$ and $|111\rangle$, with $|0/1\rangle$ being the eigenstates of $\sigma_{a_u}$ (and the quantization axis being $a_u$). Furthermore, from the discussions above, there is a stabilizer operator for the post-POVM state, as $-\sigma_{a_u}^{[2]}\otimes\sigma_{a_u}^{[2']}$ commutes with $\tilde{F}_{u, a_u}$, where $2$ denotes the virtual spin-1/2 on site $u$ that connects $2'$. Thus, the only two possibilities of the joint state of $u$ and the connected qubit $2'$ can be only $|(000)_u 1_{2'}\rangle$ and $|(111)_u 0_{2'}\rangle$, as they satisfy
\[eqn:encoding1\] $$\begin{aligned}
&&-\sigma_{a_u}^{[2]}\otimes\sigma_{a_u}^{[2']}|(000)_u
1_{2'}\rangle=|(000)_u 1_{2'}\rangle, \\
&&-\sigma_{a_u}^{[2]}\otimes\sigma_{a_u}^{[2']}|(111)_u
0_{2'}\rangle=|(111)_u 0_{2'}\rangle.\end{aligned}$$
This means that the two physical spins $u$ and $2'$ constitute the encoding of an effective qubit.
[l|c|c|c]{}
---------
POVM
outcome
---------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
& [$z$]{} & [$x$]{} & [$y$]{}\
------------
Stabilizer
generators
------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
&
----------------------------------------------------------------
$\sigma_z^{[1]}\sigma_z^{[2]}$, $\sigma_z^{[1]}\sigma_z^{[3]}$
and -$\sigma_z^{[2]}\sigma_z^{[2']}$
----------------------------------------------------------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
&
----------------------------------------------------------------
$\sigma_x^{[1]}\sigma_x^{[2]}$, $\sigma_x^{[1]}\sigma_x^{[3]}$
and -$\sigma_x^{[2]}\sigma_x^{[2']}$
----------------------------------------------------------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
&
----------------------------------------------------------------
$\sigma_y^{[1]}\sigma_y^{[2]}$, $\sigma_y^{[1]}\sigma_y^{[3]}$
and -$\sigma_y^{[2]}\sigma_y^{[2']}$
----------------------------------------------------------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
\
-------------
Logical
Pauli ${X}$
-------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
& $\sigma_x^{[1]}\sigma_x^{[2]}\sigma_x^{[3]}\sigma_x^{[2']}$ & $\sigma_z^{[1]}\sigma_z^{[2]}\sigma_z^{[3]}\sigma_z^{[2']}$& $\sigma_z^{[1]}\sigma_z^{[2]}\sigma_z^{[3]}\sigma_z^{[2']}$\
-------------
Logical
Pauli ${Z}$
-------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
&
----------------------------------------
$\sigma_z^{[1]},\sigma_z^{[2]}$,
$\sigma_z^{[3]}$ or $-\sigma_z^{[2']}$
----------------------------------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
&
-----------------------------------------
$\sigma_x^{[1]}, \sigma_x^{[2]}$,
$\sigma_x^{[3]}$ or $ -\sigma_x^{[2']}$
-----------------------------------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
&
----------------------------------------
$ \sigma_y^{[1]}, \sigma_y^{[2]}$,
$\sigma_y^{[3]}$ or $-\sigma_y^{[2']}$
----------------------------------------
: \[tbl:encoding\]Table for local encoding. Please refer to Fig. \[fig:figEncoding\]a for the qubit labeling {1,2,3,2’} at a site. The stabilizer generators determine the effective two levels, e.g., in the case of $z$-outcome: $|(000)1\rangle$ and $|(111)0\rangle$, where the qubits are listed in the order of labeling {1,2,3,2’}. The logical Pauli ${X}$ induces transition between the two, i.e., ${X}\sim |(000)1\rangle\langle(111)0|
+ |(111)0\rangle\langle(000)1|$. The logical Pauli ${Z}$ operators can differ by a sign due to the convention, e.g., one chooses ${Z}=\sigma_z^{1}$ and thus $ {Z}|(000)1\rangle=|(000)1\rangle$ and ${Z}|(111)0\rangle= - |(111)0\rangle$. If two consecutive sites share the same POVM outcome, e.g., $z$, then the encoding extends to two sites of total 8 qubits (6 virtual ones). If the site is at the end, as in Fig. \[fig:figEncoding\]b, a corresponding table of encoding using five qubits can be similarly constructed.
Now that we have identified the encoding of a qubit, we would like to seek the encoding of Pauli X and Z operators. Let us suppose $a_u=z$ and thus the two states $|\overline{0}\rangle\equiv|(000)_u
1_{2'}\rangle$ and $|\overline{1}\rangle\equiv|(111)_u
0_{2'}\rangle$ (with the basis $|0/1\rangle$ such that $\sigma_z|0/1\rangle=\pm|0/1\rangle$) constitute the basis states of a logical qubit. There are four equivalent choices of Pauli $Z$: (1) $\sigma_z^{[1]}$, (2) $\sigma_z^{[2]}$, (3) $\sigma_z^{[3]}$ and (4) $-\sigma_z^{[2']}$, as these satisfy that $Z|\overline{0}\rangle=|\overline{0}\rangle$ and $Z|\overline{1}\rangle=|\overline{1}\rangle$. The four choices are equivalent, as any two of them are connected by a stabilizer operator, e.g., $\sigma_z^{[2]}=\sigma_z^{[1]}(\sigma_z^{[1]}\otimes
\sigma_z^{[2]})$. To obtain the effective Pauli X, which has action that takes $|\overline{0}\rangle$ to $|\overline{1}\rangle$ and vice versa, we can check the following combination works, $$\label{eqn:zX}
X\equiv\sigma_x^{[1]}\otimes\sigma_x^{[2]}\otimes\sigma_x^{[3]}\otimes\sigma_x^{[2']}.$$
On the other, when $a_u=x$, the two basis states are $|\overline{0}\rangle\equiv|(+++)_u (-)_{2'}\rangle$ and $|\overline{1}\rangle\equiv|(---)_u (+)_{2'}\rangle$, where $\sigma_x|\pm\rangle=\pm|\pm\rangle$. The four equivalent choices of effective Pauli $Z$ are: (1) $\sigma_x^{[1]}$, (2) $\sigma_x^{[2]}$, (3) $\sigma_x^{[3]}$ and (4) $-\sigma_x^{[2']}$, as these satisfy that $Z|\overline{0}\rangle=|\overline{0}\rangle$ and $Z|\overline{1}\rangle=|\overline{1}\rangle$. The effective Pauli X can be chosen to be $$\label{eqn:xX}
X\equiv\sigma_z^{[1]}\otimes\sigma_z^{[2]}\otimes\sigma_z^{[3]}\otimes\sigma_z^{[2']},$$ as $X|\overline{0}\rangle=|\overline{1}\rangle$ and $X|\overline{1}\rangle=|\overline{0}\rangle$. Effectively, the POVM outcome $a_u$ indicates the new quantization axis for the effective qubit. For a summary of stabilizer generators, effective Pauli $X$ and $Z$ operators, please refer to Table \[tbl:encoding\], which also includes the case of $a_u=y$ outcome.
As exemplified in Fig. \[fig:figEncoding\]b, if the center spin-3/2 is located at either end, it has two virtual spin-1/2’s connected to it. The three sites form the basis of the qubit encoding: $|(000)_u 1_0 1_{2'}\rangle$ and $|(111)_u 0_0
0_{2'}\rangle$.
Now suppose the POVM’s on several consecutive sites of center spin-3/2 result in a same outcome; see the example in Fig. \[fig:figEncoding\]c for two sites with $a=a_u=a_v$. Those spin-3/2’s and the connected virtual spin-1/2’s together form the encoding of a logical qubit. This is due to additionally that there is a stabilizer operator $-\sigma_{a}^{[3]}\otimes \sigma_{a}^{[4]}$ for the virtual qubits on the two of the neighboring center sites $u$ and $v$ with the same POVM outcome $a$ and that $-\sigma_{a}^{[3]}\otimes \sigma_{a}^{[4]}$ commutes with both $\tilde{F}_{u, a}$ and $\tilde{F}_{v, a}$. Therefore, the two blocks that consists of two spin-3/2’s ($u$ and $v$) and two spin-1/2’s ($2'$ and $5'$) altogether only encode one qubit with two basis states being $|(000)_u 1_{2'} (111)_v 0_{5'}\rangle$ and $|(111)_u
0_{2'}(000)_v 1_{5'}\rangle$. This result generalizes to any number of consecutive center sites having the same POVM outcome [@Honeycomb]. When all spin-3/2 sites along a chain has been performed of POVM, there is a sequence of POVM outcomes, e.g., $xxyzxzzzy\cdots.$ Consecutive sites of the same outcome (e.g., $xx$ and $zzz$) are grouped into what we call a domain.
We remark that by single-spin measurements, the encoding of a logical qubit by a domain can be reduced to a single site. For example, if one measures the spin at site $v$ in the basis $|\pm\rangle\equiv (|0\rangle\pm|1\rangle)/\sqrt{2}$, a state $\alpha|(000)_u 1_v\rangle +\beta|(111)_u 0_v\rangle$ will be reduced to $\alpha|(000)_u\rangle \pm\beta|(111)_u \rangle$, depending on the outcome of the measurement. Similarly, if one measures the spin at site $u$ in the basis $(|000\rangle\pm|111\rangle)/\sqrt{2}$, which is, in terms of spin-3/2 language, $(|+3/2\rangle\pm|-3/2\rangle)/\sqrt{2}$, the post-measurement state becomes $\alpha|0_v\rangle \pm\beta|1_v
\rangle$. Thus, an encoded cluster state can thus be reduced by local measurement to a cluster state, where each site is effectively a qubit. For simplicity, from now on we shall focus on cases where no neighboring sites sharing the same outcome for illustration.
Cluster-state stabilizer
------------------------
 Cluster-state stabilizer operator. The example shows POVM outcomes on the center sites $u$, $v$, and $w$ are $a_u=x$, $a_v=z$, and $a_w=x$, respectively. It can be shown that for the post-POVM state there is a stabilizer operator defined on the three blocks $U$, $V$, and $W$: $\overline{Z}_U \overline{X}_V \overline{Z}_W$, up to a possible sign.](figZXZ.png){width="8cm"}
To show that the post-POVM CMDB state is an (encoded) cluster state, let us take the example shown in Fig. \[fig:figZXZ\]. Let us labels the three center sites in blocks $U$, $V$ and $W$ by the lower-case symbols $u$, $v$ and $w$ respectively. Suppose the POVM outcomes on these sites are $a_u=x$, $a_v=z$, and $a_w=x$, respectively. First note that $-\sigma_x^{[3]}\sigma_x^{[4]}$ commutes with $\tilde{F}_{u,x}$ and $-\sigma_x^{[6]}\sigma_x^{[7]}$ commutes with $\tilde{F}_{u,x}$. Note also that $-\sigma_x^{[5]}\sigma_x^{[5']}$ is a stabilizer operator of the singlet between $5$ and $5'$, but it does not commute with $\tilde{F}_{v,z}$. However, if we multiply all the above operators, we obtain $$K_V\equiv- \sigma_x^{[3]}
\sigma_x^{[4]}\sigma_x^{[5]}\sigma_x^{[5']}\sigma_x^{[6]}
\sigma_x^{[7]}.$$ Because $K_V$ commutes with $\tilde{F}_{v,z}$, due to the identity $$\begin{aligned}
&&\sigma_x\otimes\sigma_x\otimes\sigma_x\,
(|000\rangle\langle000|+|111\rangle\langle111|)\nonumber \\
& =&(|111\rangle\langle
000|+|000\rangle\langle111|)\nonumber\\
&=& (|000\rangle\langle000|+|111\rangle\langle111|)\,
\sigma_x\otimes\sigma_x\otimes\sigma_x,\end{aligned}$$ it is a stabilizer operator of the post-measurement state. In terms of logical Pauli operators ${Z}_U\equiv \sigma_x^{[3]}$ , ${Z}_W\equiv \sigma_x^{[7]}$, ${X}_V\equiv
\sigma_x^{[4]}\sigma_x^{[5]} \sigma_x^{[6]} \sigma_x^{[5']}$ (see the examples given in the previous section for the effective Pauli operators), we arrive at the stabilizer operator $K_V=-{Z}_U {X}_V
{Z}_W$. This is (up to a sign) the stabilizer operator defining a linear cluster state [@Cluster]. We note that for completeness of the qubit encoding for blocks $U$, $V$ and $W$, the corresponding conjugate operators $Z$ or $X$ can be chosen as follows: ${X}_U\equiv \sigma_z^{[3]}$, ${X}_W\equiv \sigma_z^{[7]}$ and ${Z}_V\equiv \sigma_z^{[4]}$ and that they satisfy the required anticommutation with their conjugate operators.
Note that the choice of three consecutive sites (or domains) is arbitrary. Furthermore, if the above example is changed to a four-site problem, e.g., with the POVM outcomes being $xzzx$, i.e., with middle two sites having the same $z$ outcome. These two sites form a single logical qubit, as discussed earlier in Sec. \[sec:encoding\], and the encoded Pauli $X$ operators will span across the two sites. The above example can be straightforwardly generalized to a general proof that the state after the POVM is, under local unitary transformation, equivalent to an encoded cluster state, similar to the case of 2D AKLT state on the honeycomb lattice [@Honeycomb]. (The encoding of logical qubits can be reduced to single sites by suitable local measurements, as remarked earlier.) As a further illustration, let us consider another example of three sites in Fig. \[fig:figZXZ\] but with $a_u=x$, $a_v=z$, and $a_w=y$, i.e., the last site has a different outcome $a_w=y$ than the above example. Because of this, one now considers $-\sigma_y^{[6]}\sigma_y^{[7]}$ instead of $-\sigma_x^{[6]}\sigma_x^{[7]}$ and can show that the follow operator is a stabilizer generator: $$K_V\equiv- \sigma_x^{[3]}
\sigma_x^{[4]}\sigma_x^{[5]}\sigma_x^{[5']}\sigma_y^{[6]}
\sigma_y^{[7]}.$$ Now, one can choose ${Z}_W\equiv \sigma_y^{[7]}$, ${Z}_U\equiv
\sigma_x^{[3]}$ , ${Z}_W\equiv \sigma_y^{[7]}$, ${X}_V\equiv
\sigma_x^{[4]}\sigma_x^{[5]} \sigma_x^{[6]} \sigma_x^{[5']}$, and $Z_V\equiv \sigma_z^{[6]}$ (see Table \[tbl:encoding\]) and obtain $$K_V=-{Z}_U ({X}_V i{Z}_V) {Z}_W=-{Z}_U {Y}_V {Z}_W.$$ Although the stabilizer operator $K_V$ is not of the canonical form of the cluster-state stabilizer ${Z}_U {X}_V
{Z}_W$ , they are related by local unitary transformation that leaves $Z_V$ invariant.
The hidden cluster state in the ground state of the AKLT quasichain is hence revealed by the POVM (\[POVM1\]) or equivalently (\[POVM2\]). The original 1D spin-1 AKLT state has previously been shown to be locally converted to a 1D cluster state by a similar spin-1 POVM [@Honeycomb] and by a different alternating POVM [@Chen10].
Quantum computational universality of the 2D Cai-Miyake-Dür-Briegel state {#sec:2Dcluster}
=========================================================================
After understanding that the quasichain AKLT state can be converted to an (encoded) 1D cluster state, arbitrary single-qubit rotations can be implemented along every quasichain in the usual one-way computation linear cluster states [@Oneway]. What remains to be seen for the quantum computational universality is whether entangling gates such as control-NOT or control-phase can be implemented between the two logical qubits on two neighboring quasichains. The answer is affirmative. The two spin-1/2 $b$ particles on two neighboring chains, which are the two virtual qubits of the merged $B$-type spin-3/2 particle, are used as either (1) a disconnecter or (2) a connecter so that either in case (1) the two neighboring logical qubits evolve independently (without being acted upon by an entangling gate) or case (2) an entangling gate acts on them. Either functionality is achieved by measurement on a $B$-site particle or equivalently by the joint measurement of two $b$ particles; see Fig. \[fig:fig2D\].
 2D structure. The two spin-1/2 $b$ particles (labeled $1$ and $2$) on two neighboring chains, are the two virtual qubits of the merged $B$-type spin-3/2 particle. By measuring the $B$ spin, two spins $u$ and $v$ will (i) evolves independently or (ii) be acted upon by a control-phase gate. ](fig2D.png){width="8cm"}
Connecting/disconnecting neighboring logical qubits
---------------------------------------------------
In the case of a disconnecter, the two virtual spin-1/2 particles (of the single spin $B$) are each applied an effective Pauli X gate $X=|0\rangle_a\langle 1|+|1\rangle_a\langle 0|$ [@applyX] before being measured in the basis of respective $\ket{\pm}_a$, where the axis label $a$ can be either $x$, $y$, or $z$ (depending on the POVM outcome on the neighboring spin-3/2 particle) and $\ket{\pm}_a\equiv
(\ket{0}_a\pm\ket{1}_a)/\sqrt{2}$ with $\sigma_a|0/1\rangle_a=\pm|0/1\rangle_a$; see Fig. \[fig:fig2D\]. Suppose the outcome of the measurement on the spin-1/2 connected to the spin-3/2 $u$ is labeled by $(-1)^{m_1}$ with $m_1=0/1$, and similarly for the one connected to $v$: $(-1)^{m_2}$. (Together, $m_1$ and $m_2$ characterize the measurement outcome of the merged spin-3/2 $B$.) Then the effect of measuring the spin $B$ on neighboring $u$ and $v$ is that single-qubit gates $Z_u^{m_1}\otimes
Z_v^{m_2}$ have been applied to $u$ and $v$, where $Z_u=|3/2\rangle_{a_u}\langle 3/2|-|-3/2\rangle_{a_u}\langle -3/2|$ and similarly for $Z_v$. Note that in the three-virtual-qubit picture, $|+3/2\rangle_{a_u}=|000\rangle_{a_u}$ and $|-3/2\rangle_{a_u}=|111\rangle_{a_u}$. Furthermore, the measurement on 1 and 2 corresponds to a local measurement on the spin-3/2 $B$. The logical qubits on neighboring chains evolve independently, i.e., no entangling gate has been applied to $u$ and $v$.
In the case of a connecter, the two spin-1/2 particles are first applied effective Pauli X gates: $X=|0\rangle_a\langle
1|+|1\rangle_a\langle 0|$ and then a control-phase (CP) gate: ${\rm
CP}_{12}= |0\rangle_{{a_u}}\langle 0|^{[1]}\otimes \openone^{[2]} +
|1\rangle_{a_u}\langle 1|^{[1]}\otimes Z_{a_v}^{[2]}$, where $Z_{a_v}=|0\rangle_{a_v}\langle0|-|1\rangle_{a_v}\langle 1|$. These operations correspond a single-spin unitary transformation on the merged $B$ spin. Then, a measurement in their respective $|\pm\rangle_{a}$ basis is made as in the previous case, and the effect is that an entangling gate has acted on the two associated spin-3/2 particles $u$ and $v$ (which are effectively two qubits), up to Pauli gates. Using the measurement labels $m_1$ and $m_2$, the entangling gate that has been applied is $Z_u^{m_1}\otimes
Z_v^{m_2}\, {\rm CP}_{uv}$, where $${\rm CP}_{uv}= \Big\vert \frac{3}{2}\Big\rangle_{a_u} \Big\langle
\frac{3}{2}\Big\vert^{[u]}\otimes\, I^{[v]}_{a_v}\, +\, \Big\vert
-\frac{3}{2}\Big\rangle_{a_u} \Big\langle
-\frac{3}{2}\Big\vert^{[u]}\otimes \,Z^{[v]}_{a_v},$$ where $I^{[v]}_{a_v}=|3/2\rangle_{a_v}\langle3/2|+|-3/2\rangle_{a_v}\langle-3/2|$ is the effective qubit identity operator and $Z_{a_v}=|3/2\rangle_{a_v}\langle3/2|-|-3/2\rangle_{a_v}\langle-3/2|$ is the effective Pauli Z operator. The logical qubits on neighboring chains have thus undergone a control-phase gate up to Pauli Z’s.
We remark that the approach of the joint measurement on the two virtual qubits has also been used recently in Refs. [@Cai10] and [@Li] and was employed earlier in Ref. [@GottesmanChuang]. In summary, an entangling gate can indeed be applied on two logical qubits residing on the two neighboring quasichains. Thus, we see that CMDB state is a universal resource for MBQC.
 Converting the Cai-Miyake-Dür-Briegel state to a 2D cluster state. (a) The shaded boxes enclose sites that share the same POVM outcomes on $A$ sites. The $B$ sites are not shown explicitly and only dashed lines are shown. (b) The solid vertical lines denote the locations where CP gates are applied. Boxes labeled with ‘Y’ indicate subsequent logical Pauli Y measurements to be made. (c) After the Pauli Y measurements, the left and right neighboring logical qubits, represented by boxes, are linked. This gives rise to a 2D cluster state. ](ToCluster.png){width="8cm"}
Converting to a 2D cluster state
--------------------------------
The whole system can be further converted to a 2D cluster state on a honeycomb lattice. First, a structure which is topologically equivalent to a honeycomb (or brick-wall) lattice can be identified. Second, by suitable disconnecting or connecting measurements on $B$ sites and then Pauli measurements on $A$ sites, the structure can be reduced to a honeycomb lattice. Shown in Fig. \[fig:ToCluster\] is the example of five quasichains. In Fig. \[fig:ToCluster\]a, the shaded boxes enclose sites that share the same POVM outcomes on $A$ sites. The $B$ sites are not shown explicitly and only vertical dashed lines are used to indicate the possible connecter/disconnecter roles by $B$ spins. In Fig. \[fig:ToCluster\]b, the solid vertical lines denote the choice of a connecter (and the remaining dashed vertical lines in Fig. \[fig:ToCluster\]a denote disconnecters) and hence a control-phase gate acts on two neighboring $A$ sites connected by solid vertical lines. The dangling spin-1/2’s sites are omitted. Those boxes with a ‘Y’ represent a subsequent Pauli-Y measurement to remove the qubit on the sites and to link its two neighboring blocks, resulting in a graph state that has the brickwall structure, as shown in Fig. \[fig:ToCluster\]c. This illustrates and generalizes to a proof that a 2D cluster state can be distilled from the CMDB state.
Concluding remarks {#sec:conclusion}
==================
In summary, we provide an alternative understanding of the quantum computational universality of the 2D state constructed by Cai, Miyake, Dür and Briegel [@Cai10]. A crucial step is the preprocessing given by the POVM (\[POVM1\]) on the central $A$ sites of all chains, which converts each chain to an encoded 1D cluster state and thus arbitrary single-qubit rotation can be implemented. Entangling gates, such as control-phase and control-NOT gates, between neighboring two logical qubits can be implemented by measuring the linking spin-3/2 $B$ sites. The whole system can also be further converted to a 2D cluster state.
The quantum computation in the correlation space proposed by Gross and Eisert [@Gross] was initially regarded as a scheme that belongs to the so-called CC-universality [@CCCQ], where the quantum computer takes classical input and delivers classical output. Many of the resource states constructed in Ref. [@Gross] were later shown to be locally convertible to cluster states [@Cai09; @Chen10], thus enabling the so-called CQ-universality, in which a quantum computer takes a classical input but can deliver a quantum state as a output. Quantum computers of CQ-universality seems potentially more powerful than those of CC-universality. By showing that a 2D cluster state can be distilled by local operations, we have in turn shown that the Cai-Miyake-Dür-Briegel state enables a CQ-universal quantum computation. Whether CQ-universality class is indeed more powerful than CC-universality class in general remains open. In view of resource states, this raises the question whether or not there exists a resource state for which measurement-based quantum computation can only be carried out in the correlation space but cannot be done in the Hilbert space of physical spins.
[**Acknowledgment.**]{} We thank Maarten Van den Nest for useful discussions. This work was supported by NSERC (T.-C.W. and R.R.), MITACS (T.-C.W. and R.R.), CIFAR (R.R.), the Sloan Foundation (R.R.), IARPA (R.R.) and National Research Foundation and Ministry of Education of Singapore (L.-C.K.).
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0_b\rangle$ and $|(111)_A 1_b\rangle$, respectively, is for convenience of later analysis. One then investigates the effect on $A_1$ and $A_2$ due to the measurement on the associated $b_1$ and $b_2$ in the $|\pm\rangle$ basis. In the case of a connecter, an additional control-phase gate is applied to $b_1$ and $b_2$ before measurement.
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|
Contrast encoding in retinal bipolar cells: current vs. voltage.
To investigate the influence of voltage-sensitive conductances in shaping light-evoked responses of retinal bipolar cells, whole-cell recordings were made in the slice preparation of the tiger salamander, Ambystoma tigrinum. To study contrast encoding, the retina was stimulated with 0.5-s steps of negative and positive contrasts of variable magnitude. In the main, responses recorded under voltage- and current-clamp modes were remarkably similar. In general agreement with past results in the intact retina, the contrast/response curves were relatively steep for small contrasts, thus showing high contrast gain; the dynamic range was narrow, and responses tended to saturate at relatively small contrasts. For ON and OFF cells, linear regression analysis showed that the current response accounted for 83-93% of the variance of the voltage response. Analysis of specific parameters of the contrast/response curve showed that contrast gain was marginally higher for voltage than current in three of four cases, while no significant differences were found for half-maximal contrast (C50), dynamic range, or contrast dominance. In sum, the overall similarity between current and voltage responses indicates that voltage-sensitive conductances do not play a major role in determining the shape of the bipolar cell's contrast response in the light-adapted retina. The salient characteristics of the contrast response of bipolars apparently arise between the level of the cone voltage response and the postsynaptic current of bipolar cells, via the transformation between cone voltage and transmitter release and/or via the interaction between the neurotransmitter glutamate and its postsynaptic receptors on bipolar cells. |
### Application Module Android Specific Properties
The application module provides a number of Android specific properties to access the Android app, context and activities.
<snippet id='app-class-properties'/>
### Using the Android Application Context
In the extended example below, the Android context is used to get the absolute path to Files directory.
We are accessing methods from the Android SDK (like `getCacheDir` and `getFilesDir`)
<snippet id='app-android-dirs-code'/>
### Registering a Broadcast Receiver (Android)
NativeScript can send/receive messages and system information though broadcast receivers.
More on broadcast receivers in Android [here](https://developer.android.com/guide/components/broadcasts).
<snippet id='app-android-broadcast-code'/>
### Unregistering a Broadcast Receiver (Android)
<snippet id='app-android-broadcast-unregister-code'/> |
WASHINGTON – The publication that announced a boycott of Donald Trump campaign news, then covered it only in its entertainment section before finally looking for any way to trash him with invectives that would put MSNBC to shame, became the first to publish a political obituary on the flailing campaign of Hillary Clinton.
Titled "Why Hillary Lost: A Premature Obit" and written by the Huffington Post’s "global editorial director" Howard Fineman, formerly Newsweek's chief political correspondent, senior editor and deputy Washington bureau chief, begins: "On the high, crenelated ramparts of Castle Clinton, a chill breeze is stirring – a faint but gnawing sense that the White Walkers are coming, wearing 'MAKE AMERICA GREAT AGAIN' baseball caps on their skinless noggins."
"Partners in Crime: The Clintons' Scheme to Monetize the White House for Personal Profit" is available at the WND Superstore!
TRENDING: 'Greater shakings': Jonathan Cahn foresaw 2020 trouble, warns of even more
It marked another bad week for Mrs. Clinton, who took to blaming her opponent for ISIS-inspired terrorist attacks in New York, New Jersey and Minnesota over the weekend.
"If Donald Trump does sack the fortress, no one who lost the battle will want to admit it was Hillary Clinton's fault," Fineman writes. "It will have had nothing to do with, say, 'transparency' or calling bearded villagers 'deplorables' or the Iraq War vote or the simple fact that middle-of-the-road Clintonism ran out of gas as a public philosophy. No, other individuals, groups and forces will have to be blamed. In fact, they already are, pre-emptively. If Trump wins, we're all going to be too busy moving to Canada to read the postmortems (or write them), so we offer them to you now:"
Among the amusing blame-game excuses the more-progressive-than-thou Fineman cites:
"THE RUSSIANS ARE COMING: Actually, they arrived long ago and got into her phone," the Huffington Post muses.
"BERNIE SANDERS: Remember when people worried that running unopposed in the primary would hurt Clinton?" Fineman asks rhetorically. "It's going to be an endless wail about how Sanders should have withdrawn sooner."
"BILL CLINTON: You know how this will go down: Best campaigner of all time and he couldn’t close the sale. He lost his mojo."
"OBAMA PEOPLE: If they could delete all of David Axelrod's tweets, they would."
"JAMES COMEY: He might as well have indicted her for real, like he did in the court of public opinion. Extremely careless."
"DEBBIE WASSERMAN SCHULTZ AND THE DNC: Her Soviet-style approach to boosting Clinton was something that Hillary's campaign was happy to countenance. But the former DNC chair should have left room for dissent rather than let it bottle up."
Some of the other reasons from the 68-year-old Fineman could not be published in a family news site.
Get the hottest, most important news stories on the Internet – delivered FREE to your inbox as soon as they break! Take just 30 seconds and sign up for WND's Email News Alerts!
The founder of the Huffington Post, Ariana Huffington, recently retired from the site, which, after buying massive amounts of traffic and building up its revenues to $146 million at its peak and a partnership with AOL, failed to turn a profit. |
5 Sightseeing Suggestions for Houston ‘Bleisure’ Travelers
Business travel doesn't need to be all work and no play. Increasingly, travelers are blending business and leisure, resulting in a trend dubbed "bleisure" travel.A 2014 surveyby Hotwire.com found that nearly half of Americans who travel for work tack leisure time onto their business trips.
"You might have to travel for business, but it doesn't mean you have to let much-deserved leisure trips fall by the wayside," said Henrik Kjellberg, president of Hotwire.com.
Not surprisingly, sightseeing rates as the top activity for bleisure travelers, the Hotwire.com survey shows. To help bleisure travelers make the most of their time in Houston, we've assembled a list of five must-see sightseeing spots in the Bayou City.
Space Center Houston
While you can't enter NASA's Johnson Space Center - a major hub for the U.S. space program - without a security clearance, you can visit Space Center Houston.
The visitors' center features more than 400 space artifacts, permanent and traveling exhibits, attractions and theaters "related to the exciting future and remarkable past of America's human space-flight program ... ."
Each year, more than 800,000 people tour the 183,000-square-foot education and entertainment complex. Are you ready for an out-of-this-world experience?
Downtown tunnels
Twenty feet below the streets of downtown Houston, you'll find a system of tunnels stretching about 7½ miles. Hundreds of shops, restaurants and retailers are scattered throughout this underground destination.
Want to make the trek to the tunnels? Only Wells Fargo Plaza and the McKinney Garage on Main Street provide direct street-level access. Otherwise, you'll have to make your way underground via stairs, escalators and elevators inside office buildings linked to the tunnels.
The tunnels are open weekdays but not on weekends. Guided tours are available, making it even easier to explore this underground maze.
The Galleria
A shopping center can be a sightseeing attraction, right? It certainly can be if it's The Galleria.
The largest shopping center in Texas and one of the largest in the U.S., The Galleria contains 2.4 million square feet and features more than 400 stores and restaurants, along with a full-size ice rink. The Galleria complex also includes two hotels and three office towers.
The Galleria, Houston's most popular retail and tourist destination, sits at Westheimer Road and Post Oak Boulevard in the Uptown area. Happy sightseeing - and shopping!
Discovery Green
Discovery Green, next to the George R. Brown Convention Center and the Hilton Americas-Houston hotel, is one of the new kids on the park block.
The 12-acre park, which debuted in 2008, was carved out of an urban eyesore as part of a $182 million revitalization project. Highlights of Discovery Green include Kinder Lake, a jogging trail, gardens, two performance spaces, two fountains, a playground, two restaurants, artwork, a putting green and plenty of green space.
"The park was envisioned by several committed Houston philanthropists who saw the space as a once-in-a-lifetime opportunity to create an urban park that would redefine the landscape of downtown," according to the Discovery Green website.
In 2017, Discovery Green will host numerous events leading up to the Super Bowl. But, of course, you don't have to wait until then to be bowled over by Discovery Green.
Astrodome
Yes, it's been shuttered since 2008. But even from the outside, the "Eighth Wonder of the World" still is a wonder. The National Trust for Historic Places calls it "an iconic piece of 20th century Americana."
The Astrodome - once home to the Houston Astros baseball team and Houston Oilers football team - opened in 1965. The vacant 1 million-square-foot stadium, formally known as NRG Astrodome, is next to NRG Stadium. The address: 8400 Kirby Drive.
"As the world's first indoor, air-conditioned domed stadium, the 18-story multipurpose structure set the bar for arena design and construction for decades to come," the National Trust for Historic Places says. |
ARRL Propagation Bulletin ARLP024 (2003)
SB PROP @ ARL $ARLP024
ARLP024 Propagation de K7RA
ZCZC AP24
QST de W1AW
Propagation Forecast Bulletin 24 ARLP024
From Tad Cook, K7RA
Seattle, WA June 13, 2003
To all radio amateurs
SB PROP ARL ARLP024
ARLP024 Propagation de K7RA
Geomagnetic disturbances continued this week, but at a lower level
than the previous seven days (our reporting week runs from Thursday
through the following Wednesday). The average daily planetary A
index for the week dropped to 21 from 37.1 the previous week. The
average daily sunspot number rose from 67.4 to 149.4, reaching a
peak of 207 on Tuesday, June 10. Solar flux increased as well, the
weekly average rising from 117.4 to 150.5. Solar flux peaked at
192.9 on Wednesday, June 11. Solar flux over the weekend is expected
to be 150, 140, 130 and 120 for Friday through Monday.
With all of the recent geomagnetic disturbances, there is hope for
HF operators with the predicted planetary A index of 12 for June 13
and June 16. This is only slightly unsettled, much better than the A
index of 20 to 30 we've seen recently. However, be aware that flares
can pop up and conditions can change, as it did recently on May 30,
which was forecast for so long to have quiet conditions. Now it
seems there was a coronal mass ejection that could hit earth on June
13, causing a rise in geomagnetic indices.
A couple of large sunspots were news this week, causing the rise in
sunspot numbers and some flares as well. A good view is Tuesday's
solar disk, seen at
http://science.nasa.gov/spaceweather/images2003/10jun03/midi512_blank.gif.
Notice the "10jun03" characters in that URL. You can change those to
11jun03, then 12jun03 and 13jun03, then click "back" with your
browser to display as a simple animation.
Check out Project Jove at http://radiojove.gsfc.nasa.gov/. Dick
Flagg, AH6NM and Jim Sky, KH6SKY built a spectrograph that scans
18-28 MHz, recording radio noise from the Sun and Jupiter. They are
about to release software that lets anyone view spectrograms in real
time from data streamed via the internet. Recently they observed a
solar burst during flare activity, and just prior to the burst you
can see HF signals present between 18-28 MHz. Right after the burst
is nothing, due to a radio blackout. The images were on
http://www.spaceweather.com yesterday, and unfortunately are now
gone. Perhaps by next week we can come up with a link to the images.
Bob Sluder, N0IS says he has a very simple 6 and 2-meter setup with
only a 2-meter loop and a 6-meter Halo in his attic. But on
Thursday, May 5 he heard stations from around North America on
2-meters and on 6-meters the North and South America openings lasted
24 hours. Bob writes, "So, bring on another BIG BLAST from the sun
and lets see what happens. Hooray for high K's. Too bad about those
high A numbers, but then, if you are on VHF, you would not care."
Going a little further back into May, Bill Cullen, WH6DQ who lives
3,500 feet up the side of Kilauea on Hawaii's Big Island reports
that on May 23 around 0100z he heard the 147.09 MHz repeater on
Catalina Island in California. He listened to a couple of California
stations converse, broke in, but wasn't copied, even though he could
trigger the repeater. He observes that the two California hams would
have been excited if they only knew where he was. So, if you were on
147.09 MHz in Southern California around 0100z on May 23 and heard a
not quite copy able station break in, it was Bill.
Rodney Vorndam, K9ROD wrote to say that last Saturday, June 7 was a
great day for him on 6-meters in Colorado. He made 25 contacts
across the south and central parts of the U.S., and one on 6-meters,
while running just 10-watts. He's noticed great 6-meter conditions
coinciding with large storm centers moving across the U.S. in the
summer.
Dan Jeswald, W4NTI also commented on large storm fronts, saying he
has good luck during the summer E-skip season aiming his 3-element
homebrew 6-meter Yagi at storms. On the same day K9ROD in Colorado
was having so much fun, W4NIT in Anniston Alabama was hearing
France, Italy and Portugal at S5-S7 on 6-meters. K9ROD wrote again
to say that Tuesday, June 10 was his best night on 6-meters ever.
The band was full and he made 26 contacts across the U.S.
The day prior, Monday June 9, Al Olcott, K7ICW in Nevada reported an
all day 6-meter opening that suddenly intensified. He noticed a lot
of QRM on broadcast television frequencies, and at 2319z he heard
W5HOT in Arkansas at S9. On 2-meters shortly after this he noticed
pandemonium. He made 11 W5 contacts in Arkansas, Louisiana, Texas
and Oklahoma. He tried 222 MHz, but got no response. He believes
there was a highly reflective ionospheric cloud in the E-layer
centered over DM83 on the Texas-New Mexico border.
Carl Luetzelschwab, K9LA had some interesting insight regarding
trans-equatorial propagation during high geomagnetic activity,
mentioned in last week's bulletin. He writes, "There's been much
study in the area of how geomagnetic storms affect the ionosphere.
One piece of knowledge to come out of this is that all geomagnetic
storms are not equal, and thus the effect on the ionosphere can
vary."
He continues, "For gradually evolving storms, driven by slowly
increasing southward IMF, the low to mid-latitude ionosphere tends
toward an increase in ionization at night - sometimes up to a 50%
increase in foF2. So there really is an ionospheric basis for
enhanced north-south propagation. On the other hand, storms with an
initial compressive phase and rapidly evolving main phase tend to
deplete nighttime mid-latitude ionization." Thank you, Carl!
For more information on propagation and an explanation of the
numbers used in this bulletin see the Propagation page on the ARRL
Web site at http://www.arrl.org/tis/info/propagation.html. You can
write to the author of this bulletin at k7ra@arrl.net.
Sunspot numbers for June 5 through 11 were 95, 98, 125, 167, 176,
207, and 178, with a mean of 149.4. 10.7 cm flux was 113.6, 125.6,
133.2, 153.4, 158.3, 176.5, and 192.9, with a mean of 150.5.
Estimated planetary A indices were 13, 13, 24, 27, 28, 27, and 15,
with a mean of 21.
NNNN
/EX |
As Alan Pardew shook hands with Steve Clarke at the final whistle he had only one word for his West Bromwich Albion counterpart. "Sorry," said Newcastle United's manager after seeing his side secure a most flattering three points thanks to Papiss Cissé's inadvertent late winner.
"I won't make any bones about it, we didn't deserve it," said Pardew. "They were pushing for a win at the end and we didn't have too many ideas. We were tired in the second half, we had no rhythm and I was messing about with my team, but Sammy shot and if you shoot, you never know what will happen."
Newcastle's manager initially opted for a 4-3-3 formation featuring Shola Ameobi to the right of Demba Ba and Ben Arfa on the left. Once again there was no starting slot for Cissé while, further back, James Perch assumed the suspended Cheik Tioté's enforcer role.
All dribbles, nutmegs and clever dodges, Ben Arfa was Newcastle's best player and he very nearly helped supply an early lead. After meeting Ben Arfa's pass Ameobi Snr crossed invitingly towards Ba but despite making a decent connection the Senegal striker headed uncharacteristically wide.
Emboldened by this reprieve, Clarke's swift-breaking Albion players offered a typical counter-attacking riposte. Graham Dorrans's smart through-pass found the excellent Romelu Lukaku and Tim Krul did well to parry his shot.
Foster was left with no scope for similar heroics when, shortly afterwards, he was beaten by Ba's volley following Ameobi's headed flick and poor defending on the part of Jonas Olsson and Gareth McAuley.
Clarke must have rued the failure of Claudio Yacob to pass a fitness test in time to join Youssouf Mulumbu at the base of midfield in his 4-2-3-1 formation. Yacob has been Albion's stand-out individual lately and, during the first half, Newcastle highlighted James Morrison's out of position deployment in the absent Argentinian's holding role.
Albion's manager may also have reflected on how much has changed since the days when he served as first-team coach at St James' Park; some say that Ruud Gullit's most inspired act as Newcastle's manager was the elevation of Clarke from a junior role.
Lukaku equalised 10 minutes after the interval when Zoltan Gera, exploiting Danny Simpson's defensive negligence, crossed left-footed for the Chelsea loanee – who Robert Di Matteo is pondering recalling in January – to head beyond Krul. "West Brom have real assurance about them and Lukaku's a big talent," said Pardew. "He was a real problem for us."
That goal proved to be virtually the last acto of the Belgian before his controversial replacement by Shane Long. By then Pardew had introduced Cissé and Gabriel Obertan, switched to 4-4-2 and rather desperately began pushing assorted tactical buttons.
He found himself forced into further change when Ba, whose vulnerable left knee took a hefty knock in the first half, limped off. "Hopefully Demba's not a major concern but he may struggle to play at Liverpool next week," said Pardew. "We think he's damaged a nerve in his shin."
On came Sammy Ameobi but with Newcastle missing Tiote's tackles and West Brom suddenly coping well without Yacob, the power-balance had altered significantly. Or so everyone thought until Ameobi's shot and Cisse's back did the rest. "We were the best team," said Clarke. "But football's a cruel game." |
/* Redline Smalltalk, Copyright (c) James C. Ladd. All rights reserved. See LICENSE in the root of this distribution. */
package st.redline.core;
import st.redline.classloader.SmalltalkClassLoader;
public class PrimSubclass extends PrimObject {
public static final PrimObject PRIM_SUBCLASS = new PrimSubclass();
private PrimObject theMetaclass;
protected PrimObject invoke(PrimObject receiver, PrimContext primContext) {
System.out.println("PrimSubclass invoke: " + String.valueOf(primContext.argumentJavaValueAt(0)));
assert receiver.equals(primContext.receiver());
String subclassName = String.valueOf(primContext.argumentJavaValueAt(0));
PrimObject superclass = primContext.receiver();
PrimClass newClass;
PrimClass newMeta;
boolean bootstrapping = isBootstrapping();
if (bootstrapping) {
newClass = (PrimClass) superclass.resolveObject(subclassName);
if (newClass == null)
throw new RuntimeException("New class is unexpectedly null.");
} else {
newClass = new PrimClass(subclassName);
newMeta = new PrimClass(subclassName, true);
newClass.selfClass(newMeta);
newClass.superclass(superclass);
newMeta.superclass(superclass.selfClass());
newMeta.selfClass(theMetaclass);
}
// TODO - Add other definitions to appropriate objects.
//System.out.println("TODO - Add other definitions to appropriate objects.");
if (!bootstrapping) {
SmalltalkClassLoader classLoader = classLoader();
String fullQualifiedName = makeFullyQualifiedName(classLoader, subclassName);
classLoader.cacheObject(fullQualifiedName, newClass);
}
return newClass;
}
private String makeFullyQualifiedName(SmalltalkClassLoader classLoader, String name) {
String instantiationName = classLoader.peekInstantiationName();
if (instantiationName != null && instantiationName.endsWith(name))
return instantiationName;
throw new RuntimeException("Current instantiating class name not found.");
}
public void metaclass(PrimClass metaclass) {
theMetaclass = metaclass;
}
}
|
Pages
When creating updates remember to build for rawhide and Fedora 25 (devel)
When ever we branch for a new release of Fedora I, and others, end up spending a non trivial amount of time ensuring that there’s a clean upgrade path for packages. From the moment we branch you need to build new versions and bug fixes of packages for rawhide (currently what will become Fedora 26), for the current stabilising release (what will become Fedora 25) as well as what ever stable releases you need to push the fix for. For rawhide you don’t need to submit it as an update but for the current release that’s stabilising you do need to submit it as an update as it won’t just automagically get tagged into the release.
As a packager you should know this, it’s been like it for a VERY LONG TIME! Yet each cycle from the moment of branching right through to when a new release goes GA I still end up having to fix packages that “get downgraded” when people upgrade between releases!!
So far this cycle I’ve fixed about 20 odd with the latest being bash-completion (built but not submitted as an update for F-25) and certmonger (numerous fixes missing from F-25 and master branch).
The other silly packaging bug I end up having to fix quite a bit is NVR downgrades where even though it’s a newer package the way the NVR is handled makes rpm/dnf/yum think the newer package is a lesser version than the current version and hence you’re new shiny fix won’t actually make it to end users. I see this a lot where people push a beta/RC package to a devel (F-25/rawhide) release. Just something to be aware of, there’s lots of good docs around the way rpm/dnf/yum handles eNVR upgrades. |
Bharti Airtel said its revenues from India operations grew2.8 per cent to Rs 15,345 crore in Q1
Bharti Airtel on Thursday reported a net loss of Rs 2,866 crore in the April-June period, as against a net profit of Rs 97.3 crore in the corresponding period a year ago. In a regulatory filing after market hours, the private sector telecom company said its revenue from operations stood at Rs 20,737.9 crore in the quarter ended June 30, up 4.74 per cent compared to the year-ago period. Analysts had on an average expected the company to report a loss of Rs 1,017 crore, news agency Reuters reported citing Refinitiv data.
Bharti Airtel said its revenues from India operations grew 2.8 per cent to Rs 15,345 crore in the June quarter. Its Africa revenues rose 10.2 per cent. Bharti Airtel has operations in 18 countries across Asia and Africa.
“The first quarter of the year has begun with a healthy and equitable growth across all our lines of businesses. Headline pricing remained stable, albeit at low levels," said Gopal Vittal, managing director and CEO, India & South Asia, Bharti Airtel.
New Delhi-based Bharti Airtel said its mobile average revenue per user stood at Rs 129 in the first quarter of financial year 2019-20. However, its monthly churn rate in mobile services business - a measure of the number of customers it lost - grew to 2.6 per cent for the quarter, compared with 2 per cent a year ago.
"We continue to remain focused on providing value to customers through our rewards platform, Airtel Thanks. This has led to the second consecutive quarter of ARPU (average revenue per user) increase."
In a statement, Bharti Airtel said its consolidated mobile data traffic on network grew 94 per cent compared to the corresponding three-month period a year ago.
Shares in Airtel ended 4.10 per cent lower at Rs 323.95 apiece on the Bombay Stock Exchange (BSE), underperfomring the benchmark Sensex index which fell 1.23 amid a broad selloff tracking global cues.
In the fourth quarter of financial year 2018-19, Bharti Airtel had posted a net profit of Rs 107.2 crore, up 29.31 per cent on a year-on-year basis. Its net profit stood at Rs 409.5 crore in the financial year ended March 31, as against Rs 1,099 crore in 2017-18.
(With inputs from Reuters) |
A practical technique for measuring human biofluid conductivity using high gain-frequency characteristics.
Currently, the study of ion composition and performance in human biofluids plays an important role in biomedical engineering research and technology. This field may become universal for human diagnostics; it allows early detection of different diseases in humans by measuring changes in ion behaviour in human biofluids. Practical experiments were conducted to analyse the liquid composite electrolyte conductivity in an alternating electric current field. These experiments allow the contribution of separate types of ions to the overall conductivity to be estimated. The method of estimating the concentration of active ions contained in biofluids is also introduced; it illustrates the possibility of performing qualitative and quantitative analysis over a wide range of concentrations and compositions. The authors present a procedure to determine the concentration of active liquid ions based on conductivity gain-frequency characteristic curve tracing. The experimental results validate the practical use of the proposed method. The results of this research are promising, and further investigation is required to further improve the method. |
Alteration of midkine expression associated with chemically-induced differentiation in human neuroblastoma cells.
Midkine (MK), a neurotrophic polypeptide of which expression is developmentally regulated in embryogenesis, is expressed in malignant tumor tissues including neuroblastoma (NB). A retinoic acid analogue, E5166, and dibutyryl cyclic AMP (dbcAMP) are known to induce differentiation in NB cells. This study showed that MK mRNA expression increased in association with differentiation by E5166, but not by dbcAMP in SK-N-SH and KP-N-RTBM1 human NB cell lines. We concluded that MK could be an important factor in differentiation of NB cells, and further, that there could be at least two pathways in differentiation of NB cells at molecular mechanism. |
Comparison of lumbar sagittal alignment produced by different operative positions.
This study is a prospective evaluation of the effects of commonly used spinal tables on lumbar sagittal alignment. The objective was to determine the differences, if any, in lumbar sagittal alignment produced by different positions on routinely used spinal operating tables. Earlier studies have documented the advantages of the knee-chest position in lumbar decompressive procedures. When simultaneous fusion is performed and augmented with internal fixation, intraoperative position is the critical determinant of sagittal plane balance. Other investigators have documented an association between the knee-chest position and decreased lumbar lordosis. Ten asymptomatic volunteers underwent a series of four lateral lumbar radiographs, as follows: standing, prone on the Jackson (Orthopaedic Systems, Inc., Hayword, CA) spinal table, and prone on the Andrews (Orthopaedic Systems, Inc.) table with the hips flexed 60 degrees and 90 degrees, respectively. Intervertebral body angle measurements were obtained from L1 to S1. Lordosis values were compared and analyzed for each of the positions. Standing lordosis was assumed to be physiologic. Physiologic lordosis values were produced only on the Jackson operative table. Both positions on the Andrews table resulted in a statistically significant decrease in lumbar lordosis. Decreasing hip flexion on the Andrews table from 90 degrees to 60 degrees produced a statistically significant increase in lumbar lordosis. However, this change did not reproduce physiologic values. When instrumentation is used to augment lumbar fusions, positions incorporating hip flexion should be avoided to ensure maintenance of sagittal plane balance. |
Hello everyone. It’s been a couple of months since we announced the incoming closure of the Katbox as a web host. We’ve been very busy on our end, mostly with life and work but also with trying to help our friends find new homes for their works. As promised, the remaining Katbox funds are being employed to helping these new spaces start up and the results are promising.
Hello everyone. I’m sorry it’s been so long since the last update, and there’s been a reason for that.
In many ways the katbox has been doing very well. Despite community activity dropping off drastically in the forums, the discord has been taking off spectacularly. We also experienced a record showing at Anthrocon this year, meeting scores of you wonderful people that have helped make this place a positive experience over the years.
Yet in the shadow of that great weekend the cumulative issues that have been going on with the site & community have come to a head, and I’m personally burned out beyond the point I think I can recover. I came to realize this shortly after arriving home from Pittsburgh. After talking with some people close to me I came to possibly one of the hardest decisions I’ve had to make. One I should have maybe made at the start of the year, when the burnout began to set in. I’m doing it now, though.
Over the coming months, possibly up till near the end of the year, the Katbox is going to be winding down operations and moving artists off site. I feel that I’ve made every reasonable effort to avoid doing this. Late last week it looked as if we were going to be able to take on a new administrator so I could just retire, but that fell through Thursday evening when they looked over everything and decided they couldn’t fix the site’s issues either.
We’re going to do everything we can to ensure that all the Katbox artists will have a home to go to before this is all over. We’ll be using whatever remaining funds the site has to try to cover expenses and make this as painless as possible. Already about half of the artists have found new places to host their content and we will be letting everyone know where those places are.
The patreon will be kept up a little longer, your continued support will help us defer the costs of hosting and to pay expenses for people who need new hosts. Once it’s all done, though, the katbox front page will be all that remains, linking to the artists who helped make it what it was. I still want to support them as much as I’m able. For the foreseeable future the discord server will also remain, though it will become a more general purpose art and culture community.
To the people who have sent inquiries to me I need to apologize for not responding. As I became more burned out I have been a lot less diligent in checking email and responding to messages.
The Katbox is not going to be for sale. This site has been my home on the internet for 15 years. It’s my precious. I may want to bring it back someday for something, but for now a new chapter begins. I look forward to what happens next and wish everybody the best. I’m sorry to the community that I was not able to fix the site’s issues and make it the best place it could be. If you want to support the artists of the Katbox, their patreons could use your patronage more than ever. |
Q:
Does CC.NET detect modification when a build script performs a checkin
I've been doing some research into finally automating our Development builds and still have one nagging question that I'm hoping the StackOverflow community can solve for me.
My understanding is that an IntervalTrigger when setup properly will check VSS every X seconds for changes and if it finds a modified file, will run my tasks. One of my tasks would be to checkout the AssemblyInfo files and update the version numbers. After these files are updated they would be checked back into VSS.
Thinking about this solution it doesn't make much sense because in my mind, I'm forcing the check for changed files to true every time the trigger fires. Am I missing something here? Is there a way of doing this without triggering an automatic build on the AssemblyInfo check-in?
A:
You can use a Filtered Source Control Block to exclude certain files from the trigger.
|
# interfaces(5) file used by ifup(8) and ifdown(8)
# Please note that this file is written to be used with dhcpcd
# For static IP, consult /etc/dhcpcd.conf and 'man dhcpcd.conf'
# Include files from /etc/network/interfaces.d:
source-directory /etc/network/interfaces.d
auto wlan0
iface wlan0 inet dhcp
wpa-conf /etc/wpa_supplicant/wpa_supplicant.conf
auto usb0
iface usb0 inet static
address 10.13.37.1
netmask 255.255.255.0
|
Nevers is a quiet town, capital of the department of Nièvre. The streets are along the Loire. Among its points of interest include the Palais Ducal, the Cathedral Saint-Cyr Sainte-Julitte and the Church of St. Bernadette of Banlay. In
The Nevers Magny Cours is the big prize of the French Formula 1 which has been held every year for decades.
It is an unpretentious international circuit, as Magny-Cours suffers from a lack of funds to place them among the greats. The |
Chemicals Market Research Reports & Industry Analysis
Chemicals are known forms of matter that have properties that consist of constant characteristic properties and chemical compositions. It's impossible to separate chemical substances into components without having the chemical bonds broken. This is typically done using physical separation methods. Chemicals can be found in various states, including plasma, solid, gas and liquid, and are able to change between these states when temperatures and pressures change.
There are various industries that chemicals are a commodity to including life sciences, materials, agricultural, defense, energy, industrial, pharmaceuticals, some product manufacturers and defense.
Chemicals are placed in various categories based on their functional and industrial significance, including ceramics, inorganic and organic chemicals, oils, esters, surfactants, acids, oleochemicals, alcohols, solvents, source gases, neutral gases, process gases, petrochemicals, ceramics, polymers, salts, dyes, bases, colorants and dyes. The oil and gas sector provides various specialty chemicals. Other chemical producers also provide chemicals to consumers through the use of various chemical synthesis and production methods, which are combined through related chemical outputs and inputs. The transport industry that ships chemicals throughout the world is a trillion-dollar-annually market.
Chemicals Industry Research & Market Reports
... data available through July 2015. This update provides the data necessary to make informed forecasts and business planning after the recent seasonal changes in output. This 164-page report includes the most recent information on the ...
|
read more...
... cost and pricing, and trends during the current environment, including the output and shipment changes over the past months. At 175 pages with over 150 charts and tables, the report covers topics such as current ...
|
read more...
... demographics. The report features 2015 current and 2016 forecast estimates on Industrial inorganic chemicals materials used by the Polystyrene foam mfg industry nationally and for all 50 U.S. States and up to 900 metro areas.
|
read more...
... features 2015 current and 2016 forecast estimates on Industrial chemicals (chemical reagents, acidizing mat, etc) materials used by the Tire Mfg. industry nationally and for all 50 U.S. States and up to 900 metro areas. ...
|
read more...
... applications and industry chain structure.The Agricultural Inoculants market analysis is provided for the international markets including development trends, competitive landscape analysis, and key regions development status. Development policies and plans are discussed as well as ...
|
read more...
... inventory data available through July 2015. This update provides the data necessary to make informed forecasts and business planning after the recent seasonal changes in output. This 160-page report includes the most recent information on ...
|
read more...
... inventory data available through July 2015. This update provides the data necessary to make informed forecasts and business planning after the recent seasonal changes in output. This 174-page report includes the most recent information on ...
|
read more...
... cost and pricing, and trends during the current environment, including the output and shipment changes over the past months. At 210 pages with over 150 charts and tables, the report covers topics such as current ...
|
read more...
... and trends during the current environment, including the output and shipment changes over the past months. At 164 pages with over 150 charts and tables, the report covers topics such as current macroeconomic trends, granular ...
|
read more...
... and inventory data available through July 2015. This update provides the data necessary to make informed forecasts and business planning after the recent seasonal changes in output. This 166-page report includes the most recent information ...
|
read more...
... inventory data available through July 2015. This update provides the data necessary to make informed forecasts and business planning after the recent seasonal changes in output. This 164-page report includes the most recent information on ...
|
read more...
... trends during the current environment, including the output and shipment changes over the past months. At 170 pages with over 150 charts and tables, the report covers topics such as current macroeconomic trends, granular product ...
|
read more...
... pricing, and trends during the current environment, including the output and shipment changes over the past months. At 165 pages with over 150 charts and tables, the report covers topics such as current macroeconomic trends, ...
|
read more...
... and pricing, and trends during the current environment, including the output and shipment changes over the past months. At 173 pages with over 150 charts and tables, the report covers topics such as current macroeconomic ...
|
read more...
... In addition, the report reviews the major U.S. and international regulatory, technological, economic, demographic, and social trends with potentially significant impact on the paints and coatings industry during the next five years, including discussion of ...
|
read more...
... (2015 - 2020) The Term Explosion refers to an unanticipated rise in the energy (chemical, mechanical or nuclear) of the system in an unbridled way accompanied by increase in temperature and release of gases. There ...
|
read more...
... applications and industry chain structure.The Adhesive Resin market analysis is provided for the international markets including development trends, competitive landscape analysis, and key regions development status. Development policies and plans are discussed as well as ...
|
read more...
... industry chain structure.The Biolubricants market analysis is provided for the international markets including development trends, competitive landscape analysis, and key regions development status. Development policies and plans are discussed as well as manufacturing processes and ...
|
read more... |
Q:
На странице есть input (выбор установкой галочки), так вот нужно убрать этот выбор и вместо
На странице есть input (выбор установкой галочки), так вот нужно убрать этот выбор и вместо этого установить значение будто галочка уже стоит
код на странице:
<input type="checkbox" id="toggle_animation" value="on" <? if ($_COOKIE["pronto-animated"] == "true") echo 'checked="checked"'; ?> /><label for="toggle_animation">Use Page Transitions</label>
а это выполняющийся скрипт:
var useAnimation;
$(document).ready(function() {
useAnimation = (Cookies.read("pronto-animated") == "true");
// Init pronto
$.pronto({
requestDelay: (useAnimation) ? 500 : 0,
selector: "a:not(.no-pronto)"
});
// Bind pronto events
$(window).on("pronto.request", requestPage)
.on("pronto.render", initPage)
.on("pronto.load", destroyPage);
// Remember to init first page
initPage();
$("#toggle_animation").on("change", function() {
if ($(this).is(":checked")) {
Cookies.create("pronto-animated", "true");
} else {
Cookies.create("pronto-animated", "false");
}
window.location.reload();
});
});
function requestPage() {
if (useAnimation) {
$("#pronto").stop().animate({ opacity: 0 }, 500);
}
}
function initPage() {
// bind events and iniitalize plugins
if (useAnimation) {
$("#pronto").stop().animate({ opacity: 1 }, 500);
}
var href = window.location.href;
$("nav a").removeClass("active").each(function() {
var url = $(this).attr("href");
if (href.indexOf(url) > -1) {
$(this).addClass("active");
}
});
}
function destroyPage() {
// unbind events and remove plugins
}
// Cookie controls
var Cookies = {
create: function(key, value, expires) {
var date = new Date();
date.setTime(date.getTime() + (expires * 24 * 60 * 60 * 1000));
var expires = "; expires=" + date.toGMTString();
var path = "; path=/"
var domain = "; domain=" + document.domain;
document.cookie = key + "=" + value + expires + domain + path;
},
read: function(key) {
var keyString = key + "=";
var cookieArray = document.cookie.split(';');
for(var i = 0; i < cookieArray.length; i++) {
var cookie = cookieArray[i];
while (cookie.charAt(0) == ' ') {
cookie = cookie.substring(1, cookie.length);
}
if (cookie.indexOf(keyString) == 0) return cookie.substring(keyString.length, cookie.length);
}
return null;
},
erase: function(key) {
Cookies.create(key, "", -1);
}
};
A:
$('#checkbox_ID').attr('checked',true);
$('#checkbox_ID').val('true');
|
# @TEST-EXEC: zeek -b no-warnings.zeek >no-warnings.out 2>&1
# @TEST-EXEC: TEST_DIFF_CANONIFIER=$SCRIPTS/diff-remove-abspath btest-diff no-warnings.out
# @TEST-EXEC: zeek -b warnings.zeek >warnings.out 2>&1
# @TEST-EXEC: TEST_DIFF_CANONIFIER=$SCRIPTS/diff-remove-abspath btest-diff warnings.out
@TEST-START-FILE no-warnings.zeek
type blah: string &deprecated;
global my_event: event(arg: string) &deprecated;
global my_hook: hook(arg: string) &deprecated;
type my_record: record {
a: count &default = 1;
b: string &optional &deprecated;
};
type my_enum: enum {
RED,
GREEN &deprecated,
BLUE &deprecated
};
type my_other_enum: enum {
ZERO = 0,
ONE = 1 &deprecated,
TWO = 2 &deprecated,
};
event zeek_init()
{
print ZERO;
print ONE;
print TWO;
print RED;
print GREEN;
print BLUE;
local l: blah = "testing";
local ls: string = " test";
event my_event("generate my_event please");
schedule 1sec { my_event("schedule my_event please") };
hook my_hook("generate my_hook please");
local mr = my_record($a = 3, $b = "yeah");
mr = [$a = 4, $b = "ye"];
mr = record($a = 5, $b = "y");
if ( ! mr?$b )
mr$b = "nooooooo";
mr$a = 2;
mr$b = "noooo";
}
event my_event(arg: string)
{
print arg;
}
hook my_hook(arg: string)
{
print arg;
}
function hmm(b: blah)
{
print b;
}
global dont_use_me: function() &deprecated;
function dont_use_me()
{
dont_use_me();
}
function dont_use_me_either() &deprecated
{
dont_use_me_either();
}
@TEST-END-FILE
@TEST-START-FILE warnings.zeek
type blah: string &deprecated="type warning";
global my_event: event(arg: string) &deprecated="event warning";
global my_hook: hook(arg: string) &deprecated="hook warning";
type my_record: record {
a: count &default = 1;
b: string &optional &deprecated="record warning";
};
type my_enum: enum {
RED,
GREEN &deprecated="green warning",
BLUE &deprecated="red warning"
};
type my_other_enum: enum {
ZERO = 0,
ONE = 1 &deprecated="one warning",
TWO = 2 &deprecated="two warning",
};
event zeek_init()
{
print ZERO;
print ONE;
print TWO;
print RED;
print GREEN;
print BLUE;
local l: blah = "testing";
local ls: string = " test";
event my_event("generate my_event please");
schedule 1sec { my_event("schedule my_event please") };
hook my_hook("generate my_hook please");
local mr = my_record($a = 3, $b = "yeah");
mr = [$a = 4, $b = "ye"];
mr = record($a = 5, $b = "y");
if ( ! mr?$b )
mr$b = "nooooooo";
mr$a = 2;
mr$b = "noooo";
}
event my_event(arg: string)
{
print arg;
}
hook my_hook(arg: string)
{
print arg;
}
function hmm(b: blah)
{
print b;
}
global dont_use_me: function() &deprecated="global function warning";
function dont_use_me()
{
dont_use_me();
}
function dont_use_me_either() &deprecated="function warning"
{
dont_use_me_either();
}
@TEST-END-FILE
|
/*
*******************************************************************************
*
* Copyright (C) 2005, International Business Machines
* Corporation and others. All Rights Reserved.
*
*******************************************************************************
* file name: pkg_imp.h
* encoding: US-ASCII
* tab size: 8 (not used)
* indentation:4
*
* created on: 2005sep18
* created by: Markus W. Scherer
*
* Implementation definitions for data package functions in toolutil.
*/
#ifndef __PKG_IMP_H__
#define __PKG_IMP_H__
#include "unicode/utypes.h"
/*
* Read an ICU data item with any platform type,
* return the pointer to the UDataInfo in its header,
* and set the lengths of the UDataInfo and of the whole header.
* All data remains in its platform type.
*/
U_CFUNC const UDataInfo *
getDataInfo(const uint8_t *data, int32_t length,
int32_t &infoLength, int32_t &headerLength,
UErrorCode *pErrorCode);
#endif
|
JESSICA VILCHES
Born in Chile, Jessica first began her healing journey through psychotherapy at a very early age. Years later, while studying Healing Arts at the Theatre School University of Arts, Sciences & Communication UNIACC, her life was forever changed upon her discovery of Yoga. From there, her journey continued to unfold with 4 years of study at the Contemporary Dance College University of Arts & Social Sciences , where she explored the healing power of Movement Therapies.
Life embraced me, raised me to the sky, and shook me so strongly, that I had to wake up
She achieved a degree in Cultural Management at the Catholic University of Chile, which has since allowed her to create and facilitate numerous Healing Arts projects that have greatly improved the realities of vulnerable and underprivileged communities in her home country of Chile.
In 2009 Jessica traveled to India for the first time and felt an immediate kinship with its ancient culture and yoga based traditions, and knew in her heart that she would soon be calling India home. She settled in the holy city of Varanasi, where over the next 4 year she attended the Benares Hindu University for Yoga and Performing Arts. During her time there, she devoted herself to the absorption and exploration of India’s wealth of ancient wisdom, passionately immersing herself in Yoga, Ayurveda, Tantra, Devotion through Singing & Indian Classical Dance, as well as Buddhist Vipassana Meditation and Yogic/Ayurvedic/Buddhist Psychology.
Life is perfectly beautiful, generous and simple. If we leave our attachments behind, our fears will also dissolve, and we will be free to embark on the magical and transformational journey of experiencing life at its fullest
Over the last few years she has facilitated numerous courses and retreats in countries across the globe, including India, Nepal, Thailand, Australia, Bali, Peru, France, Italy, and Switzerland.
The focus of her retreats is the awakening of consciousness through ancient practices and healing arts. Her work assists in releasing stored trauma and bringing awareness and balance between our inner and outer worlds, between our minds and our hearts. Her aim is to guide her students towards embracing themselves fully— recognizing and loving their uniqueness— allowing for the integration of all facets of their being and the subsequent discovery of their innate sense of aliveness.
Through her own profound personal experiences with healing, she’s come to see and understand how by using these ancient modalities an individual can be transformed and awakened. This is the reason she continues to be in service.
"I am blessed for finally breathing who I am. For being in love with myself and having a heart full of gratitude for everything that brought me to this awareness of who I am." |
id Software's new shooter Quake Champions is out now on Steam Early access and via the Bethesda.net launcher, and its release for PC is right on schedule. You can play the game right now by purchasing the $30 Champions Pack, which includes all characters available now and in the future. When Quake Champions leaves Early Access, the price of the pack will go up to $40. Another thing to know is that Quake Champions will be free-to-play later in the future, so buying the Champions Pack is a way to start sooner and get extras, but not the only way to play.
As with other Early Access games, you should be aware that Quake Champions is unfinished. As such, you might encounter bugs or other technical issues.
Quake Champions' current character roster includes: Ranger, Visor, Scalebearer, Nyx, Anarki, Clutch, Sorlag, Galena, Slash, BJ Blazkowicz, and Doom Slayer. As for future characters, there are at least six more coming before the end of 2018, and more could come after that. Additionally, everyone who buys the Champions Pack gets the skin "diehard Ranger," which is only available while the game is in Early Access.
Finally, the Champions Pack includes three loot chests, which are called Reliquaries in Quake Champions. They can include things like skins, shaders, and weapon personalisation items.
As for the content in the Quake Champions Early Access version, there are eight maps, the 11 aforementioned champions, four modes, character and weapon customisation options, custom game support, and more. Go to the game's Steam page to learn more.
Quake Champions has only been announced for PC. If the game does come to console, it could be a while before that happens. |
/*
* This program is free software; you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License, version 2.1 as published by the Free Software
* Foundation.
*
* You should have received a copy of the GNU Lesser General Public License along with this
* program; if not, you can obtain a copy at http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html
* or from the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
*
* This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
* without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
* See the GNU Lesser General Public License for more details.
*
* Copyright (c) 2001 - 2013 Object Refinery Ltd, Hitachi Vantara and Contributors.. All rights reserved.
*/
package org.pentaho.reporting.engine.classic.core.modules.gui.commonswing;
import java.awt.Component;
import java.awt.Dimension;
import java.awt.event.ComponentAdapter;
import java.awt.event.ComponentEvent;
/**
* A small helper class to limit the maximum size of an element to the elements maximum size. If the element is resized,
* the defined maximum size is enforced on the element.
*
* @author Thomas Morgner
*/
public class WindowSizeLimiter extends ComponentAdapter {
/**
* The current source.
*/
private Object currentSource;
/**
* Default-Constructor.
*/
public WindowSizeLimiter() {
}
/**
* Invoked when the component's size changes.
*
* @param e
* the event.
*/
public void componentResized( final ComponentEvent e ) {
if ( e.getSource() == currentSource ) {
return;
}
if ( e.getSource() instanceof Component ) {
currentSource = e.getSource();
final Component c = (Component) e.getSource();
final Dimension d = c.getMaximumSize();
final Dimension s = c.getSize();
if ( s.width > d.width ) {
s.width = d.width;
}
if ( s.height > d.height ) {
s.height = d.height;
}
c.setSize( s );
currentSource = null;
}
}
}
|
Jimmy Rogers (basketball)
Jimmy Rogers (born c. 1950) is an American former professional basketball player. He and fellow American Curtis Carter, who signed with KR, have been credited for revolutionizing the Icelandic basketball scene after they became the first foreign born professional players in the Icelandic Basketball League in 1975.
Early life
Rogers was born in Thompson, Texas and grew up in Houston with seven other siblings.
Iceland
In September 1975, Rogers became the first foreign born professional basketball player in Iceland when he signed a three-month contract with Ármann in preparations for their games against Honka Playboys in the FIBA European Cup Winners' Cup.
His first games for Ármann where during the annual Reykjavík Basketball Tournament. Ármann finished second in the tournament, behind reigning national champions ÍR, and Rogers led all players in scoring with 113 points in five games for an average of 22.6 points per game.
On October 30, Rogers scored 24 points for Ármann in a disappointing 65-88 loss against the Honka Playboys in the first leg of the FIBA European Cup Winners' Cup.
The first meeting between Rogers and Curtis Carter on December 16 was highly anticipated and did not disappoint. It was a tightly played and ended with an 86-81 victory for Ármann. But with 54 seconds remaining in the game, with the score tied at 81-81, Carter got into a fight with Rogers and knocked him down. The punch was caught on a picture and made the front page of Dagblaðið the day after, as well as the headline in Þjóðviljinn "Jimmy won the duel - The Truck won the boxing". Both players received a one-game suspension for the fight from the disciplinary court of the Icelandic Basketball Federation and where threatened with a six-game suspension for any future fights. The verdict was highly criticized, both for the short suspension and for the threat of a longer suspension that only applied to them, as referees were worried that opposing players would try to harass them and goad into a fight.
In the end, Rogers and Ármann came out on the top in the league after beating KR in the last game of the season, guaranteeing them the first place and the national championship. Rogers came second in the race for the scoring title, finishing with 365 points behind Carter's 451 points.
On April 1, 1976, Ármann won Njarðvík, 98-89, in the Icelandic Cup finals behind Rogers 32 points.
Rogers resigned with Ármann the following season, He was again the leading scorer during the Reykjavík Basketball Tournament with 135 points but Ármann again finished second in the standings, this time behind KR.
He was granted a leave of absence from the club in middle of December, with Ármann undefeated in first place, to return to the United States due to personal reasons. In January 1977, Ármann announced that he would not return.
Titles, awards and achievements
Titles
Icelandic champion: 1976
Icelandic Basketball Cup: 1976
Achievements
Reykjavík Basketball Tournament scoring champion: 1975, 1976
References
Category:1950s births
Category:Living people
Category:American expatriate basketball people in Iceland
Category:American men's basketball players
Category:Úrvalsdeild karla basketball players
Category:Forwards (basketball) |
Official box description: The cooler months spell for the perfect time to brighten up skin, even out complexions and target pesku dark spots! Whatever shade of the rainbow your skin colour is, optimise your skin’s radiance and clarity for luminous, glowing skin. Now that summer is coming to an end, lay off the bakin’ and pull out our ultra-brightening and super potent Snow White box! Discover Princess Snow White’s ultimate secret to beautifully bright skin that made her a beauty legend!
Snow White box contents:
Nella Fantasia Oneday Whitener (this is very popular in Asia!), 120ml rrp $29
Original raw First Essence (red version), 110ml rrp $26
Daltokki Whitening Essence, 100ml rrp $35
5 Seeds Apple Water Brightning Scrub, 80ml rrp $26
Faceflux Anti-wrinkle Revitalize cream, 30g rrp $38
Morningtree Revitalizing Whitening Deep Spot, 20ml rrp $34
These whitening products sound very scary initially, whitening makes you think the product might contain bleach for skin! I personally have been using whitening products for years and it has not change my skin shade. I have stayed around NC25 to NC30.
6 full size products with retail value of $188. Good value. But to be honest, I wouldn’t pay $29 for a body lotion! But is always nice to try 🙂
Second box is the Princess box#2 Sleeping Beauty! Who doesn’t want to wake up with the most gorgeous skin every morning?! Let the products work for you while you sleep! Genious!
Princess Edition #2 Sleeping Beauty memebox
After thought…I will probably get woken up by my cats meowing and not a prince’s kiss! 😛
Official box description: Break out of your beauty rut and pamper yourself in the PM for an instant beauty transformation! Revitalise dull and tired looking skin with ultra-moisturising, and super nutritious formulas to lock in hydration and essential vitamins and minerals! Give yourself the ultimate skin care therapy with beauty goodies that re-texturize, repair, and renew skin for petal-soft, radiant skin the next morning! Don’t fall asleep on your beauty potential, but jump start your beauty with this Sleeping Beauty box! Transform your skin with the right overnight products – and without the wait.
This box contains few sleeping packs, night creams, and 2 aloe items. I love Aloe but I am very keen to try out the neck cream. It is one of those products that you don’t realise you needed it until it’s too late.
Sleeping beauty box contents:
ReinPlatz Intensive Moisture Pack, 23g rrp $4
Vella Neck Tight Cream, 50ml rrp $30
D’Ran Aqua Wonder Recovery Cream, 25g rrp $35
Dermahouse Aloe Vera Gel, 150ml rrp $29
eChoice Aloe Vera cream, 10g rrp $3
Dewytree Aqua Collagen Peptide Sleeping Mask, 150ml rrp $28
6 full size products but 1 of them is one-use. . So I count that as 5! This box has retail value of $129.
Another good value box but rrp value is nothing if the products don’t work!
Although there are no real cute Princess themed items, nothing too pinky too girly… I’m not complaining as the contents seems to be what I’m looking for and willing to try ;D
I’ve enjoyed using and testing all the previous memebox items. It really has upped my skincare game. I can see a difference already 🙂
I hope you like this unboxing post and gotten a feel of what these boxes are like. I did not get the Rapunzel box, it is all for beautiful, strong hair and it looked like a very good box as well! If you are interested in any of these boxes, you might be able to catch a restock of them! Just stalk the “Ship Soon” page like I do every-single-day :p
Thanks for reading! Enjoy the rest of your week 😀
8th Nov update: Sleeping Beauty box has been restocked. There are currently 7 boxes left.
This post contains affiliate links.
From now until 31st January 2015. Get $3 off any order over $30 (excluding shipping and tax), use the discount code: O8WNBL |
Had my Anti D injection
I was off sick from work since wed , had the worse head ache and had a MW app on thursday afternoon, urine was fine BP a little high but she said nothing to worry about but could be cause of my head ache and just to rest so stayed home on friday as well. I finally after 5 weeks of having that lump under my arm and scared to death I was dying asked her what the hell it was and I am pleased to say it's a milk gland
I also had to have my bloods done again and she REALLY hurt I have had a few bloods done now and got my head round them as they don't really hurt but she went for a vien thats never been used before and it hurt so much and bleed so much, this then got me all worked up for the anti d as I was thinking I thought she was good with needles and if this hurt then what will the anti d be like.
She told me not to look at the needle (which did not help) and go and stand by the bed and bend over as she was going to put it in my bum, so I did that but I started to come over all hot and faint, then I felt her behind me and she said I will just help myself and pulled my bottoms down, at which point I freaked out and said I just cannot do this and worried I was going to bolt she just stuck it in me, it was over before I knew it and did not hurt at all!! The only thing is she did it in the side of my back rather than my bum check as she heard me say I cannot do this and wanted to get it in fast!
I had a huge brusie where the bloods were taken and nothing from my anti D!!! I have been in pain a little as well as Rose is laying so funny with her little bum right under my ribs on the right hand side and it's really painful, I have not been sleeping well because of it and my back has been really sore as well.
Awww!! Well I can definatley say your a lot stronger than me lol!! I had to have an anti d at about 14 weeks ish becuase of bleeding, she put it in my arm and it REALLY stung!!! :'( I must say I let the nurse know that I thought she should have told me just how much it was going to sting!! I think I must have made a bit of an impression lol because she remembers me on a first name basis every time I go back to the hospital now lol!
Oh bless her, well Lyn my MW was not my MW to start with but I did not like the ones I had before and a girl at my NCT class told me Lyn was wonderful with injections and I should go to her.
So I did and she is LOVELY and as I am hoping for a home birth she will be the lady who will deliver Rose but I must say the blood test really really hurt and I have never had one like that before, I really think it's becasue she went for aside vein thats not been done before.
The anti D I can hoensly say I never felt a thing and it was out as soon as it was in. I have spent since I was 18 weeks worrying about having that injection as well.
I heard the arm can be painful as well thats why I was pleased she said she was going to put it in my bum, only it ended up in my back due to be about to bolt!! LOL
at least your anti d is out of the way, can i ask why you were going to have it in your bum cheek? i thought it was in the arm? i have mine in about 7 weeks, i was really worried, but you say it didnt hurt so thats good. sorry to hear about your bloods being painfukl though, hopefully you wont need anymore taken?
Ashyashy1986 - Well I was told they are mainly done in your bum or leg though I have heard a few girls on here say they had it in the arm. I was told the more fat the better and a few girls said it really hurt in the arm so maybe ask her to go for the bum cheek. I honestly did not feel a thing just her sticking the needle in that was it so you will be just fine honey don't you worry at all ok .
I have got the worst needle phobia ever, and didn't get my first bloods done until 29 weeks whe I found out that I was RH negative, so missed my first dose of anti D. Had mine at 34 weeks in my arm and it stung like hell. I didn't get a choice to have it in my bum or leg Also had to have more bloods done that day cos they lost 2 lots of the first ones I was so angry cos they promised I only had to have one lot done. I had my hypnobithing midwife with me when I had the injection done which helped a little bit, but she wont be there if I have to have another one after the birth and I'm really scared I hated it so much x
I've had both of my anti d injections now. I'm used to needles due to an existing illness but these stung! The needle going in was fine, I never really feel them - it was the liquid that stung.
I might have to have a 3rd injection depending on who's blood the babies have taken. If it's mine, i'll need another one, if it's my oh's I won't! Fingers crossed for them having my partners blood! :lol:
I think i was so worked up that i felt it go in and thats all i felt. I must say she was very good when putting it in but I am not looking forward to having it again afer birth but with what we would have just been through it will be fine |
A lawyer says he will ask the US Supreme Court to overturn the 12-year prison sentence given to an African American man in Mississippi for carrying his mobile phone into a jail cell after he was arrested on a misdemeanour charge.
The Mississippi Supreme Court said on Thursday that it will not reconsider its earlier decision to uphold the sentence of Willie Nash.
More:
Southern Poverty Law Center lawyer Will Bardwell told The Associated Press news agency that an appeal to the nation's high court is his next step.
Critics have slammed the sentence as an example of racial injustice. When the Mississippi Supreme Court initially upheld Nash's sentence in January, nationally syndicated Miami Herald columnist Leonard Pitts wrote that Nash was "the latest victim of a 'just us' system that promiscuously discards black life".
Pitts urged readers to call Mississippi Governor Tate Reeves and tell him to "let my people go".
Within days of the January ruling, Bardwell filed another appeal asking the Mississippi high court to reconsider.
In rejecting the request on Thursday, justices revised a portion of their analysis about previous court decisions on sentencing but did not change the outcome for Nash.
The sentence Nash received in August 2018 for possessing a cellphone in jail is longer than Mississippi courts would impose for second-degree arson or poisoning someone with the intent to kill, Bardwell wrote in his January appeal.
Bardwell also wrote that there was no proof Nash was searched for a cellphone before being booked into jail. The appeal said Mississippi is one of only three states where a 12-year sentence for having a cellphone in jail is even possible, and research found no cases of such a long sentence being given in the other two states - Arkansas and Illinois.
Nash did not seek to overturn his conviction, but argued that the sentence was so grossly disproportionate that it violates the constitutional ban on cruel and unusual punishment.
A 2012 Mississippi law sets a sentencing range of three to 15 years for inmates found with deadly weapons, cellphones or components of cellphones in state jails and prisons.
"Though harsh, Nash's sentence falls within the statutory range," Justice James Maxwell wrote in January.
The only African American justice on Mississippi's nine-member court, Leslie King, joined in the unanimous ruling in January but wrote that the prosecutor and trial judge could have avoided punishing Nash entirely.
Corrections officials have said for years that contraband cellphones are a problem. During an outbreak of violence that left five inmates dead and an undisclosed number of others injured in January, inmates shared cellphone photos and videos that showed prisoners sleeping on the floor of a crowded cell and smoke filling a corridor and cells at the Mississippi State Penitentiary at Parchman. |
Tammy Schneider
Tammy Schneider (born November 12, 1982, in Regina, Saskatchewan) is a Canadian curler from Kronau, Saskatchewan. She currently plays third for her sister, Kim.
Career
Juniors
Schneider grew up in the small village of Kronau, Saskatchewan, outside of Regina. She and her sister and teammate Kim were the daughters of 1990 provincial champion lead Larry Schneider.
In 1998, Schneider won a silver medal at the Saskatchewan Winter Games. Schneider played in three Saskatchewan junior championships, but never won. In 2003, she was invited to play as the alternate for team Canada at the 2003 World Junior Curling Championships. Schneider played in just one match, but the team (skipped by Marliese Miller won a gold medal. In 2004 and 2005 she would play in the University national championships.
2004-2012
After juniors, Schneider played for Cindy Street, playing in the 2004 and 2005 women's provincial championship. For the 2005/06 season Schneider would leave to play with Amber Holland.
In 2008, the team won their only Grand Slam event, the 2008 Players' Championships.
In 2009 the team would earn a spot in the Canadian Olympic Curling Trials, after defeating Marie-France Larouche in the C Qualifier. The team would finish round robin with a 4-3 record, tied for third place. They would lose the second tiebreaker to Krista McCarville in an extra end.
Together the team played in their first Saskatchewan Scotties Tournament of Hearts in 2008 and again in 2009. They would not find success until the 2010 Saskatchewan Scotties Tournament of Hearts, when they would finally break through and represent Saskatchewan at the 2010 Scotties Tournament of Hearts. They would miss the playoffs, finishing with a 6-5 record. The team would repeat as Saskatchewan champions in 2011. At the 2011 Scotties Tournament of Hearts, the team would finish round robin first with a 9-2 and advance to the playoffs. They would lose the 1-2 game to team Canada, before winning the semi-final, over team Ontario. In the final, they would again face team Canada (Jennifer Jones), and this time would come out victorious, stealing the win in the 10th end, winning the Canadian Championship. This was the first time since 1997, that a team from Saskatchewan would win the National Championship. Together the team would win a silver medal at the 2011 Capital One World Women's Curling Championship.
Returning to the Scotties in 2012, the team was looking to repeat and win their second Canadian Championship, however they would finish the tournament with a disappointing 6-5 round robin record, failing to reach the playoffs. This was the first time since 2008, Team Canada did not reach the playoffs.
After seven years of playing with her Canadian Championship winning team, Holland announced that she would leave her squad. Holland told her team she wants to go in another direction. Heather Kalenchuk has since decided to step away from the game for a few years, leaving Tammy and her sister Kim Schneider pondering their curling future. This departure by Holland left the four players ineligible for $72,000 worth of federal funding earned from winning the 2011 Scotties Tournament of Hearts, and they will forfeit their spot earned in the Olympic Curling Pre-Trials.
Personal life
Schneider is an office manager for CCR Construction Ltd.
References
Sources
Extra End Magazine 2009-10, pg 56
Curling runs in the family - Regina Leader-Post
Hollandcurlingteam.com
Canada's Olympic women's candidates - Edmonton Journal
External links
Category:1982 births
Category:Living people
Category:Curlers from Saskatchewan
Category:Sportspeople from Regina, Saskatchewan
Category:Canadian women curlers
Category:Canadian women's curling champions
Category:Canada Cup (curling) participants |
---
abstract: |
In this paper, we formulate and prove linear analogues of results concerning matchings in groups. A matching in a group $G$ is a bijection $\varphi $ between two finite subsets $A,B$ of $G$ with the property, motivated by old questions on symmetric tensors, that $a\varphi (a)\notin A$ for all $a\in A$. Necessary and sufficient conditions on $G$, ensuring the existence of matchings under appropriate hypotheses, are known. Here we consider a similar question in a linear setting. Given a skew field extension $K\subset
L$, where $K$ commutative and central in $L$, we introduce analogous notions of matchings between finite-dimensional $K$-subspaces $A,B$ of $L$, and obtain existence criteria similar to those in the group setting. Our tools mix additive number theory, combinatorics and algebra. The present version corrects a slight gap in the statement of Theorem \[thm:matching property\] of the published version of this paper.
author:
- |
Shalom Eliahou[^1] and Cédric Lecouvey[^2]\
LMPA Joseph Liouville, FR CNRS 2956\
ULCO, B.P. 699, F-62228 Calais cedex\
Univ Lille Nord de France, F-59000 Lille, France
title: 'Matching subspaces in a field extension: an update'
---
**Keywords.** Linear Matchings; Additive combinatorics; Systems of distinct representatives; Hall theorem; Matroids; Free transversals.
Introduction {#matchgroup}
============
Throughout the paper, we shall say *field* for a skew field or division ring, and *commutative field* for a field in which the product is commutative.
Let $G$ be a group, written multiplicatively. Let $A,B \subset G$ be nonempty finite subsets of $G$. A *matching* from $A$ to $B$ is a map $\varphi :A\rightarrow B$ which is bijective and satisfies the condition $$a\varphi(a)\notin A$$ for all $a\in A$. This notion was introduced in [@FanLos] by Fan and Losonczy, who used matchings in $\mathbb{Z}^{n}$ as a tool for studying an old problem of Wakeford concerning canonical forms for symmetric tensors [@Wak]. Obvious necessary conditions for the existence of a matching from $A$ to $B$ are $|A|=|B|$ and $1\notin B$. The group $G$ is said to have the *matching property* if these conditions on $A,B$ suffice to guarantee the existence of a matching from $A$ to $B$. What groups possess the matching property, and when are there automatchings from $B$ to $B$? The following answers were first obtained by Losonczy [@LOs] in the abelian case, and then extended to arbitrary groups in [@EL1].
\[TH\_matchAB\]Let $G$ be group. Then $G$ has the matching property if and only if $G$ is torsion-free or cyclic of prime order.
\[TH\_matchA\]Let $G$ be a group. Let $B$ be a nonempty finite subset of $G$. Then there is a matching from $B$ to $B$ if and only if $1\notin B$.
Theorem \[TH\_matchAB\] and \[TH\_matchA\] were established using methods and tools pertaining to additive number theory and combinatorics. Specifically, the additive tools used are lower bounds on the size of the product set $$AB = \{ab \mid a \in A, \; b \in B\}$$ in $G$, and the main combinatorial tool is Hall’s marriage theorem. See also [@Hamidoune] for more results on matchings in groups.
Now, various additive theorems bounding $|AB|$ have recently been transposed to a linear setting, in the following sense. Given a field extension $K
\subset L$ and finite-dimensional $K$-subspaces $A,B$ of $L$, analogous lower bounds on the dimension of $\langle AB \rangle$ were established, where $\langle AB \rangle$ is the $K$-subspace spanned by the product set $AB
$ in $L$. See [@Xian; @Hou; @EL2; @ELK]. Suitable hypotheses on the extension may be needed, such as commutativity or separability. Two main results in [@EL2], which play a key role here, only require $K$ to be commutative and central in $L$.
The purpose of this paper is to show that Theorem \[TH\_matchAB\] and [TH\_matchA]{} also admit linear analogues in a field extension $K \subset L$. As in [@EL2], we only assume that $K$ is commutative and central in $L$. In Section \[defs\], we introduce a specific notion of matching bases of finite-dimensional subspaces $A,B$ of $L$, and state the main results of the paper, namely Theorem \[thm:matching property\] and \[thm:automatching\]. They are analogous to Theorem \[TH\_matchAB\] and \[TH\_matchA\], and give existence criteria for such matchings. The possibility of matching a given basis of $A$ to some basis of $B$ is reformulated in Section \[dims\], in terms of suitable dimension estimates. In the process, we use a linear version of Hall’s marriage theorem, derived from a more general theorem of Rado on the existence of independent transversals in matroids. Section [linearized]{} presents the linear versions in [@EL2] of results in additive number theory, that will allow us to deal with the required dimension estimates of the preceding section. This is achieved in Section \[proofs\], where Theorem \[thm:matching property\] and [thm:automatching]{} are finally proved. In the last section, we introduce and study a related notion of strong matching between subspaces of $L$.
Definitions and main results {#defs}
============================
Throughout the paper, we shall consider a field extension $K \subset L$, where $K$ is commutative and *central* in $L$, i.e. such that $\lambda x=x\lambda$ for all $\lambda \in K, x \in L$. Let $A,B \subset L$ be finite-dimensional $K$-subspaces of $L$. Ideally, a matching from $A$ to $B$ would be an isomorphism $\varphi : A \rightarrow B$ such that $a\varphi(a)
\notin A$ for all non-zero $a \in A$. However, we need to introduce somewhat subtler requirements in order to obtain existence criteria analogous to those of Theorem \[TH\_matchAB\] and \[TH\_matchA\].
To start with, observe that if $0 \not=a \in A$ and $b \in B$, then $$ab \notin A \; \Longleftrightarrow \; b \notin a^{-1}A \cap B.$$ This motivates the use of the subspace $a^{-1}A \cap B$ of $B$ in the definition of matched bases below.
\[def matched\] Let $A,B$ be $n$-dimensional $K$-subspaces of the field extension $L$. Let $\mathcal{A}= \{a_1,\ldots,a_n\}$, $\mathcal{B}=\{b_1,\ldots,b_n\}$ be bases of $A,B$ respectively. We say that $\mathcal{A}
$ is matched to $\mathcal{B}$ if $$a_i b \in A \; \Longrightarrow \; b \in \langle b_1, \dots, \widehat{b_i},
\dots, b_n \rangle$$ for all $b \in B$ and all $i = 1, \ldots, n$, where $\langle b_1, \dots,
\widehat{b_i}, \dots, b_n \rangle$ is the hyperplane of $B$ spanned by the set $\mathcal{B}\setminus \{b_i\}$; equivalently, if $$\label{match}
a_i^{-1}A \cap B \; \subset \; \langle b_1, \dots, \widehat{b_i}, \dots, b_n
\rangle$$ for all $i = 1, \ldots, n$.
If $\mathcal{A}$ is matched to $\mathcal{B}$ in the above sense, then it follows that $$a_ib_i \notin A,$$ and hence $a_ib_i \notin \mathcal{A}$, for all $i = 1,\dots, n$. In particular, the map $a_i \mapsto b_i$ is a matching, in the group setting sense, from $\mathcal{A}$ to $\mathcal{B}$ within the multiplicative group $L^\ast$.
Moreover, we now show that if $\mathcal{A}$ is matched to $\mathcal{B}$, then $B$ cannot contain 1. This necessary condition exactly mirrors the corresponding one in the group setting.
\[1 notin B\] Let $A,B$ be $n$-dimensional $K$-subspaces of the field extension $L$. If a basis $\mathcal{A}$ of $A$ can be matched to a basis $\mathcal{B}$ of $B$, then $1 \notin B$.
Let $\mathcal{A}=\{a_1,\dots, a_n\}$, $\mathcal{B}=\{b_1,\dots, b_n\}$ be bases of $A,B$ respectively. Assume on the contrary that $1 \in B$. Then we have $$1 \; \in \; \bigcap_{i=1}^n (a_i^{-1}A \cap B).$$ On the other hand, it is clear that $$\bigcap_{i=1}^n \langle b_1, \dots, \widehat{b_i}, \dots, b_n \rangle \; =
\; \{0\}.$$ Therefore, the inclusion $a_i^{-1}A \cap B \,\subset \, \langle b_1, \dots,
\widehat{b_i}, \dots, b_n \rangle$ required in (\[match\]) cannot hold for all $i=1,\ldots, n$, and hence $\mathcal{A}$ cannot be matched to $\mathcal{B}$.
With the notion of matched bases at hand, we now introduce that of matched $K
$-subspaces of $L$.
Let $A,B$ be $n$-dimensional $K$-subspaces in the field extension $L$. We say that $A$ is matched to $B$ if every basis $\mathcal{A}$ of $A$ can be matched to a basis $\mathcal{B}$ of $B$.
By the above lemma, if $A$ is matched to $B$, then $1 \notin B$. Conversely, is the condition $1 \notin B$ sufficient to guarantee that any subspace $A$ of the same dimension as $B$ is matched to $B$? We shall see that the answer depends on properties of the field extension $K \subset L$.
Let $K \subset L$ be a field extension. We say that $L$ has the linear matching property if, for every $n \ge 1$ and every $n$-dimensional subspaces $A,B$ of $L$ with $1 \notin B$, the subspace $A$ is matched to $B$.
We shall prove the following results in Section \[proofs\].
\[thm:matching property\]Let $K\subset L$ be a field extension, with $K$ commutative and central in $L$. Then $L$ has the linear matching property if and only if $L$ contains no proper finite-dimensional extension over $K$.[^3]
Let $L$ be a commutative finite-dimensional Galois extension of the (commutative) field $K$. Then $L$ has the linear matching property if and only if $L$ is an extension of $K$ of prime degree.
In contrast, no special hypothesis on $L$ is needed to guarantee that any $n$-dimensional subspace $B$ avoiding 1 is matched to itself.
\[thm:automatching\] Let $K \subset L$ be a field extension, with $K$ commutative and central in $L$. Let $B$ be a finite-dimensional subspace of $L$. Then $B$ is matched to itself if and only if $1\notin B$.
The proofs of these results involve delicate linearized versions, obtained in [@EL2] and recalled in Section \[linearized\], of classical addition theorems due to Kemperman and Olson.
Dimension criteria for matchable bases {#dims}
======================================
Let $K \subset L$ be a field extension, with $K$ commutative and central in $L$, and let $A,B \subset L$ be $n$-dimensional $K$-subspaces of $L$. In this section, we reformulate the property of a basis $\mathcal{A}$ of $A$ to be matchable to some basis of $B$, in terms of suitable dimension estimates.
\[thm:dim\] Let $\mathcal{A}=\{a_1,\ldots,a_n\}$ be a basis of $A$. Then $\mathcal{A}$ can be matched to a basis of $B$ if and only if, for all $J
\subset \{1,\ldots, n\}$, we have $$\label{eq:dim estimates}
\dim \bigcap_{i \in J} (a_i^{-1}A \cap B) \; \le \; n-|J|.$$
For the proof of this equivalence in Section \[proof thm:dim\], we shall need a linear version of the classical marriage theorem of Hall [@Hall].
Free transversals {#sec:Rado}
-----------------
Let $E$ be a vector space over the field $K$ and let $\mathcal{E}=\{E_{1},E_{2},\dots,E_{n}\}$ be a collection of vector subspaces of $E$. A *free transversal* for $\mathcal{E}$ is a free family of vectors $\{x_{1},\dots ,x_{n}\}$ in $E$ satisfying $x_{i}\in E_{i}$ for all $i=1,\dots,n.$ The following result of Rado [@Rado] gives necessary and sufficient conditions for the existence of a free transversal for $\mathcal{E}$, very similar to those of Hall’s marriage theorem. See also [@Mirsky; @Arocha; @Moshonkin].
\[TH\_Lin8hall\]Let $E$ be a vector space over $K$ and let $\mathcal{E}=\{E_{1},E_{2},\dots,E_{n}\}$ be a family of vector subspaces of $E$. Then $\mathcal{E}$ admits a free transversal if and only if $$\dim\underset{i\in J}{+}E_{i}\geq\left| J\right| \label{LMC}$$ for all $J\subset\{1,\dots,n\}.$
It is not too difficult to prove this result directly, by properly mimicking a proof of its classical counterpart. In the above-mentioned paper of Rado, Theorem \[TH\_Lin8hall\] arises as a particular case of a more general theorem concerning the existence of independent transversals in (possibly infinite) matroids. A finite version would read as follows [@Oxley Chapter 12.2].
\[Rado\] Let $F$ be a finite set, let $\mathcal{F}=\{F_1,\ldots,F_n\}$ be a family of subsets of $F$, and let $M$ be a matroid over $F$ with rank function $r$. Then the family $\mathcal{F}$ admits a transversal which is independent in $M$ if and only if one has $$\label{eq:rado}
r(\bigcup_{i \in J} F_i) \ge |J|$$ for all $J \subset \{1,\ldots,n\}$.
Theorem \[TH\_Lin8hall\] can be derived from Theorem \[Rado\] as follows. For each $1 \le i \le n$, pick a basis $F_i$ of the subspace $E_i$, let $\mathcal{F}=\{F_1,\ldots,F_n\}$, and set $$F = \bigcup_{1 \le i \le n} F_i.$$ As matroid $M$ over $F$, we consider the collection of linearly independent subsets in $F$, with rank function $r$ defined by $$r(S) = \dim_K \langle S \rangle$$ for all subsets $S \subset F$. Here, as earlier, $\langle S \rangle$ denotes the subspace of $E$ spanned by $S$. We now apply Theorem \[Rado\] in this situation. It is clear, from the definition of the rank function $r$, that $$r(\bigcup_{i \in J} F_i) = \dim\underset{i\in J}{+}E_{i}.$$ Thus, conditions (\[LMC\]) and (\[eq:rado\]) are equivalent, and an independent transversal for $\mathcal{F}$ given by Theorem \[Rado\] yields a free transversal for the family $\mathcal{E}$.
Proof of Proposition \[thm:dim\] {#proof thm:dim}
--------------------------------
We shall use the following standard notation. We denote by $$B^{\ast}=\{f:B\rightarrow K\mid f\text{ is linear}\}$$ the *dual* of $B$. Moreover, for any subspace $C\subset B$, we denote by $$C^{\perp}=\{f\in B^{\ast}\mid C\subset\ker f\}$$ the *orthogonal* of $C$ in $B^{\ast}$. Recall that $\dim C^{\perp} =
\dim B - \dim C$.
We now prove Proposition \[thm:dim\], using Theorem \[TH\_Lin8hall\] as a key ingredient.
$\Rightarrow$) Assume first that $\mathcal{A}$ is matched to the basis $\mathcal{B}=\{b_1,\ldots,b_n\}$ of $B$. It follows from condition ([match]{}) that $$a_i^{-1}A \cap B \; \subset \; \langle b_1, \dots, \widehat{b_i}, \dots, b_n
\rangle$$ for all $1 \le i \le n$. This implies, for any $J \subset \{1,\ldots,n\}$, that $$\bigcap_{i \in J} (a_i^{-1}A \cap B) \; \subset \; \bigcap_{i \in J} \langle
b_1, \dots, \widehat{b_i}, \dots, b_n \rangle \; = \; \langle \mathcal{B}
\setminus \{b_i \mid i \in J\} \rangle.$$ It follows that $\dim \bigcap_{i \in J} (a_i^{-1}A \cap B) \; \le \; n - |J|$, as claimed.
$\Leftarrow$) Assume now that, for all $J \subset \{1,\ldots,n\}$, we have $$\dim \bigcap_{i \in J} (a_i^{-1}A \cap B) \; \le \; n-|J|.$$ Taking the orthogonal in the dual space $B^\ast$, we get $$\dim \left(\bigcap_{i \in J} (a_i^{-1}A \cap B)\right)^\perp \; \ge \; |J|,$$ and hence $$\dim \sum_{i \in J} (a_i^{-1}A \cap B)^\perp \; \ge \; |J|.$$ By Theorem \[TH\_Lin8hall\], the linear version of Hall’s theorem, the above dimension bounds imply the existence of a free transversal $$\varphi_1,\ldots,\varphi_n \; \in \; B^\ast$$ for the system of subspaces $\{(a_i^{-1}A \cap B)^\perp\}_{1 \le i \le n}$. In other words, we have $$\label{perp}
\varphi_i \in (a_i^{-1}A \cap B)^\perp$$ for all $1 \le i \le n$, and $\{\varphi_1,\ldots,\varphi_n\}$ is free and hence a basis of $B^\ast$.
Let $\mathcal{B}=\{b_1,\ldots,b_n\}$ be the unique basis of $B$ whose dual basis $\mathcal{B}^\ast$ equals $\{\varphi_1,\ldots,\varphi_n\}$, i.e. such that $b_i^\ast=\varphi_i$ for all $i$. By (\[perp\]), we have $$b_i^\ast \left(a_i^{-1}A \cap B\right) \; = \; \{0\},$$ whence $a_i^{-1}A \cap B \; \subset \; \langle b_1, \dots, \widehat{b_i},
\dots, b_n \rangle$ for all $i$, as desired.
Linear versions of some additive theorems {#linearized}
=========================================
In order to exploit the equivalence given by Proposition \[thm:dim\], we shall need tools to establish the required dimension estimates (\[eq:dim estimates\]). These tools will be conveniently provided by two results in linearized additive number theory, both established in [@EL2].
Our first tool is a linear version of a classical theorem of Kemperman [Kem]{}.
\[th\_AB\]Let $K \subset L$ be a field extension, with $K$ commutative and central in $L$. Let $A,B$ be finite-dimensional $K$-subspaces of $L$ such that $K\subset A\cap B$. Suppose there exist subspaces $\overline{A},\overline{B}\subset L$ such that $$A=K\oplus\overline{A},\text{ }B=K\oplus\overline{B}\text{ and }K\cap (\overline{A}+\overline{B}+\langle\overline{A}\,\overline{B}\rangle )=\{0\}.$$ Then $$\dim\langle AB\rangle\geq\dim A+\dim B-1.$$
For the proof of Theorem \[thm:automatching\] in Section \[proofs:auto\], we shall actually use the following corollary.
\[corKem\] Let $U,V$ be finite-dimensional $K$-subspaces of $L$. Assume that $U$, $V$ and $UV$ are all three contained in a $K$-subspace $X$ of $L$ such that $K\cap X=\{0\}.$ Then $$\dim X\geq\dim U+\dim V.$$
Let $A=K\oplus U$, $B=K\oplus V$. Then $K\cap(U+V+\langle UV \rangle)=\{0\}.
$ Therefore Theorem \[th\_AB\] applies, and gives $$\dim\langle AB\rangle\geq\dim A+\dim B-1.$$ Since $\langle AB\rangle=K\oplus(U+V+\langle UV \rangle)\subset K\oplus X$, this gives $\dim\langle AB\rangle\leq\dim X+1$. With the equalities $\dim
A=\dim U+1$ and $\dim B=\dim V+1$, we then derive $$\dim X\geq\dim\langle AB\rangle-1\geq\dim A+\dim B-2\geq\dim U+\dim V,$$ as desired.
Our second promised tool from [@EL2] is a linear version of a classical theorem of Olson [@Ols]. It will be used in the proof of Theorem [thm:matching property]{} in Section \[proofs:match\].
\[TH-Ol8lin\]Let $K \subset L$ be a field extension, with $K$ commutative and central in $L$. Let $A,B$ be finite-dimensional $K$-subspaces of $L$ distinct from $\{0\}$. Then there exist a $K$-subspace $S$ of $\langle AB\rangle$ and a subfield $M$ of $L$ such that
1. $K\subset M\subset L,$
2. $\dim S\geq\dim A+\dim B-\dim M$,
3. $MS=S$ or $SM=S$.
Proofs of the main results {#proofs}
==========================
Let again $K \subset L$ be a field extension, with $K$ commutative and central in $L$. Let $A,B$ be $n$-dimensional $K$-subspaces of $L$. The above linearized versions of additive theorems will allow us to fulfill, under appropriate circumstances, the dimension estimates required by Proposition \[thm:dim\], and thereby to prove Theorem \[thm:matching property\] and \[thm:automatching\].
Proof of Theorem \[thm:automatching\] {#proofs:auto}
-------------------------------------
\[th-match1\]Let $B$ be a finite-dimensional $K$-subspace of $L$. Then $B
$ is matched to itself if and only if $1\notin B$.
We already know from Lemma \[1 notin B\] that if $B$ contains 1, then $B$ cannot be matched to itself. Conversely, assume $1 \notin B$. Let $\mathcal{A}=\{a_1,\ldots, a_n\}$ be any basis of $B$. For $J \subset \{1,\ldots,n\}$, denote $$V_{J}=\bigcap_{i\in J}(a_i^{-1}B \cap B)=\{x\in B\mid a_i x\in B\text{ for
all }i\in J\}.$$ It follows from Proposition \[thm:dim\] that $\mathcal{A}$ can be matched to another basis of $B$ if and only if $$\label{eq:cond}
\dim V_J \; \le \; n-|J|$$ for all $J \subset \{1,\ldots,n\}$. Denote now $B_J$ the subspace of $B$ spanned by the subset $\{a_i \mid i \in J\}$ of $\mathcal{A}$. Then we have $\dim B_J = |J|$, and $$B_J V_J \subset B$$ by construction. Since $1\notin B$, Corollary \[corKem\] applies, with $U,V,X$ standing for $B_J, V_{J}, B$ respectively. This gives $$\dim B_J +\dim V_{J} \; \leq\; \dim B,$$ i.e. exactly condition (\[eq:cond\]). By Proposition \[thm:dim\], the basis $\mathcal{A}$ can be matched to another basis of $B$. Therefore, the space $B$ is matched to itself.
Proof of Theorem \[thm:matching property\] {#proofs:match}
------------------------------------------
We now turn to the characterization of all field extensions satisfying the linear matching property.
Let $K\subset $ be a field extension, with $K$ commutative and central in $L$. Then $L$ has the linear matching property if and only if $L$ contains no proper finite-dimensional extension over $K$.
Assume first that $L$ is neither purely transcendental nor an extension of prime degree. Then there is an element $a\in L$, of finite degree $n\geq2$ over $K$, such that $K(a)\varsubsetneqq L$. In particular, we have $$K(a)=\langle 1,a,\ldots,a^{n-1} \rangle.$$ Set $A= K(a)$. Let now $x\in L\setminus K(a)$, and set $$B=\langle a,\ldots,a^{n-1},x \rangle.$$ We claim that $A$ is not matched to $B$. Indeed, consider the basis $\mathcal{A}=\{1,a,\ldots,a^{n-1}\}$ of $A$. Since $A=K(a)$ is a subfield of $L,$ we have $$a_{i}^{-1}A\cap B=A\cap B=\langle a,\ldots,a^{n-1} \rangle$$ for all $1 \le i \le n$. Therefore, the condition $\dim \bigcap_{i \in J}
(a_i^{-1}A \cap B) \; \le \; n-|J|$ of Proposition \[thm:dim\] does not hold for $J = \{1,\ldots,n\}$, for instance. It follows that $\mathcal{A}$ cannot be matched to a basis of $B$.
Conversely, assume that the only finite-dimensional subfields of $L$ extending $K$ are $K$, and $L$ itself if it is finite-dimensional over $K$. The field $L=K$ contains no proper intermediate extension and vacuously satisfies the linear matching property. Assume now $L\neq K$. Let $A,B$ be $n
$-dimensional $K$-subspaces of $L$ with $1\notin B$. Let $\mathcal{A}=\{a_{1},\ldots ,a_{n}\}$ be any basis of $A$. For any $J\subset \{1,\ldots
,n\}$, denote $$V_{J}=\bigcap_{i\in J}(a_{i}^{-1}A\cap B)=\{x\in B\mid a_{i}x\in A\text{ for
all }i\in J\}.$$By Proposition \[thm:dim\] again, we know that $\mathcal{A}$ can be matched to a basis of $B$ if and only if $$\dim V_{J}\;\leq \;n-|J| \label{eq:cond2}$$for all $J\subset \{1,\ldots ,n\}$. As earlier, denote $A_{J}$ the subspace of $A$ spanned by the subset $\{a_{i}\mid i\in J\}$ of $\mathcal{A}$. Then we have $\dim A_{J}=|J|$, and $$A_{J}V_{J}\subset A.$$Set $W_{J}=K\oplus V_{J}$. We have $\dim W_{J}=\dim V_{J}+1$, and still $A_{J}W_{J}\subset A$ by construction. By Theorem \[TH-Ol8lin\], applied to the subspaces $A_{J}$ and $W_{J}$, there is an intermediate field extension $K\subset M\subset L$ and a subspace $T\subset \langle A_{J}W_{J}\rangle $ such that $$\dim \langle A_{J}W_{J}\rangle \geq \dim A_{J}+\dim W_{J}-\dim M,
\label{Hall5}$$and $MT=T$ or $TM=T$. We cannot have $M=L$, for otherwise $T=L$; but as $T\subset A_{J}W_{J}\subset A$, this would imply $A=L=B$, contradicting the hypothesis $1\notin B$. It follows that $M=K$, and inequality (\[Hall5\]) yields $$\dim A\geq |J|+\dim V_{J},$$since $\langle A_{J}W_{J}\rangle \subset A$, $\dim W_{J}=\dim V_{J}+1$ and $\dim M=1$. Therefore conditions (\[eq:cond2\]) are satisfied, implying that $\mathcal{A}$ can be matched to a basis of $B$. It follows that $L$ has the linear matching property.
Let $L$ be a commutative finite-dimensional Galois extension of the (commutative) field $K$. Then $L$ has the linear matching property if and only if $L$ is an extension of $K$ of prime degree.
Indeed, for a Galois extension of degree $n$, the intermediate extensions are in reversing bijection with the subgroups of the Galois group $G$ of order $n$. Thus, if $n$ is not a prime number, then $G$ will have proper subgroups $\{1\} \not= H \not= G$, thereby yielding proper intermediate extensions $L \supsetneq M \supsetneq K$.
\[Rem\_Gap\] For any non-prime integer $n>1$, there exists a field extension $K \subset L$ of characteristic $0$ and degree $n$ admitting no proper intermediate extension. It can be constructed as follows. Take $L=k(X_{1},\ldots ,X_{n})$ the field of rational functions in the commutative variables $X_{1},\ldots ,X_{n}$ over an arbitrary field $k$ of characteristic $0$. Set $S=L^{S_{n}}$ the subfield of $L$ of rational symmetric functions. The field $L$ can be regarded as the decomposition field of the polynomial$$P(T)=\prod_{i=1}^{n}(T-X_{i})\in S[T].$$Therefore $L$ is a normal extension of $S$. Since $L$ is of characteristic $0$, it is a Galois extension of $S$. Its Galois group is $S_{n}$ so $L$ has degree $n!$ over $S$. The subgroup $S_{n-1}\subset
S_{n}$ is maximal. Therefore, if we set $K=L^{S_{n-1}}$, the invariant subfield under the group $S_{n-1}$, then $L$ is an extension of $K$ of degree $n$ with no proper intermediate extension.
A refinement
------------
Even if the extension $K \subset L$ does not satisfy the linear matching property, it is still possible to match some subspaces $A,B$ of $L$ under suitable circumstances. Let $n_0(K,L)$ denote the smallest degree of an intermediate field extension $K \subsetneq M \subset L$. Thus $n_0(K,L) \ge 2
$, and $n_0(K,L) = \infty$ if the extension is purely transcendental. Slightly adapting the proof of Theorem \[thm:matching property\] yields the following result.
\[refin\] Let $K \subset L$ be a field extension, with $K$ commutative and central in $L$. Let $A,B \subset L$ be $n$-dimensional subspaces of $L$, with $1 \notin B$ and $n < n_0(K,L)$. Then $A$ is matched to $B$.
Let $\mathcal{A}=\{a_1,\ldots, a_n\}$ be any basis of $A$. We proceed as in the proof of Theorem \[thm:matching property\], and use the same notation $V_J, A_J, W_J=K\oplus V_{J}$ for $J \subset \{1,\ldots,n\}$. In order to ensure that $\mathcal{A}$ can be matched to a basis of $B$, it suffices to check the condition $$\label{eq:cond3}
\dim V_J \; \le \; n-|J|$$ for all $J \subset \{1,\ldots,n\}$. We have $A_J W_J \subset A$. By Theorem \[TH-Ol8lin\] applied to $A_J$ and $W_J$, there is an intermediate field extension $K\subset M \subset L$ and a subspace $T\subset \langle A_J W_J
\rangle$ such that $$\label{Hall6}
\dim \langle A_J W_J \rangle \ge \dim A_J+\dim W_{J}-\dim M,$$ and $MT=T$ or $TM=T$. This means that $T$ is either a left of a right $M$-module, whence $\dim M$ divides $\dim T$. But since $T \subset \langle A_J
W_J \rangle \subset A$, it follows that $\dim M \le n$. Now, our assumption $n < n_0(K,L)$ implies $M = K$. Therefore, inequality (\[Hall6\]) yields $$\dim A\geq|J|+\dim V_{J},$$ since $\langle A_JW_{J}\rangle\subset A$, $\dim A_J = |J|$, $\dim W_{J}=\dim
V_{J}+1$ and $\dim M=1$. Thus (\[eq:cond3\]) is satisfied, implying that $\mathcal{A}$ can be matched to a basis of $B$.
Strong matchings
================
Here we turn to a related, but much stronger notion of matching between subspaces. An existence criterion for such matchings is much easier to establish, as we do now, independently of the preceding results.
Let $K\subset L$ be a field extension, and let $A,B$ be finite-dimensional $K
$-subspaces of $L$ distinct from $\{0\}$.
A strong matching from $A$ to $B$ is a linear isomorphism $\varphi:A\rightarrow B$ such that any basis $\mathcal{A}$ of $A$ is matched to the basis $\varphi(\mathcal{A})$ of $B$, in the sense of Definition [def matched]{}.
We start with an easy equivalent reformulation of this notion, and then proceed with the promised existence criterion for strong matchings.
\[Lem\_strongmatch\]Let $\varphi:A\rightarrow B$ be an isomorphism of $K$-vector spaces. The following two statements are equivalent.
1. The map $\varphi$ is a strong matching from $A$ to $B.$
2. For any $0 \not=a\in A$ and any subspace $H\subset A$ such that $A=\langle a \rangle\oplus H,$ we have $a^{-1}A \cap B\subset\varphi(H).$
Assume $\varphi$ is a strong matching. Let $0 \not=a\in A$, and let $H\subset A$ be any $K$-subspace such that $A=\langle a \rangle\oplus H.$ Let $\{a_{2},\ldots,a_{n}\}$ be any basis of $H.$ Then $\mathcal{A}=\{a,a_{2},\ldots,a_{n}\}$ is a basis of $A.$ Hence $\mathcal{A}$ is matched to $\varphi (\mathcal{A})=\{\varphi(a),\varphi(a_{2}),\ldots,\varphi(a_{n})\}.$ This implies that $a^{-1}A \cap B$ is a subspace of $\langle
\varphi(a_2), \ldots, \varphi(a_n) \rangle=\varphi(H).$
Conversely, assume statement 2 holds. Let $\mathcal{A}=\{a_{1},a_{2},\ldots,a_{n}\}$ be a basis of $A$. For any $i=1,\ldots,n,$ set $H_{i}=\langle a_1,\ldots, \widehat{a_i},\ldots, a_n \rangle$. Then we must have $a_{i}^{-1}A \cap B\subset\langle \varphi(a_1),\ldots, \widehat{\varphi(a_i)},\ldots, \varphi(a_n) \rangle$. This proves that the basis $\mathcal{A}$ is matched to $\varphi (\mathcal{A)}$. Hence, the map $\varphi$ is a strong matching from $A$ to $B$.
Let $K\subset L$ be a field extension. Let $A,B$ be $n$-dimensional $K$-subspaces of $L$ distinct from $\{0\}$. There is a strong matching from $A$ to $B$ if and only if $AB\cap A=\{0\}.$ In this case, any isomorphism $\varphi:A\rightarrow B$ is a strong matching.
Assume $\varphi: A \rightarrow B$ is a strong matching. By Lemma [Lem\_strongmatch]{}, we obtain for any $0 \not= a\in A$: $$a^{-1}A \cap B \; \subset\; {\bigcap\limits_{H}} \varphi(H)\; =\;
\varphi\left({\bigcap\limits_{H}}\, H \right),$$ where $H$ ranges over all subspaces of $A$ such that $A=\langle a
\rangle\oplus H$. But of course, the intersection of all such subspaces $H$ is reduced to $\{0\}$. Hence, we have $a^{-1}A \cap B=\{0\}$ for any $0
\not=a\in A$. This means that $AB\cap A=\{0\}.$
Conversely, assume $AB\cap A=\{0\}$, and let $\varphi:A\rightarrow B$ be any isomorphism. Then, for all $0 \not= a \in A$, we have $a^{-1}A \cap B=\{0\}$, whence $a^{-1}A \cap B \subset \varphi(H)$ for any subspace $H \subset A$. It follows from Lemma \[Lem\_strongmatch\] that $\varphi$ is a strong matching from $A$ to $B$, as claimed.
**Acknowledgement.** We are most grateful to Professors Akbari and Aliabadi for having pointed out to us the now corrected gap in our published version of Theorem \[thm:matching property\].
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[^1]: eliahou@lmpa.univ-littoral.fr
[^2]: lecouvey@lmpa.univ-littoral.fr
[^3]: Our original statement of Theorem \[thm:matching property\] in the published version of this paper \[Journal of Algebra 324 (2010) 3420-3430\] was incorrect, as pointed out to us by Professors Akbari and Aliabadi. It mistakenly stated that the linear matching property was equivalent to $L$ being either transcendental or an extension of prime degree over $K$, thereby missing all finite-dimensional extensions of non-prime degree having no proper intermediate extensions. (See Remark \[Rem\_Gap\]).
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Tuesday, June 14, 2011
Read this and after you are finished screaming obscenities, please read my comments.
Anti-Gay Bigots: Homos Are Bullying Us!
This takes the damn ass fucking cake, but it's no surprise to those of us on Twitter.
As the gay-rights movement advances, there's increasing evidence of an intriguing role reversal: Today, it's the conservative opponents of that movement who seem eager to depict themselves as victims of intolerance. To them, the gay-rights lobby has morphed into a relentless bully — pressuring companies and law firms into policy reversals, making it taboo in some circumstances to express opposition to same-sex marriage. "They're advocating for a lot of changes in the name of tolerance," said Jim Campbell, an attorney with the conservative Alliance Defense Fund. "Yet ironically the tolerance is not returned, for people of faith who don't agree with their agenda." Many gay activists, recalling their movement's past struggles and mindful of remaining bias, consider such protestations by their foes to be hollow and hypocritical.
Not agreeing over equal marriage is one thing. What these people are doing is quiet an other.
First I want to remind you that they are Hate Groups for repeatedly spreading known misinformation and out right lies against the LGBT population.
They use derogatory language at every turn. They rely on discredited "facts" and studies that are manipulated to fit their agenda. Several of the writers of these studies that they twist are coming forward to protest how the Hate Groups are using their findings.
They compare being gay with so many horrible things that I can't bear to write them. You all know what they are.
They blame us for everything under the sun that goes wrong, from the economy to natural disasters.
They say that homosexuals are worse than terrorists and should die. That homosexuals have no Family Values and want to make all their children homosexuals too. If homosexuals are allowed to marry, our kindergartners will be taught about homosexual sex. Homosexuals hate christians. Homosexuals hate God! Bullying is wrong...unless you want to tell a homosexual they are going to hell.
Got the picture?
Now you can lie all you want out here but you can not lie in court. The anti-marriage defence is lame at best and the courts keep finding in favor of fairness to all.
They are scared. They know they will loose. They will do or say anything to win including waving the religion card. The FACT that the Catholic church is dumping money into the "war" and every board member is catholic may have something to do with that. The Fact that they are fighting about disclosure of funding in several states raises some good questions.
Homosexuals are taking away your freedom of religion. You will not be able to spread the word that God hates homosexuals. Homosexuals want to take away your rights.
Now they are the victims?
I think the fact that the Supreme Court allows for Phelps and the WBC to continue to do their thing is proof that religious freedom is just fine. The only thing that will change is " If you receive public funds, you can not discriminate against the public." They can discriminate all they want as long as it is with their own money.
That we are "making it taboo in some circumstances to express opposition to same-sex marriage." That is not true. They can say what they want in their homes and house of worship. They can stand on the street corner and public protests.
There is no change in their freedom of speech or religion.
These Hate Groups want people to believe that exposing their lies, exposing their twisted "facts", exposing their hate toward gays, and proving that we are NOT all those nasty things is bullying.
Lama Surya Das, who contributed to the script of the Journey Into Buddhism films,
has written this brilliant new book. It is deeply wise and elegantly practical, and has the remarkable
quality of giving you both greater amounts of time and timelessness. A gift for anyone.
.
Lama Surya Das, who contributed to the script of the Journey Into Buddhism films,
has written this brilliant new book. It is deeply wise and elegantly practical, and has the remarkable
quality of giving you both greater amounts of time and timelessness. A gift for anyone.
“From early morning to late at night, from preschool to retirement, we rush through our lives in order to scrimp on time. But what if time did not control us? What if we felt that our time and our lives were our own? —
From Buddha Standard Time
HarperOne, an imprint of HarperCollins Publisher
May 2011 | Hardcover |$25.99 | ISBN: 9780061774560
Discover the Power of Living Fully in the Now
BUDDHA STANDARD TIME
Awakening to the Infinite Possibilities of Now
By Lama Surya Das
National Bestselling Author of Awakening the Buddha Within
Life in the 21st century moves at break-neck speed. Yet despite our slavish dependency on instant coffee, express buses, ATMs, and 140 character tweets, we’re all strapped for time and desperately wish for more hours in the day. What if someone had a solution for how busy and stressed out we’ve all become?
Now in BUDDHA STANDARD TIME: Awakening to the Infinite Possibilities of Now, Lama Surya Das, national bestselling author and one of the foremost Western Buddhist teachers, offers an alternative to the ceaseless hustle and bustle of modern American life.
The problem begins, Surya Das says, with our relationship to time—we experience it linearly by moving forward doing and accomplishing things. But we are human beings not human doings, and the thinner we spread ourselves the more disconnected we become. That leaves us vulnerable to high blood pressure, heart attacks, stroke, insomnia, digestive ailments, and depression. We must eschew the notion that stress will melt away if only we could adapt to the frenetic pace of life. Instead the aim is to experience the Eternal Now, or what Surya Das calls “Buddha Standard Time”— the realm of timelessness where every choice, every action, and every breath can be one of renewal and infinite possibilities.
With “Mindful Moments” exercises and “Time Out” meditations, Surya Das equips readers with tools to cure the “disease to please,” kick addictions, reconnect with nature, and gracefully embrace loss, sickness, and death. When we incorporate Buddha Standard Time, stress melts away, and we find greater focus, fulfillment, creativity and even wisdom. Buddhists and non-Buddhists alike will find inner peace and live more sanely and joyously by realizing we have all the time in the world.
“This book is Lama Surya Das in his most tone-perfect Western guru voice: authoritative, inviting, generous, funny, poetic, imaginative and informative and totally accessible. For newcomers to Buddhism (and non-Buddhists interested in universal wisdom!) and ‘old hands’ at practice, this is a delightful read. It promises nothing less than a liberated life, freed from the angst over the tyranny of time, though the practice of loving presence. The ‘To Do’ sections are remarkable interesting and inspiring.” — Sylvia Boorstein, author of Happiness Is An Inside Job
“Lama Surya Das is one of our best teachers of universal wisdom. Buddha Standard Time is fairly dripping with insights. It’s like a treasure to keep near you at all times.”
— Marianne Williamson, author of The Age of Miracles
“Buddha Standard Time is a welcome antidote to the often frenetic pace of modern life. Drawing from the broad scope of his poetic, social and scientific interests, as well as the great depth of his Buddhist training, Lama Surya Das offers a wise and sane way to navigate these times. This pragmatic book will be illuminating and helpful for anyone wishing to find the timeless amidst the rush of time.”
— Joseph Goldstein, author of One Dharma and A Heart Full of Peace
“A wealth of inspiration and practical tips for enjoying the Kingdom of God, the Pure Land of the Buddha, *now*.” — Bestselling author Thich Nhat Hanh
ABOUT THE AUTHOR
Lama Surya Das is the national bestselling author of Awakening the Buddha Within and Buddha Is As Buddha Does. A renowned Western Buddhist meditation teacher and scholar, he teaches and lectures around the world, conducting dozens of meditation retreats and workshops each year. Based on his relationship with His Holiness the Dalai Lama, Surya Das founded the Western Buddhist Teachers Network and has organized three week-long conferences of Western Buddhist Meditation Teachers with the Dalai Lama in Dharamsala, India. He also teaches regularly at Esalen, Open Center, Omega Institute, Interface, at universities in the United States and abroad.
Earlier this week I reported that the Archdiocese of Boston had moved to cancel a planned "All Are Welcome" Catholic mass in honor of gay Pride. Yesterday the Boston Globe reported that the local priest behind the idea is standing up to his bosses.
Sunday Mass at St. Cecilia’s Church in the Back Bay brought the first standing ovation any parishioner could remember. During the first Mass since the Archdiocese of Boston canceled one planned for next weekend in support of St. Cecilia’s gay and lesbian churchgoers, the Rev. John J. Unni preached a fiery message of unconditional love and what he called “acceptance of all." “You are welcome here, gay or straight, rich or poor, young or old, black or white,’’ Unni said as he paced up and down the center aisle. “Here, you all can say, ‘I can worship the God who made me as I am.’" Unni finished his homilies at the 9:30 a.m. and 11 a.m. Masses to thunderous applause.
The "All Are Welcome" special mass remains canceled, but members of the Rainbow Ministry will gather on the sidewalk outside the church next Sunday.
"If Tracy Morgan is truly sorry for what he has done, then he should make the effort to learn the damage that is caused by homophobic parents and help to educate others about the terrible harm caused by parental rejection. He heard the crowd cheering him on. What if one of them has an LGBT child? I would advocate that his employer, NBC, join in this effort. Their power to reach millions is obvious. There is no more valuable effort that can be done for LGBT youth than to work to help them be loved and protected in their own homes." - Ali Forney Center executive director Carl Siciliano, writing for the Huffington Post.
RELATED: Morgan has agreed to meet with Siciliano and GLAAD.
During a call with GLAAD President Jarrett Barrios and members of GLAAD’s staff today, Morgan committed to meet this week in New York City with LGBT youth from the Ali Forney Center who have been hurt or left homeless by parental rejection as well as family members who have lost children to anti-gay violence. Those he will meet include Elke Kennedy, the founder of Sean’s Last Wish. Elke’s son Sean was killed by anti-gay violence in 2007 at the age of 20 in South Carolina, when another man called him a f*ggot and punched him so hard it broke his facial bones and separated his brain from his brain stem. Since that day, Elke has traveled more than 140,000 miles to speak in states across the country about hate violence and bullying. Morgan also committed to participate in GLAAD’s upcoming ‘Amplify Your Voice’ PSA campaign to combat anti-LGBT bullying.
Last year Seattle's iconic Space Needle flew the rainbow flag in recognition of gay Pride. But officials at the landmark said earlier this month that they would not be repeating the honor this year. That may change.
In response to a ground swell of support requesting the Rainbow Flag being raised again on Seattle Pride Weekend, the Space Needle has issued an exciting new fundraising challenge. If the community can raise $50,000 for 4 local charities, the Space Needle will raise the Rainbow Flag on Sunday of Seattle Pride weekend in Seattle. The Space Needle will also kick off the challenge with an inaugural donation of $5000.00.
The four beneficiaries of the campaign: Greater Seattle Business Association (GSBA) Scholarship Program, Lambda Legal, It Gets Better for the Trevor Project and Mary's Place. Contribute here.
The U.S. Bankruptcy Court for the Central District of California has declared DOMA to be unconstitutional. The ruling arises from a case in which a married gay couple was denied the right to jointly declare bankruptcy. Chris Geidner at Metro Weekly provides the court's money quote:
This case is about equality, regardless of gender or sexual orientation, for two people who filed for protection under Title 11 of the United States Code (Bankruptcy Code). Like many struggling families during these difficult economic times, Gene Balas and Carlos Morales (Debtors), filed a joint chapter 13 petition on February 24, 2011. Although the Debtors were legally married to each other in California on August 20, 2008, and remain married today, the United States Trustee (sometimes referred to simply as “trustee”) moved to dismiss this case pursuant to Bankruptcy Code § 1307(c) (Motion to Dismiss), asserting that the Debtors are ineligible to file a joint petition based on Bankruptcy Code § 302(a) because the Debtors are two males.
A coalition of LGBT groups including GetEQUAL and Truth Wins Out is demanding an apology from the Southern Baptists Convention. Q Notes has the press release:
“We call on the Southern Baptist Convention to stop misusing the Bible to promote religion-based bigotry and start recognizing the enormous pain and suffering caused by its mistreatment of LGBT people, particularly vulnerable youth,” said Dr. Jack McKinney, a former Southern Baptist minister and spokesperson for Faith in America. “History has not been kind to the Southern Baptist Convention’s record on minorities, and it is making the same awful mistake today by perpetuating abuse against gay people.”
“The anti-gay teachings of the Southern Baptist church nearly led me to suicide,” said Dr. Jerry Stephenson, a former Southern Baptist minister and board member for Truth Wins Out. “I entered an ‘ex-gay’ ministry that falsely claimed I could change my sexual orientation and this led to a deep depression. Only after I accepted my true self was I able to reconcile my faith and sexual orientation. The Southern Baptist Convention needs to apologize because its policies are hurting real people.” This petition drive is being organized by the Association of Welcoming and Affirming Baptists, Believe OutLoud, Faith in America, GetEQUAL, Soulforce and Truth Wins Out.
Later today, at noon ET/9 AM PT, a federal judge in San Francisco will hear motion to overturn the Prop. 8 case because Judge Walker has a boyfriend. It's another pathetic, last-ditch effort by the increasingly desperate haters to thwart equality. Ted Olson and David Boies will be in the court room defending the Prop. 8 decision. We're still waiting for the California Supreme Court to answer the standing question (there's a hearing in September) before we get a decision from the Ninth Circuit. Yeah, it's procedurally complicated. But, the ultimate goal is a win for equality in the U.S. Supreme Court.
According to the NY Times, the federal case involving Prop. 8 is preventing movement on a 2012 marriage referendum in California.
But with a pending federal court case showing promise and major donors reluctant to step forward, it is unlikely that California voters will revisit same-sex marriage anytime soon.
“I’m not aware of a single donor who would support a ballot measure campaign,” said Chad Griffin, the co-founder and board president of the American Foundation for Equal Rights. “A ballot would be unwise, foolish and, in fact, dangerous.”
That danger, according to several leaders in the gay community, comes from the potential impact that a failed effort in 2012 could have on the federal case, which was brought in 2009 by Mr. Griffin’s group. Mr. Griffin, an experienced fund-raiser, hired the high-powered legal team of David Boies and Theodore B. Olson to pursue a constitutional challenge to the law, and last August, a federal judge — Vaughn R. Walker of the Federal District Court for the Northern District of California — sided with opponents of Proposition 8, finding that the voter-approved law violated constitutional guarantees of equal protection and due process.
But the legal machinations continue on several fronts: Judge Walker’s decision has been appealed to the United States Court of Appeals for the Ninth Circuit, and on Monday, there will be a hearing before another district court judge regarding a motion to vacate Judge Walker’s decision because of his sexual orientation. (Judge Walker, who retired in February, is gay.)
Regardless of how the lower courts rule, most legal analysts believe the Boies-Olson case will eventually be decided by the United States Supreme Court. No one seems to want anything to happen outside the courtroom to prejudice judges at any level.
I agree with that strategy. We've already got one referendum on the ballot in Minnesota. I'd rather take my chances with Olson and Boies than go the voters again. We know that public opinion is increasingly on our side. But, I don't think we need the risk right now. It would be a very, very, very expensive gamble -- and too risky, as far as I'm concerned.
Today, I'm at the Federal Court Building in San Francisco, to watch the hearing on the Prop. 8 proponents motion to vacate Judge Walker's decision -- because Judge Walker has a boyfriend. The first part of the hearing related to a motion by the Prop. 8 side to order a return of the trial tapes. They really don't want anyone to see the actual testimony. Judge Ware, who has taken over Judge Walker's case load, said he will probably deny the motion to order return of tapes.
The hearing then moved on to the motion to vacate. Charles Cooper from the Prop. 8 defendant/intervenors began by trying to define what kind of interest required recusal by a federal judge. He wanted to link the pecuniary interest to other non-pecuniary interests.
Cooper then got into the meat of his argument. He cited the plaintiffs' brief, noting how it read that "at the heart" of the plaintiffs claim is that they are similarly situated to opposite-sex couples in wanting to get married. According to Cooper, "it now appears Judge Walker..occupied those same shoes as the plaintiffs." Cooper said that Walker "was similarly situated to the plaintiffs." That's because he was in a "long-term, committed relationship."
Judge Ware maintained that the plaintiffs wanted to change their relationship to be allowed to marry. He repeatedly asked Cooper for evidence that Walker wanted to change his relationship. There is none. But, Cooper apparently thinks the very fact that Walker didn't disclose his relationship is evidence enough.
Throughout his time, Cooper made it clear that this motion to vacate revolves around the fact that Walker has a boyfriend. To that Ware said, "Long-term relationship is your marker for wanting to marry." But Cooper also argued that if Walker had no interest in marrying his partner, he would have to disclose that too.
I'm livetweeting here. During the break, I ran into AFER's Board Chair Chad Griffin and the organization's Senior Project Director, Adam Umhoefer. AFER is livetweeting here. Courage Campaign's Rick Jacobs is also at the Court House. He's is liveblogging here.
Our side's lawyer, Theodore Boutrous Jr., just started after the break. First line is that this motion is frivolous and offensive. Yep.
As I wrote earlier, I was at the Federal Court House in San Francisco today to watch the hearing on the anti-gay side's motion to vacate the Prop. 8 ruling because of Judge Walker's status as a gay man. There was also a hearing on whether the parties had to return the tapes of the trial. Looks like the Judge already decided not to ask for their return.
The lawyer for the Prop. 8 proponents, Charles Cooper, tried really hard to make his case. He couldn't. As in the Prop. 8 trial, there were no facts to back up his assertions. It was really astounding. Cooper kept saying their motion was about disclosure. It was not. It's about blatant homophobia.
The lawyer for the Prop. 8 proponents, Theodore Boutrous, Jr., was excellent. Olson and Boies get a lot of the attention for this case, but the whole legal team is filled with superstars. I watched him at the press conference following the hearing, too. He said of the other side, "Their claims in support of Proposition 8 are baseless. They had no evidence. That's why they filed this motion. This was a desperate, Hail Mary pass they are throwing because they think they are going to lose. And, they should lose." He also said in court and at the presser several times that this motion is "frivolous." It was. Lawyers get sanctioned for filing those kinds of motions, but Boutrous and his colleagues declined to file a complaint.
Judge Ware told the lawyers that he'd be issuing a written decision within 24 hours.
And, I had a chance to talk to two of the plaintiffs, Paul Katami and Jeff Zarrillo, after the hearing to get their thoughts:
I also met the other two plaintiffs, Kristin Perry and Sandra Stier. I thanked all of them for putting themselves on the line for the rest of us. And, also let them know that there's enormous interest in their case outside of California, too. |
Anointing the Sick
Anointing of the sick may take place wherever it is needed: at home, in the hospital, or before or after the worship service.
Depending on the wishes of the person being anointed, an anointing ceremony may involve only one officiant, or it might include several members of the congregation. Where members of the opposite sex are involved, it is mandatory that at least three people be present.
A brief prayer might precede the anointing, thanking God for his grace and love and for hearing the prayers of his people in their need.
The officiant should then lay his or her hands on the sick person’s head or shoulders, or simply hold the person’s hand, and pray for healing.
The sick person may then be anointed with oil (preferably olive oil) by dipping a finger or thumb in the oil and applying it to the person’s forehead while saying words to the effect of: “We anoint you for healing in the name of the Father, and of the Son, and of the Holy Spirit. Amen.”
Sample prayer:
Our Father, we pray on behalf of [name of sick person] that you will in your mercy and power do what is right and good in his/her life. In the bond of the Holy Spirit, who ministers to us your love, and in union and communion with Jesus Christ, your beloved Son, we pray as one that [name of person being anointed] would be made whole now, as we know that he/she will be made whole in the life to come. We pray in Jesus’ name. Amen. |
Hоw to Kill Black Mоld
Not learning how to find, prevent and kill black mold саn bе a vеrу serious рrоblеm in most households. It is еvеn regarded as a роtеntiаl hеаlth hаzаrd. Nevertheless, thеrе аrе ѕignѕ that саn help уоu сhесk if уоur hоmе iѕ bеing invaded by blасk mold. |
My goal by the time i'm 18 is to make it into a DII college for tennis. I have a 3.6GPA and am currently a junior in highschool. I started playing tennis when I was 10 and I recently got rated a 4.0 from my coach (USTA certified). Anyway, would a solid 4.5 NTRP player be good enough to make into a DII tennis school if I kept my grades up?
I mean I want to be realistic, and I know that getting to the 5.0 or 5.5 level is very slim for me. However, I do think a solid 4.5 is not out of the question by the time im 18. I am almost 16 years old and have 2 more years of highschool. I know that I'm not blessed with crazy talent like some other players, but I'm a fit/athletic guy. Oh and if this helps, I am in the top 110 for juniors ranked 16- in Colorad (hopefully will break into top 100 soon)
If anyone knows any youtube videos that show DII college players playing please post them, and please any input regarding how good you have to be to make into a DII school would be appreciated. I mean I guess if I have to play DIII then that's fine, but I want to try to make into a DII school first
Easy 5.0 for you...you're 6'2" and growing, play tennis 5 days a week, have the general strokes and temperament to improve, and is athletic already and trained in other sports too.
Just depends whether you need to be numero uno, or can settle for just making the team. Luck is a big part of that draw. Luck as in exactly how good you get, how good the other player's are, how much you're involved with your G/F, how your body holds up, and how much you stay interested in playing serious tennis. And whether your car holds up, or you can afford to play tennis.
As a short, old fart, easy for me to make Div111 singles top 3 for CityCollege of SanFrancisco, SanFranciscoState, DiabloValleyJC, or Laney around here after 3 years of tennis. Your younger, stronger, better trained, taller, possibly as athletic, and only YOU can hold yourself back.
Is there any reason you don't think you could become a 5.0 in a little over 2 years? I don't wan't to make it sound like it's easy to become a 5.0 because it's not but if you are playing at 4.0 at 15 with a lot of hard work and good instuction it's not out of the realm of possibility. The chance is as slim or as likely as the effort you put into it. I encourage you to keep training and set your goals high both in your education and in tennis.
My goal by the time i'm 18 is to make it into a DII college for tennis. I have a 3.6GPA and am currently a junior in highschool. I started playing tennis when I was 10 and I recently got rated a 4.0 from my coach (USTA certified). Anyway, would a solid 4.5 NTRP player be good enough to make into a DII tennis school if I kept my grades up?
There are so many of these threads. Take the time to search a bit. The bottom line, there is no real answer to this question. Doesn't matter the division...there is a huge range of players in each division. There are D-I schools who are much weaker than many D-III schools, consequently the players are much weaker.
There's certainly no formula related to USTA ratings, especially since most colleges don't give a crap about these ratings; they care about rankings. I know of a D-II team that was absolutely horrible last year - their #1 player was about #35 sectionally in a fairly weak section. Their #s 5 and 6 were basically beginners. Other D-II teams I watched had players that could easily play for some of the better D-I teams.
If you really want to play tennis and you're willing to do the research to find the right fit, you can play. It may not be at a school you've ever thought about or even have ever heard of.
Send e-mails/letters to coaches - not to one or two, but to lots (hundreds) of coaches. Visit college websites and fill out recruiting forms - again, not one or two but dozens or even hundreds. Perhaps you'll get a bite and perhaps you'll find the perfect fit.
Easy 5.0 for you...you're 6'2" and growing, play tennis 5 days a week, have the general strokes and temperament to improve, and is athletic already and trained in other sports too.
Just depends whether you need to be numero uno, or can settle for just making the team. Luck is a big part of that draw. Luck as in exactly how good you get, how good the other player's are, how much you're involved with your G/F, how your body holds up, and how much you stay interested in playing serious tennis. And whether your car holds up, or you can afford to play tennis.
As a short, old fart, easy for me to make Div111 singles top 3 for CityCollege of SanFrancisco, SanFranciscoState, DiabloValleyJC, or Laney around here after 3 years of tennis. Your younger, stronger, better trained, taller, possibly as athletic, and only YOU can hold yourself back.
Thanks LeeD. Yeah I'm playing 6 times a week and I have lessons ever once in a while.Im not sure maybe its too early to be thinking of this stuff, maybe when I'm 16-17 ill have a better idea. thanks for the encouragement though, I hope I can make it to a 5.0. I mean I just want to set a realistic goal. I don't want to say I'm going to be a 5.5 after 1 year of playing like some crazy juniors around here. I mean i don't know if 2 years is enough to go from a 4.0 to a 5.0, but I'll put in all the effort my body can muster and we will see.
Quote:
Originally Posted by BorisBeckerFan
Is there any reason you don't think you could become a 5.0 in a little over 2 years? I don't wan't to make it sound like it's easy to become a 5.0 because it's not but if you are playing at 4.0 at 15 with a lot of hard work and good instuction it's not out of the realm of possibility. The chance is as slim or as likely as the effort you put into it. I encourage you to keep training and set your goals high both in your education and in tennis.
Like I said above, I have lessons every once in a while and I practice hard and with intent 6 times a week. I just want to set a realistic goal, and it seems from what I've seen that 5.0s are just damn good players, cream of the crop players. I hope I can get there, but just want to stay realistic I guess. I will keep training and working on grades, thanks for the advice
There are so many of these threads. Take the time to search a bit. The bottom line, there is no real answer to this question. Doesn't matter the division...there is a huge range of players in each division. There are D-I schools who are much weaker than many D-III schools, consequently the players are much weaker.
There's certainly no formula related to USTA ratings, especially since most colleges don't give a crap about these ratings; they care about rankings. I know of a D-II team that was absolutely horrible last year - their #1 player was about #35 sectionally in a fairly weak section. Their #s 5 and 6 were basically beginners. Other D-II teams I watched had players that could easily play for some of the better D-I teams.
If you really want to play tennis and you're willing to do the research to find the right fit, you can play. It may not be at a school you've ever thought about or even have ever heard of.
Send e-mails/letters to coaches - not to one or two, but to lots (hundreds) of coaches. Visit college websites and fill out recruiting forms - again, not one or two but dozens or even hundreds. Perhaps you'll get a bite and perhaps you'll find the perfect fit.
I'm sorry, I didn't take the time to search out a thread that was my fault. I'm not usually like that, sorry to make another thread. Seems like there's alot of research involved in this, so I guess id better start now. Thanks so much for the advice though it really helped alot, and I'll make sure to search the other threads out there
The physical part of your game is there to get to 5.0 and maybe even a 5.5 level but you probably are not getting enough formal lessons to improve your technique which may be your biggest hurdle at the moment. Lessons are expensive so I understand why. I'm a short aging fart who never would have made it to 5.0 without 4 years of twice a week (1 private, 1 group) lessons as a junior. I also received frequent beatings in junior tournaments here in Florida by Vince Spadea and others which helped me improve.
A few of my friends in high school were very athletic and I taught them how to play tennis. They were good enough based on my advice and some practice to play lines 4 and 5 on our high school team. One of them was so athletic and developed such a heavy serve that he could almost win sets off me. In fact, the last time we played about a year ago he was up 5-2 on me in the 2nd set before I came back. So your athleticism alone should help you get to a strong 4.5 level.
The physical part of your game is there to get to 5.0 and maybe even a 5.5 level but you probably are not getting enough formal lessons to improve your technique which may be your biggest hurdle at the moment. Lessons are expensive so I understand why. I'm a short aging fart who never would have made it to 5.0 without 4 years of twice a week (1 private, 1 group) lessons as a junior. I also received frequent beatings in junior tournaments here in Florida by Vince Spadea and others which helped me improve.
A few of my friends in high school were very athletic and I taught them how to play tennis. They were good enough based on my advice and some practice to play lines 4 and 5 on our high school team. One of them was so athletic and developed such a heavy serve that he could almost win sets off me. In fact, the last time we played about a year ago he was up 5-2 on me in the 2nd set before I came back. So your athleticism alone should help you get to a strong 4.5 level.
Yeah technique isn't coming easy for me, but I've been trying. Your right I don't get enough lessons and I try to make up for it by researching on here, but really there's no substitute for 1on1 coaching. However, I have found a retired open-level player who has been hitting with me 3 days a week and coaching me for free, and it's been helping alot. He is old, but he knows more than me about tennis
And that's good to hear that being athletic will help. I've always been like this ever since I was in elementary school, loved to run, spent all my time outside playing tag, basketball, always staying active. And by the time I hit highschool I was on the varsity track team doing pretty good. Keeping my fitness where it is is no problem, because I enjoy running/working out
And yeah the beat downs I've received at tournaments have helped alot too like you said. You just learn alot from those really good players and you learn alot about yourself and your game.
Well I start applying to colleges late junior year, so I'll prob be making more threads on this then. By the way Mike, I'm looking to go to a school in Florida. I did a little research and I found small universities like the University of Western Florida and other small DII schools, many that I haven't heard off but seem like good schools. Always been my dream to live in Florida
Yeah technique isn't coming easy for me, but I've been trying. Your right I don't get enough lessons and I try to make up for it by researching on here, but really there's no substitute for 1on1 coaching. However, I have found a retired open-level player who has been hitting with me 3 days a week and coaching me for free, and it's been helping alot. He is old, but he knows more than me about tennis
And that's good to hear that being athletic will help. I've always been like this ever since I was in elementary school, loved to run, spent all my time outside playing tag, basketball, always staying active. And by the time I hit highschool I was on the varsity track team doing pretty good. Keeping my fitness where it is is no problem, because I enjoy running/working out
And yeah the beat downs I've received at tournaments have helped alot too like you said. You just learn alot from those really good players and you learn alot about yourself and your game.
Well I start applying to colleges late junior year, so I'll prob be making more threads on this then. By the way Mike, I'm looking to go to a school in Florida. I did a little research and I found small universities like the University of Western Florida and other small DII schools, many that I haven't heard off but seem like good schools. Always been my dream to live in Florida
That's cool that the guy is helping you out for free. I doubt he'd spend the time if he didn't think you could improve.
Those tournaments really helped me show what I needed to work on. Most of the juniors kept picking on my backhand, so I became obsessed with it. First I switched to the 1 hander and then I practiced high backhands all the time to neutralize that shot.
As for Florida, c'mon down and play tennis year round! I grew up here, went to school out of state and then came back. There are a lot of small schools here that I'm sure you could play for. My high school nemesis who was probably a 5.0+ played for some small school in Boca Raton. I went to a D1 school so I had no shot at making that team.
I was a 3.5 when I was 15, by the time I was done with high school I ended up a 5.0, went to a DIII college and played #2 singles.
you definitely have the time to make it to 5.0
thats where i am at right now(just turned 15) maybe borderline to 4.0 and this rating i self rate myself is based off consistency if i was consistent enough(which im working on) then i would easily be a 5.0 because when i am on i really am good, 6 months ago i took a 5 star(not bluechip) recruit to 3 sets and lost 3-6 7-5 4-6. but honestly lately i have been horrible loosing 0 and 0 to a 1 star(to his credit he was ranked #3 in boys 16s) and 4 and 5 to an unrated guy but this was post-highschool season and in high school you rarely play anyone good at #1 jv and #3 or #2 singles. our #1 went to states so we had a solid team
__________________
~Real Men Don't Use Shock Absorbers~
Personal Statement: I might not be a G.O.A.T, but i certainly enjoy eating GOATS.
Easy 5.0 for you...you're 6'2" and growing, play tennis 5 days a week, have the general strokes and temperament to improve, and is athletic already and trained in other sports too.
.
Don't listen to this. True 5.0 is FAR frome easy, it takes hard work and time, BUT it definitely sounds like a real possibility for you!
Don't aim for 5.0 for now. Just set the small goals, and work hard. If you do, wherever you end up, will be your best effort, and it won't be shocking if it is 5.0! I've worked with many juniors who were able to go from around 4.0 at about 16 to 5.0+
does anyone know about what your level has to be to make it to a a lower ranked D1 school . i started playing my freshmen year and now i will be a junior in the fall. i played 2nd singles on varsity my sophmore year and i play about 5 hours a day 6 or 7 days a week and now i am playing usta right now I am about a 4.0
does anyone know about what your level has to be to make it to a a lower ranked D1 school0
I've seen D-1 schools with 4.5 singles players. Fordham for example. But if a school has a ranking at all, you have to be pretty good to play singles for them. This is the guy who played number 6 singles for 75th ranked William and Mary College (75 is as far as the rankings went at the site I visited):
Quote:
PREP/JUNIORS
Advanced to the Virginia Group AAA semifinals in singles each of his final three seasons ... A semifinalist in the Virginia Group AAA doubles tournament as a senior ... A three-time Beach District and region singles champion, becoming the first player in 17 years to accomplish the feat ... Won the district and regional doubles championship in 2007 ... A career record of 72-1 against regional opponents during his high school tennis career ... Finished his high school career with an overall record of 94-4 ... Named high school MVP during all four seasons of his career ... Ranked as high as No. 79 in the USTA Rankings ... Ranked in the top 10 from 2003-07 in the Mid-Atlantic Section of the USTA ... Won USTA National Open Doubles Championship in 2003 ... Ranked No. 157 nationally, No. 27 in the Middle Atlantic Region and No. 2 in the state of Virginia according to the Tennis Recruiting Network ... Played volleyball and ran cross country in high school as well ... Recipient of the E.T. Penzold, Jr. Memorial Outstanding Metro Scholastic Men’s Tennis Award from the Norfolk Sports Club in 2005, 2006 and 2007.
As much as you play, assuming you improve as much as I would think somebody playing that much should improve, I'm sure you could make a D-1 team someplace. Probably not ranked team though.
As for Florida, c'mon down and play tennis year round! I grew up here, went to school out of state and then came back. There are a lot of small schools here that I'm sure you could play for. My high school nemesis who was probably a 5.0+ played for some small school in Boca Raton. I went to a D1 school so I had no shot at making that team.
Haha give me 2 years and I'll be down there for sure, can't wait to graduate highschool and get started with the college life. I dont want to get too ahead of myself here, but I'm really excited to go to college |
Postnatal development of the suprachiasmatic nucleus in the rat. Morpho-functional characteristics and time course of tyrosine hydroxylase immunopositive fibers.
According to earlier data, the suprachiasmatic nucleus of neonatal rats is highly innervated by serotonin- and tyrosine hydroxylase-immunopositive fibers [Ugrumov M. V. (1992) Zool. Sci. (Tokyo) 9, 37-45], while the latter were no longer observed in adults. This study has attempted to evaluate the timing of the innervation of the rat suprachiasmatic nucleus by tyrosine hydroxylase-immunopositive fibers, as well as to specify some morpho-functional characteristics of these fibers. According to our semi-quantitative light microscopic immunocytochemical data, few tyrosine hydroxylase-immunopositive fibers were observed in the suprachiasmatic nucleus as early as the second postnatal day. They highly increased in number neonatally reaching a maximum at the 10th postnatal day, and then decreased dramatically in adulthood. These data suggest either the provisional character of the tyrosine hydroxylase-immunopositive fibers themselves or the transient expression of tyrosine hydroxylase within permanent fibers. The tyrosine hydroxylase immunopositivity in the fibers points to their catecholaminergic nature, while the overlapping in the distribution of tyrosine hydroxylase- and serotonin-immunopositive fibers might also suggest the transient expression of tyrosine hydroxylase in serotoninergic neurons. In order to check this hypothesis, the neurotoxins of catecholamine- and serotoninergic neurons, 6-hydroxydopamine and 5,7-dihydroxytryptamine, were intraventricularly injected at the second postnatal day, while their effects were specified by the semi-quantitative immunocytochemistry eight days later. 6-Hydroxydopamine did not modify the content of tyrosine hydroxylase-immunopositive fibers in the suprachiasmatic nucleus. Conversely, the treatment with 5,7-dihydroxytryptamine resulted in a significant increase in the number of the tyrosine hydroxylase-immunopositive fibers, while reducing the amount of the serotoninergic ones.(ABSTRACT TRUNCATED AT 250 WORDS) |
Thursday, May 29, 2014
Kate Spade
My new baby, I've been in the market looking for a new wallet ever since I got my first wallet 5 years ago. My white Betty Boop wallet has seen better days but is still in working condition. I used my trip to Buffalo as an opportunity to get something I wouldn't buy in Toronto.
I love the colour which I would say is a Tiffanys blue and the name plate. Simple and cute and the best part is I got the wallet on sale from $149 to $70. I can never pass up a good bargain. |
Q:
Mule Server 3.6 > Anypoint Studio > CloudHub > 405 Not Allowed
I am encountering the error when trying out my app. It works fine on my local instance as well as on a stand-alone Mule Server, but not on CloudHub. Any reason why this problem occurs?
Update
The app doesn't have any issues running from Studio on my local machine. The problem only occurred after I deployed it to CloudHub. I am not able to access the app from CloudHub and encounter a 405 Not Allowed (nginx) error page.
CloudHub logs shows the app has started successfully as far as I understand it. See the CloudHub deployment logs below:
19:29:02.272 | 07/10/2015 | SYSTEM | Deploying application to 1 workers.
19:29:05.450 | 07/10/2015 | SYSTEM | Provisioning CloudHub worker...
19:29:07.277 | 07/10/2015 | SYSTEM | Deploying application to 1 workers.
19:29:08.325 | 07/10/2015 | SYSTEM | Provisioning CloudHub worker...
19:29:25.696 | 07/10/2015 | SYSTEM | Starting CloudHub worker at 52.74.74.41 ...
19:29:32.862 | 07/10/2015 | SYSTEM | Starting CloudHub worker at 54.169.12.90 ...
19:30:49.027 | 07/10/2015 | SYSTEM | Worker(54.169.12.90): Starting your application...
19:30:50.715 | 07/10/2015 | INFO |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Initializing app 'myapp' +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
19:30:50.958 | 07/10/2015 | INFO | Monitoring enabled: true
19:30:50.958 | 07/10/2015 | INFO | Registering ping flow injector...
19:30:50.975 | 07/10/2015 | INFO | Creating the PersistentQueueManager. Asynchronous VM queues will be persistent.
19:30:50.984 | 07/10/2015 | INFO | About to create the PersistentQueueManager with environment: scope: 55824160e4b0f5ecab93e207_559f73dfe4b02b744ec0f626 bucket: ch-persistent-queues-us-east-prod accessKey: AKIAIYBZZZI7M2PAT4WQ region: ap-southeast-1 privateKey: no
19:30:53.393 | 07/10/2015 | INFO | Apply ap-southeast-1 to the client com.amazonaws.services.sqs.AmazonSQSClient@5c6c69b6
19:30:53.393 | 07/10/2015 | INFO | New sqsClient is created com.amazonaws.services.sqs.AmazonSQSClient@5c6c69b6
19:30:53.412 | 07/10/2015 | INFO | Apply ap-southeast-1 to the client com.amazonaws.services.s3.AmazonS3Client@4a1e0237
19:30:53.469 | 07/10/2015 | INFO | New s3Client is created com.mulesoft.ch.queue.sqs.clients.S3Client@20d271f6
19:30:53.470 | 07/10/2015 | INFO | Done with SQSQueueManagementService() instance
19:30:53.505 | 07/10/2015 | INFO | Initialising RegistryBroker
19:30:53.760 | 07/10/2015 | INFO | Refreshing org.mule.config.spring.MuleArtifactContext@44b5763: startup date [Fri Jul 10 11:30:53 UTC 2015]; root of context hierarchy
19:30:57.438 | 07/10/2015 | WARN | Schema warning: Use of element <response-builder> is deprecated. HTTP transport is deprecated and will be removed in Mule 4.0. Use HTTP module instead..
19:30:57.630 | 07/10/2015 | WARN | Schema warning: Use of element <header> is deprecated. HTTP transport is deprecated and will be removed in Mule 4.0. Use HTTP module instead..
19:30:58.537 | 07/10/2015 | INFO | Using files for tx logs /opt/mule/mule-3.6.2-R43/./.mule/myapp/queue-tx-log/tx1.log and /opt/mule/mule-3.6.2-R43/./.mule/myapp/queue-tx-log/tx2.log
19:30:58.538 | 07/10/2015 | INFO | Using files for tx logs /opt/mule/mule-3.6.2-R43/./.mule/myapp/queue-xa-tx-log/tx1.log and /opt/mule/mule-3.6.2-R43/./.mule/myapp/queue-xa-tx-log/tx2.log
19:30:58.632 | 07/10/2015 | INFO | Initialising model: _muleSystemModel
19:30:59.749 | 07/10/2015 | INFO | Initialising flow: myappFlow
19:30:59.749 | 07/10/2015 | INFO | Initialising exception listener: org.mule.exception.DefaultMessagingExceptionStrategy@4fe27195
19:30:59.856 | 07/10/2015 | INFO | Initialising service: myappFlow.stage1
19:31:00.389 | 07/10/2015 | INFO | Registering the queue=55824160e4b0f5ecab93e207_559f73dfe4b02b744ec0f626_2D1531125C052F65252D3BF0500990 with display name=seda.queue(myappFlow.stage1)
19:31:00.402 | 07/10/2015 | INFO | Configured Mule using "org.mule.config.spring.SpringXmlConfigurationBuilder" with configuration resource(s): "[ConfigResource{resourceName='/opt/mule/mule-3.6.2-R43/apps/myapp/myapp.xml'}]"
19:31:00.403 | 07/10/2015 | INFO | Configured Mule using "org.mule.config.builders.AutoConfigurationBuilder" with configuration resource(s): "[ConfigResource{resourceName='/opt/mule/mule-3.6.2-R43/apps/myapp/myapp.xml'}]"
19:31:00.430 | 07/10/2015 | INFO | Apply ap-southeast-1 to the client com.amazonaws.services.sqs.AmazonSQSClient@1c5e47e5
19:31:00.430 | 07/10/2015 | INFO | New sqsClient is created com.amazonaws.services.sqs.AmazonSQSClient@1c5e47e5
19:31:00.448 | 07/10/2015 | INFO | Apply ap-southeast-1 to the client com.amazonaws.services.s3.AmazonS3Client@7b8419b2
19:31:00.468 | 07/10/2015 | INFO | New s3Client is created com.mulesoft.ch.queue.sqs.clients.S3Client@2c611f62
19:31:00.473 | 07/10/2015 | INFO | Done with SQSQueueManagementService() instance
19:31:00.504 | 07/10/2015 | INFO |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Starting app 'myapp' +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
19:31:00.561 | 07/10/2015 | INFO | Starting ResourceManager
19:31:00.561 | 07/10/2015 | INFO | Starting persistent queue manager
19:31:00.562 | 07/10/2015 | INFO | Started ResourceManager
19:31:00.574 | 07/10/2015 | INFO | Successfully opened CloudHub ObjectStore
19:31:00.590 | 07/10/2015 | INFO |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ DevKit Extensions (0) used in this application +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
19:31:00.591 | 07/10/2015 | INFO | Starting model: _muleSystemModel
19:31:00.594 | 07/10/2015 | INFO | Starting flow: myappFlow
19:31:00.595 | 07/10/2015 | INFO | Starting service: myappFlow.stage1
19:31:00.881 | 07/10/2015 | WARN | HTTP transport is deprecated and will be removed in Mule 4.0. Use HTTP module instead.
19:31:00.947 | 07/10/2015 | INFO | Initialising connector: connector.http.mule.default
19:31:01.156 | 07/10/2015 | INFO | No suitable connector in application, new one is created and used.
19:31:01.158 | 07/10/2015 | INFO | Connected: HttpConnector
{
name=connector.http.mule.default
lifecycle=initialise
this=5f68f6a9
numberOfConcurrentTransactedReceivers=4
createMultipleTransactedReceivers=true
connected=true
supportedProtocols=[http]
serviceOverrides=<none>
}
19:31:01.158 | 07/10/2015 | INFO | Starting: HttpConnector
{
name=connector.http.mule.default
lifecycle=initialise
this=5f68f6a9
numberOfConcurrentTransactedReceivers=4
createMultipleTransactedReceivers=true
connected=true
supportedProtocols=[http]
serviceOverrides=<none>
}
19:31:01.159 | 07/10/2015 | INFO | Starting connector: connector.http.mule.default
19:31:01.169 | 07/10/2015 | INFO | Initialising flow: ____ping____flow_____76326334
19:31:01.169 | 07/10/2015 | INFO | Initialising exception listener: org.mule.exception.DefaultMessagingExceptionStrategy@66551924
19:31:01.186 | 07/10/2015 | INFO | Initialising service: ____ping____flow_____76326334.stage1
19:31:01.380 | 07/10/2015 | INFO | Starting flow: ____ping____flow_____76326334
19:31:01.381 | 07/10/2015 | INFO | Starting service: ____ping____flow_____76326334.stage1
19:31:01.387 | 07/10/2015 | INFO | Registering listener: ____ping____flow_____76326334 on endpointUri: http://localhost:7557/____ping____
19:31:01.459 | 07/10/2015 | INFO | Loading default response transformer: org.mule.transport.http.transformers.MuleMessageToHttpResponse
19:31:01.542 | 07/10/2015 | INFO | Initialising: 'null'. Object is: HttpMessageReceiver
19:31:01.559 | 07/10/2015 | INFO | Connecting clusterizable message receiver
19:31:01.563 | 07/10/2015 | WARN | Localhost is being bound to all local interfaces as specified by the "mule.tcp.bindlocalhosttoalllocalinterfaces" system property. This property may be removed in a future version of Mule.
19:31:01.575 | 07/10/2015 | INFO | Starting clusterizable message receiver
19:31:01.575 | 07/10/2015 | INFO | Starting: 'null'. Object is: HttpMessageReceiver
19:31:01.644 | 07/10/2015 | INFO | Listening for requests on http://localhost:8085
19:31:01.645 | 07/10/2015 | INFO | Mule is embedded in a container already launched by a wrapper.Duplicates will not be registered. Use the org.tanukisoftware.wrapper:type=WrapperManager MBean instead for control.
19:31:01.675 | 07/10/2015 | INFO | Attempting to register service with name: Mule.myapp:type=Endpoint,service="____ping____flow_____76326334",connector=connector.http.mule.default,name="endpoint.http.localhost.7557.ping"
19:31:01.676 | 07/10/2015 | INFO | Registered Endpoint Service with name: Mule.myapp:type=Endpoint,service="____ping____flow_____76326334",connector=connector.http.mule.default,name="endpoint.http.localhost.7557.ping"
19:31:01.686 | 07/10/2015 | INFO | Registered Connector Service with name Mule.myapp:type=Connector,name="connector.http.mule.default.1"
19:31:01.689 | 07/10/2015 | INFO |
**********************************************************************
* Application: myapp *
* OS encoding: /, Mule encoding: UTF-8 *
* *
* Agents Running: *
* DevKit Extension Information *
* Batch module default engine *
* Clustering Agent *
* JMX Agent *
**********************************************************************
19:31:01.754 | 07/10/2015 | INFO | Registering the queue=55824160e4b0f5ecab93e207_559f73dfe4b02b744ec0f626_515E160FC244EB5157E8E7C8B162E0 with display name=seda.queue(____ping____flow_____76326334.stage1)
19:31:02.561 | 07/10/2015 | SYSTEM | Worker(54.169.12.90): Your application has started successfully.
19:31:09.295 | 07/10/2015 | INFO | Mule system health monitoring started for your application.
19:31:59.537 | 07/10/2015 | SYSTEM | Worker(52.74.74.41): Starting your application...
19:32:01.200 | 07/10/2015 | INFO |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Initializing app 'myapp' +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
19:32:01.525 | 07/10/2015 | INFO | Creating the PersistentQueueManager. Asynchronous VM queues will be persistent.
19:32:01.526 | 07/10/2015 | INFO | About to create the PersistentQueueManager with environment: scope: 55824160e4b0f5ecab93e207_559f73dfe4b02b744ec0f626 bucket: ch-persistent-queues-us-east-prod accessKey: AKIAIYBZZZI7M2PAT4WQ region: ap-southeast-1 privateKey: no
19:32:07.054 | 07/10/2015 | INFO |
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
+ Stopping app 'myapp' +
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
19:32:07.056 | 07/10/2015 | INFO | Stopping flow: ____ping____flow_____807729792
19:32:07.056 | 07/10/2015 | INFO | Removing listener on endpointUri: http://localhost:7557/____ping____
19:32:07.057 | 07/10/2015 | INFO | Stopping: 'null'. Object is: HttpMessageReceiver
19:32:07.059 | 07/10/2015 | INFO | Disposing: 'null'. Object is: HttpMessageReceiver
19:32:07.059 | 07/10/2015 | INFO | Stopping service: ____ping____flow_____807729792.stage1
19:32:12.028 | 07/10/2015 | SYSTEM | Worker(52.74.74.41): Your application has started successfully.
19:32:15.041 | 07/10/2015 | INFO | Mule system health monitoring started for your application.
19:32:33.488 | 07/10/2015 | INFO | Stopping flow: myappFlow
19:32:33.489 | 07/10/2015 | INFO | Stopping service: myappFlow.stage1
19:32:37.061 | 07/10/2015 | SYSTEM | Application was updated successfully with zero downtime. The new version of your application has been launched and the old version has been stopped.
19:32:37.545 | 07/10/2015 | SYSTEM | Your application is started.
A:
I found the solution to my problem. From the deployment logs:
19:31:01.644 | 07/10/2015 | INFO | Listening for requests on http://localhost:8085
The host should have been the default All interfaces [0.0.0.0], and the port 8085 is not allowed on CloudHub. And I must use the default port 8081.
I was running multiple Mule apps on my local machine at the same time, that's why I had used a different port for this app, and I wasn't aware that port 8085 is not allowed on CloudHub.
Thank you all for the response.
|
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